BOUGHT WITH THE IKCOME FROM THE SAGE ENDOWMENT FUND THE GIFT OF Hetirs m. Sage 1891 i^.a7g^(,^ mli3 Cornell University Library MT 50.G59M4 1913 The material used In musical composlton > 3 1924 021 806 207 Cornell University Library The original of this book is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924021806207 THE MATERIAL USED IN MUSICAL COMPOSITION A SYSTEM OF HARMONY DESIGNED ORIGINALLY FOR USE IN THE ENGLISH HARMONY CLASSES OF THE CONSERVATORY OF MUSIC AT STUTTGART BY PERCY GOETSCHIUS AUTHOR OF EXERCISES IN MELODY-WRITING; THE THEORY AND PRACTICE OF TONE-RELATIONS; MODELS OF THE PRINCIPAL MUSIC FORMS ; THE HOMOPHONIC FORMS OF MUSICAL COMPOSITION ; APPLIED COUNTERPOINT; ELEMENTARY COUNTERPOINT; LESSONS IN MUSIC FORM; ETC. NEW (FOURTEENTH) EDITION COMPLETELY REMODELED AND RE-WRITTEN NEW YORK: G. SCHIRMER BOSTON: THE BOSTON MUSIC CO. 1913 S COPYEIGHT, l88g, S^. SCHIRMER Copyright, i8gs, by G. Schirmer Copyright, 1913, by G. Schirmer 23878 . PREFACE TO THE NEW (FOURTEENTH) EDITION. The first draft of this book was made in 1879, while the author was teaching, and still studpng, at the Conservatory of Music in Stuttgart, Germany. It was many times rewritten before being first issued in 1882, in Stuttgart. In this original form it was used until 1889, when, in completely re- modeled form, it was pubUshed by Mr. Schirmer in America. In 1895 it was again partially revised. For the present edition it has been again thoroughly revised, rearranged and re-written. The object of this latest revision was, to record the experience gathered during the past twenty years of uninterrupted teaching; to correct prolix and clumsy diction; to increase the exercise-material, especially in melody harmonization; and to introduce and systematize, as far as possible, the novel experiments and achievements of modern harmonic thought. Also, to present the book, as a whole, in a more attractive and useful form. New York, October, igi2. PERCY GOETSCHIUS. EXTRACTS FROM THE PREFACE TO THE FIRST AND SECOND EDITIONS. The author is not inclined to the sanguine beUef that such a subtle and imaginative art as that of composition can be acquired by those not possessed of the innate faculty, by simply studying from books. But it is certainly true, that even those who are born to compose are not exempt from the necessity of a careful training, systematic arrangement and studious development of their ideas. It is therefore essential that the musical student be guided in his studies by some method in which the primitive laws of the art (as instinctively recognized by genius), and the subsequent experiences and inventions of distinguished minds (as transmitted through classic productions), are compriehensively and truthfully recorded; and that method which most lucidly, concisely and systematically imparts such information is the one from which the scholar will derive the greatest benefit. In opposition to the still popular impression that such books as these are written only for the use of composers, and that only those who intend or hope to become composers ever need to study harmony, the author avers his belief that none of the many branches of musical discipUne is so indispensable as that which treats of the Science of music; and hp therefore wishes to be understood as having pre- pared this treatise more particularly for the musician in general f than for the very small minority of com- posing musicians. #*##:)(: The students in whose hands this book is to be placed, are assumed to have completely mastered all the elements of notation; to be reasonably expert in piano plajdng, and in reading at sight (for which the easier Sonatas of Mozart or Haydn may be offered as tests); and to be somewhat familiar with classic literature. If this is not the case, they are urged to devote a few months to the acqui- sition of this indispensable knowledge before commencing harmony; for neither from this nor from any other book can the study of harmony be successfully pursued by any student whose attention is still partly engrossed by the rudiments of music. ill IV This method of harmony is based upon the method of Prof. Dr. Immanuel Faisst, for a detailed account of which the author is indebted to the interest and kindness of Dr. Faisst himself. (See the following Preface.) The present author's knowledge of harmony was obtained solely through this channel, and he takes pleasure in avowing that what he has since learned is due to the influence of Dr. Faisst's incom- parable mode of instruction. But in the preparation of this book the course of instruction received by the author has undergone many, in part radical, modifications. * * * * Chief among these, — as defining the main standpoint assumed in this method in distinction to all others, and as indicating the source from which the laws of harmonic action and logical tests of euphony are deduced, — are paragraphs 12,* 13, 18, 24, 34, 46c, 59, 68, 69, 70> 78, loi, 171, 198, 259, 262, 267, 302, 307, 315, 323, 339, 346, 358, 376, 390, 40s, 4i4-4i9» 425, 427, 462. These, and the fundamental laws of melody; the treatment of melody-harmonizing; the treatment of the altered and mixed chords; and the fundamental laws and processes of modula- tion, — the author beUeves to have originated. This second, re- written edition differs from the first one in the following respects: The different subjects of study have been more distinctly and methodically systematized; the explanatory notes and illustrations are more copious; and the exercises have been made easier, so that every ordinarily gifted scholar may have the gratification of correctly solving them, with a fair amount of application and patience. * * * The course of study is divided into Lessons (weekly, or semi-weekly) in such degrees as the author has found to be most convenient in his own practice; but it is left to the judgment of the teacher to modify this division as occasion prompts. It will oftener be found necessary to devote the time of two lessons to one alone, than to merge two lessons in one: haste is of little avail in the study of harmony. Each lesson terminates with an exercise, or a set of exercises, and a synopsis of the fimdamental principles of the subject under treatment. The author recommends working out all the given basses and other exercises, upon the ground that "practice will make perfect." The adop- tion of the given positions (upper figures) facilitates the solution of the basses very materially, of course, and they are really intended only for the use of weaker pupils. Those who are ambitious to profit most by the given exercises will simply ignore all such auxiliaries, i.e., will copy out the given basses without paying any attention to the upper (position) figures. The fundamental principles should be memorized. The references to other paragraphs (which may appear at first glance unnecessarily profuse) have been made with the studied purpose of impressing certain points more deeply upon the scholar's mind, by dint of frequent repetition. Therefore, he is required to make conscientious use of them, despite the slight interruptions they may cause. In the other references (to other works) the author has limited himself as much as possible to such compositions as are accessible to every scholar, and, with very rare exceptions (in favor of some particularly striking examples), to pianoforte music alone. The printed examples, of which those not otherwise marked are original, are the more pointed illus- trations of the matter in question, and are so copious that the references, if unobtainable, may be dispensed with. •These paragraph numbers refer to the present, latest, edition. PREFACE OF DR. FAISST. The method of harmony upon which the present work of Mr. Percy Goetschius (published with my assent) has been based, was originally prepared by me in 1847, for the purpose of instruction in a musical Institute; and was subsequently — certain parts repeatedly — revised. After having used it in this manner for a period of ten years, the establishment of the Stuttgart Conservatory of Music, and my acceptance of the proffered position among its faculty, gave me occasion for a new and more extended application of my method, by reason of which it naturally grew more and more complete; albeit I gave the lessons without the aid of manuscript notes, and extemporized the examples and exercises directly upon the blackboard. In one of these Conservatory-courses, my system of instruc- tion was written down as accurately as practicable in text and notes by a scholar who was afterwards engaged in my stead as teacher of the branch in question, and who gave the lessons according to his manuscript copy. Through a similar medium, Mr. Goetschius, to whom I subsequently had the pleasure of imparting instruction personally in the higher branches of composition, came into posses>- sion of this part of my method. As I have been unable as yet for lack of time, and may possibly never find time, to elaborate this branch of study consistently with my wishes for publication, I would not oppose the author of the present work in his intention of preparing a system of harmony, which, though based upon the method which I have applied, contains various modifications and original additions. But, on the other hand, it may be no more than just that I should, in this place, support my right of invention and application to such subjects and such modes of treatment as^to the best of my knowledge, distinguish my method from prior modes of instruction; especially in view of the possibility that parts of this method which are peculiar to myself, might later be adopted in other — perhaps even German — didactic books. The points which I believe I have originated, are as follows: The adoption of an "absolute" figuring for all the chords. That is, a designation m numbers, which, without the necessity of a written bass, indicate the species of the chords and their exact situ- ation in the key; not only in reference to their roots, but also to their denomination (as triad, chord 7 9 of the seventh or ninth), and to the grade of inversion; — for illustration, IIi, 0V3. Further, the npting down of exercises in numbers according to this system, to be worked out in dififerent keys. The abbreviated denomination of all the chords, according to the numbers used in this "abso- lute" figuring; e.g., the Two-seven-one. The regard paid to the eminent influence which in all chords (above all in the concords) the con- dition of the soprano exerts upon the admissibility and effectiveness of the chord-progressions; and, in consideration of this influence, the investigation and judgment of all the diatonic harmonic pro- gressions, with regard to every possible soprano-position; furthermore, in the same connection, incit- ing and guiding the scholar to a melodious progression of the soprano, in every kind of exercise. The institution of rules for voice-progression, which are not limited to a succession of two tones, but apply to the connection of a protracted series of tones. The application, throughout, of each part of the harmonic material, in a threefold manner: (a) In working out flgured basses; (6) In the invention, by the scholar, of original phrases and periods; in both cases with special regard to the acquirement of these simple, elementary forms in regular construction, — for which reason, the suitability of the momentary chord-material for semi-cadences is also indicated; VI (c) In harmonizing given melodies, chiefly in these elementary forms, or in other related forms proceeding from them. The determination of the relations existing between the laws of rhythmic progression, and the prolongation or change of chords and bass tones. Many rules of voice-progression for special combinations of chords; particularly in reference to covered, interrupted, and oblique consecutive octaves and fifths. The distinguishing between different kinds of parallel fifths, according to their size, and the condi- tion of the voices. Precise definition of the harmonic relations and general use of the different six-four chords of the key. Thorough exposition of the free resolutions or progressions of discords, and their use; also the free resolutions of suspensions. Regulations respecting the practical application of the diminished triads, and their inversions; of the chords of the ninth, and inversions; the chord of the seventh upon the 7th step in major, with its inversions; of the altered and mixed chords. The derivation of the chord of the seventh upon the 4th step, from the chord of the ninth upon the 2nd. The distinction between, and separate treatment of, diatonic modulation (based upon the funda- mental principle that certain chords are common to different keys) and chromatic or enharmonic modu- lation; diatonic modulation to remote keys, direct and indirect; precise exposition of the different chromatic chord-progressions, and their modulatorpfcgnificance. Rviles for determining the admissibility of cro^-relimons. Detailed treatment of harmonic and mixed figuration. The transition from the harmonic (homophonic) style of writing to the polyphonic, by means of inharmonic tones. *~ All these characteristics, which I believe to be peculiar to my method, have been adhered to with more or less fidelity by Mr. Goetschius in the presentVork. But, while it would be groundless to regard each individual point in the presentation and treatment of these subjects in this book as proceeding from me (inasmuch as Mr. Goetschius has deviated in many respects), it would be still less just to overlook what he has done to complete certain parts of my method, and present it in a fitting shape for practical instruction; besides the addition of those parts, in reference to which he in his preface lays just claim to having advanced original views, the significance of which will not be denied even by those who are unable promptly and easily to appropriate them. May this book then, which has been prepared with so much intelligence and assiduity, prove to be a successful guide to very many in their musical studies. Dr. IMMANUEL FAISST. Stuttgart, October, 1882. TABLE OF CONTENTS. PART I. DEFINITIONS AND RULES. Rhythm Modes of Accentuation Melody The Key The Scale 5 Rules of Melody 6 Harmony. — Intervals 10 Consonance and Dissonance 12 Pagb I 2 3 3 Page Chords 13 The Voices or Parts 15 DupUcation of Chord-Intervals 16 The Positions of a Chord 17 Rules of Part-writing ... 18 The general Exception 20 Qualification of Tones, Chords, and Chord-in- tervals 21 PART II. THE SUCCESSION OR CONNECTION OF CHORDS. Division A. Concords. Section i. Triads. Section 2. The Chords of the Sixth. The Tonic Triad, I. — The Dominant Triad, V 22 The succession I-V 22 The reversed succession, V-I 24 The Perfect Cadence 24 The Phrase 25 The Subdominant Triad, IV 28 "Connection of the Subdominant and Dominant Triads 31 The Principal Triads in the Minor Mode. . . . 33 The Subordinate T.iads in Major 35 The Second-dominant Triad, II 36 The Submediant Triad, VI 39 The Mediant Triad, III 4X The Subordinate Triads in Minor 43 The Period-form 44 The harmonizing of Melodies. Principal triads . 45 Melodies, with Subordinate triads 47 The Inversions of the Triads 49 The Principal Chords of the Sixth. . . . The Subordinate Chords of the Sixth . . Consecutive Chords of the Sixth . . Triad and 6th on the same Bass tone . . Melody harmonizing. Chords of the sixth Harmonizing successive tones together . SI 54 S6 57 60 61 Section 3. The Six-four Chords. The connections of Six-four Chords. First con- nection 53 Second connection g^ Third connection 65 The Plagal Cadence 68 Six-four Chords as Passing-chords 68 Melody harmonizing. Six-four chords 72 vm TABLE OF CONTENTS. Division B. Discords. Page The Classification of the Discords 74 The Resolution of a Dissonance 74 Section i. The First Class of Discords. A. The Chord of the Seventh upon the Domi- nant 75 The Introduction of the V 76 The Inversions of the Dominant-Seventh-Chord 78 Irregular Resolutions of the Dominant-7th- Chord 81 The Passive Resolution 82 Other Irregular Resolutions 83 B. The Incomplete Chord of the Dominant- seventh , 8s (The n in Minor) 86 Melody harmonizing. Dominant seventh . C. The Chord of the Ninth upon the Dominant Introduction and Resolution of the Five-nine . The Complete Inversions of the Five-nine ... D. The Incomplete Chord of the Dominant- ninth . . . 88 90 91 93 94 g P-*°" The oV in the Major Mode 94 9 The oV in the Minor Mode 96 Melody harmoiiizing. Dominant-ninth . . .99 Section 2. The Discords of the Second Class. 7 A. The II and its Inversions 102 7 B. The IV and Inversions 103 The Digression into the next higher Class ... 104 Section 3. The 3rd and 4th Discord-Classes. A. The Discords of the Third Class 107 Irregular Passive Resolution 108 B. The Discords of the Fourth Class no 7 The III in Major no The m, III and III in Minor in Table of the Harmonic System of a Key . . .113 Sequences 113 Harmonizing of Unfigured Basses 115 Division C. The Altered and Mixed Chords. Section i. The Altered Chords. Section 2. The Mixed Chords. A. In Major 117 B. In Minor 121 A. In Major 126 B. In Minor 129 PART III. MODULATION. Section i. Key-relations. Key-relations '. 131 General Rule of Modulation 132 Section 2. The process of Modulation. Fundamental Rule of Modulation 13 5 Altered Chords as modulatory mediums .... 137 Extraneous Modulations (i; Through Next-re- lated Keys) 138 Extraneous Modulations (2. Direct) 140 The Modulatory Stride 140 Modulation to the Opposite Mode 141 Modulation at Cadences, and in Sequences . . 145 Section 3. Chroniatic Progression, as a Special modulatory agent. Rules of Chromatic progression 149 Chromatic Chord-progressions 150 TABLE OF CONTENTS. IX Page Section 4. Enharmonic Modulation. Simple Enharmonic Changes with the Dim. Seventh 159 Other Resolutions of the Chord of the Dim. Seventh 161 Other Enharmonic Chords 164 Compound Enharmonic Changes 166 Pivotal Modulations. Page 167 Section S- The Harmonizing of Melodies, with Modulations. ist. Melodies with Indicated Modulations . . and. Melodies with Intimated Modulations . . 3rd. Melodies with Optional Modulations. . . . 171 172 174 PART IV. THE INHARMONIC (NON-HARMONIC) INTERVALS. The Inharmonic (Non-harmonic) Intervals . . 178 The Irregular Anticipation . . . Section i. The Organ-point. Hints and Directions 180 The Pastoral Organ-point 183 Irregular Organ-points. — The Mediant Organ- point .... 185 The Short Organ-point 186 Section 2. The Suspension. Hints and Directions Harmonic Suspensions Suspension-Chords Irregular Resolutions of the Suspension . Irregular Introduction of the Suspension The Harmonizing of Melodies ... 189 190 191 193 197 199 Section 3. The Anticipation. Hints and directions 201 Harmonic Anticipations 202 Syncopation . . 203 . . . 207 Section 4. The Neighboring-notes. The Neighboring-note proper, as "Local" Em- bellishment 209 The Passing-notes, as "Progressive" Embellish- ment 211 Embellished Melody, and Running Parts. . . . 212 Embellished Harmony 215 Irregular Neighboring-notes. The Appoggia- tura 219 The Double-neighbor 220 Harmonic Embellishment, continued 222 Other Licences 225 The Harmonizing of Embellished Melodies, and Basses 231 Wandering Harmonies. Modulation with In- harmonic tones 234 Warning Note 239 Analysis . . . . 239 PART V. VOCAL AND INSTRUMENTAL HARMONY WITH AN IRREGULAR 'NUMBER OF PARTS (FEWER OR MORE THAN FOUR). STYLE. Section i. Vocal Harmony. Three-part Harmony 241 Two-part Harmony . . 242 Five- to Eight-part Harmony 244 Section 2. Instrumental Harmony. Figuration or Broken Chords. Accompani- ments 246 Harmonic Figuration 246 The Registers of the Figural part 247 Hints and Directions 249 Melodic (or mixed) Figuration 254 Two-part.Figuration 255 One-part Figuration 256 Irregular Part-writing 258 Figural Motives with Supplementary tones . . 259 Rhythmic Figiuration 260 Double, Compound and Complex Figuration . 262 Triple and Quadruple Figuration 263 Paraphrasing; or simple Variation 265 PART I. DEFINITIONS AND RULES. 1. Music is the association of tones. A tone is a fixed sound. The point in the domain of sound at which it is fixed is called its pitch. Tones may be indicated in a number of ways. The oldest and most common way is to denote the tones by letter. For this purpose the first seven letters of the alphabet are used. This is all that is required, as the key contains only seven tones. Names for all other tones are obtained by inflecting these seven letters with accidentals (sharps and flats). Tones are also indicated by notes, placed upon the stafi. The identity of the tone (its letter-name) is fixed by a letter- sign, called the clef, placed upon some fine of the staff. Tones are also indicated by numbers indicating the vibratory rapidity which defines their pitch {e.g., middle C = 261 pulses in a second) ; and also by numbers indicating their place in the scale (as scale-steps). The study of musical material embraces the consideration of the three essential factors of music: Rhythm, Melody and Harmony. Rhythm. 2. Rhythm is engendered by the motion of the musical pictiu-e, and manifests itself in the associa- tion of differing time-values. It treats, first, of the division of the time required for the expression of a musical idea into absolutely regular and equal units, of which the most convenient and commonly adopted representative is the "beat." Secondly, rhythm treats of the grouping of a certain number of these units or beats in sjmimetrical measures. This grouping is effected by a regularly reciurring emphasis, called the accent, always laid upon the first unit of each group. The beats are absolutely similar in duration, but differ in quality, some being heavy and others light. This is the vital principle of rhythm, as it estabUshes a distinction between the beats, and gives the otherwise monotonous and mean- ingless series of similar strokes a recognizable form. 3. The rhythmic groups consist of either two or three units or beats, and constitute the simple measiu-es of written music. When theire are two beats in a group (heavy and light beats in regular alternation) the rhythm is duple : - Ex. _J j I j |^_J J-l J J I (heavy-light I). When there are three beats in a group (an irregular alternation of one heavy and two light beats) the rhythm is triple : A I A I Ex. _- g . m • • (heavy-light-light I). J*, r r r I r r r I 1 a 8 i a s a. The following are examples of simple groups or measures, in duple and triple rhythm: | (i.e., a group of two units of the value of quarter-notes); | (a group of three units of the value of eighth-notes); | or $ (alia breve); i; 2, etc. I THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 4. 5. Compound measures are multiplications of these simple groups. For instance, two groups in duple time: | + I = * or B; or I + I = I; I + i + i = ?; | + | = | (not to be confounded with i), etc. c. Simple measures have only one accent; compound measures have an accent for each rhythmic group that they contain: Ex 2. Xj-l A g a .Sm. 1-4 133 4Se 780 7-e 4 measure is pre- d. The only difference between simple and compound measure is, obviously, the number of bars. cisely the same as | with the alternate bars omitted. The first accent of a compound measure is the strongest, as the exponent of the first of the two or three groups which compose the measure, and is called the primary accent; the other accent or accents are secondary. e. Diversity of time-value is obtained by dividing beats, or by adding them together. The division of a quarter- note into two equal fractions gives eighth-notes; into three equal fractions, the triplet; into four fractions, sixteenth-notes. The addition of two quarter-notes gives a half-note. A dot lengthens a note one-half its time-value; and so on. Ex. S. ^^ Divided beats Added beats S ^^3 -»-r- MoDES OF Accentuation. i^ 4. The accent which falls upon the first unit of each group is called the natural or grammatical accent, and is fixed by counting. But an arbitrary stress may be imparted to any individual beat, for diversity of effect. These optional emphases are not "accents," but "accentuations," and may be produced as follows; ist, dynamically, by simple emphasis; 2nd, metrically, by a tone of longer duration, representing the sum of two or more beats or fractions of beats; and 3rd, harmonically, by a change in the combination of tonesT] Thus: Dynamic accentuation Metric accentuation \i^=m^ Harmonic accentuation AAA ^ J/Z V V V V 6. Those rhythms are most natural and comprehensible, in which the dynamic and metric accentuations coincide with the natural accent, — that is, fall upon the first unit of a rhythmic group; if not constantly, at least for such a period and in such frequency as to render the rhythmic intention unmistakable. For example: Ex; 5. \A^^^:^^^ti=n^d^^^^ Measures b, c, d, are satisfactory in effect, because the longer notes coincide in position with the natural accent. This arrangement of time-values, — the heavier notes at the heavy beats, or the lighter notes at the lighter beats, — is there- fore known as regtdar rhythm. Measure a, consisting of uniform time-values, is regular, because there is no evidence of irregularity. Measures /, g, h, i, are illustrations of irregular rhythm, because the arbitrary metric accentuations do not confirm the natural accents; that is, the heavier notes occupy lighter beats, or fractions. Such shifting of the natural rhythm is Par. 6. MELODY. 3 generally known as syncopation, and it is extremely effective when recognizable as such. In order to be understood, it should appear in connection, or alternation, with sufficiently marked regular rhythm. See par. 390, 392. Measure e is slightly irregular; the primary and secondary accents are exchanged. Melody. 6. Melody is any succession of single tones. The quality of the melody depends upon the degree of congruity or affinity of the tones for one another; also upon the degree of uniformity in the grouping of the tones, both with regard to pitch and to time-values; also upon other, scarcely definable, conditions that do not concern the beginner. The fundamental requirement is, no doubt, that of relation; those tones which belong together will be most likely to sound well together. 7. A melody is a line of tones; a line whose successive points are fixed sounds, which define its flexions, its rising, fall- ing, poising, in various rhythmic forms. Melody is therefore the same element in music that the line is in a pictvure or drawing of any character, simple or complex. These tone-lines determine all the tangibly impressions imparted to an in- telligent mind by the music; and they represent so nearly the sima of what is indicated by a musical sentence, that it may be said that the lines (that is, the melodies) are the music. With this conception of njusic, as a system of tone-lines, the student can not become too deeply impressed; for he must learn, sooner or later, that whatever he may desire to express in tones, must be conveyed through the lines of tone. He can assure himself of this by listening thoughtfully to any ex- ample of good music and analyzing his mental attitude, — observing what it is that gives him definite impressions of the music. Whether consciously or not, he will discover that he is tracing the tone-lines. It is this fact of musical formula- tion that gives to melody its supreme importance, and makes rhythm and harmony subservient. The Key. 8. A key is a family of tones. The term "family" is used advisedly, because it suggests a simple and exact analogy. The key is a group of related tones; tones which inevitably congregate, in obedi- ence to the law of relation or affinity. 9. The vital principle of musical art is Tone-relation. Every association and progression is defined by it. A solitary tone has no more meaning than a single letter or character of speech has; both acquire significance only upon association with other characters, whereby a relationship is established, involving mutual obligations and actions. 10. The classification of the grades of tone-relation is not a matter of conjecture or opinion, but may be tmdertaken with mathematical exactness, because each tone represents a definite number, — the number which indicates the velocity of the tone-waves that fix the pitch of the tone. 11. The fullest degree of tone-relation is exhibited by two tones that have exactly the same velocity of vibration. This is the unison; the numbers, and therefore the pitch, are identical; the vibratory ratio is i : i, and it is quite impossible to distinguish the tones from one another by pitch. The next, somewhat less complete, degree of relation is exhibited by two tones produced by a certain velocity and exactly double that velocity. This is the octave; the vibratory ratio is the simplest imaginable, 1:2; and though there is an actual diflference in pitch, it is not entirely easy to distinguish the tones from one another. These tones are there- fore regarded and treated in music as practically identical, as the same musical /oc/or (in the chord, the key, — sometimes even in the tone-line), manifesting a distinction but not a difference. The next, somewhat more remote, degree of relation is exhibited by two tones whose vibratory velocities represent the next simplest ratio, 1: 3, or 2: 3. This is the so-called perfect fifth. There is not only a difference in pitch, but it is easy to distinguish the tones from one another, — in fact, not possible to confound them. The personality of each is com- plete, the result is two actually distinct factors, which, nevertheless, constitute the most intimate affinity that can exist be- tween actually different tones. Unison Octave Perfect fifth -<2 ffl s W- S- -&- S- -9- 1:1 1:2 1:3 2:3 THE MA TERIAL USED IN MUSICAL COMPOSITION. Par. 12. 12. It is with this significant tone-relation, the perfect fifth (to which the name harmonic degree might be given), that nature initiates the entire system of tone-combinati§n. The miison and octave are used for dupUcation and extension into higher or lower registers, but the perfect fifth is the basis of generation. It is the necessary simple point of departure for every association and every action in the domain of tone; from it radiates the whole tone-complex, like a web, ramifying and extending infinitely. It is this interval which determines the tones that must assimilate and congregate (in a sense, gather as a clan) in the group or family of tones called a key. The perfect fifth may be located on the keyboard by counting upward eight "keys," or half-steps; thus from c ; c-c#-d-d#-e-f-f it-g. The upper tone must, moreover, be the fifth letter from that of the lower tone. Thus, Ab-Eb (not D#); B-F# (not Gb). 13. The key or family of C (for example) is formed by beginning with C (as head of the family) and defining his two nearest relatives, — the perfect fifth both upward and downward, — the tones G and F. The process of tone-generation operates upward, and therefore the next member of the family will be the perfect fifth upward from G, — the tone D. (The lower perfect fifth of G confirms the keynote C). The next member is the upper fifth of D, the tone A; then its fifth, the tone E; then the fifth of the latter, the tone B. The following perfect fifth, the related tone of B, is F-sharp. There is no particular reason why this tone should not be a member of the family of C, excepting that it conflicts sharply with the F-natural, whose relation to the keynote C is too intimate to be overpowered by the remote relative, F-sharp. The observant student is surely aware that this F-sharp, while not a legitimate member, is nevertheless a very frequent guest in the family of C. Excluding the F-sharp, because of its hostility to the closely related F-natural, this key will be found to contain the following seven tones: i Keynote #- -<5>- -19- -9- ^m Ex. 6. IE _not a member of CI F D (F#) 14. The nucleus of the key is formed by the five relatives, C, G, D, A, E, — five contiguous tones in the chain of perfect fifths. In this nucleus the lowermost tone is the keynote. Any combination of these five tones results either in consonance, or the mildest dissonance (whole step; for example, C and D together); nowhere does a harsh dissonance appear. These are the five tones of the most common 5-tone scale (the Scotch scale, for instance). These nucleus-tones are the ones used by Beethoven in the first period of the theme of his "Leonore" overture (prob- ably with singularly true musical instinct) : C-G-D-A-E i ^» Ex. m w m To these five nucleus- tones a perfect fifth is added at each end (F below the C, and B above the E). These additional tones result, by combination with the others, in the more harsh dissonance of the diatonic half-step (F-E, and C-B), and beyond this the "family," as a body of reasonably harmonious members, apparently can not extend. Hence the limitation of a key to seven members, as shown in Ex. 6. Par. 15. THE SCALE. 5 15. Any tone may be adopted as keynote, and the members of its key or tone-family found, as above, by adding one perfect fifth below, and five successive perfect fifths above. Thus, for the key of At: — A|,-D b-Et-B b-F-C-G. For the key of E: — E-A-B-F#-C#-G#-D#. All keys have the same series of seven letters, beginning at different points. For the key of C it is the established custom to use ^lain letters; all the other keys require the inflection of one or more of the letters (by sharps or flats), and the niunber of such inflections defines the signature of the key. In the key of At>, for instance (see above), four letters are flatted, therefore the signature of A|> is four flats. In the key of E four letters are sharped, hence its signature is four sharps. The Scale. 16. a. A scale is any succession of whole steps and half -steps. h. The whole step, as seen, is the difference in pitch between tones of the key which he two harmonic degrees (perf. fifths) apart, — reduced by the octave to closer proximity; Ex. 8a. The diatonic half-step is the difference in pitch be- tween tones that lie five harmonic degrees apart; Ex. 8J. The chromatic half-step is seven harmonic degrees removed; Ex. 8c. i a. Whole step b. Diat. half-step -gyg- c. Chrom. half-step :r= I Ex. 8. -7>9- 2 deg. d. -s>- l f# (The term diatonic refers to the scale, and means "agreeing with the scale.'' The term chromatic refers to the inflection of a scale-step by an accidental.) 17. There are therefore as many possible scales as there are possible combinations of the whole and half-steps. But of all these varieties, there is only one scale that is natural (that has its origin in a natural arrangement of tones), and that is the so-called major scale. 18. The major scale is not "constructed," but is derived from a natural source, — from the key or original tone-family. The major scale consists of the seven tones of the key, arranged in progressive pitches ; that is, reduced by the octave to successive close proximity. Thus (C major) : Ex. 9. r\ C major. as key or tone-family or, closer together AsC major scale , /■ J 1 1 I 7" I a ■ I 1 ft \ f^ „ ,.3 =^ 1 11 1 \^ ) n '^ ^ 1 1 ^ II %-> F C G D A E B F C G D A E B -e- c D E F G A B (C D Eetc. 1 c\- '^ 1 1 '- 1. 1 \ -^ □ 1 \ 1 ej ' 19. When thus defined, by direct derivation from the key, the natural (or major) scale is found to represent the following succession of whole and half -steps: whole steps between scale-steps 1-2, 2-3, 4-5, 5-6, 6-7; half-steps between scale-steps 3-4, 7-8. Thus: T Scalei-steps 3 4 s e 7 8 Ex. ) II ^ , 2> 1 10. ft \ ^ <> '^ II \^ T ^ e> 1 1 «-. (S- ^ O THE MA TERIAL USED IN MUSICAL COMPOSITION. Par. 20. The reason for this apparently inexplainable arrangement of steps is in reality very simple: — the tones simply assume these pitch-spaces when the original key-members are thus reduced to scale-form; it is not devised as a scale, but "comes out that way" by agreement with the tone-family. No further demonstration need be sought. 20. The scale-tones are called steps, or, rather, scale-steps; and are numbered upward from the keynote. Their names are as follows: a. The first, and most important, step is called the Tonic (or keynote); The next in importance is ihe fifth scale-step (the perfect-fifth derivative from the tonic), called the Dominant; The next in importance is the perfect fifth below the keynote, the fourth scale-step, called the Subdominant. These three tones, tonic, dominant and subdominant, are the principal members of the key and scale. The rest are subordinate, and their names, in the order of importance, are as follows: b. The second scale-step is the perfect-fifth relative of the dominant; in a sense, "the dominant of the dominant," — wherefore it is called the Second-dominant; The sixth scale-step lies midway between the tonic and subdominant, and is therefore called the Submediant; The third scale-step Ues midway between tonic and dominant, and is called the Mediant; The seventh scale-step is called the Leading-tone. C major. Ex. m n.^ -S>^ -•- -0- ■ Tonic Dominant Sub- Second- Sub- Mediant Leading- dominant dominant mediant tone REVIEW OF FUNDAMENTAL PRINCIPLES. Rhythm is diversity of time-values, and of dynamic force. There are only two species of beat-groups: duple and triple. Rhythm is regular when the heavier (longer) notes appear on the heavier pulses, and vice versa. Melody is a succession of single tones, a tone-line; and the most significant element in music. A key is a family of seven tones, associated in harmonic degrees (perfect fifths). The only true, natvural, scale is the so-called major scale, which is derived from the key by placing the tones in progressive pitches. The principal tones of a scale or key are the tonic, dominant and subdominant. EXERCISE ONE. a. Write out every key in its original form, as in Ex. 6. b. Write out every major scale, first as in Ex. 10; then as in Ex. 11, attaching the name to each scale-step. Rules of Melody. 21. It may seem impossible to establish definite rules for the mechanical invention of a melody, because this pre- eminent musical element isthe mysterious product of many and varied natural principles, whose subtle interactions must be perceived by instinct rather than by reason. Nevertheless, there certainly are general laws and rules of melodic move- ment which can and must be learned. As stated in par. 6 (which review), the most vital requirement is that of relation. Hence the first rules of good melodic conduct: Par. 32. THE SCALE. 22. a. A melody may follow the line of a Scale. And: h. A melody may follow the line of any good (important) Chord. (The scale is explained in par. i8; for the definition of the chord, see par. 43, 47. be found in thorough detail in the author's Exercises in Melody Writing.) For example: All of the rules of melody will 23. There are, however, some limitations to each of these rules. In following the scale-line, it is necessary to con- sider the natural inclination of certain scale-steps to rise or fall. These tendencies are partly inherent in the relations of the several scale-steps to their keynote, and are partly due to impulses acquired through association with other tones. The former (natural) tendencies are defined as follows: 24. a. The seven tones of the scale or key may be divided into two classes: into Active tones ^ which possess a pro- nounced inclination to proceed in a certain direction; and Inactive tones, which possess no melodic tendencies them- selves, but represent the aim and fulfillment of the tendencies of the others. Ex. 13. Active tones Inactive tones Or -g— sr- 1^^ Steps 7 6 4 1 -5'- -g-:>-s^ 5 Interior Exterior Interior 6. The inactive tones are those which form the chord of the key, or which are generated (as "overtones") out of the kesmote, and which therefore share with it the attribute of rest which distinguishes the keynote from all the other tones of the key. The inactive tones lie, so to speak, at the center of harmonic repose. C. The active tones are the other four scale-steps, which lie outside of this harmonic center, and therefore tend, more or less urgently, to regain the condition of repose. They thus simply respond to the same law of gravity which governs the swinging, and final stopping, of a pendulum. d. The direction of each active scale-step is determined by its proximity to an inactive tone, being most strongly attracted by that inactive tone to which it lies nearest. Thus: The '/th scale-step ascends (preferably one step, to the 8th) ; The 6th scale-step descends (preferably one step, to the 5th) ; The 4th scale-step descends (preferably one step, to the 3rd). The 2nd scale-step is unquestionably active, but, lying as it does equally distant from the inactive first and third scale-steps, the direction of its movement is not positively definable. For illustration: ,, 7 6 4 3 Ex. 14. ^m s^^ ^"-2^-^^ ^ i This rule is illustrated in the following examples: a. Haydn Mendelssohn ^^ Ex. 15. H*>*«-» 8 6 5 4 3 Brahms 8 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 25. 25. These are the natural movements of the scale-steps, and they will be made, unfailingly, as long as the active steps are not subjected to pressure. In good, smooth melody these impulses must and do prevail, 'as all the acknowledged good and satisfying melodies of the classic masters attest. 26. But the natural tendency of any active tone may easily be overcome by pressure in the opposite direction. Thus, the 7th scale-step will descend to step 6, ij approached from step 8. In other words, the succession 7-6 alone is unnatural and irregular, but the whole line 8-7-6-5 is justifiable. The same rule applies to the 6th scale-step, which can be pushed upward into step 7, if approached from step 5. And step 4 will move upward into step 5, if preceded by step 3. Thus: Ex. 16. i ^ ^ m. Par. 2130 -J-JIJ J J ja ^ good The sign ■^ means "wrong." For fuller details, see Exercises in Melody Writing. 27. Moreover, an artificial tendency may be imparted to any scale-step, by various means: Approaching it along the scale in rapid rhythm; so arranging the accompanying tones that it becomes a dissonance (par. 197); by chromat- ically raising or lowering it (par. 265). In this way, the tendencies of the active scale-steps may be either counteracted or intensified; and the inactive scale-steps may acquire tendencies in either direction. The natural tendencies (defined in par. 24^) are the most significant, if not the most urgent, and should generally be respected in preference to acquired tendencies. 28. The limitation to the rule of the chord-line is as follows: Successive skips in the same direc- tion must continue in the same chord-line. That is, if one skip follows another, the second skip must, — if the chord changes^ — be made in the opposite direction. Thus: good i ! J ^ :^ good good m i Ex. 17. i:^ I ^ * Chord C g -•- g-b-d c- e- g 29. The importance of the chord-line as basis of melodic figiures, is shown in the following: a. Beethoven, Sym. III. b. ^iri EE Beethoven, Sym. V. Ex. 18. i^E* I i .equivalent tn "^^S ±^ V^ m fe^ ^ ,-T>. -r -r ^ S m -* SS ^®i ±z J^^'jJ Par. 30. d. FUNDAMENTAL PRINCIPLES. ^P ti^rFJT! ^ star-spangled Banner ffF^Fe ^ — # i^ *«: ^ :;?»- ZJiV Wacht am Rhein ^^m ^ -a- 30. The narrow leap involves no obligation. But after a wide leap (beyond a third: see Ex. 21), the melody usually turns. This is almost imperative when the leap is made to an active tone, less so when made to an inactive scale-step.- Also, it is not necessary when the melody continues in the same chord-line (par. 28). For example: kU-Mf^ 1-J 1 1 J ^ Ex. i9.as j^-^^ -^-^^h^ (?) good better good 31. If the wide leap is made to an active tone in the direction of its natural tendency, it is im- possible to turn without violating this tendency. Hence the rule, that a wide leap to an active tone should be made in the direction contrary to its tendency; that is, dcmm to scale-step 7, and up to scale- steps 6 and 4. (Always excepting when the chord-line is unchanged.) * ± Ex. 20. I f::^ 3^ w better (?) better good possible. good. Test these rules by examining tlie given melodies in the book, — Exercise 16, etc. FUNDAMENTAL PRINCIPLES. A melody may follow the scale-line, and a good chord-line. The natural tendency of scale-step 7 is to ascend; of scale-steps 6 and 4 to descend. The natural tendency of an active tone may be overcome by approaching it along the scale in the other direction. Successive skips in the same direction should be made along the same chord-line. After a wide leap, the melody usually turns. A wide leap to an active tone is best made in the direction opposite to its tendency. EXERCISE TWO. First study par. 43, 44,. S^- Then write a large number of melodic sentences, either 4 or 8 measures in length, with strict observance of the above rules, and imitating the style of the given melodies (Exercises 16, 17, 22, etc.). lO THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 32. HARMONY. 32. Harmony, in its narrower sense, is the combination of single tones; in its wider sense, the association and succession of such harmonic bodies. 33. The combination of any two tones constitutes an Interval. The term interval, or "space," can obviously not be applied to tones, as tone-associations are not defined by distance, but by relation only. The word "interval" does, however, apply to the notes, which lie upon the staflE (and in the scale) at varying distances from one another. The names of these spaces, — between the notes on the staff, — are simply adopted as names for the various tone-associations, or synonyms of the tone-relations. INTERVALS. 34. Intervals are always counted from the lower note upward, as the major scale goes, and are de- termined by the number of steps of the scale included by the two notes. i pnme or unison second third fourth fifth sixth eighth or seventh octave ninth tenth 9 Ex. 2t. 5^ -s>- letc.z: sz^- The first eight are simple intervals; the last two and all that follow (beyond an octave) are compound, — consisting of an octave and a second, octave and third, etc. Such intervals are always reduced to simple ones, and called, with omission of the octave, simply "second," "third," etc.; for, as already observed, these terms indicate strictly the relation- ship between the letters, which is always the same without regard to distance, as long as the letters do not exchange places. Thus, C-D is a "second," whether written ^m^'-mm and even D-C i g^): is but slightly different. 35. These intervals, which follow the major scale, and therefore represent the simple scale-rela- tions of the several steps to their keynote, may be called natural or diatonic intervals. They are divided into two classes: perfect and major. The unison, fourth, fifth and octiLve, from the keynote of any major scale^ are called perfect. The second, third, sixth, and seventh from the keynote are called major. C major. a. Perfect. g 8ve 6. Major. 6th 7th Ex. 22. rUnison. ~^t h 5th- -3rd- That is to say, the interval c-f (for instance) is a fourth, because / is the 4th letter or step in the scale of C; and it is a perfect foiirth, because it exactly agrees with the natural scale of C, and because "perfect" is the term used to qualify the natural or diatonic 4th. The interval e-c# would be counted along the scale of E, and, as c# is the 6th letter from e, it is a, sixth; furthermore, a major 6th, because it exactly agrees with the scale of E, and because "major" is the term applied to the natural sixth. Par. 36. INTERVALS. II 36. A perfect interval, when extended by an accidental (0 #'*), the letters remaining the same, be- comes augmented; when contracted by an accidental (B [> bb), it becomes diminished. For example: Perfect 5th Augmented 5th Diminished 5th Ex. 23. w m i It is obvious that if the letter were to be changed, the quantity of the interval would be altered. Therefore the g# (Ex. 23) must not be regarded as equivalent to a\>, nor g\> to/#. 37. The perfect intervals are so called because they represent the best (most nearly "perfect',') relations, — the asso- ciations of the htyaote with its dominant and subdominant, the three principal tones of the key (par. 20). Ex. 22a. The associations of the keynote with the other scale-steps are less perfect ("imperfect") relations, and to these the term major (the "greater") is given, because they represent the larger of two sizes that are constantly being assumed by what is prac- tically the same relation. The "smaller" of these sizes is called minor, and it is obtained by contracting the major interval by an accidental. There are therefore four minor intervals, derived from the four major ones (Ex. 22 b). Maj. 2nd Min. 2nd 3rds 6ths 7ths Ex, 24. ■S w d7=^ Maj. ^ ±S =g^ i -s>- Min. Maj. -19- Min. -f9- Maj. -S>- Min, As stated, the major and minor sizes represent practically the same relation. That is, there is no radical difference between major and minor; none that affects their treatment as musical factors. They are merely different aspects of the same tone-relation. But, on the other hand, the inflection of any interval into its augmented or diminished form does result in a radical difference, both in relation and treatment. 38. A major interval, when extended by an accidental, becomes augmented, precisely like the per- fect intervals. When contracted it becomes, as has been seen, not diminished, but minor. A minor interval, when contracted, becomes diminished. Thus: Ex. 25. Major 3rd Augm. 3rd Minor 3rd Dimin. 3rd ^^ ^ m i From this it appears that the perfect intervals become diminished by one contraction, whereas the major intervals must be contracted twice to become diminished. 39. In defining the quantity and quality of a given interval, the student must start from the only infallible standard, the major scale, and erect it upon the lower of the two notes. The number of the upper note in the scale gives the quan- tity. If the upper note agrees with the scale in question, the interval will be either perfect or major (par. 35). If not, it will have become minor, augmented or diminished, according to the inflection that has taken place (par. 36, 38). This, and a few other conditions, are shown in the following example: i 12 8 4 5 b. grij j^^nis g ^ g ■ i ^^' -''- \ m ^ m h^ Ex. 26. =5=*= G maj. scale D|> maj. scale At a, the interval is a sth in quantity; the scale-note d being changed to (i#, the natural "perfect" sth has been ex- tended to an augmented sth. At b, quantity, a 7th; being altered from c to cb, the natural "major" 7th has been con- tracted to a minor 7th. 12 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 40. In cases like c, where the major scale of the lower tone is unfamiliar and inconvenient, the simplest process is to shift the interval to a convenient place by cancelling an equivalent accidental from both notes. At i: This somewhat rare interval would be called a "double-augmented" 4th. At e: Instead of the contradictory "diminished prime" (g-gb), one should designate its equivalent, the "diminished odaw." EXERCISE THREE. A. Erect the dimin. octave, minor second, dimin. third, perfect fourth, augm. fifth, minor sixth, and dinun. seventh, _ upon each of the notes E, A, D, G, B, F#, C, Git, F, and Bb: B. And determine the names of the following intervals: and the augm. octave major second, minor third, dimin. fourth, perfect fifth, augm. sixth, and min. seventh. on the notes fDb, ^, C, F. Bb Ab D, Eb, GK ^^i^ is I ^^^^^S^^^^^^^^^^^^ -|^|s^'J^ ' §> '{faWz^ ^&- "Xg~ fc t>g-g'- i I m ^ ir m IE P= w^ -ZSr Consonance and Dissonance. 40. Besides the relation of generation (explained in par. 11), which determines the right of the tones to associate as independent factors, in their operations within a key, there is another quality of tone-relation or affinity known as con- sonance. This refers to the degree in which the tones blend with each other, as soimds, and determines their right to ap- pear in simultaneous union. (All the tones of a key are related by generation to their tonic, but if all sounded together at once there would be a disagreeable excess of dissonance; so it is evident that the first relation does not fully guarantee the other.) 41. The distinction of consonance and dissonance is defined by the vibratory ratio of the sound-waves which pro- duce the sensation of tone. a. It has been seen that the ratio i : 2 gives the octave, and 2 : 3 the perfect fifth (or harmonic degree). The next ratio, 3 : 4, gives the perfect fourth. Then follow 4:5 — the major third; 5:6 — the minor third. h. Thus, as the tones approach each other in pitch, the ratios become more complex; there is a gradual increase of conflict between the sound-waves, resulting in proportionate decrease in consonance, or tone-blending. The ratio 8 : 9 gives the major second (or whole step), and 15 : 16 gives the minor second (or diatonic half-step). c. In musical theory, the ratios up to 5 : 6 produce consonances; those which follow produce dissonance. Therefore, the minor third is the smallest consonant interval. d. The consonances are divided into two classes, however, because of the appreciable difference in their degrees of blending. The octave and fifth (direct and inverted, — par. 42) are called perfect consonances; the others (thirds and sixths, both major and minor), are called imperfect consonances. e. All seconds and sevenths, and all augmented and diminished intervals, are dissonances. Par. 42. CHORDS. 13 42. The inversion of an interval is its complement within an octave. Thus: 8ve 7th 6th 5th 4th 3rd 2nd Unison Ex. 27. -O- Unison P 2nd 3rd 4th 5th 6th 7th ive In the inversions, one tone is simply transferred past the other to a higher or lower octave, therefore (on the grounds of par. 11) an interval and its inversion are practically identical. A perfect interval when inverted remains perfect; the inversion of major becomes minor; the inversion of augmented becomes diminished. Chords. 43. A chord is the combination of more than two tones, so chosen that the intervals are entirely or preponderantly consonances (par. 41^). The English word "chord," possibly owing to a confusion of derivation, has the same meaning as the word "accord " (" Akkord," "accordo ") used in continental Europe, and signifies a body of tones which accord with each other. 44. Consonant chords, or concords, containing none but consonant intervals, can not embrace more than three tones, combined as follows: a. 6. c. d. e. f. '->S>-K Ex. 28. ^ijji=Uft)-^^^i^P (Eb may be substituted for E, and A b for A, because the intervals 3 and 6 may be either major or minor. The inter- vals s and 4 must, however, be perfect to be consonant.) The fopns 3.td,e, and/, are identical with a, b, and c, respectively. The forms 6, and c, are merely modifications of the first and natural form a, by inversion. For illustration : :1E Ex. 29. W- c=^ — (§-) 3 ^)S- =S) From which it appears that Ex. 28a, in which the tones lie one above another in thirds, is the pri- mary chord-form, from which all others are derived. 45. a. If another third be added /K » i9& -\ H (the ear sanctions ib in preference to 611) the new tone le lowest. forms a dissonant interval (7th) with the lowest. b. If still another third be added there will be three dissonant intervals. 46. a. Chords like these, which contain one or more dissonances, are called dissonant chords, or discords. Their use in harmony is not only sanctioned but demanded; because, on account of the obligations associated with a dissonance, they are more active than consonant chords. And, besides, their slight harshness affords a necessary contrast to the purer but less attractive concords. b. Still, the dissonant intervals miist be introduced in judicious proportion to the consonances, which must largely predominate. The addition of still another third to the above chords would inaease the number of dissonances to such an extent (as shown by the lines) that there would barely be a predominance of consonant intervals. 14 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 47- c. To such tone-combinations as these, which extend beyond s tones and contain an undue proportion of dissonances, a place is assigned and to such tone-bodies as do not conform to the structure of tliirds (for example i among the so-called Inharmonic elements, where they can be much more simply and satisfactorily analyzed. 47. The concise definition of a "chord" is, then, a combination of three, fotir or five tones, in in- tervals of thirds {or reducible to such). 48. A chord of three tones is called a Triad (usually a concord); a chord of four tones is called a Chord of the Seventh {discord); and a chord of five tones is called a Chord of the Ninth {double- discord). Triad Chord of the 7th Chord of the 9th Ex. 30. i 49. The tones which constitute a chord are called, separately, the Intervals of the chord (or chord-intervals), the term "interval" here again signifying the harmonic relationship of the upper tones to the lowest. The lowest chord-interval (the one upon which the structure of thirds is erected, and from which the whole chord emanates) is called the Root. The other tones are called the chord-third, chord- 5th, chord-7th, and chord-pth, respectively, according to their distance from the root. Ex. 31. _Fifth_ IThirdZ I^Rootl -^ Ninth Seventh! -IS- Root- I 50. A major third and perfect fifth constitute a major tried; a minor third and perfect fifth, a minor triad. The augmented triad has an augmented 5th and a major 3rd; the diminished triad, a diminished Sth and minor 3rd. Major triad Minor triad Augm, triad Dim. triad Ex. 32. i w ^ i There are a few other distinctions made in the species of triads, and the varieties of four- and five-tone chords reach a high number. But as it is not the shape and sound of a chord, but its location in the scale and consequent relation to its tonic which defines its treatment, no further attention need be paid to these distinctions. 51. A triad may be erected upon each tone of the diatonic scale, excepting the leading-tone, and each triad takes its name from the step of the scale which its root occupies. Ex. 33. i C-major w -rg- I Tonic Dominant ^ triads, or Principal triads. Subdominant ) i Second-Dom. Submediant Mediant I triads, or Subordinate triads. Par. 53. THE VOICES OR PARTS. IS The first three are principal, because they emanate from the principal tones of the scale (par. 20 a), i.e., the tonic or keynote itself, and those other two tones which stand in the relation of the harmonic degree (perfect fifth) to the tonic. These are the fundamental harmonies of a key, and, being major triads, they characterize and give the name "major" to their key. The last three are subordinate, because they he more remote from their tonic; and, being tmnor triads, they contradict and oppose the prevalent major character of their key, and can therefore appear only as subservient and contrasting elements. 62. For convenience, the triads are designated by Roman nimierals, coinciding with the situation of their roots in the diatonic scale, as follows: Ex. 34. ^, ^ , , ;; t^ mm II III IV V VI Spoken: "the One," "the Two," "the Three," etc. 63. The triad upon the leading-tone must be set aside for the present, for reasons which will appear in due time. FUNDAMENTAL PRINCIPLES. Intervals which agree with the scale-steps are perfect or major. There is no radical difference between major and minor intervals. An interval and its inversion are practically identical. A chord is the combination of from three to five thirds. The leading-tone cannot be a root. EXERCISE FOUR. Write out the six triads of every major key in the order given in Ex. 33, attaching the name, in Roman numerals, to each. The Voices or Parts. 64. Music of every description is based upon the succession of chords, in such harmonic order as the various tone-relations (and the melody) dictate, and in such metrical order as the character of the piece requires, or the fancy of the composer suggests. For the adequate expression of such a suc- cession of chords, four distinct tone-lines, called voices or (especially in instrmnental music) parts, are necessary, and are usually employed. a. Chords of three tones furnish material for but three parts, it is true, but it is advantageous to duplicate one of these three tones, in order to define the chord and the key with greater distinctness, and for this duplication a fourth part is required. And, on the other hand, chords of five notes, being somewhat unwieldly, are almost always deprived of one unimportant interval, so that even for such chords four parts are sufiScient. 66. These four voices or parts are called (from the lowest upward) Bass, Tenor, Alto and So- prano. As vocal parts they have the following average compass: Bass _^. (^) Tenor >rz: ZZ Alto Soprano J .J. -^^^^^^m T>r ^ ^ IG - C i6 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 56. 56. The female voices (soprano and alto) correspond respectively in compass to the male voices (tenor and bass), but difiEer just about an octave in register. The highest and lowest of each class (soprano and tenor — alto and bass) are therefore called paraUel parts. The compass here given is a safe average, and is bounded, as will be observed, by the tonic and dominant of C. In instrumental music the compass of the parts depends entirely upon the instrument employed; for pianoforte music the compass is almost unlimited, and the terms soprano, alto, tenor, bass, refer merely to the relative position of the differ- ent parts, the highest being always "soprano," the lowest always "bass,'' etc. The parts are usually written upon two staves, the female voices in the G-clef, the male voices in the F-clef ; and the stems' of the notes are turned respectively upward and downward to distinguish the parts which occupy the same staff, — as shown in Ex. 36. 57. The most important of these four tone-lines is, generally speaking, the soprano, as its tones are more prominent than those of the lower lines, and it therefore generally carries the "melody" proper, the air or tune of the sentence. The next in importance is the bass line, as it defines the chords, and supplies the harmonic basis of the composition. The__two inner parts are comparatively unimportant, as individual Unes; they accompany the outer parts, and com- plete the harmony. The arrangement and progression of the four parts or melody-lines which co-operate in the expression of a musical thought, are illustrated in the following example: Ex. S6. & Melody f= im-. f= i -^Soprano -»Alto ^-1-1-1- J a ZBASSft f^T X ->Tenor ■»Bass X 58. Rtde I: The parts shotild not cross (e.g., the soprano line should not be carried below the alto; and the same with the other parts). Ride II: The alto should not he more than an octave from either of its two neighbors, soprano and tenor. For example: good Ex. 37." rtfc^^,^^^# ^ ^ ^ 59. Duplication of Chord-intervals. The best notes to double are the principal tones of the scale (the tonic, dominant and subdomi- nant), wherever they occur; — excepting, first, when they are the chord- fifth in a triad, which interval is not entitled to the prominence which duplication gives to a tone; and, second, when they represent a dissonant interval (par. 2ood). By thus emphasizing the chief elements of the scale, the identity of the key is maintained throughout in the most consistent maimer. The result is as follows: Par. 60. Ex. 38. m THE POSITIONS OF A CHORD. b. . c. 1 17 ?? a. IE it -9&- I ^m IV II VI III IV II 60. From this it appears that in the principal triads the root (Ex. 38a), and in the subordinate triads the chord-third (Ex. 386), should be duplicated, as a general rule. As seen in Ex. 38c, the chord-fifth of the I, and also of the IV, are principal tones of the scale. But they should never- theless not be doubled, because of their quality as chord-fifth. In subordinate triads the chord-fifth is a subordinate scale-step, and therefore its duplication is still more questionable. Also, for the same reason, the chord-third of a principal triad should not be doubled, as a rule (Ex. i&d). 61. There are two additional, exceptional possibilities, as follows: a. In the subordinate triads the root may be doubled (though a subordinate tone of the scale), be- cause it is the principal interval of the chord. (Ex. 39a.) b. In the principal triads the chord-fifth may be omitted, and the root tripled. (Ex. 396.) Ex. 39. i a. Good /Better atto ditto ^ ^ ^ II V~z^ II VI III I IV The Positions of a Chord. 62. In view of the prominence and significance of the uppermost tones (par. 57), it is evident that much must depend upon the choice of chord-interval assigned to the soprano part. This choice, which also defines the principal melodic line, determinfes the so-called position of the chord, as follows: a. When the root is in the soprano, the chord is in octave-position. "Octave" is here synonymous with "root," and appUes to the root in any part above the bass. b. When the chord-third is in the soprano, the chord is in the position of the third (not "third- position"). c. When the chord-fifth is in the soprano, the chord is in the position of the fifth. Thus: Position of the 8ve 8 Position of the 3rd Fosifion of the 5th Soprano. , Alto. Ex. 40. Tenor. Bass. ^Octave (Root) ; :3r'L -5th- :5thi ■3rd I 9- -#-5th- i Octave (Root) i Octave f :Rooti ^ :Root: ^ IRooC i I8 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 63. FUNDAMENTAL PRINCIPLES. The principal tones of the key should be doubled, as a" rule. Any root may be doubled. The chord-fifth, in principal triads, may be omitted; but not doubled. The "position" of a chord is defined by the soprano. EXERCISE FIVE. Erect the six triads of G major in successive order (I, II, III, IV, V, VI), in their three positions, according to the following model: i Octave-position 8 I Position of the 3rd Pos. of the 5th 1,83 I , J i A =J FPFf i^ C major I good (s\h I I II 60 613 The root must always be in bass. Strict regard must be paid to the compass of the parts (Ex. 35), and to the dupli- cation of Intervals (par. 60, 61). The following examples are wrong: ^ ^ ^ ^ Uv^Mm- J ^ Ml 1/ = I I 58, Rule 2 Ex. 381^ Ex. 38c Ex. 35 Rules of Part-writing. 63. The conduct of the four voices or parts, the tracing of the four tone-lines which co-operate in the combination of harmonic bodies, is guided by the following four fundamental laws of voice-pro- gression: 64. Rule I. a. Each part should move as evenly, connectedly, (diatonicaUy, "horizontally") from one chord-interval to another as circumstances will permit. h. Wide leaps should be avoided as much as possible. c. A tone that is common to successive chords generally remains unchanged. d. This rule applies chiefly to the inner parts. Both soprano and bass may be treated with more freedom. Par. 65. RULES OF PART-WRITING. 19 For example: Ex. 4.1." J^J I Jl i r-f ' r-f 'r-f ' r~f " ^-J i ^ j J- J , ^ =^ f^Mf=4 i N.B. Each of these measures is an example by itself, and is not to be connected with the one that follows. 65. Rtile n. a. No two parts (neither outer, inner, adjacent nor parallel parts) should move in parallel motion {i.e., direction) from one perfect fifth to another perfect fifth; nor from one perfect octave, or unison, to another perfect octave, or unison. In other words, parallel or consecutive fifths, octaves and unisons, in the same pair of voices, are prohibited. b. Successive chord-fifths sound disagreeable because of the comparatively impleasant sound of the interval of a per- fect fifth. The ear accepts one of these at a time (especially when softened by the presence of a third), but rejects two in close and evident succession. As will be seen, the effect of even one fifth alone, when rendered conspicuous by any means, may be decidedly unwelcome; and inversely, whatever serves to conceal or disguise the fifth, proportionately re- moves the objection. c. Successive octaves do not offend the ear; but when two distinct parts make the selfsame movement at the same time, the individuaUty of each part is momentarily lost. In successive unisons, one part disappears entirely. Persistent successive octaves, on the contrary, which duplicate an entire melodic figure or line, do not convey this disappointing im- pression, and are therefore good, — the intention being obvious. d. Consecutive seconds and sevenths are forbidden by common sense, and are therefore not included in the rule. Con- secutive fourths are as disagreeable as fifths, but apparently less distinct; they seldom occur alone, and whatever accom- panies them generally overpowers them. 2nds 3rds 4ths 5ths 6th5 ^ths Sths St Paralld ™,U 6, 7). 24 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 77. THE REVERSED SUCCESSION, V-I. 77. a. From the octave-position of the V. h. From the position of the third, c. From the posi- tion of the fifth. a. 76a b. 3 ^^ par. 67 lA^l-Ul 76* ^^ Ei £Si ^ f=f=frr T ^'T ^Vr F-rT=f Ex. 50. ..)i JJ J i J J i i i*i J*i J i J, ^ etc. p^ g V I 1 i I *i) The leading-tone, in the tenor, is led downward, to g, instead of upward (67).- This is permissible on two con- ditions: first, that it occurs only in an inner part; second, when it is preceded by a higher tone, — that is, when it is on the way down, as in Ex. 16. See Ex. ^id, e. Further, it must not descend with any wide leap, — excepting, always, during chord-repetition. 78. As stated in par. 73J, the above progression, from V to I, is one of the most urgent, most nearly inevitable chord-movements in music. This, and all similar successions, in which the chord falls one harmonic degree, will be distinguished in this book as the Nonnal progression. FUNDAMENTAL PRINCIPLES. The tonic triad (I) can progress to any other chord. Every chord can progress to the dominant triad. The dominant chord is characterized by the leading-tone. Successive octaves in contrary motion are allowed, but not fifths. Successive positions of the 5th are not good. The Normal progression of a chord is a harmonic degree (perfect fifth) downward, — from root to root. EXERCISE SIX. Connect, as in the above examples, the I-V in G major; the V-I in B-flat major; the I-V in E major; and the V-I in D-flat major. Each in as many ways as possible, but carefully avoiding all errors or doubtful movements. Review par. 64. The Perfect Cadence. 79. A cadence is an interruption or momentary pause in the rhythmic movement; a stopping- place, or point of repose in the sentence, which indicates the end of a melodic member or section of the composition. A cadence is made with at least two chords; the final one of these is called the cadence-chord. All cadence-chords fall on an accented beat. Cadences differ in force or weight, partly according to the importance of the cadence-chord, and partly to its length. In order to interrupt the rhythm, the cadence-tones should be somewhat longer than those which adjoin. Par. 80. THE PHRASE. 25 80. The perfect cadence, or full stop, which occurs at the end of the entire sentence, is the com- bination of the four following conditions: i, The tonic triad; 2, in octave-position (root in both outer parts); 3, on an accented beat; 4, preceded by the dominant triad {in any position). For illustration: 8 8 8 T- i Jn-^-Hf " I ^'^ J-i^ -4 i=i fe^ 2_(or_4.) ^Y ^"F=^='^^ p-' r r r ' fU ^ Ex.. 51. J i ^/^ lA I I ^ .-J-J. ^ ^.^^^^ I ife ^(or_^)- ^ AVAV I f-h2 — (S. f=^ a) r Par. loi. THE PRINCIPAL TRIADS IN THE MINOR MODE. /■ -5 ♦a) 8 33 ^^EfSE^E^'^f^^ ^^=^^^^ ^■ D major. | I IV V I IV IV V »3) ^ P =f= I I *i) The Foreign progressions are indicated by brackets throughout these basses. The melody is found according to par. 99. — *2) The irregular progression V-IV. — *3) Value, dotted quarter. — To this exercise, add a number of Original phrases, as before. The Principal Triads in the Minor Mode. 101. The derivation of the major scale was shown in par. 18. The so-called minor scale (or mode) is not a natural, but an artificial scale. It is a modification of the natural major form, and is obtained by chromatically lowering the 6th and 3rd scale-steps of major. See Ex. 68. This practice of "bending" the natural scale is extremely conunon in music, and yields significant results, which will be considered in their proper place. Glance at par. 265, etc. It is the process through which every possible irregular scale-form is obtained. See par. 16, 17. 102. The lowering of the 6th and 3rd scale-steps is the simplest and easiest method of alteration, because these are the only changes which do not impair any one of the principal triads. These changes merely contract the chord-third of the I and IV from major to minor intervals, — see text below Ex. 24. (The lowering of the 7th scale-step is also possible, in the V, but strong melodic reasons forbid tampering with the leading-tone, which must remain a half-step below the tonic in order to characterize the key, and retain its vital upward tendency.) Any other scale-change would augment or diminish some interval of a principal chord, and thus impair it. This accounts for the great frequency and legitimacy of the minor mode. Of aU the "bent" forms of major, the minor mode is the most natural and common. The alterations are not merely transient (as all others are) but may be practically permanent, creating a form of the scale which is popularly assumed to be equal in importance to the true natural (major) scale. 103. The C major scale, thus altered, assumes the following minor form; and the principal chords in minor are modified accordingly: C, major form C, minor form Principal triads.*l) i Ex. I m is 68. =^ ^ IV "i) The I becomes a minor triad; the IV becomes minor; the V remains, as in the major mode, a major triad (as a rule, at least). 104. This form of minor is called the harmonic minor scale, because it coincides with the principal harmonies of the key; also in distinction to the melodic form, to be explained later. 105. There are no specific signatures for the minor modes; key-signatures are peculiar to major key-notes. Often the same signatiure is used for both modes; but it is customary to borrow another signature for minor, — merely for convenience. The one thus chosen is the signature of the third scale-step of minor: for C minor the signature of e-flat, its (lowered) third step, — three flats. 34 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. io6. This "customary" signature is the most convenient one that can be found; but it attacks the 7th scale-step also, and therefore an accidental must always precede the leading-tone, in the harmonic minor, to restore it to its proper place in the scale. Thus: C, harmonic minor Witli customary signature V Ex. 69. » g g ^ „ K> "- | ^^--_ g ^ r, ^ ^'^ ^ ■- - ^ ^^.^-^ t -^ I N.B, It must be distinctly understood that this signature does not indicate E-flat major. It is borrowed from that key, for convenient application to C minor. (The keys whose signatures thus correspond, are called "relative" major and minor. See later.) 106. The downward tendency of the 6th scale-step is made more urgent in minor (in consequence of lowering it), for which reason it might be called the "dominant leading-tone." a. In minor the 6th scale-step {dom. leading-tone) must progress downward, — excepting in chord- repetition; and it should not be doubled. b. It is forbidden to progress from one leading-tone to the other (7th scale-step to the 6th, or 6th to 7th). 6th 7th 7th 6th ^^ } ^^r^^--^P=^^-\^^ H Not only because each of the tones would progress in the wrong direction, but because the succession involves an imnatural chromatic interval (an augm. 2nd) which it is difficult to sing true, and which sounds peculiar. This error is best avoided by close attention to par. 67a, 6. This succession may be produced on an instrument, it is true, but it always sounds unnatural, and is appropriate only where a weird efiect is desired. * 107. The chord-progressions in minor are of precisely the same quality as in major, and are exe- cuted in precisely the same manner, according to the same rules (par. io6a merely emphasizes a former rule). FUNDAMENTAL PRINCIPLES. The minor scale is derived from the major scale of the same tonic. rThe harmonic minor scale differs from the major at the 6th and 3rd steps, which are lowered a half-step. The dominant chord is alike in both modes. The 6th scale-step in minor must progress downward. The two leading-tones (6th and 7th steps) must not succeed each other in the same part. There is no essential difference in the treatment of the major and minor harmonies. EXERCISE TEN. The signatures prove that the following basses are in minor. The accidentals below certain bass tones refer to the thkd of, the chord (in bass a,/#, the leading-tone; comp. Ex. 69), and are rendered necessary by the absence of the cor- responding accidental in the signature. Review par. 105. The accidental must appear in that upper part which has the leading-tone. Par. to8. sa THE SUBORDINATE TRIADS, IN MAJOR. FaISST *._8 8*1) *a) 35 m i ^ I r I ' rJJ ' L-L i^ *2) +8 ase r r r ^^ rT^ rf. *3) ^ I S t 1 +3 a^ ^ *2) i=P= 3 :^ /• 3 P fr^?= i ffi ? ita= -z;*- F# minor. 4 I V *3) 8 I IV 3 +3 V I IV 5 +8 3 I I IV V I I I V V I V I *4) I 1 I •i) io6a. — *2) 996. — *3) Rhythm [ | , of course. — *4)' The bracket 1 1 indicates that both chords belong to one beat. The tie ' -" signifies here, as elsewhere, that the chord is to be held, not reiterated; the rhythm of this measure is therefore I J ri J I °r I J J^ J 1 • To this exercise, add a number of Original phrases. The Subordinate Triads, in Major. 108. See Ex. 33. The three subordinate triads should not be regarded as new and independent harmonies, but merely as modified forms of the principal chords. They are the relatives or parallels of the latter, and serve chiefly as substitutes for them, for variety. The relation is defined by the principal scale-step which each subordinate chord contains. In the VI of C major, for example, the most important of its three tones, in the key, is its chord-third, the tonic note c: C major Ex. 71, principal tone VI This proves that the ruling element in this chord is the tonic, which places it among the chords of the tonic class. The same test, with the other two subordinate chords, C major. ~^> y prin. Ex. 72. prin, tone. II $ prin. tone. Ill shows that the II belongs to the subdominant, the III to the dominant class. That is: The I and VI together represent the Tonic class; 36 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. log. The IV and II together represent the Subdominant or Second-dominant class; and The V and III together represent the Dominant class. See par. 70. VI III b. Ex. 73. \ a. (Ex. 9) III o *l) =^= -gr- IS IV V VI IV II =i^ III -gr- -related- -related— -related- m *i) It will be observed that the "related" chords are the exponents of those major and minor modes which have the same signature. 109. The functions of the related triads, though not identical, are so very similar as to justify this classification. The subordinate chords act mainly as subsHtuies for their respective principal chords, and deduce almost all their har- monic regulations from the latter. The Second-dominant Triad, II. 110. a. This is in reality the fundamental representative of the subdominant or Second class, as will be seen later on. Comp. par. 90. b. The best position is that of the third. c. The octave-position, in a subordinate triad, is more objectionable than in a principal one, because undue promi- nence is given to a subordinate step of the scale, in placing it thus in both outer parts. Still, the octave-pos. of the II is not forbidden, because it is the best of the subord. triads. d. The position of the fifth is very objectionable in this triad. 111. Either the third or root may be doubled. No interval can be omitted. Review par. 59, 60, 6ia. 112. Being a subdominant chord, the II contains the 4th and 6th steps of the scale. Care must be taken to lead them downward, — especially in soprano. 113. The following examples illustrate the progressions of the II, in the order of natural preference. See par. 109. a. The Normal progression, II-V (par. 78). J. 76a s, " possible m ^ 71^ better ll ^^ i II V Measure No. 3 is good, because of the skip down to the leading-tone (par. 31). No. 5 illustrates a very common move- ment, — the deferred resolution. (The term "resolution" is applied to the progression which fulfils the tendency of any active tone.) The 4th scale-step in soprano reaches the 3rd step indirectly, after the interposition of one convenient tone. No. 4 is doubtful, because the resolution is entirely evaded. No. g is an unusual exception to several rules: the alto has the deferred resolution of step 4; the soprano may be justified by Ex. 16-2. Par. 1x4. THE SECOND-DOMINANT TRIAD, II. 17 b. The progression to the tonic triad. This is a Foreign progression, and a rare one. It is rather singular, that no other chords can progress into the I excepting the V and the IV (the two triads re- lated to it by the harmonic degree). The II abhors the direct progression into the I, always preferring to move first into the V. 1 112 Ex. < 75. II-Ll h=^==^ -J, i Ex. 16-3, 8 ¥. :t ^ »i) J-A 99^ rrr r, r f i r ' r r'r ^^¥^ I I ?? i II I '1) In every foreign progression excepting IV-V (Ex. 66, where both are prin. triads) it suffices to lead two upper parts contrary to the bass; the other one moves in srds parallel with the latter. c. The progression to the IV. This progression, from the II into its own principal triad, is not good. When the two representatives of the same class are connected, the subordinate triad should follow, not precede, its own principal triad. In other words: of the two parallel chords, the principal triad comes first. Thus, the IV can pro- gress to the II, but the II cannot progress to the IV. And the same applies to the other classes; I-VI is correct, but VI-I is wrong; V-III is allowed, III-V is incorrect. Ex. 76. II-IV. J J J *l) ^ n r~r-T U ^ i*i^ i X I 9i ?^ t ^ II IV VI I III V *i) This is a rare exception to par. 73c. 114. The triads which introduce {i.e., precede) the II are exhibited in the following examples; ar- ranged, as before, in the order of preference. a. From its relative prin. triad, the IV. Ex. 77. IV-II. i w^ t »l) ^ J- r * 4 —r 4 I *a) ^m I i ^^ .^i ^ J^ I I (?) tet -SH f= j'-'i i A. A. fB^t ff^^^ IV II *i) The coimection of relative triads is considered nearly equivalent to chord-repetition. Therefore, the licences of par. 68 are valid here, with slight limitation. This accounts for the wide leaps in the soprano in these three measures, — even measure 6, from the chord-fifth c. It also tends to excuse the'pos. of the fifth in the II (measure 7). — *2) Comp. Ex. 74-g. 38 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 115. 6. From the tonic triad: a Foreign progression. Ex. 78. I-II i »8) m -*-zz r r ' /-^-^ ;+rT r r ' r I I 1 I , ' I ? , ? ' m. i^ ^P3? L\iUJU Mr f ' r nr r ^ ^ II 2) These wide skips are a little less objectionable than usual, because both tones (/-<;) are 'i) Ex. 75, Note *i). - principal steps of the scale c. From the dominant triad. This Progression (V-II) is the counterpart of Ex. 67 (V-IV), because the IV and II are parallels, and in each case the V does not progress, as it should, to a tonic chord (par. 1006). Nevertheless, the progression V-II may be more readily effected than V-IV, on account of the relation of a harm. ^ degree which the triads represent ' V II The first measure of the following example shows the most rational connection, similar to Ex. 67-4, 5- i IE :J^J=i r f r ' r ^i IIO* J J *i) J *2) n *3) , I X X VS^^EE^ V (II) V *i) The skip from the leading-tone is wrong, because it is not chord-repetition. *2) This soprano is wrong. Only when the V progresses to a tonic chord, has it the effect of a dominant chord. In this measure it sounds like the I of G major, and the/O in soprano (instead of /#) is therefore disagreeable. When the/ is introduced with a skip from below, as in the first two measures, the impression of G major is weakened. — *3) Here the incorrect progression of the leading-tone, followed by the forbidden position of the 5th, renders the false impression of the key still more palpable. 115. The following melody illustrates the predominance of the position of the third in the II. i 't M-^ j^i-^ ^ *i) 2=P= =?s^^ ^ * II — V V — II •i) In adding the inner parts, the third of this chord must be doubled. II — V r^ i Pai. xi6. THE SUBMEDIANT TRIAD, VI. 39 FUNDAMENTAL PRINCIPLES. The VI is a tonic chord, the II a subdominant or Second-class chord, and the III a dominant chord. In the II, the position of the 3rd is the best; that of the sth rare. The downward tendency of scale-steps 4 and 6 must be respected in all second-dominant chords. A subordinate triad does not progress into its own principal triad. The V should progress to a tonic chord, — not to the second-dominant chords. +s *l) i EXERCISE ELEVEN. 5 *1) 3 * m iZfil EPe s ^m ^^s d d -* 3tZt tcf d. ^ m'ln r f ju ^ I ^ =3e=t * ' • 2 -8 13 S Dl? major. 4 I I I IV II I V V I I I 1 IV IV I II V I I V I I *i) Par. 112. Bass e should be worked out in several other keys, with other positions. To this exercise, add a number of Original phrases. The Submediant Trlad, VI. 116. Review par. 109. a. The best position is that of the third. b. The octave-position is forbidden. c. Third or root may be doubled. Par. 6ia. 117. The progressions of the VI are exhibited in the following examples, in the order of their preference. a. The Normal progression (to the II). s Ex. 81. VI-II i 1 l ^:J' | J-1 I J iith b. To the V: Foreign progression. 8 Ex. 75, Note. 1 * I fi U ^ i^ . ^ j WWf^ Ex. 82. VI-V J I J J, 99" fm- * i VI 11 II VI V 40 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 1 1 8. Ex. 83. VI-IV c. To the IV. 4- i *l) *3) *3) IE \ — d h \ ^^^^ — \ 1 \ H-/" ^ \_i I J-' I J J I j..-^ I ( ^ t r- ? ? >- !► -f- i I r r J ^T r ■d 1 — r I /"i , /"i ^ I VI IV ' I ' I ' I *i) Par. 31 excuses these wide leaps in soprano. — *2) Also excusable, though the first tone (e) is a chord-fifth. — *3) Not very good, because of the wide leap down to step 6, and the irregular duplications. d. To its own relative, the I. Forbidden progression. See Ex. 76. 118. The VI may be introduced (preceded) by the other triads, in the following order: a. By its relative, the I. (Comp. Ex. 77.) ■J I i j_i-! J I , . ^J^^ • g tei ! r' r 7 f' f -f=^ J J- ^ 4 * i I * ^J-^ -J- i 763 VI =r-t *i) See Ex. 77, Note *i). b. By the II : an ascending harmonic degree. 8 Ex. 85. II-VI i IE r r^ J*!) g± ^^ J-^, J i" J ^m II VI ' ' *i) The soprano is unnatural, because it stumbles beyond the expected half-step progression, f-e (as in the measure before). The 4th and 6th steps should proceed diatonically downward, whenever they can. c. By the V: Foreign progression. d. By the IV. *i) i I -J i ^J^ r V VI I I I I r I IV VI *i) These two measures violate par. 99a, but are excused by the quality of the tones in the leap, — tonic and domi- nant. Comp. par. 76c. — *2) Ex. 85, Note *i). Par. iig. THE MEDIANT TRIAD, III. 41 119. The chord-progression in Ex. 86 is no contradiction of the spirit of par. 73J. The VI is a tonic chord, and therefore is quite as apt to follow the V as is the I itself. It is often called the De- ceptive progression, — V-VI, where V-I is expected. EXERCISE TWELVE. *■ +3 f^^V=^=f^ 5W ^ f= ^^i=W^ 3^ d. 8 ^^fe ^ # ^ F=F — • — ^ — — p- ^" r ^ ^ ^ ^^^ EjnJXd '-^T rrr /. G major, and other keys. +« 3 -5 3 H ill I ri V I VI II V I I VI IV IV I ii~ii V i 1! I I To this exercise, add a number of Original phrases. The Mediant Triad, III. 120. This chord lies most remote from the tonic centre, and is therefore the weakest, least frequent, and most embarrassing of all the triads. See par. 696; Ex. 730. It is usually brief, and creates the impression of an intermediate "passing" chord, in the following connections. 121. The III may progress: a. to the VI (the Nonnal progression) ; and h. to the IV, i.e., the nearest pin. triad (Foreign progression). 122. It may be preceded: a. by the I (because the I can pass into every chord, — par. 71) ; h. by the VI (an ascending harm, degree); — and c. by its own principal triad, the V. 123. The position of the III depends upon the chord which /oZ/oici it. a. Before the IV, the III takes the position of the fifth (exceptionally the pos. of the third). b. Before the VI, the III takes the position of the third. c. The triad which follows the III is always best in the position of the third. Thus: III— IV, or III— IV; and III— \^. 42 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 124. From the I : into the IV ; into the VI. From the VI : into the IV ; into the VI. From the V : to the IV; to the VI. Ex. 88. ^^ r"r Exceptional : i -J- i \^^^ ^ ^ ^^=^ -i -i n m -h^ ?^¥^^ I ^ 1 J: < rnn~nr- -•— i-^- ^ i IV VI IV VI 8 IV VI J J hJ lu^^ w .-^ -'/ji.-j- j^j.j'\ (?) JXi IV 124. a. From this it is seen that the III has no connection with the II. The progression would he foreign, and both chords are subordinate. Ex. 88-4 is somewhat doubtful, because there are too many weak chords in direct succession. b. The Foreign progression of the III (into the IV) is more common, and apparently better, than its Normal pro- gression (into the VI), — probably because the weak III obtains more support from the principal triad (IV), especially as it lies nearer. Compare par. 396. 125. The 7th scale-step, as chord-fifth in the III, seems to forfeit much of its characteristic quahty as leading-tone. As seen in Ex. 88, its movement is generally downward (as in Ex. 16-1), — invaria- bly so when the IV follows, on account of successive 5ths with the bass. FUNDAMENTAL PRINCIPLES. The I passes into all other chords. The V passes into I and VI. The IV passes into every chord, excepting into the III. The II passes into V and VI; and follows the IV, I and VI. The VI passes into every chord, excepting the I; and follows every triad. The III passes into IV and VI; follows the I, VI and V. The best position for all triads is that of the third; especially for subordinate triads. In the VT, the octave-position is forbidden; in the II, the position of the fifth is poor. In the in, the leading-tone usually descends. ^^ EXERCISE THIRTEEN. *l) +3 Faisst m fa 3*3) *3) +3 i '& fW^ Par. 126. 3 3 s [3 t} I f ,4r rifE SUBORDINATE TRIADS IN MINOR. -8 5+3 S ''• 43 1 1 L--__l. ^^^^ ^ ^ EBS^ -i» 35 S 8 /. »4) *5) *5) *4) FaISST 8 _-8 3 +8 . ^ •— ^ ?=-P-#-Mt ^ i; ^• *4) *4) SSfefe m 4 4 8 *3> 5 ^ I -5 +3 8 8 S »a) §^ g^7^ "^ y tt wa; it 1» — f=- ^i: fa a. g •P=p: ^2- ^ te Tl— f3 »6) *4) g a* J:;.^=^ *i) Double the 3rd in this chord. — "2) Par. 112. — '3) Position of the third. 116J. — *4) 1230. — *s) 123c. * 6) 1236. — To this exercise, add a number of Original phrases. The Subordinate triads in Minor. 126. The intervals of these triads are defined according to the harmonic minor scale (Ex. 69), and are as follows (6th and 3rd scale-steps lowered) : Ex. 89. C minor IE ig: ~t?z^ VI II III 127. The VI is a major triad, the II a diminished, and the III an augmented triad (see par. 50). The latter two are discords (although only three-tone chords), because they contain respectively the dissonant intervals of a diminished and an augmented fifth (460). Therefore, their consideration must be deferred until the next Division. Review the text following Ex. 24. 128. The VI is, then, the only subordinate triad that may be used in minor, at present. Its treat- ment in minor is precisely the same as in major, — excepting in its connections with the 11 and III, which are regulated by the rules of discords, and are omitted here. Review par. 106a, b. 44 THE MATERIAL USED IN MUSICAL COMPOSITION. EXERCISE rOURTEEN. 8 Par. 139. Faisst IS i=p= « — ^ ^ :t ^ m ^ > • ^ 1=F=^ I ^i^S +3 85 3-3 5 Pi TOiLU i ^^n^j r ; i d:^ i^ i r \ * ! t) Q D To this exercise, add a number of Original phrases. The Period-form. 129. The period, or double-phrase, consists of two phrases, and is therefore usually eight measures in length. The first of these is called the Antecedent phrase. It has its cadence, like any phrase, on an accent of the fourth measure; but as it is only the first half of the entire sentence, its cadence must be less complete than the final (perfect) cadence. Review par. 79. Every such lighter rhythmic interruption is called a semi-cadence. The second phrase is called the Consequent, and closes with the perfect cadence. 130. A semi-cadence differs from the full stop only in the choice of chords. As a rule, any succession of fairly strong chords will constitute a semi-cadence, but the most appropriate and common chord is the dominant, — preceded by any suitable chord (I, IV, II, VI). The cadence-chord falls on an accent, of course. 131. There is a close general relation between the two phrases, which represent "question" and "answer." They are likely to begin on the same beat, and close on corresponding accents. The fol- lowing example is the outline of an 8-measure period, in 3-4 time, with the dominant semi-cadence: ] Antecedent phr. 4 measures | *l) 1 *2) J Consequent phr. 4 measures m it -I- i I t=^=^ ^=t I i I h4:-f- I V r V I J Ex.. 90. a I I I e t=^= I I ^^ I ^ ^ (V VI III IV I VI V) *3)- Semi- (IV II V I VI III IV VI ) Perfect [Cadence. ) [Cadence.^ •i) This semi-cadence, I-V, is harmonically the reverse of the perfect cadence (V-I) and therefore constitutes the most consistenti''aiitithesis to the latter. The V may, however, be preceded by any other good chord. A semi-cadence Par. 132. THE HARMONIZING OF MELODIES. PRINCIPAL TRIADS. 45 upon the IV is heavy; its relative, the II, although a subordinate chord, is better. The I can be employed as seihi- cadence chord, but not in octave-position. It is not very good, however, as it furnishes too little contrast with the perf. cadence. Its relative, the VI, is somewhat better. The III, as intimated, is too weak (par. 120). The student can substitute these different forms of the semi-cadence for the one given in Ex. 90, and judge of their comparative effect. *2) Here the unusual succession V-IV is turned to account at the point where the narrow relation of chord to chord is overbalanced by the broad relation of phrase to phrase. Comp. par. 876, which indicates exactly the same principle. *3) This longer note is necessary for the semi-cadence chord, in order to interrupt the rhythmic movement. FUNDAMENTAL PRINCIPLES. Of the subordinate triads in minor, only the VI is a concord. The semi-cadence is any succession of good chords, in cadential location, that do not form the perfect cadence. The best semi-cadence chord is the V. EXERCISE FIFTEEN. A. Complete Ex. 90, in C, Bb, A\> and F# major; using a different semi-cadence in each version. B. Pointout the general errors in the following: AdE ^i=f: ^^d m J j J J 1 — r^ - ZSH- 4J: f^f 3EE* ^-^--M^^ 1 i ^ m Time-signature ? Cadences ? Cliord-successions ? Positions ? Duplications ? Consecutives ? C. Write a number of Original periods. The Harmonizing of Melodies. Principal Triads. 132. The harmonizing of a melody consists in assigning to each successive tone its proper chord. The scale-steps which each principal triad contains are shown in the following table: Ex. 91 i C major. Principal triads : I V IV m Scale-steps : Steps of the scale : a I IV Frin. triads -rr ±: IV IV The first scale-step occurs in two primary chords, the I and IV; and the fifth scale-step occurs both in the V and the I. At these places, of course, choice must be made between the two chords; but all the other steps of the scale repre- sent, originally, but one primary chord. 46 THE MA TERIAL USED IN MUSICAL COMPOSITION. Par. 133. 133. The application of this table to any given melody defines the harmonic basis, or bass part. Thus: Scale-steps * 3 3 4 2 3 Melody: ^ 1 I I Ex. 92. ^ W M -^ -iM^ i Harmony : 1^ t I IV IV t!v liv 134. Where a choice is to be made between two possible triads (at the ist and 5th scale-steps) the following rules must be considered: a. The very first chord is the I; the last two chords the V-I (par. 8ic). 6. The rules of chord-succession and chord-repetition must be respected (par. 1000, par. 85). c. The chords must not be so chosen that any two successive melody-notes would be chord-fifths; successive roots (octave-positions) are also hazardous, but not impossible, — Ex. 47, Note *3). See also par. 99a, b. d. A wide leap in the melody almost always indicates chord-repetition (par. 84). Applied to Ex. 92 the result is: Ex. 93. fe J ^- I i^^^ I I »2) IV I *3) I »4) *i) The V is cancelled by par. 13411. — *2) The IV would make parallel 5ths with both the preceding and following chord. See also i34— 'S- m -s)—eH-7^ M^d=^T=p;^ « ^^ ==i^ S I s ^&te^^ m ■*-t- w. Ex. 100-5. Ill # J | J J I J i S T' n-n i se: e ^ ^m if- IMiB^feJ -J^t ^ m i *=C3 VI VI M^m BiMl.:i \ '-^^fi^ ^m Also Ex. 93. V VI The Inversions oe the Triads. 141. "Inverting" a chord means, simply, placing some other interval than the root in the lower- most part. Thus, the triads, which have three intervals, may appear in three different shapes, as re- gards the condition of the bass, namely: a. As original triad or fundamental chord, with the root in bass; b. As first inversion, with the third in bass; and c. As second inversion, with the fifth in bass. Fundamental chord ist Inversion 2nd Inversion Ex. 101.' i I &t^= s:=Rootz Ie. S;=Thirdr 1*5): *i) Spoken: "Tonic triad, ist Inversion"; or more conveniently "One-one." *2) Spoken: "Tonic triad, 2nd Inversion"; or more conveniently "One-two." 50 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. i42> Changing the chord-interval in bass does not alter the fundamental harmony, any more than the change of position in soprano does. Therefore the above forms are all named "the I." 142. In order to distinguish the bass notes as chord-third, or chord-fifth, from the bass note as root, figures are attached below them, which indicate the interval or intervals jrom the bass note to the upper tones, and define the shape and general denomination of the chord. Thus: Triad Chord of the Sixth *2) Chord of the Six-four *3) *i) The figures (intervals) s and 3 are always understood, imless contradicted by 6 and 4 respectively; therefore they are usually omitted. The figure (interval) 8 signifies duplication, and is usually understood, in triads. *2) So called, because the column of intervals (from the lower tone upward) contains a sixth, — 3 instead of 3. *3) In agreement with the bass-figuring, or shape of the column of intervals, |. EXERCISE EIGHTEEN. Attach the names (in Roman numerals) to the following chords, as indicated in the first measure. When there are no figures, the bass note is a root. When marked 6, the bass note is a chord-third, the chord is a ist inversion, and the root, and name, is found a 3rd bdow. When marked |, the chord is a 2nd inversion, and the root, and name, is foimd a jth below. (See par. 51.) Eb major. I IV3 VI, s =9^ ^ ;)=^) B major. a ^^ m -19- And write the following chords in figured bass notes, as above: D major I2-III-IV1- V2-IIi-VI-Ii-VIi-ni2-IV-Il2- V1-VI2-III1-IV2-II; and the same chords, in reversed order, in Gt> major. SECTION 2. THE CHORDS OF THE SIXTH. C major. *i) Ex. 103. ^ i III nil IV, VI, *i) These chords will be limited principally to the major mode, at present. Only those examples in which neither the II nor the III (or their inversions) occur, can be appUed to minor also. 143. The first inversions appear most naturally as substitutes for their respective fundamental triads. The chord-third being a lighter interval than the root (par. 69c), it follows that the ist in- versions are lighter and more fleidble than triads. Par. 144. THE PRINCIPAL CHORDS OF THE SIXTH. SI The Piuncipal Chords or the Sixth. 144. The chords of the sixth are classified, like the triads, as principal and subordinate. The prin. chords of the 6th are, naturally, the first inversion of the three prin. triads. 146. a. The best position for every chord of the 6th is that of the octave (i.e., root in soprano, — see i45d). Thus the quality of the bass tone as chord-third (instead of root, as the ear is apt to assume) is most dearly defined. 6. In the principal chords of the 6th, however, the root, being a prin. tone of the scale, can he in an inner part without endangering the identity of the chord, in which case the soprano may take the fifth. c. The position of the third should be avoided, as it doubles an inferior chord-interval in the outer parts. d. The position of a chord is always reckoned from the root, no matter what interval the bass part chances to have. For example: Octave-position 8. ^ Ex. 1 04.' Pos. of the 5th S ^ Prin. note_ Pos. of the 3rd 'A ^ — " Prin. note_ u 9i e _Subord. note_ -4 =\= Subord. note_ r =i ti\ 2____Subord. note l__f2_^_Subord, note_ T -J- 1 m 146. a. As a rule, it is best to double the principal tones of the scale (par. 59). b. But in chords of the sixth almost any tone (excepting the leading-tone) may be doubled in order to obtain smooth voice-progression. Therefore, the prin. tones may be doubled, whether root or fifth. It is least desirable to double the bass note (i.e., the third) in principal chords of the 6th. c. No chord4nterval is ever omitted, in any inversion. 147. a. The inverting of a triad is attended by the following advantages: It facilitates the coimections of the chords to such a degree that almost any of the foregoing forbidden progressions become possible, when the second chord, or both chords, are inverted. Thus, V-IV is doubtful, but V-IVi is good, and Vi-IVi still better; VI-I?, VI-Ii good; and so on. b. As seen above, it simplifies the rules of dupUcation. c. It simplifies the rules of melodic progression so that successive positions of the sth or 8th are allowed when one (especially the second) chord, or both chords, are inversions; and wide skips to the sth in soprano are less objectionable than in triads. d. It conduces to the melodic smoothness of the bass part, which has precisely the same melodic choice of root, third (or fifth), as the soprano has. Compare the basses in the following exercises with those of the preceding ones. 148. The following tables exhibit the progressions of the three prin. chords of the 6th into triads, in the order of preference. Review par. 75. ^ ^j i - 1 io^j i n Ex. I06. Ii U i W [jTrnr nr Mr fir r i / r ir-f i r ^^ a IV 8 II O VI 8 52 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. I49- Ex. I06. 'M9 ^fc *i) 4- r I - ly i j J fej ElfT'T ' f'T ^ F^ 3)(?) 1^, ^ e V a VI an e III « IV Ex. 107. rf= ^ *i) i r 1 I 6 IV ^ *3) I I ^ ^ i a V 6 sue III *i) Exactly the same in C major and C minor. — *2) Par. 147c. — *3) Major only. — *4) See Ex. 79, and compare par. 147a. — *s) Par. 670. — All the measures covered by Note "i) must be played in C minor also. 149. The introduction of these chords (choice of preceding chord) is effected according to the same general principles, and can be found by simply reversing each measure of the above examples, — plajmig the second chord before the first. Particular attention is, however, called to the following exceptional cases: I?? . I 3, - ..... 3. J-i 1 EE f r'f r *3) ', good I J V I i f ,*2) , , , ,(?) , -\ -5, f*!)"^ Ex. 108. ~ Ex. No. 8 Ex. 105, No. 9 u Ex. 105, No. 10 I 1 J- i i P^ r- a a II Ii »3) VI I, *4) ^ Ex. 106, No. 6 ^ Ex. 107, ]Sto. 2 *a)| 9^ f^ IV r ^ Ex. 107, No. 4 *2) a i II 6 "i) Perfectly good, because the second chord is inverted (par. 147c). — *2) These four cases show hOw an irregiilar chord-succession is rectified by inverting the second of the two chords (par. 1470). — *3) Like Ex. 85, Note *i). This illustrates how and when the position of the 3rd of the Ii may be necessary. — *4) The bass may leap down to the leading- tone, but not up (par. 31). Par. 150. THE PRINCIPAL CHORDS OF THE SIXTH. 53 150. All of the above examples show that chords of the 6th prefer to progress and to enter smoothly, — without wide leaps in the bass. Compare the fast two or three measures of Exs. 105-107 with the later ones. FUNDAMENTAL PRINCIPLES. The best position for every chord of the 6th is that of the octave. In principal 6ths, the position of the fifth is permitted. Any chord-interval may be doubled, — excepting the leading-tone. No interval is ever omitted in an inversion. Every irregular chord-succession is excused by inverting the second one of the two chords, or both chords. EXERCISE NINETEEN. A. Add the soprano and inner parts to the following basses. The student is reminded that the figures bdow the bass are always reckoned upward from the bass note; on the con- trary, the figures above the bass refer to the position, and are always reckoned /row the root of the chord. Comp. par. 142, and 145(2. a. . - X " '■-' - - - - ~ ^ ^ T-a m m s=t ^ tit *i) s B e a 5 ^ ^^ =i=^ ^ d. _3 iBi-fcft g , 6 _ 8 2+i «• 3 - +8*2) o T^r ^w o *3) 3^8 a +5 S 3 ^m. /■ F minor. 2 4 I Vj I I V VI Ii I IV I IVi IV I V I VI IV Ii I IV I Ii I V I IVi V I I »*) *i) Par. 145a. — '2) Par. 676; 1456. — *3) Par. 147c. — *4) Brackets indicate divided beats. — *s) Time-value? B. Transpose (at the piano, at sight) the following two fragments (separately) into every other major key, and also into each corresponding minor key: 3 I ^ '■i^. . r =p=i= nil A I ^m a a I Ii V Vi I I IV, V V, I '1 ' *i Observe the positions and chord-progressions, and the transposition will be easy, C. Add a number of Original phrases. 54 THE MA TERIAL USED IN MUSICAL COMPOSITION. Par. 151. The Suboedinate chords of the sixth. 151. The only good subordinate 6th is the first inversion of the II. The VI^ and III^ are extremely rare. 162. Subordinate 6ths are limited almost wholly to the octave-position; because their roots, being subordinate tones, need to be in one of the outer parts, in order to be recognizable as roots. Par. i45fl. The exceptions to this rule are: a. The IIi — which sometimes takes the position of the third, (because it is a principal tone and endures duplication, even in outer parts). 6. The IIIi — which, when followed by the IV, may (like the III itself) take the position of the fifth, c. During chord-repetition, any position can be taken, of course. The II The III j-j I J J J i J ,U^ ^m Repetitions 8 s, ^E^^ i m Ex. 109.< r , I J. I I jii I *i)i f-H-!-^ f ir m rj u I r *i) This is an exceedingly rare example of the doubled leading-tone. It is excused mainly by the fact that it is the III, and not the V, — see par. 125; partly, also, by the smoothness of the voice-progressions in soprano and tenor. 153. The progressions of the three sub. chords of the 6th, to triads, are as follows (in major only) : Ex. 1 10. Hi ^ 1520 3 124a 150 L^l-^ i- J- J- \ ^ 5^^?c: III III — ii ?? I r-r I r-T I f-.^ i "i a II 8 VI i IE ^ *i) *3) par. 150 4=t ^ FprfFPPTTf 6 VI e II s III a IV a Pf i Par. 154. Ex. I 1 12. y III. \ Rare. J ( THE SUBORDINATE CHORDS OF THE SIXTH. 5 Ex. 109-4 par. 150 55 1,1 6 - |J ,1 ' I I , I \l I ! J- i I J 1 J s — W: UX4 ^ ^ in. — i I — II III, 6 III 6 VI 8 IV a *i) A succession of two weak chords. — *2) Also in minor (par. 128). ^ 154. The introductions will be found, as before (par. 149), by playing each of the above measures in reversed order. The following exceptional cases require special attention: Ex. 79 »i) 147a 147a ^ J I I J Good :^ :^ i ^^ n- "^ r r No. 5 Ex. 112, J I Nos.3,4 I ^m Ex. 112, V a I a IV a a II V a IV a VI II a *i) Good, because the bass leap is made from the I (comp. par. 71). A strong chord can move with greater freedom than a weak one. 155. These examples again show that the movements of the chords of the 6th are dictated largely by proximity of bass tones. Comp. par. 150. The subordinate 6ths, especially, abhor wide leaps in bass. In this respect the inversions differ somewhat from the triads, whose harmonic actions are determined chiefly by chord-relations. The thorough student must become fully familiar with all of these chord-movements. The above logical inferences will probably be of assistance, although, if need be, he must simply memorize each individual succession. FUNDAMENTAL PRINCrPLES. The only good subordinate 6th is the IIi. Subordinate chords of the 6th take the octave-position. Chords of the 6th, especially when subordinate, should make no wide leaps in bass. EXERCISE TWENTY. Faisst , ^ m *l) 3 -J- m izSb F f 19-^ m C. *l) «l) /^ *a) 3-3 g^ *— F ^ 56 ^^ s i-P: T//E MATERIAL USED IN MUSICAL COMPOSITION. Par. 156. »3) 1^+3 3 -8 tt^ u m #-•■ g s i *i^ :s^* ■"^ e $ e » JJ^s / -S 3 **) +3 -3 *l) -3 Eb major. | I I^ I V^ V Vi | II IIj II VIj VI VI^ | II Vj I IVj V IIIi | VI 11^ V I || »s) •i) Par. 152. — *2) This line denotes that the soprano note is to be held. — *3) Par. 1526. — *4) Par. 676. — *s) Also other major keys. To this exercise, add a number of Original phrases. Consecutive chords of the sixth. 156. The progression of one chord of the 6th into another (instead of into a triad, as in the foregoing lesson), is one of the most graceful, effective, and common chord-connections, and can be effected with great ease, especially when the bass moves smoothly (par. 155). Here the advantage of inversion is again exhibited; for when, as in successive sixths, both chords are inversions, the chords are connected without regard to their relations (see par. 147a). For instance, the triad-progressions V-IV-III-II are wrong; but as chords of the 6th (Vi-IVi-IIIi-IIi) the succession is perfectly good. Thus: •^ ■$■ good i^i: sr- 6 6 V IV III II 6 6a 157. a. The soprano generally moves in sixths parallel with the bass, each chord taking the oc- tave-position. Occasional exceptions (par. 1456, 1520) are admissible. b. The rule of smooth voice-progression must be strictly observed, and attention must be paid, especially, to par. 66. c. At least one part should move in contrary direction to the others, irrespective of duplications (1466). 158. The following table illustrates the connections of the Ii with other chords of the 6th, in the order of preference; each measure can be reversed (as shown in par. 149). a ^ **) m-^lT-^ ^zk ^^^ \4^Ekk^B * T^^f r ^-T 1^ m-^ H^ ^ I I i 5 s 4 a *4) IE S EJ^ N^^M ^ -r- I ^=J r r ^ ^^ a n^ J. IV It ??^ ^^ i Par. 159. TRIAD AND SIXTH ON THE SAME BASS TONE. 57 *i) Either one of these three tenor progressions can be taken; and the same with the two alto progressions in the fol- lowing measure. — *2) Comp. Ex. 109-4. — *3) These wide bass leaps are good only with principal 6ths. — *4) Also in minor. 159. The other successions of 6ths are made in the same manner, — best when diatonic, or with narrow leaps. The geries may extend to three or even more chords, in which case parallel octaves and fifths must be guarded against. See par. 157c. i ^U=i=f i ^^J^^^J =J J 4: ^^PP 1 f T^ Pf r^ r ' r Ex. 1 15. Major. »l) i m^m ^ f r r r r i J^i: J^U 'f^^sm *2) I J i J- f=^ I 666e 61 aaas eseee 8 I ' 6 8 "i) The soprano runs in 6ths parallel with the bass. For three beats the alto moves contrary; then the inner parts turn, and the tenor runs opposite to the other three parts. — *2) All four parts ascend, as it cannot be avoided; but there are no parallel 8ves or sths. Triad and Sixth on the same bass tone. 160. According to par. 155, it is apparent that a chord of the sixth will connect very readily indeed with that triad which has the same bass tone, — for example, the Ii and the III (bass tone e, in C major, — Ex. 116). 161. Chords which are so nearly alike as these (with only one note of difference), are very often connected during one beat, instead of using a separate beat to each chord. Thus: III Ex. I 16. i s^ — ^ ^m v^r. S 66 S6 The figure 5 denotes the triad, and is not understood in this The chord of the 6th may precede or follow the triad case, because of the 6 which accompanies it. 162. Rules: ist, the notes of difference 6 and 5 (c and b in this instance) are connected in one the same part — usually in the soprano; 2nd, when connected on a single beat, the first of these notes should not be doubled. For example: Rule I Rule 2 "i) The lower three parts simply hold their tones. — *2) The notes of difference are less effective in an inner part than in soprano. — *3) Much too uncjuiet. — *4) If the first tone (c) is doubled and then held; it makes a dissonance with the second tone (6), to be avoided for the present. — *s) The second of the above rules applies only to the rapid con- nection, in a single beat; when each chord has its full beat, it is treated independently of the other. S8 THE MATERIAL USED IN MUSICAL COMPOSITION. 163. The other chords of the 6th make this connection in the same manner: P«r. 163. Ex. 1 18. i w^ '^ ^ Si *i) -J- J- ^^ ^^ 65 II, 56 nil 65 IVi 65 VI, *i) As usual, separate measures. — *2) These two couplets are perfectly correct, but they will not appear in the following exercise, because they involve chords which have not yet been explained (par. 53). — *3) One or two exceptions of this kind (the second tone doubled) are justifiable. Observe the bass figuring; the horizontal rows (8-6, 5-6) indicate the course of the upper parts. 164. a. The rapid diatonic passing-notes {i.e., the notes of difference), whether they lie in soprano or in an inner part, must run on diatonically in the same direction, if the following chord contains the required tone. Thus: Ex. 1 19. i i par. 6yd L i^j , {^^,^ i~^ p« i *i) Here the soprano is right, because it fulfills the impulse of the rapid diatonic notes, and conforms to par. 26. — '2) These two measures are awkward. b. If, however, the succeeding chord should not contain the required tone, then the rapid part is more likely to turn, than to progress in the same direction with a skip, or remain on the same tone. Thus: J Msk & m *i) ^ m ^ ?? ^ J, J ^' n ^ ^F^ 7q i *i) Compare measure 1. This soprano makes parallel sths with the bass part, which are as objectionable as if the second eighth-note (d) were not between; because unaccented fractions of beats do not fully intercept consecutive sths. The same applies to intercepted octaves. Par. X64. TRIAD AND SIXTH ON THE SAME BASS TONE. S9 FUNDAMENTAL PRINCIPLES. In successive chords of the sixth the soprano generally moves in 6tJis parallel with the bass; and one inner part runs contrary to the other three parts. The couplet 6-5 or 5-6 should be placed unbroken in some part, — usually soprano; and the first tone should not be doubled. Rapid diatonic tones generally rim on in the same direction. EXERCISE TWENTY-ONE. It is well to complete the soprano before filling out the inner parts. a. *i) *s) ^i* m T W 4: t 66 6 a *i)*a) *s) ^■ e e e +8 #2) e e 6 «s) 3 ^ I ^m^ r r fN V f rnjtr f r r ff ' r i r r r Ji rfj^ ftg ^ ^a 6 65 56 6 6 6 65 C. +3 *l) *2) ^ i2i 6 6 65 6 6 65 56 *5) -3 6660 666 -6 65 56 56 ~ey d. *a) ^^ ^^ m «4) ■m— e $ o ^^^1 Faisst t 6 6 6 "^r^'p't^? *5) iw i m S 56 56 /• *6) *2) 5 65 a 8 *6) ^^^^ ^ ^^iig^=^ g- +8 6 6 56 *9) *5) 6 6 *7) FE :^=(E m^ ^=^=w i=5C i a ^r* *8) «6) h. »3) 2 »6) 8 F major. | I VI IVj I IIi V IIIi I I^ IV IVj I I 1 II Vj V I I Vj IV^ III^ I IIj V I I 11 I I I I I I I I I I I I ' ' " *i) Par. 162. — "2) 1640. — *3) 1570, and c. — *4) Par. 67J. — *s) 1646. — *6) The line below the bass note in- dicates that the soprano holds its tone, — perhaps one or both inner parts also. — *7) The line denotes that the soprano note is to be held. — *8) This bass illustrates diversity of rhythm, somewhat like Ex. 95, Note *i). — *9) 1230, and c. To this exercise add a number of Original phrases. Par. 165. 60 THE MATERIAL USED IN MUSICAL COMPOSITION Melody-harmonizing. Chords of the sixth. 165. The use of chords of the sixth, in hannoniziiig a melody, is controlled by the following general principles: a. The choice of chord is made almost precisely as before, according to the table, Ex. 99, — which review, thoroughly. h. The chord-third is used in bass most commonly when the soprano (melody) has the root of the chosen chord. (Comp. par. 72 and par. 1450, — "root in bass, third in soprano; root in soprano, third in bass.") This is almost invariable in subordinate chords. c. The first inversion may, however, be used when the chord-fifth is in soprano; but only in prin- cipal chords. The following table, showing inversions only, may be added to Ex. 99: 6 _ _ _ _ - i Scale-steps : 1 3 Ex. 121. i p n. (nil) IVi ("l) (iVi) No 6th For example: *8) ^ ^^j , rjj , j. || ,. a^j^^^y^ *3) n I I Ex. 122. -i<-*- I Ii V I IViV Ii III V I I Ii IV III V Vj I IVi V Ii Vi I Ij— IIiV I *i) "Root in soprano, third in bass." — "2) Here, and two beats later, the chord of the sixth is used with the chord- fifth in soprano, — being principal chords. — *3) The chord is repeated over the accent, but the bass changes, — par. 166. 166. There is little or no objection to the repetition of a chord over the bar or accent, if the bass part moves into a new form of the chord. This does not necessarily contradict par. 85, for there (and in par. 87) constant stress was laid upon the application of the rule to the repeated bass tone only. But this apparent exception now modifies par. 134^, and increases the student's freedom. 167. Besides the above fundamental directions, there is: a. The more exceptional line of siKcessive sixths (par. 156) — which may be used (sparingly) when the melody-tones run smoothly, as successive roots; and 6. The couplet 6-5 or 5-6 above the same bass tone (par. 160), which is self-indicating. For example: *2) a-"^ ~\ 8 8 8 «i) j^-l t^U: Ex. 123. i ^fc± Ii III "IiIVi Ii III IVi III Ii III i b. j-j^-i- m *3) rx I m rT Bass r r •i) This note is harmonized with a triad, to avoid too long a line of 6ths. *2) Observe that the successive 6ths are applied where the melody runs smoothly, and that the line usually begins and ends with a fairly strong chord. — *3) Here the sixth scale-step is harmonized with the IIi, because it is evident from the slur and wide leap that the whole beat is one chord. See par. 168. Pai. i68. HARMONIZING SUCCESSIVE TONES TOGETHER. 6r Hakmonizing successive tones together. 168. If an accented, melody-note and the following tone or tones represent the same chord, they may be slurred, as foUows, and harmonized together: *i) Ex. 124. i r" r r r I =*3)I ^m s I V I IV j^ IV V- I V VI IV V *i) The Jb and g cannot be slurred in this case because they together represent the IV, which does not follow the V. — *2) Whether the chord is merely hdi (as in the ist meas.) or repeated in a different form, is of no consequence; the principle is the same. 169. a. This principle applies particularly to rapid melody-notes which result from the division of a beat, as seen in Ex. 123, Note *3). Such rapid notes, wlmn they belong to the same beat (or group of beats), are very often intervals of the same chord, especially when they skip, and not only may but shoiUd be harmonized together. Thus: Allegretto. , Faisst ^ cad. u i Ex. 125. 1 Cc r 4 l ^^=B s tit II- V (IV?) V »2)V- *l) II- Ii V *i) Like Ex. 124, Note *i); it should be VI-IVi. — *2) See par. 166, and 87J. b. When the rapid notes (within a beat) are diatonic, they cannot belong to the same chord, and the treatment will conform to Ex. 123&, — second beat of measures i and 2, and measure 3. fundamental pkinciples. A chord of the sixth is most commonly used when the root is in soprano. A chord may be repeated over the bar, or accent, if the bass tone is changed. Rapid notes, in the same beat, are apt to be harmonized with the same chord, or same bass tone. exercise twenty-two. Add bass and inner parts to Exs. 122, 123, 124 and 125; and to the following melodies, using triads and chords of the sixth. See par. 242. •1) ^^m^^ 1 ^ ^=k\^ ! J l JJ ^ g^ -i ^ J i J J JJ ^ =P=^ i ? :5=p: 62 THE MA TERIAL USED IN MUSICAL COMPOSITION. *a) m i^ ±^ /• Par. 170. «8) ^ E5^ ^ ^ iitbt *4) i te^ffl ^^ I s :& i tf A. & *i) m i a s *6) *7) i' *8) , ^^Qj^ i ^r^ :p^ =B: :g^ SE ^ s«= Ttt -^J ^^ *S) -Q-Oh^ ^ Faisst HlP^^a^ ^^ *8) *9) *10) *i) Par. 166. — *2) 167a. — '3) Invert the IV, after the V (par. 147a). — "4) Par. 1690. — *5) Probably V-I, with successive sths in soprano; they are rectified by inverting the second chord (par. 147c). — *6) Par. 1676. — *i) Note the slur. This is not treated as in par. 1676. — *8) 1690. — *9) Like Ex. 124, Note 'i). — *io) Par. 137. Section 3. The Six-four chords. 170. See Ex. 102. These inversions stand upon the chord-fifth, as shown in par. 141. The quaUty of this chord-interval, as defined in par. 69c, is most apparent, and exerts the greatest influence upon the harmony, when it lies in the hass part, — the chief function of which is to support the harmony. Consequently: 171. a. Six-four chords are not employed independently, but must be placed in certain connec- tions with other and stronger chords, as Embellishing or as Passing chords. i. They can not occur in direct succession, because of the successive chord-fifths in bass, which are far weaker than successive positions of the fifth (comp. par. 766). c. They can neither enter nor progress with a skip (in the bass part, of course). d. For this reason, also, they are not classified, like triads and chords of the 6th, as "principal" and "subordinate" chords. The only distinction that can or need be made is as follows: *2) ^ Ex. c major, 126. f^ hM=j=H^ Fa IV, Vo vu *i) See Ex. 103, Note *i). "2) The I2, when accented (as is commonly the case), is semi-independent. The IV2 is also a fairly strong chord. The rest are all dependent, and seldom occupy accented beats. The Vj is weaker than might be expected. Par. 172. THE CONNECTIONS OF SIX-FOUR CHORDS. 63 172. o. The soprano-position of a six-four chord does not enter into consideration, being always regulated by the chord with which it chances to be connected. The soprano usually has either the interval 6 or 4 (third or root of the chord), — rarely the duplication of the bass tone. h. The hass note is almost always doubled (as intimated, usually in an inner part, — not often in soprano). 173. First The connections of Six-four chords. FIRST connection. In general, the six-four chords appear in three different connections with other chords. : A 6-4 chord may enter from, or progress to, the triad upon the same bass note. 4 The following example illustrates the I2 in this connection. See, again, par. 75. I ^^1^ »i) P ijj ii J J nnrii-T^p^ i^^ge r If r ir^ J J | J i i -«a)- -»3)- 6 fee fs is i * * " f I e i i I g I i 'i I 'i '8 I i ' *i) Major and minor. — *2) The figuires | denote the triad, and are necessary on account of the figures | which ac- company them during the same bass tone. As seen in measures i and 2, the soprano usually takes either the melodic line 565 or 343 (but compare the last three measures), and the bass tone is doubled in one of the inner parts; wherever the 6th is, the sth will follow it (as in Ex. 117), and, similarly, the 4th is followed by the 3rd. — *3) An imusual arrangement of the bass figures, as here, serves to indicate the course of the upper lines. 174. This connection of the six 6-4 chords is not allowed in the following rhythm* ^^^ on account of the repetition of the bass tone over the bar. (Comp. par. 166.) 175. Not all of the six 6-4 chords can appear in this connection. The following table shows that, besides the I2, only the IV2, II2 and VI2 can be connected with the triads of their respective bass notes. With the V2 and III2 it is impossible. The IVg _ The Ilg The Vly The Vg The Illg U^m s a s 4 8 *i) The V2 can not be used in this coimection on account of the false melodic progressions involved (Ex. 16-6). *2) With these accidentals the 6-4 chord is not a V2, but the I2 of G major or minor. — *3) Here it is a IV2 in D minor. *4) There is no legitimate triad upon the bass note of the III2 (par. 53). 64 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. \^k^^ 176. The connection of a 6-4 chord with the chord of the 6th upon the same bass note is possible, but rare. It is most common in rapid rhythm, as in Ex. 117. *i) The line denotes that the corresponding tone is to be held. SECOND CONNECTION. 177. Second : A six-four chord may appear in connection with any chord of the same root. = ^ g H - ^ i I ri -j-. I, J J r/ 1 J I m - \. r -^ #^«*>s» £ it e o a 6 a a 4, 44 d^ V Between V— Vj *3) *4) II— III VI— VIi III— nil i-- — r'^-'''- J -^ J?^| i I I e<3 a a a ^ ■■ a a 444, 4 ^ *i) The first 9 measures are the same in major and minor. — "2) From here on, only in major. — *3) Ex. 16-1. — *4) Ex. 16-8. — *s) All weak chords. ' 190. a. Second : The 6-4 chord becomes a passing chord between two different chords of the sixth. This progression is very good, and is possible in either direction; but it is comparatively rare," because there are so few places in the scale where it is practicable. 6. The soprano generally runs in 6ths parallel with the bass. i ^ Eg-r-^ ±f* i- .U: ^^ t:^zf r r f r r r ^V"r, 'T^j^ Ex. 139. -^ J -i-J- 4 ^ i ./^ -I fpf^^ferrM^ a 66 a aaae 444 a a 4 a a 4 ^o THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 191. 191. a. Third : The 6-4 chord appears as diatonically descending passing note in bass, following a triad, and progressing in the same direction into another triad, or into a chord of the sixth. Thus: b. This harmonic group is analogous to Ex. 117. The chords are so nearly alike that the combination is usually made on a single beat, and the bass tones, which are here the notes of difference, should not be doubled. Compare par. 162. After the I : After the II : III: IV: VI: f ^4t^ \r I \ i3 m i *4) ' ' 6 4 6 ' "i) Either the 3rd or sth of the triad is doubled. — "2) Ex. 117, Note *4). — *3) Compare Ex. 120, Note *i). — *4) Compare Ex. 117, Note *s). ■ Another illustration of this connection: Mozart Allegro f3 Ex. 141. i m=^ P i iSs ^ III2 VI IV VIo II IV9 V '3 -^s= FUNDAMENTAL PRINCIPLES. An accented 6-4 chord usually passes into the triad of the same bass tone. An unaccented 6-4 chord usually progresses diatonically. The plagal cadence is added to the perfect cadence, while the keynote is held in soprano, or in both outer parts. The deceptive cadence is substituted for the perfect cadence, by using the VI instead of the I. EXERCISE TWENTY-FIVE. *l) *1) *2) ^ bra I i m I 64 46 Par. igi. SIX-FOUR CHORDS AS PASSING CHORDS. 71 *3) ^SB' p^ f^^'Ti ; M J J s #TF 6 6 4 -z^ 4« *4) 8 *1) 3 fi^= • Aft A n 1^^ ^*' ^^"^^ 65 8 6 6 4 5a 6 6 4: n) ^^^^ i *s) ^ i 1^ txxrn itit 6 6 l_ 4 e >h^ 6 6 65 4 4« 6 65 4lt as 4ff »1) 3*6) ^^^ ^i5E S ^: ^ 3 ff 6 6 6 4 4 6 6 4 ^ M »1) '»6) *4) i :* fl fl fi fi R 6 6 ^^ R 6 fi6 5 ^ 6 6 4 ° I §li 6 ga J=»ti: *6) .^tl. ^^? :*=? i i P8T ^?=? 65 4$ 6 65 4 « * 65 4S «a) :P= ^^ *i) ^^ ^i^ t> l ? 4 J_ e±? -*— #- ±±t w rr^^ *-^ 6 6 6 4 *i) Par. 189a, 6. — "i) Exerdse 23, Note *i). — *3) Exerdse 23, Note *s)- — *4) Par. 190a, 6. — *s) Plagal cadence; rhythm J^ J — ^.*6) Par. igia, h. — Analyze every bass, as in the foregoing exercise. To this exercise, add a number of Original phrases. EXERCISE TWENTY-SIX. Transpose (at the piano, at sight) the first of the following examples into all other major keys; and the second, in the same manner, into all other minor and, major keys. I. ^ ± i i i J ■ ^^i c ~ m. 4 a. u n f _ — • — « — =-: — M — J \- i ffr ^ — ^r4rT^-'' ^^pp rrf rtw f Mff^ m ^ ^ Y" r 8 I Closely observe the positions and the bass figures. 72 THE MATERIAL USED IN MUSICAL COMPOSITION. Melody-hakmonizing. Six-four chords. Par. 192. 192. The fundamental chords are defined, as usual, by the scale-steps, according to Ex. 99. But for the 6-4 chords it is more convenient to single out the melodic groups which best admit of this form of chord. These are: a. The figure with scale-steps 5, 6, 5, — also 3, 4, 3, — 2, 3, 2, — 7, 8, 7, — i, 2, 1. See Exs. 127, 128. ^m 343333 or I I I 1 I 1 r.r 7 8, " -^ •- ibbU: rcLrc I .4l.a i I § ditto ^ r Bass : \ | g I § ditto i I I i b. Every line of three diatonic steps may be harmonized with the same three steps in bass, in contrary direction; and a 6-4 chord is always involved. See Ex. 138-1, 2. I -LJ J J J =i: J- =i=J=i^ Ex. 143. I'ea'l'ee e'e 6 a Bass i i J ^^ ^^ i frrffrrrrrrrrrr Discrimination is necessary here. Tlie 6-4 chord is usually in the centre of the group, but not always. Review par. 17 16. , c. A melody-note, repeated over the bar or accent, is very likely to become a 6-4 chord. See Ex. 135. I ~. -:^ 11. and Ex. 144. -^-. J- Ttlt Bass ; [ r (""''v - ^ r P^^^ X- -4 — r- I ^=t: -• — f etc. r These groups agree partly with Ex. 142. d. In a "line of 6ths" (Ex. 123a), a good 6-4 chord may be substituted for one of the 6ths. But see par. 17 16. Ex. 145. ^-^~i-^ Vic or I I • 4 ^^ H* — •- E^^ • d •- Tj^ r f r r Bass: 666 6 666 6 666 193. The tonic 6-4 chord is of peculiar importance at both the semi-cadence and the perfect cadence, — in connection with the V. Thus: Par. 193. MELODY-HARMONIZING. SIX-FOUR CHORDS. 71 a. Semi-cadence b. Perl, cadence ^^^nJ l -J^-'lx^ l J^J.KiJ ^J »8) 1 ^^ ^^ I 1 ^ ^— H- TTtt ^-1/ i-i F'^^ I La- is' — 1=2- s s r^ rr- Xa V I5J I "i) The effect of the I2 is to lighten and embellish the semi-cadence. — "2) If the melody-tone _/«*/ before the perfect cadence calls for the I, it should not be the I itself, but some inverted form, — best, the second inversion. See par. 242. EXERCISE TWENTY-SEVEN. ^ B I s * *1) «3) *4) *3) i s j l j J JJ J | J J^L^J ^ Faisst i i mi J I 1 J Tj J *i) a »e) *4) a »3) »5) *3) VI 4^,^^h^^ri\sf^\^\^^\^-\mm *7) *7) «1) ^ VI «4) rjO | jjj|jj^ i Jj^^Oij-jj i j„,(.,, ^iby «7) «8) ^ «3) ^^ ^iUt^ s ^ ±=t «4) »9) *i) Ex. 143. — '2) Par. I93- — *3) Ex. 146, Note '2). — "4) Par. 137. — "s) Ex. 142. — *6) Par. 181. — "y) Ex. 144. — *8) The two measures beneath each slur represent the same melodic figure. When transferred thus to other ■{higher, or lower) scale-steps, the reproduction is called a Sequence. The same formation is seen in melody o (meas. i, 2), and in melody e (meas. 1-3, 5-7). Sequences are usually harmonized uniformly. -^ *?) Par. 1690. 74 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 194. DIVISION B: DISCORDS. 194. A Discord is a Iiarmonic body which contains one or more dissonant intervals. 195. The simplest dissonance is the interval of a seventh, which results naturally from adding one higher 3rd to the intervals of the triad. See par. 460. The result is a four-tone chord, named chord of the seventh, after the dissonance which it contains (par. 48). 196. The chords of the 7th are the fundamental four-tone chords, corresponding to the triads, or fundamental three- tone chords. But they can not be classified in the same way as the latter, on account of the obligations connected with their dissonance, in fulfiUing which their original independence as fundamental concords is to a certain degree sacrificed. 197. A dissonance has, as the term indicates, a harsh sound which the ear will accept only on condition that it be reasonably brief, and that it be justified by the intervals which precede and (especially) follow it. By itself, a dissonance in meaningless; it demands a progression which will fulfil its obligations. This impression of expectation characterizes the dissonant intervals, and imparts an activity to them which enlivens the harmony. The CLASsiricATiON of the Discords. 198. a. The discords are divided into grades or classes representing their proportionate degrees of importance and consequent frequency. These classes are determined by the distance of their roots from the tonic, in ascending harmonic degrees (perfect fifths). Ex. 14-7. i ist class 2nd class 2nd-dom. Disc. 9^ rs _Dom. Discords_ 3rd class 4th class JSi Submed. Disc. Med. Disc. --] Tonic h. This table shows that there are only four fundamental chords of the seventh, or, in other words, discord classes. The discords which stand upon the other three steps of the scale (4th, ist, 7th) are derived from these, in a manner which will be seen. (,. The tonic class is not numbered the "first," because it is composed exclusively of concords. No tonic chord can become a discord, without losing its tonic characteristic of repose, and becoming a member of one of the four discord classes. d. Hence, the dominant chords constitute the first class, because they rest upon the first perfect fifth above the tonic note. And, similarly, the second class have the 2nd perf. fifth above the tonic as fundamental tone, and so on. e. The third and fourth discord classes are so rare that they hardly enter into consideration in harmony. They are exclusively dissonant. /. Therefore it is apparent that the tonic class (exclusively consonant) and the ist and 2nd classes (both consonant and dissonant) represent together virtually the three elements of the whole system of harmony. See par. 70. The Resolution of a Dissonance. 199. The progression which satisfies the requirements of a dissonance is called its resolution, and the chord which follows a discord is the resolving chord. 200. a. Every dissonance in music is resolved diatonically, in the majority of cases downward. Ex. 148a. The progression with a skip is very irregular, and can be justified only in repetitions. Ex. i486. Par. 201 i THE FIRST CLASS OF DISCORDS. 75 h. The dissonance of a chord-seventh shoxild not progress upward: Ex. 148c. c. The interval of a 7th should not progress into an octave: Ex. i48v| 7 j I < g >«■ J I i g>«. b J I g >• J r/ g >■ J I g Ex. 148. M F I ^S =i: i 1^ I 1^ p^T^^^ .-^-F ^p^^ 75 7 8 7 ^ ^^ f= r T r T r'r ' ' r r ' T =r 74 7 8 201. Dissonances often prove to be a modification of some consonant interval, and the direction of their resolution depends upon the nature of the modification. Augmented intervals have an upward tendency; diminished ones progress downward. The seventh of a chord may be regarded as a depression or contraction of the octave, and therefore it is al- ways resolved downward. The 2nd, as inversion of the 7th, derives its progression from the latter. ^ 7 Dim. 7th J^^ I I Dim; eth Augm. 5th I , Ex. 149. i iE f=f^f^5rf N^J \ r -G>- I SECTION I. THE FIRST CLASS OF DISCORDS. A. The chord of the seventh upon the Dominant. i IE I V*l) *8) In minor ^ =0) *3) -a- *i) Spoken: "Dominant-seventh," or "Five-seven." — "2) Ex. 102, Note *i). — *3) Par. 2036. 202. The chord of the dominant-seventh is obtained by adding another (higher) 3rd to the intervals of the dom. triad. The new interval, the chord-seventh, is the dissonance, requiring resolution. The dominant-seventh is employed in place of, or with, the triad V. The construction and treatment of the chord are the same in minor as in major, with the usual exceptions (Ex. 70). 203. a. There is no choice of position; and the chord-seventh may lie in any part. h. The chord-fifth may be omitted, and the root doubled. c. The chord-seventh progresses diatonically downward, and is not to be doubled. 7 204. a. The resolution of the V into the I (or inversions) will be called Normal, because it cor- responds to the normal progression (par. 78). h. The resolution into the VI (the relative of the I) will be called Deceptive (par. 119). c. Both the normal and deceptive resolutions are regular, because both lead into tonic chords (par. 1006). 76 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 305. Normal resolution iE± ^ N. B. M^ Deceptive resolution , 1 : 1 I ^<-i h^« J^J/ ^ i(?)J/ , I J ^ ^ re 7 6 7 3 4 B VI *i) Separate measures, as usual. Alike in major and minor. — '2) See par. 200c. This error, which may be termed " unequal octaves," is quite as disagreeable as actual parallel octaves. The error is most obvious in measure 7. — *3) The parallel sths in the inner parts are also "unequal," because the first one is diminished and the second one perfect. For this reason they are not altogether wrong, as the rule applies strictly only to successive perfect sths. When the second Sth is perfect (as here the a-e), the consecutives had, however, better be avoided. The b in tenor should ascend to c, any- way. 7 The Introduction or the V. 206. Dissonances should be not only properly resolved, but also so smoothly introduced as to avoid needless harshness. 206. The regular modes of introducing a chord-seventh are: a. Diatonically from above {i.e., the seventh preceded by the next higher tone) ; h. Diatonically from below; c. By preparation {i.e., preceded by the same tone, as interval of another chord). 207. The introduction with a skip is somewhat irregular, but possible in all chords of the First class. Being a tone which resolves downwards, the skip upward to it is better than the downward leap (par. 31). For example: Diatonically from above ^_ From below _, C. Prepared *i) In major and minor. — "2) Also "xmequal octaves," but not quite as bad as the reverse. — "3) Major only. — *4) The leap upon the 7th, in parallel direction, and in the outer parts, is harsh. The following measure (soprano and alto) is permissible. — *s) Par. 207. Pai. 207. THE INTRODUCTION OF THE FIVE-SEVEN. 77 FUNDAMENTAL PRINCIPLES. Discords are divided into Classes, according to the distance of their roots in harmonic degrees above the tonic. Tonic chords are exclusively consonant. The seventh of a chord is resolved diatonically downward, and is not doubled The fifth may be omitted, in chords of the 7th. Unequal octaves are wrong. Unequal 5ths are doubtful when the second one is perfect. The introduction of a 7th is regular when it enters diatonically, or is prepared. All reasonable licences are permissible in First-class chords. EXERCISE TWENTY-EIGHT. A. Write out the V of every major and minor key, with its two resolutions, on one staff, as follows: G maj. G min. IE -M =51= 11=^ 6i= etc. VI B. Transpose (at the piano, at sight) the following fragment, into every major and minor key: 3 i E^a^ i^^ ~zi- f 7 V 7 V I V VI V I C. Add the upper three parts to the following basses, — each chord complete, in succession, as it is no longer practi- cable to define the soprano alone. *i) +3 8^^ 3 +7^ ^ *3) **) b- ^ ^ mm sas »-4-i =F=^ a 6 4 8 e 4, g y^i-j ziy _3+3*2) S ^ -*-#-L-^- ^ a a 6 7 e 87 S * t- *s) a 87" «e) s a *7) ^ ^ & ^1F=^ II % t* 87 4« 78 *4 li ^E 1^ ^ Si ^=* ^ i 3t=t if "*" 87 7 as it 4« 57 87 78 / i* THE MA TERIAL USED IN MUSICAL COMPOSITION. Par. 208. -3+3 8-3 3 3 FAISST 1=^ ^ r^ ^ ntz* ^ 8 7 *a) 7 se a a 6 5 4 s ^ £ I g- a a 7 a 3 4 +3 G major | I | I I3 V I I^ I IIj IV VV I VI Ij 11^ I V I- V I Ii IV I, Vo I I IV, lo IV I V Ig V V I I II *i) Par. 1896. — *2) Chord-fifth omitted. — *3) Par. 193. — *4) Ex. 151^-2. — *s) Exercise 23, Note *i). — *6) The upper parts may all be held. — *i) Ex. 140. D. To this exercise add a number of Original phrases. The Inversions of the Dominant-seventh-choed. 208. All chords are inverted in the same manner, i.e., by substituting some other chord-interval for the root, in bass (par. 141). A chord of the 7th (4-tone chord) has, obviously, three inversions, as follows: ist inversion, > , , ( with the third in bass; 2nd inversion, ) l with the fifth in bass; 3rd inversion, with the seventh in bass. The inversions are figured and named according to par. 142. Thus: Chord of the seventh Chord of the six-five Chord of the four-three Chord of the second -35?- ^ ^m ai Vj *3) 7 Vo 7 V. STRoot: Z^Third^r^ ZFifthZ _Seventh_ ^ 6 I *4) (I) *i) As usual, those figures which are understood, are generally omitted. — *2) The pair of adjacent notes always represent the intervals 8 and 7, that is, root and seventh; thus: m In other words, the iipper of these two tones is the root, and consequently defines the chord. Therefore, the names of the three inversions merely indicate the intervals from the bass note to this pair of tones: f, f, and 2. — *3) Spoken: "Five-seven-one"; first the name of the chord, then its species, and lastly the number of its inversion. — '4) In minor, fuller figuring is necessary, on account of the leading-tone, which has an accidental. 209. The inversions appear, as usual, in place of the fundamental chord. The second inversion, like the 6-4 chords, is weak, but not as much so as the latter. The third inversion is beautiful and useful., 210. The inversions are treated, in general, like the chord of the seventh. The exceptions are: a. No interval should be omitted (par. 146c) ; b. The inversions are limited almost entirely to the normal resolution (into the I and Ii). The deceptive resolution (into the VI) is very rare in the first inversion, impossible in the second and third. Review par. 206. Par. aio. THE INVERSIONS OF THE DOM.-SEVENTH-CHORD. 79 Normal resolution 2o6a 2o6i 2o6f 207 ^ i 7-? ' u- r r-r ' r '.ill I r r r -J — i J i f,-, I Lj i i^ r r r ' r r ' r-r r ' ' rr i I « 5 *i) i i f=^ e 6 4 s ^ -4- ^=^(?3? *3) **^ J i r-r r i J i e V, I I -i P R^^^^ - ^ *4) I* Deceptive resolution a «a) ±3^ i=i ^ r r 'r r , r r ^ 'r-r ' c^ r 'C» ^ ^ VI v„ VI V, VI, . P ^^ .«■ =, 1 fi A ^i^ Ii I *7) ^ *8) *9) "i) The figuring ^"g equals I5, the interval 6 being doubled. — *2) E^ equals t-, the interval 4 being doubled. — *3) These unequal sths are perfectly good, because the second one is not perfect. — *4) Either the I or Ii may follow the 4-3 chord; but the I is better, as it avoids the duplication of e. — *s) Like Ex. 98-3. — *6) Obviously only the Ii can follow the third inversion, as resolution of the chord-seventh in bass. — *7) The unequal sths, though doubtful, are not as noticeable in alto and bass as in any other two parts. — *8) Wide leap in bass; comp. par. 171c. — *9) Succession of weak chords. — *io) In minor as well as major, excepting where the 6th scale-step ascends to the seventh (Ex. 70). 7 Further illustrations of the V and inversions: i M ri Beethoven Jii- Beethoven ^iiv/,,ii/i;;/yiii:'^ a P^FP Ex. 154. ^te i f i Tf , irntt i g: I ^TK' i f ij 7 A V. V3V1 IVi la IV Ii Va I Vi Vi I III la V I 80 THE MA TERIAL USED IN MUSICAL COMPOSITION. Par. an. 211. The rule of par. 85, concerning the repetition of a hass tone, is subject to an exception, as follows: An unaccented bass tone may be repeated over the bar or accent, ij it becomes a dissonance. Thus: Ex. 155." m k¥^ ^ A ■s! s er j-i IV II FUNDAMENTAL PRINCIPLES. In an inversion, no chord-interval is omitted. 7 The deceptive resolution is applied only to the V, — not to its inversions. A chord may be repeated over the bar, if its bass changes; a bass tone may be repeated over the bar, if it becomes dissonant. EXERCISE TWENTY-NINE. 7 7 A . Write out the V^ of F, G,B]>,D,E\>,A,E,A [., D\>, B, G\> majors; the Vg of et, gi, 6b, /, c#, /#, c, b, g, e, d minors ; 7 and the V3 of G, F, Bb, D, A, E\>, A]>, B, E, D\>, Fi^ majors, — with their resolutions, on one staff, as follows: i 7 Vi F w ^^ V3 Eb V3 G -f- & P^9, ^^ I etc. Il Afterwards, find these same chords and their resolutions at the piano, with the right hand alone, without reference to the table. B. Basses. (The position-figures may be ignored.) a. *i) 8 J 7 +3 ^ *2) -^-\-m- ^ S ^^^^^ ^^ 4 d -0-^^ 6. *]) 8, +3 ^m ^^ *3) ^m zM±*z ^^ m m *• # # itTT^^mr i 7ft-r 8 7 3S w Par. 213. IRREGULAR RESOLUTIONS OF THE DOM. -SEVENTH-CHORDS. 8l ^ i *i) s 4>v- ^ ^ ^ e OS « I 8 7 6 87 *»s) BT^^n^ *4) ^S i s ^ 6 6 6 6 7 64, 5 0- • - 4,6 » 4- 6 6 e«60 4 6 66 S7 4 434 3 4jj- /• i5» f M J i IE ^ ^• f • P =§^^3^ S ^Pl e^^ 6 6 I 6 4:\ 6 6 6 7 a^ FT^ ^ & 5=F= S :F=^ t - ° t i *5) *i) Positions are reckoned from the root. — *2) Par. 1230. — *3) Ex. 153, Note *i). — *4) Ex. 153, Note *2). — *s) The upper parts are held. C. To this exercise add a number of Original phrases. Irregular Resolutions or the DoMiNANT-yTH-CHORDS. 212. The majority of licences in the treatment of dependent chords and intervals appear at re- petitions, where, as has been shown, all rules are suspended. 213. The licences which attend chord-repetition are of two general classes, namely: 0. The resolution of the active tone itself is deferred, by the interposition of some other interval or intervals of the same chord; b. The active tone is transferred to another part, and there resolved. These all constitute "modified repetition." 214. a. Hence, when the chord remains the same, any convenient interval or intervals may be inter- posed between the chord-seventh and its resolving-tone. (Deferred resolution.) b. When the chord is repeated, it may change its form, its position, and the disposition of its in- tervals to any reasonable extent; the seventh is likely to be transferred from one part to another with- out any other restriction than this: being a tone with downward tendency, it is most apt, even when the chord remains the same, to progress to a lower tone. c. In all of these deferred resolutions the seventh is ultimately resolved in the part where it last ap- peared. 82 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. ai5. a. Deferred resolution »3) b. Transferred dissonance ^^ Ex. 156. »l) J i_i i 3^=3^ J^^ 9i ?»=i- m ^ r r ' r r f 7 V .J>u J| *5) T ^i J i J JiL r ^r— r^ 7 I *8) J - -J- UL 7 -ft — Z (= ^ m *i) Major and minor. — *2) The 7th moves upward; but in reality the g is only an interposed interval of the same chord, and does not interfere with the ultimate resolution into e. — *s) Here another form of the chord intervenes, before the resolution takes place. — *4) The 7th is transferred from the alto to the soprano, and is resolved in the latter part. — *5) The 7th in soprano, though transferred to the bass and resolved there, should progress downward to d or b, and not upward. The following measure is better, because the 7th in tenor is taken up by the bass in the same register. — *6) Here the chord-seventh disappears altogether for a moment. The Passive resolution. 215. Another kind of licence is a Digression or Indirect resolution, whicli consists in interposing a foreign chord before the resolution takes place. It is another form of "deferred" resolution, but less common than that of modified repetition. The foreign chord must be reasonably brief, and must be in some way connected with the discord whose progression it interrupts. 7 216. a. The foreign chords which intervene between the V and its regular resolving-chords are the two subdominant or second-class chords IV and II, in both of which the seventh of the domi- nant occurs as consonant chord-interval, thus constituting a connecting-link. For example: i m 7 V IV 7 V i II b. This chord-progression may be termed a Passive resolution, because the 7th, in becoming a consonant interval, is actually resolved, passively, through the other parts. It corresponds to Exs. 67 and 79, but is more feasible, because of the connective link which the seventh provides. 217. The consonant condition thus gained by the 7th does not compensate for the actual regular resolution. Hence: a. The passive resolution is usually only a digression from the discord and directly back to it (per- haps m a new form) ; thus: V-(IV or II)-V: or V-(IV or II)-Vi, or Vg. Compare Ex. 67, Note *2). Par. 218. OTHER IRREGULAR RESOLUTIONS. 83 h. Much more rarely, it is interposed between the discord and Us resolving-chords; thus: V-(IV or n)-I, or VI. c. Rule I. The seventh must remain stationary, i. e., in the same part. d. Rule II. The seventh should not be doubled, or otherwise disturbed, during its transient con- sonant condition. Passive resolution *6l *7) Ex. 157. l^^ S *6) *7) 5& i J ' i r 1- i §■ C r f 'r U i V IV Vi I V II 5 6 7 4 i Incorrect Exceptional I J, J | { j i j J , . ^M J J I , ^=^J=^ gnTTr f i r M f r i rr tpfi i Rule I Rule II *i) Par. 217a. — *2) 217&. — *3) The 7th must remain in the same part when the harmony changes. Par. 217c. — *4) The/ in alto is wrong, because it doubles the passive seventh. Par. 200c. — *s) These measures, in which the passive 7th changes parts, are exceptional, but admissible, because the tone remains in the same register. — *6) Major only. — *7) Major and minor. Other irregulae resolutions. 218. Besides the above hcences there are two other irregularities which are peculiar to the chord of the dominant-seventh: a. The 7th may be resolved diatonically upward, when the bass, part moves parallel with it, in yds; and b. The seventh may be doubled, when one seventh progresses to another chord-interval before the other is resolved. Thus; a. Ascending resolution 6. Doubled seventh *3) I Ex. 158. *1) f J I J I , : I i4='^^ ,^ *i) Major and minor. — *2) This licence is Umited to the chords V2-I1; in no other case would the bass move with the ascending 7th, in parallel 3rds. It is not to be confounded with the first measure of Ex. ij6j where the 7th 84 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 2i8. progresses upward, but returns to its resolving-tone. — "3) These sths are allowed. They are unequal; and they seem to be fully disguised by the parallel movement of each part with the bass (comp. par. 66). FUNDAMENTAL PRINCIPLES. When the dom. discord is repeated, it may change its form in any reasonable manner, deferring the resolution, if desired. The passive resolution of dom. discords is effected by Second-dom. chords, the chord-seventh re- maining stationary. The seventh of the dom. chord may be resolved diatonically upward when the bass accompanies it in parallel thirds. EXERCISE THIRTY. A. Basses. (The positions may be ignored.) '^- +7S*l) a 75 6 2 - 6 a- as a a 4- ^^ 87 4 se 34 ( 1 S=?E ViE3 or n ■? L 87 4 *a) 7S 87 8 »3) S7 „ « 5 *1) 7*3) ir-^f-rBM i i^ a M «5 f- 87 t- 6 7 3 8 *4) S Be ^' ?3t: ^ ^ itt T^f !£■'- e a a 4 4 8 t _ 8 a »s) 3 -^ e *^^ *^> ^m riF^ J I * i a « 8 5 3 4 8 7 » - gas 343 6 8 7 8 5 4 It" Faisst i=^ /• *3) S S -f—^ S • -^- '8 a 0— 5 4 ^ g »fffff^%t^ ^•-5, ♦3) • ^ .(^ J. A ^ ^ f-& t=:=t 7 3 7 87* 8 085 ?7 *3e5 f I ^ ° I t I f 8 1 i 5 t M « t y-f Par. 2ig. THE INCOMPLETE CHORD OF THE DOMINANT-SEVENTH. 85 h. *i) Ex. 1566. — *2) As usual, the rows of figures indicate the course of the upper parts. — *3) Par. 217c, i. — •4) Par. 2186. — *s) Par. 218a. B. Play the following chord-progressions slowly, at the piano, in different major and minor keys. At first with the right hand alone; afterwards with both hands, the bass alone in the left hand: V7/TN77/TS77/!> 7 77«>7 7'SN I-V-Vr-Ii II Vj-Vr-Ii II Vi-V-VI |1 V-I2-V3-V2-I || V-IVi-V-I || Major only (7 7 f7\\ 7 7/^7 7/T^7 /T\ Vi-IIj-V-VI-'ll V2-IV2-V1-I II Va-IV-Va-Ii 1| V-IVi-VI || Major only 7 /TN /7 /T\\ 7 7 /TS V1-IV2-I II W-IIr-VI^II V-IVi-Ir-V-Vs-Ii || C. A number of Original phrases. B. The Incomplete chord of the dominant-seventh, or, the triad upon the leading-tone. 219. a. The root is the interval upon which the identity of a chord naturally depends; but when the other chord- intervals are of such a nature that they define their chord beyond a reasonable doubt without the root, the latter may be omitted without obscuring the harmony. b. This is naturally not often the case in three-tone chords, but is not unusual in those oifour tones, and almost obli- gatory in those with Jj»e. When applied to the chord of the dominant-seventh the result is as follows: Ex. 159. i Inversions Figuring Positions *3) 8 IE -^- -Tg- -2g~ 7 V 7 «l) 7 oVj 7 0V3 I *i) Spoken: "Five-seven, incomplete." The term "Incomplete" in this book invariably signifies "without the root" and is indicated by the o. The inversions are not reckoned from the actual root, but, for convenience, from the apparent root (the third of the fundamental chord). — *2) The positions, also, are reckoned from the lowest tone of the triad, as in ordinary chords. 7 ' 220. a. The incomplete V is the triad upon the leading-tone (par. 53), with its inversions. 7 h. Like the V itself, it is alike in form and treatment in major and minor. c. It is a diminished triad, because its fifth is diminished, and therefore a discord, though but a 3-tone chord. The diminished 5th is the dissonance (par. 4oe). 221. The reasons why this chord must be regarded as a derivative of the V, instead of as an independent chord with the corresponding designation (VII), may be demonstrated as follows: 1, because it contains the leading-tone, the chief characteristic of the dominant harmonies, as apparent harmonic basis (par. 73a); 7 2, because its most natural progression (resolution) is into the I and VI, exactly like the V. This is naturally owing 7 to the tendency of its leading-tone, and to the coincidence of its dissonance (the dim. sth) with the dissonance of the V ; 86 THE MA TERIAL USED IN MUSICAL COMPOSITION. Par. 232. 3, because the comparison of this chord with the V discloses a similarity of effect not to be fowid or expected be- tween different chords. 222. a. The dissonance, being no longer an acPual 7th, is not obliged to resolve diatonically down- ward, but may (especially when approached from below) progress diatonically upward. b. Either the 3rd or 5th of the triad may be doubled. When the latter (the dissonance) is doubled, the two tones generally move in opposite directions. c. The best and far most frequent form of this dim. triad, is the chord of the sixth. The triad itself is rarely used, because of the prominence of the dim. 5th. The 6-4 chord is better than the triad, and stronger than other (consonant) 6-4 chords, and occurs in the usual three connections (par. 173, etc.). d. The resolutions correspond to those of the V complete, i.e., normal, into the I (Ii) ; deceptive, into the VI; passive, into the IV and II. For example: 7 a. Chord of the 6th (oVj ) i J J \n\ im a ^ tP^ ^m I n^t, f3t \ 4) *3) 1*1) 1*8), ' 1 I I ^ I i a Ij 6a 86 66 I 6 6 6 TV TT VI 8 ^^3 6 ^^ Ex. 1 60. ' -*- I ^ I b. The triad (qV) C. The I chord (oVg) **) , J , I Ji ' ?M I J I M r3 1 r^ I 1 I J I I I ^ -*l I ' "•". I I ' N ' ' *7) ' I ' ' ' ' »8)l irpry-r ' i ^-rw^ :f~f \ n \ f ^i£=j^u^ 6T66 VTS-eeTV 666 I n-r^r VI 5T 8 6 IV 6 6 6 65 -"^ 66 6 S 66 _ . .. _ *i) The 3rd scale-step is very often doubled in connection with these incomplete chords, as it conduces to smooth progression. — *2) The leading-tone may be thus doubled, when the two tones progress diatonically in contrary motion, as here. — *3) This skip from the dissonance (/) is justifiable in any part but soprano. — *4) Par. 162. — *s) The un- equal 5ths in bass and alto are barely excusable. — *6) Par. 1910, 6. — *^) The skips in bass from the dissonance, in this measure and the next, are irregular and unusual, but excusable on the groimd of par. 222a, and the quality of / as a prin- cipal tone of the scale. — *8) The two successive 6-4 chords (contrary to par. 1716) are allowed because one is the I2 (Ex. 126), and the other a discord (par. 222c). — *9) See Ex. 118, No. 6; also par. 137. The II IN MmoR. 223. This is also a diminished triad, and consequently a discord. It belongs properly to the 2nd Class of chords, as its root is the second-dominant (Ex. 147), therefore its treatment at this place is premature, but justified by its im- 7 portance. It resembles the incomplete V in general character and treatment. In structure it corresponds of course to the major II: ^ dt C minor i w m -27- II II, II, Par. 224. THE II IN MINOR. 87 224. a. This dim. triad differs from the incompl. dom.-7th in being a fundamental chord, and not a derivative. Therefore it is used more independently and more frequently than the former. b. Its treatment is very nearly the same as in major. The dissonance (dim. sth) is, at the same time, the dominant leading-tone (par. 106), and is resolved diatonically downward to the dominant; consequently, the resolving-chords will 7 be such as contain the dominant note, viz., the V, V, or I. The passive resolution into the IV (which contains the dis- sonance as consonant interval) is effective, as transient progression. c. As before, the best form is the chord of the 6th. The triad itself is very rare. The 2nd in- version is, as discord, stronger than ordinary 6-4 chords. Comp. par. 222c. a. Chord of the 6th b. The triad i Ex. 161. (Minor) ffi i=^ * S J J i JJJiJ % a ^-f^;-r T'- r ' r r ' r r T ' f'f ■ ; F ^m lt=t=3t iM -f2- m i i^ W=f i ^ lAiri: 1 , ^Alli V 8 I3 s i^ 56 1^ a iVj^v as a •^a 4 a n c. The I chord < fe y=t^^ n j i ^ J i^ ga m T^ r' r r r: ij f •3) ™~' I *i) a- 7 48 V a e 4 4 F=f-m-m =n a a a 4 4 "i) In major, this would be palpably incorrect; in minor it is good, because one of the 6-4 chords is a discord. — *2) Of these three successive 6-4 chords, two are discords, and the other is the I2. FUNDAMENTAL PRINCIPLES. The triad on the leading-tone is an incomplete dom.-seventh chord, and is treated accordingly. 7 The only good form of a diminished triad (qV and II in miaor) is the chord of the 6th. Successive 6-4 chords are allowed if one is a discord. EXERCISE THIRTY-ONE. A. Major. S 8 ^* 5j*8) 3 +S e 1 ^T 1^ — If t « ° 3 S 5 ^-» ■*— # S^S^ 6 5a ^^ a 4 - 4 *a) ^. i *s) ^ ^m g ^ b 4 « ^: It* I "3^ 88 d. THE MA TERIAL USED IN MUSICAL COMPOSITION. 8 -^_4^ "* Far. 225. Bi-fe:a=2=:f: I * 57 -Sl^ 6 »S)* a- se £. Minor. •5) *6) /• ^e ^ ^ ^ !r 3ti "0 6 6 6 57 .565 4 4 J- 343 ^ :?^ I a ^ f m ^ 3 i=PE: =»t ^ *-V 666 e e ^6— 6 4 <( a 6 *8) 3 a 5 4, a a 66 $66^ 66 |. -3 *7) 87 a # 67 I ^i;M ^ ^S: m ^ =P^:i= -.^— •- ^^ r sap 6 06640 Oat 7 6 6 6 6 a* " I "i) Ex. 159, Note "2). — '2) Ex. 140. — '3) The upper parts are held. — '4) Par. 1230. — "$) Par. 162. *6) Plagal. (Rhythm J J J ). — *7) Par. 157. — *8) Deceptive cadence. C. Original phrases. Melody-Harmonizing. Dominant-seventh. 225. The dominant discords appear naturally as substitutes for the concord. Therefore, the dom.-seventh chord may be used for any scale-step contained in the V. Thus: steps: _ _ a Ex. 162. i IE V or V V or V V or V The inversion depends upon circvmistances, but is easily determined. 226. Further, the dom.-seventh chord may now be used in harmonizing the fourth scale-step. This has hitherto been harmonized with the second-dominant chords (IV or II), and these will still be necessary when the 4th step ascends, or makes any other movement antagonistic to its resolution as chord-seventh of the dominant. For example: Ex. 163. i ^ '- J | j -J . J -J i ^ :J -r^-riT-J.r^ W- ^m i ■^ ( I V I - 7 Vi VI ;i 7 V 7 V 7 V 7 V 2 "1 *l) *2) ■ or Inv. *3) V V or Inv. 7 V 7 V IV - *4) *6) *o) — m — S :f^ 7 V, 7 vv - or Inv. 7 IV V II 7 7 7 V IVi Vj V IVj VI la Par. 327. MELOD Y-HARMONIZING. 89 *i) Not the Vs, because the seventh cannot be doubled in bass and soprano. — *2) Not the VI; see par. 2106. — "3) Good, if the hass note changes. — *4) This is the one possible case where the ascending 4th step may be harmonized with a dom. discord; but it is rare; see Ex. 1580. — *s) Ex. 1560. — *6) Passive resolution. 227. The Incomplete dom.-seventh may be used for the 7th, 2nd and 4th scale-steps, but is chiefly used for the 7th step, which it harmonizes with the chord of the 6th. Thus: »;i) s 434 I i Steps: 7, 3 3 2 I 1, j|]] i njrj:n i ^^-^| j ^ i 0j] Ex. izitzt 164.^ S • Bass: g sa oeees *i) This demonstrates the usefulness of the incompl. dom.-7th, in the case of these irregular melodic successions. 56 ea' 6S6 a 4 a See pars. 242, 243. i fefei *1) »2) *3) EXERCISE THIRTY-TWO. *3) b. »3) hhU ^zJ=:iU=4, E^to^ :^=ftit=^:^ I _ h I J IS «--#■ ^ • • ii -d * ^ C. «4) *6) *4) n-J J i J n ^ *7) ^^g i *6) *6) *8) «9). h^ i Ttz±±: j i ^ * 3te *-3t ^E^ ,M-«i S -P » Si *ii) *xo) ±=bt ■tS- ¥=n& |4xUfj..jJ|JJ^ l ^-/j | J7j | J-t^^^r- r r i f ^ "America" ^^ ^ ^. (In major and minor.) ^. tin major ana mmor.; , ,is v ^j ^&^ \ r^ Ji f r ^ I J JT i J'jrrirJ F ^ ^^gB i ^^■ 1 ' ^iiJ i j. r ^J i Lit^ i^ :|C ^ 90 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 228. /. Allegretto ^S w 5i 3t=t IClJ^ ^ •H) *1S) »12) _ 1 1^ I -1^^ ^^ i i I I r Popular air ^ :ti; *ia) A. Larghetto *. Larghetto ,^ *12) IV ^: Old melody W^ i It** p^ Vr-U t= *io) *i) Par. 226. — "2) Ex. 144. — *3) Par. 225. — *4) Passive resolution. — *s) Ex. 164. — *6) Ex. 163, Note *4). — *7) Par. 227. — *8) Ex. 143. — *9) Successive 6ths. — *io) Ex. 146, Note *2). — *ii) It is better not to use the discord 0} the dominant, as semi^cadence chord, but the simple V. — *i2) Same chord, unchanged, for the repeated notes. — *i3), Ex. 1 18-2. C. The Chord of the Ninth upon the Dominant. 7 228. a. This five-tone chord is obtained by adding another higher third to the intervals of the V. b. The new interval is a ninth from the root, and its most important characteristics are: ist, that, being related most directly to the seventh (upon which the last third is erected), it must always be at least g tones (7+3) from the root, and therefore can never be contracted to a 2nd. Thus: ^ Efl ; ^^'i' 2nd, that it cannot appear without the seventh. Consequently, c. The chord-fifth must be omitted in 4-part harmony; not the seventh, nor the third. No inter- val can be doubled. 229. This is the first dominant chord which differs in major and minor. In major it has a major ninth, in minor a minor ninth. Hence, a distinction is made in its treatment in the two modes as fol- lows: a. In major, the ninth should always be placed in the uppermost part (soprano). b. In minor, on the contrary, the ninth may Ue in any of the three upper parts; but, as stated above, never less than a ninth from the root. .^. Ijigf In major (229a) J In minor (229^) •i) Spoken: "Five-nine." — *2) Always figured f on accoimt of par. 2286. — *3) Par. 228c. — *4) Par. 2296. Par. 330. INTRODUCTION AND RESOLUTION OF THE FIVE-NINE. 91 Introduction and resolution of the V. 230. a. The introduction of the ninth is similar to that of the seventh, as shown in pars. 206, 207. h. The ninth is resolved exactly like the seventh, diatonically downward ; or, if a passive resolu- tion, by remaining stationary, in the same part. The two dissonances (seventh and ninth) are very commonly introduced and resolved together, in the same manner; but not necessarily. c. The normal resolution is effected by the I (I2). The deceptive resolution is not possible. The passive resolution is effected by the IVi or IV2; not by the II. Introduction. *l) Strict ( comp. Ex. 151 ): n laUi ^^^^^^P^ Free: ^^ Ex. 166. «5) J i J i J uJ-J i J i J ij -^.-^ J ^ ^ m r n?^r- ^8 10 g 7 — IV r\^ II 89 67 43 *i) When the gth is introduced diatonically from above, the leading-tone moves contrary to its natural tendency. It is chord-repetition. — *2) A skip of a seventh is hardly possible in any other connection than in chord-repetition, as here. — *3) Unequal octaves; comp. Ex. 151, Note *4). — "4) Par. 207. — *s) The student must hereafter determine for himself which of the examples are valid for both major and minor. The chief obstacle, which defeats minor, is the suc- cession of the 6th and 7th scale-steps, — as in meas. i, 2, 16 and 17. Resolution Normal : Partial : Passive : -^^^4m%^ *i) J d *2) 1 r r ' *3) hiri ^343 IV, 4,- * 'i) The pth is resolved alone. : — *2) This duplication of the stationary gth (a in soprano and bass) is excused by the ■thness of the progressions; but par. 217^ remains valid. — *$) Similar to Ex. 133, Note *2). smoothness 92 THE MATERIAL USED IN MUSICAL COMPOSITION. rar. 231. 231. There are a few licences in the resolution of the V which are to some extent peculiar to five-tone chords, as fol- lows: a. The ordinary iejerrei resolution (par. 214a), and the transferred dissonance (par. 2146). 6. The exchange of dissonances. c. When one dissonance progresses to another, or, in general, when any active tone progresses to another active tone, it evades its own resolution, the progression of the last active tone sufficing for both. It is necessary that the first active tone moves in the proper direction, unless it is chord-repetition. d. Similarly, an exchange is sometimes made during the passive resolution. i. c. , .., ^. ( ? ) Ex. 168.' r~t 3 - S 2 8 7 e 4 9 7 7 9 9 I VI *i) The exchange of the gth and 7th is possible only in minor, for the reason given in par. 229a. See also par. 214c. *2) The 9th (a) is merged in the 7th, and the resolution of the latter suffices for both. — *3) The 9th is merged in the lower leading-tone and evades its ordinary resolution. The progression upward into the leading-tone would, however, be very irregular. It is possible, but demands a different analysis. In all of these cases excepting the passive resolution the discord is merely repeated in another form (par. 212). FUNDAMENTAL PKINCIPLES. The chord-ninth must always be at least 9 tones above the root. The ninth never appears without its seventh. In major, the ninth of the dominant chord must be in soprano. The ninth is introduced and resolved exactly hke the seventh. When one dissonance progresses to another dissonance, or to another sufficiently active tone, the resolution of the latter suffices for both. *i) «i) EXERCISE THIRTY-THREE. Faisst b. *l) 3 fc *a) 3 ^ Itrfi ^4 «i) *i) ^^ ±a ^ 5 * 93 7 - B- 9 8 7 7 M _ " —, 65 6.5 959 36 43 7— *8) «3) Par. 232. ^ id2: Tff£ COMPLETE INVERSIONS OF THE FIVE-NINE. *i) ^ d. 93 d. ^ 3 7 5 * *) St 97 B7 75 a| ?! i 79 es 97 ^^ / hJ ii >" r I B ^ 98 51 S-ff 7 43 66 07 65 43 75 43 a— 86 7 6 66 8 4 7 § i —0,0 -t-y I I ^^ ^ ^ 6 3 6 4 6 6 66 *6) "i) Par. 2290. — '2) Par. 2296. — *3) As usual, the arrangement of the figures indicates the course of the upper parts. — *4) Ex. 140. — *s) Passive resolution. — *6) Rhythm J J — . To this exercise, add a number of Original phrases. The complete inversions of the Five-nine. 232. It is obviously impossible to invert the interval of a 9th,because it exceeds an octave (par. 42). But, as the in- version of a chord merely affects the bass part, it follows that complete inversions of the chord of the dom.-gth may be obtained, in the usual manner. But they are peculiar and difficult to handle, on account of the inconvenient 9-tone in- terval, which can neither be inverted nor contracted (par. 228J). The following example exhibits the possible forms: 1 *s) I Ex. 169. Minor F , f , ^ \^-J f^M" J?4k^ ^ Z^ 1^=^ J ^^ Vl Third Vg *i) Fiftli V3 Seventh *3) V^ Ninth *i) The and inversion can-be employed only in five-part harmony, as the 5th (the only omissible interval) lies in the bass itself. — *2) The 4th inversion, involving an inversion of the nine-tone interval, is an absurdity. — *3) The reso- lution of these chords corresponds to that of the Five-nine itself. D. The Incomplete chord of the dominant-ninth, or, the chord of the seventh upon the leading-tone. 233. It need not be inferred from the above paragraph that the chord of the dominant-ninth is available only in its fundamental shape. On the contrary, that is the very form in which it is most rarely used, because it is too bulky, and subject to too many restrictions. This is the case with every chord of the ninth; hence the rule: a. Five-tone chords should, in general, not be used in four-part harmony in their complete form, but must be made incomplete, by omitting the root. (Review par. 2190, b). s b. The only exception is the V, which, by virtue of its superiority as First-class chord, is occasionally used complete, — as seen in the preceding exercise. 94 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 234. 234. The incomplete Five-nine is the chord of the seventh on the leading-tone (comp. 220a) with its inversions; and it differs in major and minor, like the Five-nine itself (229): Maj. Min. i -*- -:r- ^ -@- % 8 V oVn)o *i) Spoken: "Five-nine, incomplete," and figured as usual, 7, f, |, and 2. See Ex. 159, Notes. The qV in the major mode. 236. The chord of the seventh on the leading-tone is called, in major, the "Ambiguous seventh," because it is more suggestive of the relative minor key than of its own major key, and unless carefully handled, with strict regard to the conditions of its key, it causes disagreeable confusion of scales. This is because it is a genuine chord of the 7th, with every indication that the lowest tone is its actual root. But as it cannot be a root if it is the leading-tone (par. 51), the ear assumes this lowest tone to be some other scale-step, and there- fore in some other key, — namely, the 2nd step of the relative minor. Thus: C major A minor C major g ¥ -^ yr < ^ ^^^ag^^^ -s>j:i- 7 II 7 V ^ -&- oV I li V I ^ In order to hold this chord in its major key (where it is a chord of the ninth), and counteract its tendency towards the relative minor (in which it is a chord of the seventh), it must be treated like the original "ninth," and not hke an ordinary "seventh." The rules are as follows: 236. a. The 7-tone interval from the leading-tone to the ninth represents the original 9-tone interval, thus: ^ 9 7^ therefore this interval, in major, should not be inverted (as . 97 second). In other words, the dom.-ninth, in major, must never lie below the leading-tone, thus: i C Maj. / A Min. w -gjp- ^ ^sMM: \ good b. The most effectual mode of avoiding this error is, to place the ninth in the soprano (par. 229a). c. The major ninth may, it is true, also lie in an inner part; but only when the leading-tone is in some still lower part, and when the 9th is introduced strictly. d. No interval can be omitted in these incomplete chords, and consequently none can be doubled. The following table illustrates the manner in which the Incomplete dom.-ninth and its inversions may be erected in major. C Major -V . 1 „V, 1 „V„ i „V. »2 ' f O *i) These forms are exceptional. See par. 236c. — *2) Ex. 169, Note *2) Par. 237. THE oV IN THE MAJOR MODE. 9S 237. The dissonances (7th and 9th) are introduced as in the complete V, but perhaps somewhat more strictly. Introduction : «3) m ^ ^ ^ r rrr J i ^ ^ *3) i ^ , J-J f ^ 1 J •!> i i J J J i J J J J J , *i) When the gth enters diatonically from above, the leading-tone is generally doubled. This is entirely correct in this connection, as it is simply a smooth preparation for the interval 7, — like Ex. 151, meas. i, 2. — *2) These parallel Sths are particularly apt to occur. They are best avoided by doubling the third of the I, as seen in the preceding measure. — '3) Par. 2i6c. o 238. The resolutions, also, coincide with those of the complete V, i.e., normal, into the I, Ii; pas- sive, into the IV (VI) ; deferred, by other forms of dominant discords. Resolution ; »l) *2) ^ f^ *l) 6 ' ' VT IV S IVi e "i) In the normal resolution, these parallel 5ths are especially troublesome, and must be closely watched. As before, they are generally avoided by doubhng the 3rd of the I, as in the next measure. — *2) Comp. Ex. 167, measures 4 and 5. — *3) Cqmp. par. 218a. — *4) Comp. Ex. 160, Note *^). 96 »i) THE MA TERIAL USED IN MUSICAL COMPOSITION. EXERCISE THIRTY-FOUR. 3 5*2) +8 *1) *3) , Par. 239. -+- Faisst -8 ^E ^ T-9r-»- ^ =P=f^ m li; *i) +3 6 6 7 4 6 6S 43 6 87 7S ^^ *3) te i ^ ^— * 6 6 6S 6 6 4 ^ t ^ d. *3) ,»4) ^^^ £ a- 65 84 43 3- e 7 6 65 43 a- a- a 43 |4 g- ^^ ^+3 +7 5 -8 8 7 64 6 66 6 •-•-65 ^ l_ii^ ' „ 6 6 7 -4- 43 7 a a 4 5 a a 7a- 6-6 *i) Par. 2366. — *2) The positions are reckoned as in ordinary chords of the 7th, without regard to the actual (omitted) root. — '3) Ex. 172, Note 'i). — '4) Par. 236c. — *5) Rhythm J^ — . Add a number of Original phrases. The oV in the Minor mode. 239. a. The chord of the seventh upon the leading-tone in minor is called the chord of the di- minished 7th, because it contains that peculiar interval (in C minor, 6|)-ob). Figuring : C minor Ex. 173. -bs^ 8 o 0» 0*1 6. One of its most significant features is, that the contiguous intervals are all of the same size (at least, on the pianoforte), namely, three half -steps. Thus: Ex. J 74. is: fiHr-^ '-^i=^* ^ -^ a ^ m b »— ^ _etc.__ c. Consequently: All the forms (inversions) of the chord of the dim. 7th must sound exactly alike, as they constitute each time a group of " three times three half-steps." (Test at the piano.) It is therefore impossible to distinguish the separate chord-intervals from each other, and the restriction, of the chord-ninth to the soprano (as in major) is needless. These chords are the most flexible in the whole harmonic system, and accommodate themselves with extraordinary ease and readiness to other chords. For this reason, and because of their great beauty, they are extremely important and useful. Par. 240. THE oV IN THE MINOR MODE. 97 d. The difference in the denomination or actual size of the intervals (according to the letters) is necessary for the iden- tification of the chord and key. In the above example all the adjacent tones constitute minor 3rds, excepting ob - ilj, which is an augmented 2nd, representing the intervals 8 and 7, — see Ex. 152, Note *2), — and defining the chord-name. 240. The rules are, then, as follows: a. The disposition of the chord-intervals in the four parts is entirely optional. The ninth may lie in any part, even in bass. Otherwise the treatment is about the same as in major. b. As in major, no interval is to be omitted, and none doubled. c. The introduction of the ninth diatonically from above is impracticable, on account of the false melodic succession. d. In the normal resolution, the parallel 5ths are not as bad as in major (Ex. 172, Note *i), be- cause one of the 5ths is diminished. Still, it is advisable to avoid them, as in major, by doubling the third of the resolving-chord (I). Introduction: e Par. 240a. rar. 2400. q V , I I oV|i . 1*3) , I , -J J I J J I J 1 1 ^ irVd.. I J J if^Jj^ bJ-4 Pre ^ ^^MLi^^Um^^.j-}.^. T-r t^^t^rJ ^F^=!^ ^ k ^ j=j ^ J. J I .- I J- 1 ? ^ JnV: ^ m m ^-J-rJ -* — # f=f=^ ^m ^ ^TTW-^ m- i ik A *3) rf- m ij,j. ^ii^ -I ^ ^ w^4j 2 6 2 4 6 - S 2 ^ *i) Review par. 75. — *2) These skips to the leading-tone are good. Par. 31. — *3) The ninth in bass is correct, but Resolution: g J^ ^^^#^i^#iP Ex. 176. Minor. ^^E^^^^^^ nrrTjtg^ 7 I 7 V IVa oV oV, « Ii IV2 VI^ 98 i m^ THE MATERIAL USED IN MUSICAL COMPOSITION. o 0^3 ? ^s i Far. 340. •4) S ^ S m »8)'l I f n#^=^ r w^^ . t^J -^,W 1 ^' i ^M ai^U^^ai ? Ii »a) IV ^^J ^J^j VI Chopin ^jj r I f~f < * d—d= *-^^ i sg P fiJ . J tM S "fttt f t f -^y fi I *4) ^ 3^ E IV, II *a) ^ 7 9 7 VI Vo Via Vo VIj IV V_ (261) *i) Par. 24od. In measure 7 the unequal 5ths are concealed by the inner part. In meas. 8 they are in the outer parts and therefore conspicuous. — *2) These downward skips from the 7th and gtll are justified by par. 239c. See also Ex. 160, Note *i). — *3) See Ex. 175, Note *3). The normal resolution of the bass ninth, into a 6-4 chord, is very weak. The following measures are better. — *4) Passive resolution. — *s) This irregular soprano is permissible, because it is chord-repetition. But the part that has the succession should be on the way upward. Comp. Ex. 50, Note *i). FUNDAMENTAL PRINCIPLES. Five-tone chords, with the single exception of the dominant-ninth, are not used complete in 4-part harmony, but incomplete (without the root), o The incomplete V is the chord of the 7th on the leading-tone. The incomplete V in major suggests the relative minor key, and is possible only when the ninth lies above the leading-tone. The major ninth of the dominant is best in soprano. 9 The incomplete V in minor is the chord of the dim. 7th, consisting of equidistant intervals; it is very useful, attractive and easy to connect. The chord of the dim. 7th and its inversions all sound exactly alike. The minor oth in bass is rare. 7 o 7 s The First chord-class, or dominant element, embraces the discords V, V, oV and qV, and the con- cords V and III. "" EXERCISE THIRTY-FIVE. These minor basses are all to be worked out in a number of different ways {i.e., with different sopranos). The given posi- tions may be used for the first solution, but must then be ignored altogether. a. *!)+'' . _ +8 iSE ^ m 3 - - # ^ ^^ I Par. 241. b. MELOD Y-HARMONIZING. DOMINANT-NINTH. *i)8 *8) -» 99 I s i I f a f g '^ «^ f ° f I'l « j: ift t#=^ -5-. *8) m 8+S «2) L » tiiL • » i LLLI SI i ahg- B j: "* a— J a J. Ha a * ^™ 6' s e s e 7 6 a t 4J- ^ *a) ^^ £f^ ^ E[ M^ u a u f o 170 * » « 4#4 J! » f a 87 -&-' 4. 5- ^&m *s) pi s ■)5Z- S /• +a —a -t-a —a | ^- i^E i ^ 4 « I If"**) a a 4 s n 4: 6 87 "3 65 4tl *i) The positions are reckoned as usual, from the lowest tone of the chord, without reference to the actual root. — "2) Rhythm J /3 — . *s) Comp. Ex. 176, measure 4. — *4) Comp. Ex. 90, Note *2). To this exercise add a large number of Original phrases. Melody-harmonizing. Dominant-ninth. 241. The five-nine, as stated, should be used ahnost altogether in its incomplete form; and a dis- tinction must be made as usual between its application in major and minor. a. In major, it can only be used, safely, in harmonizing the 6th scale-step, when it descends. This places the ninth in soprano, and ensures the admissibility of any legitimate inversion (Ex. 170). o b. In minor, the V (generally incomplete) may be used: T . . . ist, and in general, wherever the V and its inversions are possible. 2nd, and in particular, as in major, in harmonizing the 6th scale-step (descending). For illustration: Major and minor e Minor Maj. and minor a *l) ;> Ex. 177. V I IgoV-I oV3HI) nV,-I, 7 8 7 V V V V Almost any form 7 V V e 7 V V S V„ 9 V„ IV Vo Vo IV V lOO THE MATERIAL USED IN MUSICAL COMPOSITION. Far. 242. IIl|oV*3) L0V3 •i) Par. 166. — *■£) Passive resolution; a little troublesome in minor. be one bass tone, as in Ex. 171, meas. 2. - *3) Possible, but weak. — '4) Likely to GENERAL PRINCIPLES. 242. The following general principles and directions should always be borne in mind, in determin- ing the harmonic basis of a melody: (i) Always look forward. Never define the chord of any melody-note without considering its relations to, and possible influence upon, the following tone or tones. (2) The attention should be directed chiefly to the accented beats. The tmaccented notes are of less importance, and must accommodate themselves to the chords which the accented beats require. (3) Mark, at the outset, all those scale-steps which can be relied upon with reasonable certainty, throughout the phrase. Namely: the very first chord (I) ; the semi-cadence (generally V, or I^V) and 7 7 the perfect cadence (V-I, or V-I, or la-V-I); the 3rd step (I); the 7th step (V, etc.); and the 6th step (IV, or Vo). (4) After doing this, sing (or play) the melody. through once or twice in correct time and rhythm, and endeavor to discern its harmonic basis by instinct (by "ear"), applying slurs where successive tones (of the same beat or accent) evidently or probably belong to the same chord. 243. The following table, in which the most natural and probable harmonic basis of each scale-step is again shown, as summary of the foregoing rules, should be thoroughly memorized: 1st step 2nd_ Ex. 178. m 3rd 4th_ 5th 6th_ 7th_ ^1 ^ 1 II VI V III II (ll)("'» I (VI) IVj V etc. (IV) oVmin. (Ill) I II V Vi 7 (V) IV (II) Vetc. / II V \ V ^IV oYi/ oVi IVi V o r,V min. Ill W — V EXERCISE THIRTY-SIX. «^' »i)l «2) *'3) ' H* •' ^ 1: ^ *5) _^ s I ^Ci p VI Par. 344. THE DISCORDS OF THE SECOND CLASS. *3) d. lOI ^ M^ir^^^Jz^ fe^ rrff^ JJ^t^^^ ^ fer »6) ^^h: p:i^ ^ mM ih^m ^ n 9 — p ^^^-ii4 i - i Jnj]]^ ^ ?:-♦ 1 ttii ffi ^=±±1 ^• le^ *a) ^^^=^ *3) t^E^ fe^a^^^^^E^.^^iJT: J ^i-^ i^ *2) VI 'i) Ex. 144. — *2) Par. 168. — *3) Par. 193. — *4) Change the chord at this bar. — 's) Exercise 32, Note *ii). — *6) Passive resolution. — *i) When the leading-tone (in the melody) leaps, as here, it is evident that the dominant chord must be repeated. N.B. — The student may extend this exercise by reharmonizing all of the melodies given up to this point, with the ma- terial of this lesson. This he is warmly urged to do, as nothing is more important than facility in harmonizing melodies, and nothing makes perfect but practice. SECTION 2. THE DISCORDS OF THE SECOND CLASS. 244. The fundamental tone of this class is the second perfect 5th above the tonic, or, the second Step of the scale. Review par. 198. Therefore, the 2nd class embraces the chord of the ^\h on the second step, the chord of the 9th on the second step, and the chord of the 7th on the fourth step, as incomplete chord of the 9th, — in major and minor. ^ Major .^. .gu Minor I -e>- IE g / g a / g e/s > -zr- m g / g g /g- -tS^ L-g; -VST. 2S= M Sletc. _S2_ 7 7 7 7 ■- / 77 7 7 11 ill 11., lln II oil or IV IV, IV, IV, 7 f t a «a) •sF f i a Ex. 179. *i) Spoken: "Two-seven," "Two-seven-one," etc., and figured as usual, 7, % f, 2. — *2) The II is available in 7 4-part harmony only without its root, as IV (see par. 233a, J). — *3) Called "Four-seven" instead of "Two-nine, in- complete," on account of its relation to the triad IV. 245. To this class belong also, as concords, the fimdamental 3-tone chord II, and its parallel, the IV, which is actually an incomplete twQ-seven, — in analogy with par. 221. i ST Compare par. iioa; and see par. 259. II 7 , II S all or IV 102 THE MATERIAL USED IN MUSICAL COMPOSITION. Pai. 246. A. The II and its inversions. 246. a. These chords are not quite as common as those of the First class, but they are barely less important, es- pecially in modem harmony. They are treated, relatively speaking, almost exactly like the dominant chords, only a little 7 7 more strictly. The principal external distinction is, that the II has a minor third, while that of the V is major. More- over, the Second-class chords do not contain the leading-tone (as those of the First class do), but the 4th and 6th steps of the scale (see par. 112). b. The chord-seventh is resolved diatonically downlvard, or remains stationary (passive res.), and is 7 not doubled. In the II itself, as fundamental chord, the fifth may be left out; but in the inversions no omissions are possible. c. The normal resolution is effected, as usual, by the chords which lie a perfect sth below, namely, those of the First class (dominant). This fundamental rule operates in its most comprehensive sense. Every 2nd-class chord is normally resolved into any and every ist-class chord, concord or discord. The same is true of all the discord classes, each of which obtains its normal res. by progressing into the preceding class; the 2nd into the ist, the 3rd into the 2nd, and the 4th into the 3rd. See par. 259. d. The passive resolution, for which this discord-class evinces a decided preference, is effected by the tonic chords (I or VI), which contain its dissonance as consonant interval: i ^^^ 7 II -s^ (Comp. par. 216.) 7 II VI e. The seventh should be introduced strictly, as a rule; rarely with a skip, or diatonically from below. 7 II 7 III Ex. 180. f-^^ ^^f ^ ^i-i ^n f '^ fi ^ ^f ^ V 7 V T e °5 V V 9 7 t ) r r r i. ^^^\^ r I f if I t. > r-H^r If I r ^ r r r f T r ' r r f> r r -="^ *7) J.. Ji " *8) *0) \i.-J i-4 4i i J-i-i J i A,, i r r r i r ^irrr m^ 7 V Par. 247. THE IV AND ITS INVERSIONS. 103 7 Ha -J- Ai © i J i ^ i I *10) ^ -J- ^ eIe Tjt^ p i *ii) r" i j i jii>. F I 4 ^ — f i r r ri-F- C7) V e I III, VI *i) Major and minor. Separate measures, as usual. — *2) Normal res. — *3) This is the first case of different dis- cords in succession. The resolution into the dominant 7th or gth is better for the key, than into the triad. — '4) Passive res. —^ *s) After the pass. res. it is best to return to the same chord-class, as here. Compare par. 217a. — *6) Ex. 153, Note 'i). — *7) In the pass. res. no other part should run into the seventh. Here the soprano is wrong; the preceding measure is right. Comp. Ex. 157, Note *4). — *8) The 2nd inversion is the weakest form, naturally; it is better (stronger) in minor. — *9) When the bass progresses upward into the leading-tone, the seventh ( being the keynote ilself) may skip downward to the dominant, or move parallel with the bass in srds, as in the next measure. (See par. 2180.) — *io) The pass. res. of the seventh in bass is very doubtful. - the fifth may be omitted. *ii) These last two measures are exceptional. — *i2) In the II itself B. The IV and its Inversions, 247. a. The assignment of this chord to the Second discord-class, instead of assuming that it forms an independent class on account of the principal tone upon which it stands (the subdominant), is justified by all of its harmonic movements, by its sound, and by analogy with the development and arrangement of the First discord-class. b. The dissonances (7th and 9th, — 5th and 7th in this form) are treated like those of the dominant. The introduction is perfectly strict. c. No interval can be omitted, and none doubled (par. 22,6d). d. The chord is the same in character in major and minor. The ninth may lie in any part. J-^J i J J-J i J m j^j=± fS? r~f T- r - f -f ^ *a) *3) l» lo - -4- i Vj 7 V 7 LMJlJ-i-^ ^^-=^r h^ 7 *e) IV3 ^^^ ^1 r r ' f r ' f r ' r r r'^r- '?=^ I ,»4) --, I I »6) I I ' I , I I i S"Ili J^ 4 ^ ^ P^^ 4- ' Q a A Q A <3 I i J i f- 76 6- l^ 7 V, 3 O oVi I04 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 248. *i) These parallel sths are even more likely to occur than in the analogous resolution of the qV, — Ex. 172, Note 7 9 *i); they are best avoided by progressing into the dwcorrf^ V or qV. — *i) Passive res. — "3) Ex. 171, Note *i). — *4) Partial res. See Ex. 167, meas. 4, 5,— *s) The treatment of a 7th is less strict, when accompanied by the ninth. See Ex. 180, Note *9). — *6) The 2nd and 3rd inversions (seventh and ninth in bass) have no passive resolution. Comp. Ex. 180, Note *io). a The Digression into the next higher Class. 248. The passive resolution of the First-class discords (par. 215, 2160, which review), may also be made into the 7 7 discords II and IV, as well as into the concords II and IV. In this case the progression again represents the reverse of the normal resolution, being the upward instead of the downward direction: in the most literal sense, a "Digression" from the natural order of harmonic succession. Thus: 2nd Class- 7 7 II (IV) • ..cJh Tonic Class- 7 s instead of: V(V) -• 249. When First-class chords ascend in this manner into Second-class discords, the rules of the passive resolu- tion must be strictly respected, namely: a. The first dissonance (dom.-7th or 9th) remains in the same part; b. The progressions of the parts must be smooth; and c. After the digression, the first chord must return, in the same or in a different form. See par. 217a; 2176 is not valid in this case. 7 Ex. 182. *l) l=et i *2) *3) *5) ) ^ -g , — &■ zyg-P^zy^^-y 7 -^jr.c^^^ r^=e= *s)l 7 7 7 V IV V 7 V 7 II 7 V 7 V 7 7 II?? I oV 7 II e oV 7 II -27- -'* 7 7 V IV g oV 7 IV f 'i) Major and minor. — *2) The second dissonance, in this connection, usually enters from helow. — * 3) See 249c. Two pass, resolutions in succession are not plausible. — *4) This is unusual, but good. It corresponds to Ex. 187. — *$) Major only. — In general, par. 66 must be complied with. Further illustrations of 2nd-class chords: Ex. 183. i w SE Ex. 184 Mendelssohn It Eb f=r rr- X i I T-r ^ f ^f^=^ -zsH 7 V, IVi VI3 IV Par. 249. THE DIGRESSIO;V INTO THE NEXT HIGHER CLASS. 105 Mendelssohn ^^ ^t r^ ^^y t=fc=; P 7 7 Vi "m FUNDAMENTAL PRINCIPLES. 7 9 7 The 2nd chord-class or second-dominant element embraces the discords II, (II), IV, and the con- cords II and IV. The normal resolution of each discord-class is effected by the preceding class (a perfect 5th below). The "digression" or passive resolution is effected by the following class (a perfect 5th above). After the "digression," the first discord reappears. EXERCISE THIRXY-SEVEN. A. Basses. The given positions (upper figures) may be ignored, if desirable. «• +3 _ 8+S 5 -8*1) ^^^ -F-»- sa =f=p: ^ 6 7 B a ■l-H- « f « f * n H B 4 76 a- 67 04, 65 4q tta ^S *3) *4) ^ ^« i=p: 3 6 - 6 6 «2) 4 6 76 3 3 *4) u e 7 67 4 3 43 +8 -3 ■*- ^e^^^ =tsJ :PE a- f^ 6 6- 4 as a 1^-0 a 8 5 7 .■ia 6 34 4 76 3 56 li i'5 67 4* Plagal m ^Hrf=? ^ ^ ^ * • — ^ *-#- sa a 34 4 3- 87 87 «- 6 6 7 5 4 87 B*5) *8) 65 4* Cherubini :i!teEt t=4: 5^ 108 7 17 6 5 3 4 3 f^ io6 THE MATERIAL USED IN MUSICAI. COMPOSITION. Par. 249. / ^S *=T=t ■ *7) I ^± g- +3 8 76 s as 78 56 f7 ''« i2 6 4: 6 4 3 10 O 87 7- J(_ «4) *8) ^^ ¥ ^^ fe^ 6 65-67 **) »a) BtteT? : ^ i^S g^ ^^ #- g j f — # *ii: f^ 6 8 7 6- 6 5 4 7 2 a 8 7 4 6 5 6 7 7 7 7 /t a 5 5 3 O Bach @S g p r JI--J J|J r ^^tfr^ ^ i 1 azgz ^ S a 7 7 7 87 4,3 *i) Par. 1060. — *2) Exercise 21, Note *6). — *3) Par. 2366. — *4) Rhythm j /3 — • *S) See par. 1166. Here it is chord-repetition, and a sequence. — *6) Par. 2290. — *i) An exceptional complete Two-nine. — *8) Par. 249. B. Play the following chord-progressions at the piano, in different major and minor keys. At first with the right hand alone, and then with both hands, the bass alone in the left. 77T\ 7 IT\ 77/r\S77/T\87 O n\ I1-II-V2-I II VI-IIi-V-I II IVi-IIi-Vs-Ii II I-ns-Vi-I II I-IIs-oV-I II 7 7 7/^ 77r;>57 7/^ 77/^ II-I1-II1-I2-V-VT II I2-IV-0V2-I1 II I2-IV1-0V-I II IV-IVs-Vr-I II 7 /^7778 977/T\ VI-IV-I2-V-I II Vi-IIj-Vi-VI II 0V-IV2-V1-I II, C. A nimiber of Original phrases. 7 7 D. Melodies. The II or IV, in any convenient form, at each '- a. . f i ^V n>' ' | J I J ih PJ i\H\k^=^t^ M ^^nnvn ^ Ff^-^^3-J^^:^ J- i I J J J 9 V ■n i j ^^ 7 V, -*- * 4 ^ J J J J ^ Par. 250. THE DISCORDS OF THE THIRD CLASS. 107 SECTION 3. THE 3RD AND 4TH DISCORD-CLASSES. 260. The discords of the 3rd and 4th classes are very rare. (See par. igSe.) They are hardly ever used as essential members of the fimdamental chord-succession, but as passing chords, usually upon fractions of heats, or on short beats, between the more essential chords. Nevertheless, their actual existence as genuine harmonic bodies, their origin, and their comparative significance in their key are unmistakably apparent in Ex. 147, and therefore they claim a certain degree of consideration. Their possible existence slightly modifies par. 70. A. The Discords of the Third class. 251. a. The 3rd discord-class embraces the chord of the 7th on the sixth step (the third perfect 5th above the tonic) in major and minor; the chord of the 9th on the sixth step, and the chord of the 7th upon the first step (as incomplete ninth) in major only. Ex. 184. W- Major Minor ^^ ih it 7 "^ 7 7 VI *i) VIj VI3 VI3 ^^^ Major only *s) -ig- -^-^ e VI 9 7 7 oVIorl Ij «3) -#- I *i) Spoken: "Six-seven," and figured as usual. — *2) Spoken: "One-seven." — *3) These chords cannot appear in minor, because the ninth (i) could not be resolved diatonically downward (Ex. 70). 6. This chord-class, unlike the First and Second classes, consists exclusively of discords. The concords VI and I, which occupy the same scale-steps as the 3rd class, are the representatives of the tonic class. The most important and essential quahty of the tonic element is its inactivity, as basis or "centre" of its key; and when this quality is nuUified by the addition of a dissonant interval, it ceases to he a "tonic" harmony, in the correct sense of the term, and assumes a place among the discords. Review par. 198c. 7 7- Hence, the triads I and VI are tonic chords because they are consonant; but as chords of the seventh (VI and I) they become Third-class harmonies, and are subject to the laws of that class. 252. The rules for the treatment of these chords are as follows: a. Seventh and ninth are resolved as usual, diatonically downward, and are introduced strictly. 7 b. The normal resolution is effected by the preceding class (the Second), namely, by the II, IV, II, 7 IV. Comp. par. 246c. 7 VI 7 VIi 4^'r l ^^ ^M-JJ l| L^./ J, l /-^.^ i i J r r ^ — ^ , *2) -^—l m F^ 87 '7 II II IVi 7 II II io8 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 353. 7 7 VI3 ^^P ^ J J i -n J =^ 1—i *3) # i. i 1 i 1 i m i i 3e;5= ^¥^^ :p=s o- s Ila 7 II III 7 III 7 IV '1) Major and minor. — ■*2) The fifth of the VI itsdj may be omitted, and the third doubled. Comp. Ex. 180, Note *i2). — *3) The 3rd inversion (chord of the second) is one of the most useful forms, here as elsewhere. Ex. 186. »l) m s *2) 7 II X^rr^f^ a ^^•'W nj , k \ I I JL * .J_ !0) <7) II IV ^ ^ IV III 7 III 7 la 7 I3 l=g:a£rjdj =i=Jit *3) w I ^E=i= i i i 1 I I iS ai' ' Lj j'..'=g T III 2 IV, IV (li) I VI *i) Major only. — '2) When the leading-tone becomes a chord-seventh, it must obey the law of 7ths, and move 7 downward. — *3) This measure is not strictly harmonic; I-VI is not a genuine "resolution." It is chord-repetition, practically, and the h in bass is a passing-nbte only. Irregular Passive resolution. 263. These chords may also progress into dominant discords, in which case the succession corresponds to the passive 7 7 resolution, because, as in former cases (V-IV, II- 1), the dissonance of the first chord becomes, by remaining, a consonant interval of the following chord. But in this case the passive resolution is made irregularly: the dissonances of the 3rd dass are too weak to be held, and therefore they resolve immediately, diatonically downward, into the dissonances of the domi- nant chords. This is a very effective and important progression, and almost preferable to the regular normal resolution, as a stronger chord-class (the dominant) is quickly reached. Par. 254. i IRREGULAR PASSIVE RESOLUTION. »i) 109 i=^ -f- ^ -j I > = hg f-f ' r~r-f- Ex. 187. I -i J L J J ^ r f f ' ^-^-F ^ 7 VI 7 Vi 7 VIi 7 -.v 7 VI 7 8 oV >^ par. 66 •^ r r f ' *a) ' ig I -•^^^ ^^^ J -J- J :^ (?) *3) ± JL I I ^^ I 9 7 oV I „V 7 7 VI3 V3 "i) See par. 66. — *2) With the exception of this measure, the whole example is possible only in major, because the 7 6th step usually ascends. — '3) When the I is so brief, it is only a passing chord. Comp. Ex. 186, Note "3) 264. The "digression" from the 2nd class into the 3rd (comp. par. 248) is made as follows: '88. 1 (C) g -,,,^^ ^ *i) •«a) n ^^m w 7 7 VI II 7 7 IV VI 7 :,V 7 II 7 II *i) The progression of the VI into the qV after the digression, although contrary to par. 249c, is allowed, because the seventh g is actually resolved into /. — *2) Weak. EXERCISE THIRTY-EIGHT. (The positions may be ignored.) a. 3 7*1) ^/■mm r §B^ itjt 8 B a 6 6 a 5 *i) ^SE^ n) 8 7 -*-*- T^TT^ 7 57a. no a g^tffl THE MATERIAL USED IN MUSICAL COMPOSITION. +8 «3) Par. 355. +8 C. 8_ mi ^i ' J J 1 ^ e 3 6 3 4: a 5 3 %i 4« 87 6S ^^^^=j=^ Handel d. Faisst TTTTgrn p ES *-# a 6 e 5 4 *3) §^ ^^ =?c=l»: ^ a- *3) 6 11 « a 6 _ 4 s fj^x44..aiiu i t se e a 4 e s- 3 s a- 3 a a 7 7 7 as 543 / ^ Forsyth ^[ as =p=-» =^=^ a=t ?=p= n J. R I t:* 76 54 a- a as «4) ^S^ m -p— »- ^ ^i=T= S:=F • P a 4 a a "i) Omit the fifth. — *2) Rhythm J J^ — . *3) See par. 2180. — *4) Ex. 186, Note *2). Add Original basses. B. The Discords of the Fourth class. 266. This exceedingly rare class of discords consists of the chords of the 7th and gth upon the third step in major and minor, and the triad III vp. minor. 7 The chord of the ninth is, as usual, almost useless in 4-part harmony, and when its root is removed, the original V re- appears. This proves that the circle of chords which constitutes a key is herewith completed. Major Minor 189.1 ^) |- .g ^ l t,Hg q::g^T°' [(^^g ^^'^fi ^gz ^ ^HH 7777 7I9/18 |=v 7777 III nil Ilia Ilia III nil Ilia m •3) *i) Spoken: "Three-seven." — "2) The III in minor is an augmented triad (par. 127). It is more peculiar in sound than the diminished triads, but very effective when properly used. The III IN Major. 7 77 266. The III in major is resolved normally into 3rd-class chords (comp. par. 246c), VI (and VI) ; not into the I or I. 7 But, similar to the 2nd and 3rd classes, it prefers an irregular res., into the IV and IV. See par. 124*. The dissonance is treated like other sevenths. Par. as7. THE DISCORDS OF THE FOURTH CLASS. Ill II (Major) IIIj jjj jfj . . ' I C^ . _ . !?*■ -^^ , VT TTT VI Ex. 190.' (7) I e— ^^ ' 87 VT 7 7 87 TV 7 eS VT * <7! 3 <7) 87 T "■^ VI 05 ■*■* 43 '"■ S VI VI 65 -^1 7 7 7 VI III VI *2) a (7) 87 VIj 65 7 *i) When foUowed by the I, the III is not an actual chord, but only a combination of grace-notes resembling a chord. Comp. Ex. i86, Note *3). — *2) The "digression'' from srd-class into 4th-class chords is possible in major, but very in- ferior, and rare. The III, III AND III IN Minor. 257. a. The triad III in minor soimds, and is treated, very differently from the major III. Its dissonance (the augm. fifth), being the leading-tone of the minor scale, must ascend to the tonic. (See also par. 201.) The best resolution 7 is the normal, into the VI (or VI). The irregular resolution is hazardous, on account of the upward progression of the leading-tone; only the IVi is possible. The dissonance may lie in any part, and is introduced strictly. Ill (Minor) III, m aU: par. 66 h^ ^S fefcfe^Ste fi^JJ f f=^ j i i J f r ' r r r Ex. 191. J- -J- -1 i ^ ^^ i 5 -bV-f- *l) VI 60 7 VI IV _, 6 VI se IV, *2) Q a- ^- i III, m i^ r r -I P^^ i-t p-'f -7 I r ) iJ^-^ , y— ^ VI, I, (7) V *i) The line through the figure 5 signifies; as usual, that the corresponding note is raised. — *2) When an accidental stands alone, in the bass figuring, it refers to the figure 3. — *3) The progression of the III or IIIi into the I or V is not "hamonic"; Ex. igo. Note *i). 268. a. The chord of the III in minor is effective when properly treated. b. The III is not absolutely useless, — probably on account of its resemblance to the V. It is treated like the in itself; the seventh and ninth resolve downward. 112 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 258. in (Minor) 7 III, ^ i ^^ i r r rv r -J i.4ti^ i ^ gS3E^!| f^ 7 VI 7 VI g2 iVi ig f VI Major a, EXERCISE THIRTY-NINE. 5 I P*i« 1 -3_ *=i: S L,clJ U S :±±t ta: a 3 6- a §1 *> 87 5- n7 65 87 87 b. «4) 3 Ames ^^ ^ ^ S ■•—It- art as 7a 5- Minor g- *2) »3) gS -M-,-^-J^ £ =P=s: ^ * S5f; ir-fny 1 11^ ^ fittt a a 8 67^^ « t- 6 6 7 8- ii 5- I- 6 88 4-6 f 87 778087 4 5- ea 3 8 *i) Ex. 140. — *2) Omit the fifth. — *3) Par. 157a. — *4) Sequences in soprano, as shown by slurs; par. 260. Add Original phrases. Par. 359. TABLE OF THE HARMONIC SYSTEM OF A KEY. 113 Table of the Haemonic System or a Key. 259. The following table illustrates the arrangement and relations of the chords within each key. Dominant Second-dominant Tonic class or First class (Subdominant), or Second class CO "2 I V IV 8 VI (HI) II and inversions and inversions and inversions f Third class Fourth class s^ 01 1 oV 0^ 7 II (fi) if 7 VI (VI) I 5 ill (HI) niin / minor and inversions and inversions a. The chords in parenthesis are rare. b. The classes are a perfect fifth (harmonic degree) apart; par. 1980., c. The tonic class is inactive, the others are all active; comp. par. 2$ib. d. The normal (regular) progressions or resolutions are made by each class one grade from right to left (towards the tonic); par. 1006; 246c. e. The reversed progression (away from the tonic) is the "digression"; par. 248; also looa. This, and the progression of two grades (par. 253), are both irregular. /. Every regular progression is complete in itself, and cancels the obligations of its class. Every irregidar progression, on the contrary, is only a partial resolution, or none at all, and demands justi- fication by subsequent resolution. The best and commonest method is, after every irreg. prog., to return immediately to the former class; Ex. 67, Note *2); par. 217a. g. The movements of the triad III are eccentric. Sequences. 260. A sequence is the reproduction of a tone-figure upon other, higher or lower, steps. When limited to one part it is called a melodic sequence; when applied to all four parts at once, it is a full harmonic sequence. 261. Such shifted reproductions are possible almost anywhere, because every chord of every class is subject to the selfsame rules, as has been seen. Arid where irregularities or exceptional move- ments result, they are considered justified by the sequential {i.e., uniform) arrangement of the tones. 262. The following formulae, deduced from foregoing illustrations, will be found useful for the formation of tone- groups which may be utilized in the sequence: a. The succession 8-7 represents the introduction of a 7th diatonically from above. This, followed by the descending resolution of the yth, is always good. The interval 8 may represent a doubled root, in any two of the parts; and either of the two tones may descend to the chord-7th, the other tones being held: 114 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 263. *i) Here the body assumes the form of a 4-3 chord; and *2) here that of a chord of the second. The principle is everywhere the same; the root is doubled. -^ *3) These measures form a continuous phrase, to the heavy bar. Or the interval 8 may represent a doubled third, in any two parts, with similar treatment: Phrase^ -T -- *i) *i) Ex. 194." *3) ^^ 4 f-v f-^ s- ^-n I ^i. pr U ^ r ^Pfl zr 3 8 87 4 87 87 *i) Note the variety of results from doubling this third (e) in different parts, and allowing either of the two tones to glide downward. — *2) Note that when the chordrthird is thus doubled, two parts always glide down together in parallel thirds, or sixths. Par. 66. b. The interval 8 may, rarely, represent the chord-fifth, and in this case one part usually glides upward, — the stationary tone becoming a 7th by preparation: Ex. 196. mk^i hHfrf^ ? b2 Tl. h ^ e 6- *i) The 7th, in this case, generally remains (passive resolution). The somewhat complex bass-figuring differs accord- ing to the interval which chances to be in bass. 263. The most of these groups are limited to major, as the scale-steps 6-7 are almost constantly implicated in such general movements. But the chords may appear in any iime-valties, -^ full beats as well as fractions. 264|A. With this material, and a few other combinations, harmonic sequences may readily be formed. For example: Par. 2646. HARMONIZING OF UNFIGURED BASSES. b. ^ Ex. 196. li ^V 'K^ ^^1 5 •2) Seq. i Seq. 1 , *1) etc. »l) iJg - Jj. j J ,ui F^^ ^-ffV etc. »l) I ' etc. I , J 12 , J ^-^, ''' ' ^ "^Z ~^ r~^ '^^ ^ ^^''- S^ sTq. "5 Seq. r r r u ^, 4 J 7 - VI (Vo?) (Vo?.') V 7 V e Vn Ex. 1966. C major g^ ^ I m < g^^ 6>- Step I *i) See also par. air, and par. 226. And compare the whole table with Ex. 178. EXERCISE FORTY-ONE. Each of these imfigured basses should be worked out in at least three different ways (with new soprano). or l() and therefore foreign to the scale in which they appear, but which nevertheless, from their connections and their effect, obviously belong to the principal key, and not to that key which the chromatic (foreign) tone seems to indicate. For example, the chords 1^ m iz5«S2^ land. M ^l^^^smzz and many others, are used in C major as if they were legitimate chords of that key (despite the d#, /S and a\>), without disturbing the identity of C major by conveying a distinct impression of the lieys to which these foreign tones actually belong. 266. a. Such chords are called "altered" or "mixed," and the foreign tone, which is "borrowed" from a related scale, is defined as a chromatically raised or lowered scale-step of the original key. h. That a key and chord may embrace a chromatic tone, foreign to its scale, is a fact which, contradictory as it may appear, is confirmed on every page of classic music. The operation of this principle has already been seen, in the forma- tion of the minor mode. See par. loi. (,. The object of such foreign tones is: To enlarge and enrich the scale; to confirm, or to modify, the melodic ten- dencies of the scale-steps; and to afiihate the keys by increasing the number of common tones (for instance, by raising the 4th step of C to/#, the scales of C and G major are aflSliated). 267. It is evident that such foreign tones can be introduced into a scale only upon certain condi- tions. They are as follows: a. The altered tone must be reasonably brief; otherwise it may, by sheer length, assert its inde- pendent individuality and produce the impression of the scale to which it actually belongs. The limit will generally be one or two beats. 6. It must occur in such a connection as not to interfere with the legitimate harmonic action of the key. Hence, only certain steps of the scale can be altered, and these only in certain chords. Par. a68. THE ALTERED CHORDS IN MAJOR. 117 c. The most important condition is, that the following chord shall unmistakably indicate and con- firm the original key. That is, the altered chord will (as a rule) be immediately followed by a tonic 7 9 chord (I-Ii-Ia), or, more rarely, by a V or V. d. When the chord which follows (and, as is probable, the chord which precedes, also) confirms the original key, then no change of key takes place, and the foreign tone is merely a transient chromatic inflection of the corresponding scale-tone. In this case: i ^i^ Se=S= -/©- the accidental is not an actual /#, in its legitimate personality as leading-tone of C I G major, but merely "/-raised" or "/-altered." But if, on the contrary, the next chord corroborates the foreign tone, as tonic chord of the key which that tone seems to represent, thus: p jg .^ ?'^ % -I then it proves to be an actual r^. 7—j): ^ — ig — i /# in its genuine capacity as leading-tone of G major. G V I e. In a word, as a general fundamental rule one chord alone does not represent and indicate a whole key, any more than one isolated tone can represent a chord or scale. If a foreign chord stands isolated between two chords which are unmistakably indicative of the original key, then it also belongs to that key, — of course, as altered chord; but, if the following chord confirms the key suggested by the foreign tone, then these two chords together constitute a more or less complete modulation, or change of key. The identity of a chord depends upon what it does, — i.e., upon its progression. /. Altered chords are always defined according to the scale-step which is raised or lowered. SECTION THE ALTERED CHORDS. A. In major. 268. The altered chords have a legitimate chord-form, and therefore coincide with authentic chords of some other key. 269. The introduction and progression of altered chords are subject to the following rules: a. Lowered notes descend. Raised notes ascend. Comp. par. 201. b. Altered notes must not be doubled. c. In general, the altered chords are treated the same as if unaltered. The principal exception is par. 267c: i.e., they generally resolve into the I (or Five-seven). d. The altered note may be introduced diatonically (for instance, the tone av from g), or chromati- cally (the tone ab from a). See Note to Ex. 8. e. In chromatic successions, the first tone should not be doubled, unless the other tone (the dupUca- tion) progresses diatonically, contrary to the direction of the chromatic progression. See Ex. 198, Note *6). And the chromatic progression must be made in one single part. Ex. 198, Note *^). 270. The 6th step may be lowered, in the following chords: Altered chords *3) ^ Resolution Ex. 197. C major i dte3 b ll2gl ^ -bg=^i ~^- -Sr 9b 9b b 7b b 7b b 7b V»i) Vo II II IV IV With all inversions VI VI 1 m 7 V "i) Spoken: "Five-nine altered." three chords are possible, but rare. The flat indicates that the chord contains a lowered scale-step. — *2) These Ii8 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 271. The intr. and prog, of the thords with lowered 6th step, are effected as follows: C major C minor *s) I minor -^Ji/ I I J w f Ex. 198. C major i J -i T V •^ , J J , ^ 4 , J J J , hA-4 ^=^^ ^m p^ -|2- g^ Ob V„ 7b II IV *4) i *5) i good 7^^ i?t: ^•m S: f -J- ni i Ul- i(g i ri i J ^^ IV eb b CTTT^r-S^^Pf ¥: *6) i *i) With e[|, as I of C major, the preceding chord is altered, in C major. — *2) With eb, as I of C minor, the preceding ab is a legitimate scale-step, and the chord is authentic, in C minor. See par. 267^. — *3) This is the chord of the dimin- ished 7th, which, in this altered form, becomes as available in major as in minor. — *4) The altered scale-step may lie in any part. — *5) Comp. par. 267a. — *6) This is wrong, because the a in tenor which is about to move chromatically into a\>, is doubled in bass, where it progresses with a skip. In the next measure, where the dupUcating tone moves diatonically, the so-called "cross-relation"' is rectified. See par. 322. — *^) The chromatic inflection cannot be divided between two parts, as here in bass and soprano. 271. a. The raised 2nd step, when alone, can occur only in chords of the First class ; i.e., in dom- inant chords. b. The raised 4th step can never occur in any other than Second-class chords; i.e., in the II, 7 7 IV, II, IV. c. The 2nd and 4th steps may be raised together; but (on account of the 4th step) only in a Sec- ond-class chord. Ex. 199. C major i a. Raised 2nd step b. Raised 4th step w ffs- BSI ~^t> c^ or a< lg^ ITS -&- -S>- I V*i) I Hi la *2) -S>- IVi *3) 7t Hi Best in these inversions C. Raised 2nd and 4th steps Par. 273. ALTERED CHORDS IN MAJOR. 119 Intr. and Res. 1 1. , ^m ^EE^Est^EEsbsSEJ ^=k^ i J i f=^ * -J i i i *a) "r J- ! r *8) J ^ ? ^ V«i) % IV 7# II -^ *4) hrjr=f=«^ ^T-f-T^ i=f ^ i i i J. i i i i-=F^ *"^ *^ I 7SJf»5) II *i) Spoken "Five-altered;" the # indicates that the chord contains a raised, scale-step. — *2) It will be noticed that 7 most of the altered chords of the 2nd class progress into the I2 (6-4 chord). — *3) The progression into the V reestab- lishes the original key, and is therefore admissible; but it is rare, and does not sound genuine. The chromatic succession, in this instance, will be divided between two parts, if the raised step ascends. See Ex. 206, Note *i). — *4) In this case the/# can hardly be termed a raised 4th step of C. This progression will be explained later. — *s) The two sharps above 7 the II indicate that the chord is "double-altered." — *6) This inversion of the altered 11 is somewhat rare. The passive res. of the seventh in the lowest part is imcommon. See Ex. 180, Note *io). 272. The following alterations in major are much less common: 7 a. The Sth step may be raised ; but only in the I or I. 7 b. The ist step may be raised, in the I or VI (VI). c. The 6th step may be raised, but only in connection with the raised ist step, — never alone. d. The raised ist step, or ist and 6th steps, must be followed by a Dominant-discord, — not by the V itself. e. The 6th and 2nd steps may be lowered together, — only in the IIi (II2). /. The 7th step may be lowered (as in minor, — par. 277), — only when followed by the lowered 6th step; it is very 7 7 rare, but possible in the V, V, III, I, — see Exs. 205 and 206, which may be written, almost throughout, with el| instead of eb. a. Raised dominant b. Raised tonic C.d. Raised tonic and 6th step not C. maj. e. Lowered 6th and 2nd steps f. Lowered 7th step i ^^^ ^n^ fe^fa ^ 3=t^ ^^S bb 11, -&- »7) V =p^ 7b b I IV I20 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 27a. Intr. and res. *4) «7) good ^^^ III j l J j l -J. J . J *i) Thus marked to indicate that the fifth is raised.— *2) The resolution of the altered tone (upward into a) renders the IV necessary, as resolution. This is not directly contradictory of par. 267c, because the IV does not confirm the ^ as leading-tone of A minor. — *3) This notation denotes that the root of the I is raised. — '4) Par. z72d. See Note *6). 7 — *S) When the VI is altered, its seventh will remain stationary, — contrary to Ex. 187. — *6) If the V itself were to 7 follow, these chords would both be in G major. The V, on the contrary, reestablishes the original key (C). — "7) The peculiar progression in soprano is necessary here. In the following additional illustrations of the altered chords in major, the numbers after Mendelssohn's name refer to his "Songs without Words:" i I. Mendelssohij, No. 9 ^^^^^fe « No. 41 3". No. 16 j^ B^^lifTT"] p Wf Ex. 201. B maj. ( g[j ) A maj. ( bS dS ) A maj. (a#) ^te fe S^EEys^S I rn^i p fs =t=t '-¥ a IV 90 oVi 7J« Ha I V. p: Beethoven, Sym. No. 9 A maj. (a#) a«^ m J7 (eS) B\> maj. (gb) I ^ I (eH) =i?t ^ 1 ^^^^ ^ ^^ r^^ti r 7« 7 VIjV I IV olj Vn 7i] r IV III la Par. 273. ALTERED CHORDS IN MINOR. 5. Chopin 6. 121 w& Beethoven ;fa L ^ ^Ei tdti f f .[ >' f B maj. (g^ r Ab maj. ^ ^ a-^ g — ^ : # ^^ /bbl>\ UK/ S*^=f=f I^ I * J* 7|| 7b D I II Emaj. *i) Par. 2726. The ob in bass is an organ-point (par. 3650). See also Ex. 282, No. 6. B. Altered chords in Minor. 273. The alterations in minor are reckoneid from the harmonic form of the scale, and they tend chiefly to remove the vinmelodious progressions between the 6th and 7th scale-steps (Ex. 70). This interval embraces one and a half step, and therefore does not conform to the principle of scale-forma- tion (par. 16). In order to reduce it to a whole step, the 6th step is raised when it ascends to step 7 and the 7th step is lowered when it descends to step 6. These alterations make the scale singable through- out (see Note to Ex. 70), and produce the so-called melodic forms of minor. See par. 104. Melodic forms whole step whole st ep Ex. 202. C minor i m -m- • i^^ e+ N.B. Write out this example in every minor mode. 274. The altered chords in minor do not endanger the identity of their key as much as those in major do. Hence 7 it is not so essential that the I or V should follow immediately (comp. par. 267c). The chord which follows will de- pend upon the tendency of the altered tone, which, of course, must be fulfilled. 275. The raised 6th step, as factor of the ascending melodic minor scale, is generally introduced diatonically from below, and progresses diatonically upward (as seen in Ex. 202). It occurs in the following chords, and is invariably resolved into dominant chords. 122 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 276. b. IntT. and res. fl l fjjj ^/J l Jjjlftto U I I 71] I 7|J 7 B 70 II V II IV IV V VI VI ZjCwith inversions; *i) Neither the V nor Vq can contain the raised 6th step, because it would interfere with the resolution of the ninth 7 (downward). — *2) The altered II of minor requires a free resolution of its seventh, in order to avoid a duplication of the leading-tone. It can skip down to the dominant, or pass upward in parallel ards with the bass. Ex. 180, Note *9). — '3) The raised 6th step occasionally enters with a skip jrom above. 276. Sometimes the 4th step is raised, in conjimction with the raised 6th step, in order to im- prove the sound of the chords. 7 7 As stated in par. 2716, this alteration is limited to Second-class chords, — II-IV-II-IV. One advantage arising from this double-alteration is, that the chords can progress into the I, as well as into the V; in which case the raised 6th step is relieved of its obligations, and may progress in either direction. <^- b.\ „J J_ ,11 I I I *5), Ex. 204. C minor \\* I^ oOJ 7 \ If/ ''/Wi,JiJ J i >izi: SE _with inversions! F^g^ .Ut^ ^i J ^^ 7 IV '' ^^11 I2 «s) 7 V *i) Ex. 203, Note *2). — *2) The raised 6th step, when accompanied by the raised 4th step, may move either way. — ' *3) Ex. 199, Note *2). — *4) See Note '2). — '5) See Ex. 206, Note 'i). 277. The lowered yth step, as factor of the descending melodic minor scale, is introduced dia- tonically from ahone, and invariably progresses diat. dcrwnward. It occurs most naturally and frequently in the I — which it renders possible in minor; see Ex. 184, Note *3), — and in the III or III, which it improves in sound and treatment. b III 7b III ^ m -J-p^ i Til -j^j J with Invers.I ^^^^^™ b III IV 7b III i VI li I IV »i) *i) The lowered leading-tone resolves downward into the 6th step; consequently the resolving-chords will be the IV (7) or n. See par. 274. Par. 278. ALTERED CHORDS IN MINOR. 123 278. The lowered 7th step may, of course, also occur in dominant chords, but it is hazardous to alter the leading-tone in the very chords which it ought to characterize. Therefore, these altered dominant chords are very rare. Ex. 206. C minor ' m '^ Hggr- ^^^fey^a 7b Va 7b oV 7b i^ m .Best in these forms_ -PA,} J. iU -JjC s 7b ' 7D 7 nV II V 1 F^ I *i) Here again the chromatic succession is divided between two parts, contrary to the general rule (par. 2696). This exception is always permissible, if the first of the two tones (here 6b) moves in its proper direction, and does notskip. Comp. Ex. 198, Note *6). 279. The application of these alterations, — raising step 6 in the succession 6-7, and lowering step 7 in the succession 7-6, — makes every chord-sticcession hitherto limited to major, possible in minor also. For illustration: 1) Ex. 207. C minor ^=F^^^e^ Ex. 74-9 1^1 I Ex. 79-1 Ex. 88-1 J t ^ , _, I '' I Ex. 106-3 Ex. 115-3 J J ^^-^.'-^ . .1.1 ,1 -i J , , .J ., ,1 I i!^ m ^^ : ^jJ!^ etc. I ipn ^^^Sesl T I *i) When either step 6 or 7 chances to be doubled, discrimination is necessary. The more urgent of the two tones must be correctly written, and simply doubled. Note the aj|, which is urgent in tenor; also the following: Ex. 208. C minor ^' \ { P \ , S^ Ex. 194 «,^ i V^ Ex. 196 - H-r^- W -H J Jib^ J^ g^£J r ' Qr f The student should play eoery major example up to this point, and transform it thus into minor. 280. Further, the 2nd step may be lowered. This alteration is very common and effective, but is limited almost entirely to one single chord, — the IIi. It corresponds to par. 2726. 124 THE MATERIAL USED IN MUSICAL COMPOSITION. *l) l5. I I I , 1*2) , I pin, , I *l) Par. aSo. Ex. 209. C minor r b V I III la .^-^L-J \P=li ^ II *i) Possible, but very uncommon. — "2) The lowered 2nd step may progress directly into the leading-tone, even in vocal music, notwithstanding the peculiar interval-progression. Compare Ex. 200, Note *i). Additional illustrations of the altered chords in minor: I. Mendelssohn. No. 35. *i) 2. ^^^ No. 17 (meas. 32 — '). No. 22 M ^^ 12~ ] , J ^ Ex. 210. B minor ( g# ) A minor ^^ fr^ D minor (3) i2i Eas =*3)I 7S VI V 711 oVi VI 1 P 7)tJt 7 Va IVi II2 g Vn 4. No. 42. 5. Schubert 6. TJtq IV3 V Chopin ^ D minor ( eb ) A minor ( bb ) *3) A minor ( bb ) ^ n-—9^ i iai n v„ tS: g-4= 1" b III III *i) "Songs without Words.'' — *2) Here, both altered steps progress chromatically downward. This is unusual, and very irregular. Compare Ex. 199, Note *4). — "3) Ex. 209, Note *i). The treatment iS peculiar. FUNDAMENTAL PRINCIPLES. An altered chord must be followed by some chord which reestablishes the original key, — usually I or V (V). In major, the 6th step is the only one likely to be lowered; but nearly every step may be raised. The raised 4th step occiu-s only in second-dom. chords. The raised tonic must be followed by a dom.-5CTmiA. When the 6th step in minor rises to 7, it must be raised; and step 7 must be lowered when it falls to 6. Par. 380. ALTERED CHORDS. 125 EXERCISE FORTY-TWO. A. Play the following chord-progressions at the piano, at sight, in diferent keys; the bass part alone in the left hand, and the three upper parts in the right: eb b 7b # 7S 7S 7 Major: Ii— 0V2— I || I— IV— IIi— 12— V || I— V— 1 1| VI— II2— 12— V || Ii— Hi— V— VI || 7#« 7 7j|J 7 6 5* 5 7jf 7 8 7U 7 I— lis— Ij— V II I2— III— Is— Va- II II II— I— IV— V II I— VIl— V2 II Ii— VI2— Vb— II II B 7 7P 7 3 70 7 tit 7tl# 7 Minor: Ii— II— V— I || Ii— IV3— qV.- I III2— VI— Vi— 1 1| Ii— II— V— 1 1| I2— IIi- 12— V || 8 7tlJt 8 7b 7b 7 b s b IV— IV— I2— V II I— I— IV— I II I— I3— iiy-ij— V II VI— m— IV— V II I— Vi— iVi— V || b b I— III— Ij— V II I— Hi- V— I II B. Work out the following basses in the usual manner, and analyze them with special reference to the altered chords. Major »i) *2) »l) •lS I :^iSz f^ -z>- -TZi- u? \\ bl bes B aba 6 % »3) ,7 87 b6 eg tgSa r^ 7 8 I aa ■ f th2i iBz e ^ ^ ibt« f ^i 7r SD5 6 a * 4 6- 65 i d: ^ d. m u ^ ^^ iSa -^ — *■ 7 6 8 4 a S3 6- 6 5 as 65 43 6 6- 4- 43 *4) Minor 1;. ^' tt fe |g fi:^ ^"^^ ^S +8 1,7 6 =*=*^ ss ^ e„-e -8D7 3#8 6 ~6 g 6as *i) 8 8 J ti %4) 77a -r as _ ba 7 ,, 87 |a;gE^ H^=J^^^e^'CjV iij'^^fe j ftUtf ; i r /|J3g ^ 6- B 6 g a J - a as f a ba a 57 "f e ^T. * "s f 4 fi 7 it # b= a a a 7 .87 as • "* s 6 a bas iB +8. ^ a 7 a - a 807 4 3 126 THE MA TERIAL USED IN MUSICAL COMPOSITION. Par. 281. +5 m^ 5 « 1 i4 8- 6- 65 -t fe # 'a a a n bas as 4q *i) The accidentals in the bass-figuring refer to the figure that foUows, — *2) A line through a figure signifies, as usual, that the corresponding tone is raised. — *3) A soUtary accidental always refers to the figure 3. — "4) The upper parts are held. C. Add Original phrases. SECTION 2. THE MIXED CHORDS. A. In Major. 281. a. Mixed chords have no legitimate form, but result from "mixing" characteristic tones of different keys. Their distinctive feature is the interval of an augmented 6th, which they all contain. For this reason they are generally called "chords of the augmented 6th." b. One of the most important rules for the treatment of mixed chords is, that this interval {the augm. 6th) should not be inverted. Thus, the interval /^ — 1 ' f ,*a)_| _J_ *3) r i Kfr^J,-^^#:fe E^^i^^^ r-f ' r "rrr f^ 7*Jb II3 I3 7 V 7«b IV *i) The lowered step generally lies in bass, and one of the raised steps in soprano; comp. Ex. 212, Note *3). — *2) This irregular interval-progression (<;-d#) is allowed, into an altered step; especially in an inner part. — *3) Ex. 211, meas. 3. This irregular inversion is less objectionable in this mixed chord. — *4) The resolution into the dom.-jCTe»i& is possible. Comp. Ex. 199, Note *3); and Ex. 206, Note 'i). 285. The raised 2nd step, in these Second-class mixed chords, is often erroneously written as if it were the minor meif^ ■ ant : in C major, eb instead of thoughtless confusion of the major and minor modes. C major cannot have an eb, as that is the very tone which dis- tinguishes it from C minor, as seen in Ex. 198, meas. i, 2. The difference lies simply in the progression of the chord, to which, in analogy with par. 2676, the notation should conform. Thus: But :^ \) ^ is a C major chord, and progresses to the I of C major ^^ ^1 g l a/g* ^^ ? ■> " b ii is a C minor chord, and progresses to the I of C minor — 1!^ § -*- ( Ex. 218 l-H I *'J^« I I If in G major, then, of course, the e\> will be right: Additional examples of the mixed chords in major: I. Beethoven. Symph. 9 2. #^^p=p4ft^^=^-MM^f-^-ftej^^ Schubert i p* Ex. 217.' ri i / iSte ie 5ff=g -¥ E^^ i Bb v! 7»x E II« 7I1SX II,- P 3. Schubert :B £^^ Beethoven. Op. 18, No. 2 IE ^^^ tel: ' ^ -1 ^ ' v v^ S 1^ rfTTf:H iifzxia ^a: 133 5 LLTTlf^te-m^ G I Tb| 7bt II GoVi- i «i) SE ^ i^^ ;u^^ Wagner ^ s ^^ gyS= Q Ab V 1 1 ^ etc. -5f =1- V sBb *i) "Rheingold," ist Scene: the harmony employed where the Rhine-daughters chant their exuberant admiration of the glowing gold. — *■£) The modification of the same harmony in the final Scene of the opera, where they bewail the loss of the stolen treasure. See Ex. 318, No. 7, in which the most extreme distortion of this same harmony appears (in suggestion of intense hatred). Par. 286. MIXED CHORDS IN MINOR. 129 B. Mixed Chords m Minor. 286. There is only one group of mixed chords in minor. They contain a raised 4th step, and are consequently Second-class chords (par. 2716). The augm. 6th results from the association of the raised 4th step with the original dom. leading-tone. Compare these chords with the corresponding altered chords (with raised 6th step), in Ex. 204a. They resolve into either the I or V. Thus: _ _ _ b-«-\ h ^^ rh^^^ i :££ s . % IV 7» II n IV j^izjE I ?*l) :with inversions _ 7jf II la V IV V *i) The inversion of the augm. 6th is least objectionable in these mixed chords of minor. — *2) These irregular in- terval-progressions are allowed. Ex. 216, Note *2). — *3) The resolution of this (the most frequent) form of the IV into the V involves inevitable parallel sths. Therefore it is wise to progress, as a rule, into the I. — *4) Compare Ex. 206, Note *i). Additional examples of the mixed chords in minor: I. Mendelssohn. No. 40 Ex. 219. No. 22 m .E^ m^^^ V Mi~r^^~^ # =iiUJ- ..i II m m. *1 N* B min. ■7* i T* 'f Ila IVi II2 IVi la d I, 7a V n V IV, FUNDAMENTAL PRINCIPLES. All mixed chords contain the interval of an augm, 6th. This interval must not be inverted, unless the tones lie more than an octave apart. There are two kinds of mixed chords in major: the discords of the First class, with raised 2nd step; and Second-class chords with lowered 6th step, combined with the raised 4th, or 4th and 2nd, steps. I30 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 286. All major mixed chords, and most of the minor ones, resolve into the tonic chord. The mixed chords of minor belong to the Second class, and contain the raised 4th step. *i) EXERCISE FORTY-THREE. -7 3 i *2) ] 5 . , P Major. =^ 3=^3f fEEi 7 6 ^87 4, Bs- 6 7 6 4 3 0- a i-' 43 0" a- „8S If** H- b. ^S^g 5 +38 Jf *l) IK =WF ^ 87 If bI 6 "■ 4 a 4 =tt 6-4 a ^ s te ig jjiUij J ^ m a? »3) *^ ^ r =?= 0- 4— Is bi »3 a 807 6 ^7 * 81)7 8-87 6-85 43 1- g# *3) ^ i ^- ^ I r r r f e ^ 87 8„-7 g^S *l) 32 5*3) 8(7 5 3 W^S: ^^>^ 4i -^=^ -^ — h S 65 6 3 43 5 8 7- 5 -3 ba- a- 43 56 eb7 445 3 ns cad. 7 6- es - a 6 5 4 5 b * ci B7 J ^^ Faisst 3 — 3*2) s p aste P^ -g^ S! :±3* ±t *— #- -2^ a 87 t B- Faisst ba 65 48 70- a 3-4 4 rail. P p- ^m ^ s PE 6 ..7 Stl7 50 6 7 2| s- ii * # 6 7 6 0- 876 5 5676 a 4 87 1)6 7 j. *i) Do not overlook the resolution of the seventh. — *2) Rhythm J J^ — . *3) Rhythm j J-; — . These basses must be carefully analyzed, as usual. Add Original phrases. PART III. MODULATION. SECTION I. KEY-RELATIONS. 287. Modulation treats of the process by which a transition is made from one key or mode into an- other. This transition is effected, in general, by inflecting one or more tones of the first scale upward or downward, whereby the location of the half-steps is changed, and, consequently, the harmonic and melodic relations of the original scale-tones and chords are changed to conform to a new tonic basis. 288. All the keys in music have the same rotatory series of seven letters, a, b, c, d, e, f, g, a, b, etc. The difference between them is, that they start at different points in this series of letters, and therefore contain different sets of acci- dentals, for the adjustment of the scale-spaces. Review, thoroughly, par. 15, with reference to the origin of key-signatures. 289. The first requirement in the practice of modulation is a thorough knowledge of the Relationship between the keys, that is, their relative location in the modulatory system. For it is this which determines the quality of the various changes of key. 290. The relation of key to key agrees fundamentally with the relations between the correspond- ing triads. But in general it is more convenient to define the degrees of relationship, first, and chiefly, according to the number of tones which the scales possess in common; and second, according to certain important coincidences, or points of contact. 291. The notation of the letters, and, consequently, the number of common tones, is indicated by the signature of each scale; therefore the degree of key-relation becomes directly apparent by simply comparing the signatures. (This refers to minor as well as major signatures.) 292. The relative location of the keys, and their signatures, are exhibited in the following chart of the modulatory system. Ex. (J (Strictly speaking, the chart should present the Q ke}motes in vertical order, as in Ex. 9, and at the head of Exercise 47. But for convenience they are arranged in a circle, because at the 12 th degree the tones come so nearly together,— /# and gb, — that in musical practice they are treated as identical.) Explanation. — The outer circle represents the major keys, the inner one their relative minors. N.B. Hereafter a capital letter will indicate fhe major, and a small letter the minor key. The signatures within the circles belong to both the major and the minor key. The distance from key to key, along either circle, is a perfect fifth, or harmonic degree. Comp. par. 12. This proves that /feey-relations are, fundamentally, magnified towe-relations. The differ- ence in the size of the right and left half-circle is owing to the actual difference between /# and g\>; it is here a trifle exaggerated. 220 132 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 293. 293. The degree of relation between one key and another is indicated, fundamentally, by their distance apart in the above circles of harmonic degrees. It will be seen that each key is surrounded by five attendant keys. These are called the five next- related keys, and they are obviously directly accessible. For instance, the five adjacent keys of C major are G, e, a, d, F; of A major, D, b, f#, E, c#. They are most quickly defined by comparison of signature, as all agree most nearly with that of the principal key. See Ex. 222, Note *i). The five next-related keys of any given key are also definable as those whose tonic triads occur in the scale of that key, — in minor, in the descending melodic scale. Thus: JtX. 221. i From D major Mi^m T27 D I -^ * ^i^ From a minor *l) ^^ cl f#I GI A I bl al GI FI cidl C I #) m *a) *i) Not the tonic triad of any key. — "2) Comp. these tables with Ex. 220. 294. The next-related keys are designated as follows : ist, the dominant key; 2nd, the subdominant key; 3rd, the relative key; 4th, the relative of the dominant (dominant-relative) ; and Sth, the relative of the subdominant (subdominant-relative). Thus: Dominant Ex. Subdominant 222. Relative Dominant-relative Subdominant-relative *i) The signatures of the 5 next-related keys do not differ from that of the principal key by more than one accidental. The relative key has the same signature as the principal key; the dominant (and dom.-rel.) have one sharp more, or one flat less; and the subdom. (and its relative) have one sharp less, or one flat more. Note the manner of indicating the major keys with capitals, and the minors with small letters. Of C: Of a: key G, e, J) F, d, jj a, c, }} e, G, ?j d. F. *l) 295. Besides these five keys, there are a few others which, on account of certain important harmonic coincidences, can claim a remote degree of connection with the principal key, and can be reached more readily than other, entirely foreign, keys. They are called the remotely^dated keys, and will be explained in due time. GENERAL RULE OF MODULATION. 296. A modulation may be made directly into any one of the five next-related keys. Into the re- motely-related keys a modulation may be made directly, tmder certain conditions. Foreign keys can, as a rule, be reached only indirectly, through the intermediate related keys. EXERCISE FORTY-FOUR. Make a table, in letters (large and small), of the five next-related keys of every major and minor key, with signatures, as follows. Reference to Ex. 220 should be avoided as much as possible: Par. 297. THE PROCESS OF MODULA TION. 133 Prin. key Dom. key Subdom. . Relative Dom.-rel. Subdom.-rel.' c \ G # F b h e #■ d b c at g 2b f 4^ Eb 3b Bb 2b Ab 4b G # D 2# c H e *f b ^2# \ g 2b d b c 3^ Bb 2b F b Eb ab and so forth. SECTION 2. THE PROCESS OF MODULATION. 297. The transition from one key into another is effected most naturally and legitimately through the leading-tone 0/ the desired key; or, in other words, through those chords which contain the lead- ing-tone. 298. The leading-tone occurs in all the dominant chords (First-class concords and discords), and it is through these that the desired key should be entered. The best among them for this purpose 7 are: the V (which is ahnost absolutely characteristic of its scale); and the chord of the diminished seventh (Vq), which, as seen in Ex. 198 — Note *3), — can be used equally well in major as altered chord, and in minor as legitimate chord. (Review par. 239c.) The modulation into G major, for example, would be made through any of the following modulatory chords: *i) Resolving into : gzorlgllorrgi or any inversion I m VI *i) The V(j may, of course, be used with the major ninth, but it is more difficult to handle. These same modulatory chords would also be used in entering g minor (as well as G major). Because, as is obvious, the modulatory act is directed toward the tonic, or keynote, which is the same in both modes. See also par. 107. 299. This important rule is illustrated in the following modulations from C major into G major (the dom.-key) : i r ' r r r ' r r ^ r^'r vi'-^ j nj 1 m tSI-'- Ex. 224. I i -H-l J ,^--1 i J^i -J- J. -J- i i J- -^ a -* — \ 1 ni m W — »z. — r^ . ■ tf a — t^^ ^t = r^=^^\ . etc. i iS^ S I Pf^ -GV- 9b -GV„ - C G Vi The sign x indicates where the entrance into the new key (the "modulation") is effected. 300. a. Modulations that are thus made with a First-class chord, are the most direct. b. But it is also possible to enter the desired key through any one of its Second-class chords .77 (II-IV-II-IV), because these resolve directly into dom.-chords. Such modulations are less abrupt. c. Of the remaining class of chords, i.e., the tonic class, only one single form can be used in effecting a modulation; namely, the tonic 6-4 chord (Ig) of the desired key; and this should stand on an ac- cented beat, or accented fraction. 134 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 301. It is contrary to the fundamental principle of modulation, to enter a new key with any one of its tonic chords; but the accented /j is an important excejjtion. Review par. i860, 6, — from which it appears logical to regard the accented h as equivalent to a dominant chord. These more gradual transitions are illustrated in the following modulations from C major: m 1-4- ^^ uigxay i J i Ex. 225. «4) r -i J 4 m J J I J j-p i etc. is ^ -•—if , m *=:?= r^^rT ell V- *i) 7 ell— *l) ■All- ^k^J J I J J ^ ^i^fM *a) I m I ' nr nr —^ i i i J J. i =t« -2^ I I J"'PJ M gffi ' r T r ^ r all- alV 7 all ■ G I2 V- *i) The new key is indicated by its znd-class chord; but the modulation is evidently not complete until the dom. chord appears. — *2) This is the "ambiguous 7th" (par. 235). — *3) The I2 must be accented in order to exert modulatory force. — *4) The examples hereafter will be mostly in continuous phrase-form, — not separate measures. ' 301. The act of modulation consists maiiily in obtaining the desired key. But it is scarcely less important to decide at what point, — upon what chord, — the original key may best be abandoned. a. If the last chord of the original key is one which belongs also to the prospective key (in an- other harmonic meaning, of course), the modulation will be gradual, and there need be no chromatic inflection. Consequently, such are called Diatonic modulations (Ex. 226a, c). Each chord-move- ment, before, during and after the change of key, pursues the track of a diatonic scale. b. If, on the contrary, the last chord of the original key does not belong to the coming key, the modulation must be Chromatic. That is, a chromatic inflection will be necessary in one or more of the parts (Ex. 2266), in order to gain the new scale. These modulations are more striking, and usually more effective, than the smoother diatonic species. *i) *2) ^m w Ex. 226. CtoG J- J u i i -i J * afc I -^ \g II— V — VI chrom. Par. 30a. FUNDAMENTAL RULE OF MODULATION. 135 ^ Mendelssohn. No. 22 »3) X ^ Fto C " i^i a I -j- jn^D i 3 7 FV- ^ (F VI V V 7 -l|cii I I ^^Vo I "i) This chord, the last one in C major (as VI), may also be defined, prospectively, as the II of G. Consequently, the progression into the following dominant chord of G is as smooth and natural as if no change of key were taking place. *2) Here, the last chord in C (the 11) does not belong to the coming key (G), and therefore the chromatic change of /■ into /# (in bass, in this case) is necessary. — *3) Not only this last chord but also the three preceding chords belong to hoih ke3rs. The change of key is made almost insensibly. FUNDAMENTAL RULE OF MODULATION. 302. The simplest and most comprehensive rule, however, is, that it is best to leave a key at one of its Tonic chords (either I or VI); because these inactive harmonies, especially when accented, convey the impression of fulfillment and completion, — leave nothing unresolved or unfinished in their key, — and therefore suggest a digression into a new harmonic circle, rather than hinder it. This rule is illustrated in Ex. 224, Ex. 225, and Ex. 2i6o (c?), — in all of which the last chord of the first key is either the I, Ii, or VI. 303. If the tonic chords at the close of the first key belong also to the coming key, the progression into the modu- latory chord of the new key will be diatonic (par. 3010); otherwise the progression must be chromatic (par. 3016). The rules for chromatics will be found in par. 2696; Ex. 198, Notes *6) and *?); Ex. 206, Note *i). The following periods illustrate this fundamental rule, both in diatonic and chromatic operation: Mendelssohn I. Andante -^ ^^ ^ ^ ^. „ i m *i) *a) " "m ^ ^^% ^: i^-h* w ^^ Ex. 227.^ *3) Diatonic etc. 2 I 1 I E|? I 7 ^^Ab VI>.^^,^'E1» I /Bl,I t/EM 7Al,V 7 Ai» y-V""^ Eb II I-^""^^ Bb IV-V EbV-V AbV-V Eb I3 Vq- I d -rd-^^ ^^ i Chromatic *4) ' ' I ' i,*l 's^l I i I I l- I I l**i 1 *«) ^m t=t=fcs 9 sb 7 77 CI dVo I CVo I aV VI GV I eV 7 aV 7b 7 I Gil V 7 7b 7 I F V I Oil V ^ 136 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 303. *i) The last chord of the old key is everywhere, excepting at Note "3), a tonic chord, and in every case common to the new key; hence, the modulations are diatonic. — *2) Par. 300c. — *3) The last chord in Ab here appears to be a V instead of I. It is, however, plausible to regard the preceding chord, on the oMenl, as the one which concludes At (as I). In this case the unaccented I2 begins the following key. — *4) Here the I of the old key does not appear in the new key, hence the chromatic progressions. — *$) Par. 3006. FUNDAMENTAL PRINCIPLES. Key-relations are defined, fundamentally, by signature. The five next-related keys are those whose signatures most nearly agree with that of the principal key. It is best to abandon a key at one of its tonic chords and enter the new key through any of its dominant, — or second-dominant, — chords; rarely through the accented I2. A modulation is diatonic when the last chord of the first key belongs also to the coming key, — otherwise it must be chromatic. EXERCISE FORTY-FIVE. A. Play the following chord-progressions on the piano, in the usual manner (the bass alone in the left hand): C I— F Vi— I II C I— G V— I II C I— a V— 1 11 C I— e IIj— V— 1 1| C I— V— VI— d Vq— 1 1 1 G I— C Vs— Ii— G V— I 1 1 a I— Vi— I | e I2— IVi— V | f 1 1 F I— IVi— I2— d Vq— I— g Vq— I II b I— V— I— A lis— Vi— 1 1|. B. Modulations into next-related keys. All changes of key should be marked, and their relations analyzed; also the chords used in modulating. Do not neglect the accidentals. The accidentals make the modulations, — see par. 288. 6. «3) :?C3 i Ss sm ift: ^g?^Tr *i) 87 i s a *2) nt a 7 * « 57 *3) ^ d. *l) ^ &: IBZ3E m ^ I = 7 8 6 4 * g^^ Handel 3 5 ^ m^W%i^ m m ^- A - 7i=^ ■* — r* n 8 6 7 4 $ 6 S8 8 87 « 6 ^ a e 3 4, 3 67- 4t- Par. 304. ALTERED CHORDS AS MODULATORY MEDIUMS. g- 137 S^ S -B M 3 I te=e ^ J|J_ Mb'^f>g g ¥ 87 bfi g « f " B e a a. 7 4:g3 S as T -«- fiii ^ ^ ^ p ^ ^ a a a e .8 a 4 ,4 bs bt a it 6^-, * 6t|8 : Qj- a a e- 7 abs 54 a— tta ^ I ^ ^ * a J y f ^^^1^ t a? as ^ las f « 'i) Upper paxts held. — *2) Exercise 42, Notes *i) 2) 3). — '3) Par. 2696. C. Add a large number of Original phrases, possibly periods also. Altered Chords, as Modulatory Mediums. 304. It is evident that the altered chords, standing as they do upon the boundary-line between different keys, must constitute a very natural and efficient medium between the keys to which they actually belong (as altered chords), and the key or keys which they appear to represent (as legitimate chords). The distinction is defined in par. 267^, e, which see. This interesting phase of modulatory transition is illustrated in the following examples: I. X 2. Schubert 1*3) *1) *1) *l) «3) Ex. 228. *i) 9r » tf M l *i) *i) J.- J J J ^W^ -iM -zs-i : kt-^-iJ-i^-i J. | -d^ri^; ; fT ^ ff4. P- I m^ m s ^ f- ■s~ P' - \ A IVi-Ig Mendelssohn Bach GV (BblVi # 7 J b alV-Vo U Ilili-V gill- 7 -Vs 138 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 305. jjt. M fi t^ El J £j r — «r ^ <=- r -4- I g gVo c IV— V— I s eVo-I 9 ,eVo 7»Jt > ' C II— I, a Mendelssohn \>Tr-^ -^ 4=g= ^q ^=J J J . ^^J-i 9» :^ ^ ^ i- i- — -S- -f- ,:»- nS F^^PP^^^T^^R pa £ Bb Vo-glla— I I ^^ m ,7* ; cii a IV — V 7»J II 7«* 7 VI— V- ^ *i) This altered chord (with raised 2nd and 4th steps) is purposely used three times in succession; twice as unmistak- able altered chord in C, and then, at x , as legitimate chord in e. — *2) This modulation might, it is true, be demonstrated according to the fundamental rule (par. 302). But it is evident that the altered chords in the preceding measures were the incentive to the modulatory chord chosen for the final transition. The following example will also admit of simpler analysis; but the rest, from No. 3 to No. 10, cannot be accounted for in any other way than as modulations through altered chords. — *z) Lowered 2nd step. — *4) Here the transitional chord is first legitimate (in G), and is then trans- formed into an altered chord (with raised 6th step) in a minor, — as the progression proves. — *s) This is exactly (and purposely) the reverse of No. i. The transitional chord h first legitimate in e, and then becomes, at x, an altered chord in C. — *6) The transitional chord is mixed, in both keys. — *;) Altered in hoth keys, — raised 4th step in C, raised 6th step in a minor. — *8) Raised 2nd and 4th step in C, used as raised tonic and 6th steps in P. Extraneous Modulations. — i. Through Next-related Keys. 305. A modulation is extraneous when it extends past the next-related keys; or, in other words, into a key whose signature differs by more than one accidental from that of the abandoned key. The fundamental rule for such remote modulations is, to progress in successive stages, through the intermediate next-related key or keys, along the lines of the "circle of keys"; that is, through the signa- tures which occur successively in the direction of the ultimate key. For instance, the modulation from G major (i sharp) into A major (3 sharps) would be made through the key of 2 sharps, thus: G—D—A, or G—l—A. *l) *2) *i) It is not necessary to adhere to the same mode: on the contrary, it is advisable to alternate (more or less regu- larly) between major and minor, as at *2). Or from C (natural scale) into .417 (4 flats), through i, 2 and 3 flats, thus: C— F— Bt>— jE1>— 4b; or C—d—B]^—c— A\> (Ex. 229 — 2); or C—P—g—Ei?—A\>, etc. Par. 305. EXTRANEOUS MODULATIONS. 139 And from £ (4 sharps) into h), (5 flats), through s#, 6# or 65., thus: E—B—F^ or Gl?— Jl»; or £— g#— /?# or Gv—Vv, etc. For illustration: ^^^^^ ^^ E r Ex. 229.' C-e-b-A ^ J i See ^ P lit 79 '7 r I b VI-V A Vn I I :^=P o eV, C-d-Bb-c-Ab lb 2b 3b 4b ' ' ' ' I J77 Ja g 7 ^ i C dVo BbV c-' -^i^ i^ cVo AblV— V EXERCISE FORTY-SIX. 3*1) ^ +S 8 ^S ^^ a a a a If, t=4 ^ * S d -pH-* -si-' 4: a see ens af * *3 4 8 „ « J.9 9 6 e 6 87 6. *2) ga^pE g^^^^ g# rar I n r N t-^Jn^ f d p- ^' *3) *4) ^r— r>^ a ^M g »M=»^ 3E P^ .- _a 4,- „• -rf- 8' a 8 ba bs *''» B^ u ba a 1)3 b7 a 3 be ba ba 3 Da nL Ds Da tin nl u 87 V ''^ i— I— '" a a a e,~" I ^ FeteTfl 3 Da (7 Ds g8 qe c'7 u ^ a a a e„„ _ 7 BadeT? D a 4 Ba a a j qjj 4 "4,6 tl " 140 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 306. g. *5) +3 Igij^^^ *3). i^ -^ • ~T^ i2a6^ ip i Plagal - X* — gg S 87 00 4S 807 b4: 3 bl b b'e s B - ''g 87 b6 «''•' ^* 7 7 *i) Altered 11 of F and altered IV of d. All the modulations in this bass are made through altered chords, and must be analyzed accordingly. — *2) Unfigured bass (par. 264B). A modulation occurs at each *. — *3) During the first three measures this bass modulates in regular degrees "downward," i.e., adding a new flat each time. At *3), instead of going on into 6 flats it iwrns hack into 4 flats, and then resiunes the original downward direction. This is done to avoid the monotony of several successive changes in the same direction. At *4) the monotony is again broken by the "horizon- tal" modulation into the relative key. — *s) The signature (s#) is omitted, because of the subsequent modulation into flat keys. — *6) Here the notation is changed from 7# to sb; the key is regarded, in musical practice (and on the key- board) as the same. Add Original phrases. Extraneous Modulations. 2. Direct. 306. There are cases where, contrary to the general rule, the remote key is reached directly, instead of through suc- cessive intermediate keys. The most common of these is a modulation called, in this book, The Modulatory Stride. 307. The "stride" is a harmonic degree (perfect 5th) downward from a major keynote, or upward from a minor keynote, with change of mode. In other words, it is the subdominant-minor from major, and (exactly reversed) the dominant-major from minor. Thus: Ex. 230. min. maj. maj. EM itor Iand_ _also_ rtor d -bfii- bb J2E: Ab (db) * c# etc. The keys lie four degrees apart (c — G, 3 b — #), but the stride-relation is quite as intimate as any next-related key, — be- cause of the important harmonic coincidences; chiefly that of the I and V: i l^ Therefore, this modu- cV =G1 lation can be made with the same ease as those between next-related keys. The formula to be memorized is: any perfect fifth, of which the upper tone stands for a major kejmote, and the lower for a minor one (Ex. 230), indicates the "stride." 308. The stride is generally made according to the fundamental rule, leaving the first key at its tonic chord (the I, but not the VI, in this case), which is at the same time invariably a principal triad of the desired key. Thus, in the stride C—f, for instance: i ^:S -a— ^S= CI = fV and ^g=^ but possibly also | ( j^ bg %~~fl fI = CIV cn = fvi Par. 309. I. C— f MODULATION TO THE OPPOSITE MODE. 2. f— C 3. e— B— e 141 •" f r r r rtrfr ^[^rfff ff^^^*^ Ex. 231. *i) An altered chord (lowered 6th step of C). — *2) The facility of the stride is strikingly shown in this example, where it is made forward and backward in three beats. When, as here, the I of the old key is at the same time the dominant chord of the new one, there is no need of delaying the modulation. — *3) In this exceptional example of the stride, the order of chords is reversed; i.e., the first key is abandoned at its V, and the new key is entered through the I. ' Modulation to the Opposite Mode. (Exchange of Mode.) 309. The change called, in this book, the opposite mode, is, strictly speaking, not a change of key, but of mode only, — for example, from C major to c minor, or reversed. It is not to be confoimded with the relative major, or minor, which is a wholly different key. The opposite mode is defined in par. loi. By signature, there is a difference of three degrees between the opposite modes {E — e, 4# — #) in location, though in relation they are practically identical. This appears to place each minor key at tw» different points in the modulatory system, which may be interchanged or not, at option. Thus, c minor may rep- resent the locality (tonality) of "three flats," or it may pertain to the region of C, as transient modified form of the latter. (This has been its significance in all foregoing examples.) 310. a. The modulation to the opposite mode, either way, is generally made through dominant chords, which are mostly common tp both modes; see Ex. 68, Note *i); par. 202; 229; Ex. 198, Note *3). b. But the altered chords with lowered 6th step (in major) are also available, and extremely con- venient. Thus; good better i w- -iS'- -Tg- -\) o bz SI ^W^'^\ C V c V 7 V 7 V T7- Ob CVo e cVn 7 II I^ IV 142 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 311. c. Or the modulation may be made by a direct chromatic change from the one tonic triad to the other. Thus: i i 311. This modulation is very different from the stride, and is far from being as natural and easy as the latter. The change from minor into major is always good, but from major into minor is much more difficult. The major mode is often substituted at the very end of minor pieces, in order to obtain a stronger perf. cadence (on the major tonic); see Bach, "WeU-tempered Clavichord," prelude and fugue Nos. 2, 4, 6, etc., the last measure of each. It is also frequently used, either way, for the sake of striking contrasts. 312. When the dominant chords are used for the mod. into the opposite mode, they should appear on accented beats, and be prolonged as far as the rhythm will permit, so as to separate the conflicting mediants (maj. and min.) as widely as possible. I. Allegro *i) Beethoven ^^fe^0i i # s ii. Andante Schubert 1-^ rs-t-h I ip: g 17-4 #• 4-^4\*-^ -=^-N 4- V^ ^E? Ex. 232." major maj. maj. abl ( abV ^AbV — I \ Ebl-V— I 3. Allegro Schubert 4. Adagio Brahms i^^p^ ^i ir ^ r maj. *4) min. «6) maj. iP^ ^ig i vww^=^ DI- -dl B|,V- LlSZT 5. 8va^ Vivace 'ace &«— ^ d min. j3 „^j_ d min. etc. g^^i^?4 TWT ( dV ) DV ) r r I Par. 313. MODULATION TO THE OPPOSITE MODE. 143 *i) This dominant chord, prolonged through the measure, is common to both modes, so it is simply a question whether the distinctive mediant (the letter i) shall be major or minor in the resolving chord. — *2) Here the opposite mode is reached chromatically, — par. 310c. — *3) The stride. — *4) The change is made chromatically. It serves here to shorten the distance from 2? to Bb, which, according to par. 305, would require the intermediate keys G, C and F (or their relatives). *S) Par. 3106; rV of o minor, and altered IV of A major. — See also Ex. 235 - 3. 313. The exchange of mode, seen above, is liable to take place after any dominant chord, at any point in the phrase, — only excepting after the major dom.-gth (par. 229). The coincidence of the dom. chord-class in the two modes is thus turned to advantage for many reasons; chiefly, as a means of shortening the route into remote keys. For example: I. Allegro *i) |Beethoven. Op. 73 ■G — F — Eb, would be incorrect, were it not for the ingenious *i) The modulatory outline of this example: E — e- 7 manner in which the ambiguity of the V is utilized in substituting the minor mode each time for the expected major; thus: Ev-g [-Gv-g j--FV-f }-Eb. *2) The major mediant (c#) is substituted for c|j because of the coming i minor. See further: Schubert, "Schone Mullerin" (vocal, op. 25), No. 17, in which there is frequent exchange of mode throughout, in effective adaptation to the character of the words (see meas. 2-3, 4-5, 18, 21-22, 36-38, 40-41, 45-46, etc.). Also Chopin, 4 -minor waltz, op. 34, No. 2, meas. 53 to 84. 314. As the stride is almost exactly equivalent to a next-related modulation, it is evident that its application as intermediate key, in extraneous modulations, conforms sufficiently to the fundamental rule given in par. 305. Its use in this capacity is very advantageous, because it shortens extreme distances materially (being a direct transition of 4 signatures), and relieves the monotony of regularly succeeding signatures. For instance, instead of the long-winded and monotonous successions C — V — B]} — E7 — A\> — D\> — G\>, the same end may be reached thus: C— /— flb — Gb; or: C—P — h\> — Gb. (The 1 — 1 indicates the stride.) Also, from C to F#, thus: I i I 1 I 1 C— e— B— i?#. From D to F, thus: D—g—F (Ex. 234—2). From C to A, thus: C—a—E—A, (past the desired key, I i and back); or: C — d — A {Ex. 234 — i). For example: 144 Ex. 234. THE MATERIAL USED IN MUSICAL COMPOSITION. Jiij|iii*^,i .^ f^^^ ■#■ -^ trt»= ^V_ SS » ^r-f^ri i r fij dV-I > 7 A IV— la V (DI IgV-I 7 FV— "i) F\ in the tenor (as lowered 6th step of 4) would prolong the impression of the former key {^i minor) and make the mod. smoother. In determining the shortest route to be taken in an extraneous modulation, it is first necessary to ascertain the distance and the direction, according to the table on the margin. For instance: from Ai> to J is six degrees upward. If, as here, the distance exceeds three degrees, it is advisable to shorten the modulation by using the stride; but otherwise it is not necessary, and the route may be taken, as usinl, through successive signatures. In a remote mod. upward from a major key, the stride can not be employed directly, for obvious reasons, — the stride is downward from major; therefore a transition must first be made into a next-related minor key, from which the upward stride will be possible. The same applies inversely to a remote mod. downward from a minor key. For example, from C to g#, thus: C — e — B — ^gjj; or C — a — E~ I I I I thus: /#— D— g— 5|>; or ffff— A— d—B\,. From /# to BV, EXERCISE FORTY-SEVEN. A. Indicate, in letters (as shown above), the shortest possible routes which may be taken in effecting the following extraneous modulations. Only the stride, not the opp. mode, is to be used in shortening the distance. Maj. min. signa- tures A], m a =F#-(i!# 6# B -g# S# E -cif 4# -S A -/S SS S! D -b 2# tS- G -e # " C -a O F -d b B\,-g 2b ^ -Eb-c 3b 1 A^j 41' 1 i)l7-6b Sb 1 G\>-e\>=d'^ 6b = 6# From C to Eb " c " F " C# " g# " c^ " D " c# " F^ " D\, " g " d "A From d to Ai> " D " EV " D " g^ " eb " c " e\, " i?S*i) " E\> " d '■ E]> " Cb From E to g " E " Db«i) "/ " E " G\> " b F'H" e From /# to E\> " G\> " F " Gi>" c#*i) " G " g «8) " G " D\, " ^ " b " g " D From 4 b to G A " e a " B BV " E b\> " Sb B "f*i) b " Eb B " C *i) It must be remembered that 6b and 6i are alike. — "a) Not directly; the opposite mode is not to be used. B. Work out each of the above modulations, along the adopted route, in Original phrases or periods. Par. 315. MODULATIONS AT CADENCES, AND IN SEQUENCES. 145 C Basses. To be worked out and analyzed as usual. a. b. ^ ^ 5+8 -a _^ # ^* ^— . ; ' ¥^' ^ a a 8l)7 bvbse 7a7btia aBTfl 4 b— g •a) 87 S a - «- « - 7 *2) a Das a 87 Schubert I i2- ^ Ete£ :|i ^ ^ bg b5 bs 8b7 bs Oa b7 bs bt e 8b7 6 as t a 5 ^8 /• »4) Ega^tJ^:^^^ ;^ ^OI^jn^ s pE&* iZ3t f=t He- e 87 IJ5 p a a s * *4) * * « * » * /T\ ' S i *^) 8 Wagner i m, p^ )t=^ f i^i s ' ' g ails a X 87 X 4X3 6 f X- a 6- ti 7 a Da Us *i) C# major is substituted for c# minor. — *2) Similar to Note *i), c for C, and i? for /. — *3) IV of d#, mixed. — *4) Unfigured bass (par. 264^). Modulations at Cadences, and in Sequences. 316. a. The reason assigned in par. 302 for leaving a key at one of its tonic chords was, that the latter fulfil all the obligations of their key and leave no obstacle in the way of an exchange of basis. Also, preference is given to the tonic chords on accents, because these are the actual points of rest in the rhythmic oscillation, — the points where all cadences, transient and final, are made. 6. Nowhere is the impression of completion stronger than at the cadences themselves, or even at those points of tran- sient interruption in the course of a sentence which mark the end of a section of the form, — the "joints" between the members and figiures of which the melody is compounded. 316. Hence it is, that a modulation may be made with the greatest ease at any cadence (i.e., after the cadence-chord). And it is so reasonable to begin a new phrase, or a new melodic member, with a new key, that the transition may be made abruptly, and without regard to the fundamental rule of modvr lotion. 146 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 316. The only limitation is, that there shall be a reasonable degree of aflSnity between the two keys, — or between the melodic members (as in the sequence). The modulation may, and often is, made from the last chord of the first key (which is likely to be tonic or dominant) directly into the I of the next key. (Comp. par. 300c, where this is defined as very irregular. The cadential break of connection renders almost any change feasible.) For example: cad. Schumann 2. _ cad. 8va Schubert »l) etc. Ex. 235.' g^teg *i) tt ^ etc. mm m 5^ ^ Bl, I Gb I A I FI Allegro .^ ^ cad. i i cad. Mozart -''I— j^ -S— ^ ^ k -^ I *2) =/ I !"> -^ *3) •^ I , I etc, 8 i« ^ 1 X 1 S 1 - A I al Bb V Adagio cad. e ^ ^S Mendelssohn 5. ^^ cad. Schumann -^ — ^ »— =1- ^"^-V^ *4) etc. J- m jm, rxj i^ etc. Ibc, C ^ i ^ f^J^X l f '/ ^ ha ff S -=i — ^ FI g dV F I , Al, VI ■ 7 ■IV ■ 6. Adagio ^ ^J ^bA I _ J l Schubert g^ cad. *5) cad. I *a) etc. ^i=i ^^i-|^ cv I IV I Db in I Din I Par. 317. MODULATIONS AT CADENCES, AND IN SEQUENCES. M7 *i) An immediate progression from one tonic chord into another. — *2) The opposite mode. — *3) There is no rela- tion between these keys {a-B\>). But there is an important common tone, a, which is the tonic of the first key, and the leading-tone of the next. This affords the desirable affinity, and is, in general, a significant feature of all free modula- tion, — to be explained later in detail (see par. 346). — *4) Common tone a, third step of F, fifth step of d. — *s) Com- mon tone c, tonic of first key, leading-tone of the next. — *6) The common tone d'? is changed to <;#; the result is the same. Such modtJations as these might more aptly be called "modulatory leaps," than legitimate changes of key. 317. On this same principle, and with similar ease, modulations may be made hy sequence (par. 260, and, particularly, par. 261). The original member and its sequential reproduction are of course separated by a "joint" or transient cadence, at which any change of key may take place; and the de- sirable affinity is fully provided by the sequential agreement of the members. Mendelssohn X pf^^ Si Z^H i: m ^^ e r^ Ex. 236. *l) Seq, Mr I Vlfl VI Ab *a) Seq. aasi f— Ke =& »-=- AbV Dbl -g — b^ Schubert 3) ^ Mendelssohn ^^ir7\iti JAfh T^ Seq. -^ ^rj 'o^j-^ rtfPfip I B n^ Seq. ± ^^m isfes SSe ? GbV EbV a V d IV- 7 ■ V 4. Allei^o Chopin. «*) ^P s^ rr ^ , m .sT^^fn Ji ^ , p^ f Mr n'^-f . i ?=^ Seq. Seq. Seq. etc. -V ¥ £: m dIV II fIV II I g#IV II I blV II I m8 the material used in musical composition. 5- Allegro - ;; ^ -- ^^ Par. 317. Chopin i -i- ^ ^ ^ ^ ^^ i: -^W- w A=s^ ■0—0- :t *s) * — S?- Seq. ==^=^^' ^ S Seq. etc. m ias pB S; -« — S- -^ — S- Eb I gl Bb I dl *i) Ex. 23s, Note *i). — "2) This modulation is very abrupt, and the keys in no sense related. Such unusual transitions could scarcely be effected anywhere but at a melodic "joint," and by sequence. — *3) This third group is not an exact sequence of the preceding one, nor is this necessary. General similarity of melodic or harmonic progression, or a partial sequence, is all that the ear demands. — *4) Etude, op. 25, No. 10, 8 meas. from the end. Given here in sim- plified form. — *s) The tones marked x are "grace-notes." The student may read from par. 39s to par. 401, and is at liberty to apply them here, if he chooses. See also Ex. 235-6; Ex. 239c. There is an analogy between these examples and Ex. go. Note *2). EXERCISE FORTY-EIGHT. Modulations in sequences and at cadences, into related and remote keys. To be worked out and analyzed as usual. ^ Beethoven f a^ 5 7 3 o +9 ^ +3 B^S #-i* w iznL =t n? 5? '' C5 8 q g^ :^«=i ^ i ^ :t?P= * S^ ^ #=p^ -i-»^ ^ I " bf a a- . 4r a ,e a bs 4: bs s to m Da ba 1,7 e- a bs 4 as " cad. b7 m^.m^'X^ ^^ ii^ f^ S P^^ „/t a -Da at " 4: a a a ^4: a 6 a 4 fl3 7 Bs ^as Q flas b7 pes 7 aa Ds (t 143 4j qs |,4|j I 4J d. ^ ^ ^ ^ ^ • * ^^ 6 07 6- 7 4 * a # a || J i ^9^f^ bs - J »5 - iia ^e f iT 5^ - b4 3 Add a large number of Original phrases and periods. a 07 4 Pai. 318. CHROMATIC PROGRESSION. 149 SECTION 3. CHROMATIC PROGRESSION, AS A SPECIAL MODULATORY AGENT, 318. a. A progression is chromatic when the same letter is inflected upward or downward by an accidental, thus: g-g#, or g-g\?, and reversed. b. The resiilt of such an inflection is greater than it appears to be, and can be appreciated only by comparing the two tones as keynotes. This test proves that every chromatic progression is actually a leap of seven degrees; thus G (i#) and Gt> (6 flats); or 41? (4 flats) and 4j| (3 sharps). See par. i6b. c. The chromatic inflection, for which there is no apparent theoretical justification, is excused on practical grounds; namely, the difference in pitch is so slight that the ear readily follows the change. It is a case of "relation by proximity." 319. The chromatic progression has been used constantly, in the foregoing exercises, but merely as a result of the fun- damental rule, or other ordinary condition, of modulation. It may, however, be the direct cause of the change, and it is in this specific capacity that chromatics are here being considered. 320. Chromatic chord-progressions (those in which one or more of the parts progress chromatically) may be distinguished as simple or compound. In a simple chrom. chord-progression the chord does not change its form. In compound progressions there are diatonic as well as chromatic successions, so that the chord assumes a new shape. For illustration: b. Compound Ex. 237." Simple 1*1) '^ T~~ ^ '^^ I . I ii J-v- J "-i , J i r rrf m i i"U -fZ~ n b r f TT J..U- -U i sbs sbs b7 be "i) The simple change of e into ei> does not alter the form of the chord, which is the triad c — e — ^g both before and after the chrom. movement. — *2) Simultaneously with the chrom. change e — eir in soprano, there is a diatonic progres- sion c — bi> in bass, whereby the chord-form is changed from a triad to a ch. of the second. RULES OF CHROMATIC PROGRESSION. 321. The rules of chromatic inflection have already been given in par. 2696. They are recapitu- lated here, for convenience: a. The chrom. inflection is usually made in the same part. b. The note to be inflected should not he doubled, as a rule. If it is doubled, one part moves diatoni- cally, — not with a leap, — opposite to the direction of the chrom. change. c. The chrom. progression should be approached in the corresponding direction, if possible. Ex. 238. 1-^ not thus : ^#t ■*^''-'=i fete i^^ 322. The violation of par. 3210 occasions the so-called cross-relation. It is never wrong when the first of the two chromatic tones does not leap; and is often mitigated by other conditions, — when it occurs at a "joint" or cadence, — or when the first tone is in bass, — or when the change occurs in different parts but in the same register. For example: ISO THE MATERIAL USED IN MUSICAL COMPOSITION. Cross-relation ^^^ {a) (*) i&BI kAA.A w Par. 323. Beethoven "^ Ql I Ex. 239. «4) 9t IS /: 7 i fT4.^.i id) (Phras&-form)*6) V *a) V ^ MJimiiS-^i^i ^ ^^^^r^f^^m \ i Spontini i J- j-J- -ii i^ #--f- p^^ i J * f=Ff^f=f J J f^sMI Se -i J^ ^-(^ I r *i) These two examples are inexcusable. — *2) The leap in bass seems permissible, probably because the bass is al- ways to some extent independent of the other parts. — "3) All permitted, because the first of the two chrom. tones does not leap. — *4) Sequence modulations; the cross-relation is separated by the "joints." — *s) Limited to instrumental music; the cross-relation is present, but the ear does not detect it. — *6) These cross-relations all occur on the same beat, in successive measures, and seem justified on groimds similar to Note "4). Another peculiar case appears in Ex. 244-5. Chromatic Choed-progressions. 323. The entire system of chord-succession is divided into two radically distinct domains, the diatonic and the chromatic. To the diatonic domain pertain all relations and associations between any two chords which belong to the same key. Here, the quality and permissibility of the chord-successions may be, and are, determined by natural harmonic principles, because their relations are defined from a common centre (their tonic). These rules of diatonic chord-succession are given in Parts I and II; they are incontestably necessary and just, and must constitute the legitimate basis of all harmonic thought. " Diatonics " is. the domain of harmonic law and order. To the chromatic domain pertain all connections between any two chords which belong peculiarly to different keys. Here, no natural law of chord-succession can be laid down and defended, because the chord-relations cannot be defined from a common centre; any imaginable succession is possible, and it is difficult even to systematize, in some de- gree, the almost inexhaustible miiltitude of possibilities in this domain. "Chromatics" is the domain of harmonic law- While the chord-associations in the diatonic sphere are the unconstrained consequence of natural conditions, the chord- associations in the chromatic sphere are a direct violation of these natiural conditions, and are effected by artijicial means {i.e., by means of the apparently delicate, but in reality most powerful, chromatic "lever," which inflects the chord in such a way as to destroy its contact with its tonic and cancel its obUgations to the latter). a. The chromatic inflection may be made in either direction (upward or downward). b. It may be applied to any chord-interval (root, third, fifth; seldom seventh or ninth, and chiefly downward, in these intervals). c. It may be applied to almost any two chord-intervals at once, or even to all three (of a triad) at once. In this case the inflections are generally made in the same direction, though it is also possible to Par. 323. CHROMATIC CHORD-PROGRESSIONS. 151 inflect one interval upward and another downward; and, if all three are inflected, the chord must be in inverted form. d. It may be applied to any chord; best, to a Umk, chord, major or minor (Ex. 2410) ; or to a svb- dominant or dominant triad (Ex. 2416); or to the dominant-seventh or dom.-ninth (Ex. 241c); or even to other 4-tone chords (ir, IV, W). e. The chrom. chord-progression may, finally, be either simple or compound, more commonly the latter. For example: a. From the major triad: Raised root Lowered root Lowered 3rd Raised 3rd (and 5th) i ^^^^m Ex. 240. IE ^ GI C V D IV b VI c V Raised 5th 7 aVo A" fifll 7 AV bb is- Lowered 5th Lowered 5th and 3rd Raised root, lowered 3rd All raised All lowered S^ i^^ is^ I -25- i e Gb Ab b. From, the m.inor triad : Raised root Lowered root Raised 3rd ■G> 1 fj dIV lg= :6^ -g- -nr — gg- BSI S =it^ S Tg- 1S«2- Lowered 3rd and root "t^ Raised jth -z? tfzg- al 1 e IV e IV C VI Gil Fill Raised 5th and 3rd Lowered 5th All raised Eb f# All lowered ^^^ ±^ c. From the V : Raised root Lowered 3rd- ■• ri — S T^ 1 — ig ■a ■ — S ^ 1 ^if-- and 5th Raised 5th Raised 7th , and 5th. Lowered 7th, 5th and 3rd All raised ^ fcv All lowered IS— /I ^ I t*' fe :&§ Iff- " par At i (£ From the Vq, major: Lowered 3rd and 5th Lowered 9th Raised 5th and 7tK e. From the dim. yth: Bodily downward , upward i isi il2g= ig= etc. w JZgte: T^; iSisr- =« t "^^ It is needless and futfle to continue this table, for it is well-nigh inexhaustible. It is left to the investigation of the student. The rides governing the technical act axe given in par. 321; but the guides through this maze of "wandering" harmonies, the choice, and extent of their use, -^ these can be dictated only by the taste, tact and good judgment of the student. But see par. 324 and 325. Also par. 426. 152 THE MATERIAL USED IN MUSICAL COMPOSITION. a. From tonic chords : Par. 323. i>,, J J J I xk-J , J J | J ^, 1 J. I J J J |^=to i wr Ex. 241 iiii , ^ iiiJ J i i, j , j^ . i ij £ ^fe^ a^ S3; ^ ^i=^ F .al d, 6. From First- and Second-class chords : Wi\<^^\W M^'m\ \\'^\^ -^ .^ i j.-g^- Aj.-J .J -^ , j/^ i # ^f##f##g^^ i i Tf=F PF ,CV a, C III G I L5_Yi alVC c. From dom-.-discords : wi r I f "^ r H ^ wmm^H^mim Al rdgh u^A. ,hhiALH-^A.^^^,^^i I iM ifc • f ^ ^* p^ =*^ c V f, ,aV„ F, iCVq d| Schumann e. Schumann s 77 D I A Vo I e IV V *i) In each case the 3rd of the major I is lowered. — *2) Lowered 3rd and sth in the dom.-7th. Par. 324. CHROMATIC CHORD-PROGRESSIOI^S. 153 EXERCISE FORTY-NINE. Construct a large number of Original ptirases, utilizing the chiom. material given in Ex. 240, — but from different keys. Or the student may be guided by the text (par. 3230 — e), and make his own chromatic experiments, without refer- ence to the example. 324. Among the many curious and exceptional results' which attend the use of chrOm. changes, there are two which require special consideration, namely: a. ist: Chrom. progressions are not necessarily limited to the next-related modulations, but often lead immediately, and easily, into remote keys. Such irregularities, though possible results of chrom. agency, can of course be admitted only when obviously justified by circumstances. For instance: J I , I dEE^ *i) I I III, 11 I I I *a) ,1 Ex. 242.' hi i^ , in , i .i -^ =L,i^MJ: ^ u |C c, ' |C Dh |C F# | ' ^e i *a) ii *4) ^N^^^^^ f^^P^^^ w i 1 1 ^ A- U ^ J- J.- m J i^j-i^tf l 9- i9— F=^^ 1=^ * *i) These modulations are all made according to the fundamental rule (par. 302), — from a tonic chord. — *2) A 7 modulation of six degrees, the most distant that can be made in one move. — *$) The altered II of D. — *4) May just as well be C# major (with e# in alto). b. 2nd: By means of the chrom. inflection, the dominant-discords may evade their legitimate resolu- tion, in their own key, and be led into other keys. The conditions upon which this extraordinary (though very common) modulatory progression is allowed, are: First, that the dom.-discord should, as a rule, be led chromatically into another dom.-discord, — i.e., into a counterpart chord, with similar obligations in another key; and Second, that the obligations of the first chord should be resolved as fully as possible, — i.e., the 7th and 9th should descend, or remain stationary, and the leading-tone ascend, or remain. c. There are, naturally, some exceptions to these rules, which, in common with other peculiar successions, must be placed, roughly, to the account of "chromatics." 154 THE MATERIAL USED IN MUSICAL COMPOSITION. Far. 325. The following table illustrates the progression of the dom.-discords of C major into those of all the other keys, in the order of preference: ±=iib ± W J M l .0 ^tH 4^ *2) *4) o 7 ob 9b 7 7 77 CVoFV CVq FVo CV FVo CV aV *8) «3) *3) 9 aVo 9 7 dVo CVo d^o b-^ *3) *3) i -Sab^ -*H?# g^^^^^ *S) J=44^ *7) 'ik ^ 1 P^ f^TT^r rr^^ff^^^^ i>i ii,i j.-i ^i i.i *j -■r-J» - M r . J . J-r*- 7 of) 7 ^n ^ I I I ^t ^=t :l=t ^''^ CVoEbV eb V, eb AbV AbVo DbV BbVo bb 9b GVo g 9l1 EVo e F#V *i) These chords, excepting *4), can be connected in any inversions. — *2) The seventh is resolved diatonically down- ward. — *3) The dom.-discords, it will be recalled, are the same in major and minor. These first chords may also be c minor a.nd f minor. — *4) These progressions are good only in this arrangement of parts. — *5) Passive resolution of the seventh. — *6) The seventh progresses chromatically upward; this is very rare. — *;) An "enharmonic" change; par. 328. Comparison of these various successions will reveal the fact that the best progressions are those in which (a) the 3rd of the first dom.-jth is lowered, or (i) the root is raised. See Ex. 240c; Ex. 241c. The other chrom. inflections are possible, but all more or less rare. 325. When one dom.-discord is led chromatically into another, in this manner, the second one is generally resolved into its tonic chord. But it is also possible to progress again, chromatically, into a third dom.-chord, and so on. Such continuous chrom. chord-progressions are least confusing when they constitute more or less exact sequences; and, in any case, some thread of connection must be pursued in some part or other, best in soprano or bass; as for instance, the descending progression of the soprano in Ex. 244-1, in regular chrom. succession; and the regularly ascending chrom. succession in No. 2 (bass), No. 3 (soprano). No. 9 (bass); and the bass-sequences in Nos. 4 and 6. For illustration: i^^ m fej=^^ j=i -Z)-r- a ^ ^ E: f=^ 4=?= Ex. 244. *l) J liJ-M I etc. mrr^ r | T i i iil d^ etc 7 C V 7 FV BbV ^ 7 CV 7 7 aV DV etc. 7 eV 7 FV 7 dV Par. 325. CHROMATIC CHORD-PROGRESSIONS. 4. Allegro 155 Beethoven oQ 9l] gQ e\i EI B Vo E Vo A Vo D Vq Andante *4) ^^^ e V A Vo I GV I DVo ell V I „ Chopin BiRAHMS 0/111 8. Allegro ii= W ^r r" etc. i g • -pgL r r " ff " ff^Tr^ '^ 7 B|, I bb I Gb V 9 Vo Vo Vo etc. Wagner 8va^ ^ -(s- -s- fi ^ ^m ^ p=^ Arpegg. 4^ 4iitiS-jti: segue etc. 3 i T g ' g - 1 3 ,' are Very 'rire;'Seilia'r.3'24c. ■■ •■■ m. , . , . ■ ,■,! 156 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 326. 326. Besides the consecutive dom.-7ths and dim.-7ths, other chord-forms may appear in direct succession, through chromatic agency; but strictly according to the principle enunciated in par. 325, — some connecting thread should be pursued, in soprano or bass. a. Probably the most common of these is the chromatic succession of chords of the 6th, in either direction. Comp. par. 156. Chopin I. Allegro Ex. 245/ ^ hri±j * ii^ \ K M x*i) g^ r f r r^^^ X i^ Ab etc. m Verdi 3. Allegro i^ Chopin mr^^ "•^' n^^^^^ ^ < m*; Hm^^m^ i a: ^ Bb 7 II r *i) The notes marked x are grace-notes. — *2) Pfte. sonata in b\>, op. 35, Scherzo, meas. 37, 38; see also the follow- ing II measures. — See Ex. 282, No. 10. b. Successive dom.-7ths, uninverted; c. Successive 4-3 chords; — and so on. Allegretto Chopin Moderate ^^E^iisi ^e Schumann X S ^^ 1^ Ex. 246.' &#l f^frk i f^Vf --^^ f-» it a=? ^m felB3E S ^ i s t *i) Mazurka, op. 30, No. 4, near the end, — 4 measiu-es in succession. The very unusual array of perfect 5ths is jus- tified by general artistic conditions. Grace-notes marked x. 327. The_ above examples illustrate passing modtdations of the most transient kind. In many cases the keys are represented by no more than one single chord. This should not be regarded as a contradiction of the principle enunciated in par. 2676 (which review). It remains a fact, that one isolated chord does not completely define a key, but is dependent upon the chords which precede and (espedally) which follow it, for its absolute identification. This is demonstrated in Ex. 228. But when, as in this example, the adjoining chords are chromatic, and therefore confirmatory neithei: of the middle chord nor of each other, then of course there is no alternative but to define each single chord by conjecture, according to the key which it reasonably suggests. The choice between the two opposite modes is almost always quite optional; Ex. Par. 337. CHROMATIC CHORD-PROGRESSIONS. IS7 243, Note *3). — Finally, when the succession is as rapid as in Ex. 244, No. 8, it is a question whether any definite change of key can be fdt at all, or whether the whole is not a series of "passing chords," — see later. For interesting examples of chromatic succession the student is referred to Bach, Chromatic Fantasie, meas. 33-41; Chopin, Etude op. 10, No. 3, meas. 38-41; Schumann, Novellette op. 21, No. 3, meas. 43-49; Wagner, Overtiu:e to Tannhauser, measures 17-30. FXJNDAMENTAL PRINCIPLES. A chrom. inflection should be made in one part, and should be approached in the corresponding direction, as a rule. The cross-relation is never wrong when the first of the two chromatic tones does not leap. Through the agency of chromatics, any chord-progression becomes possible; remote keys may be reached directly; dom.-discords, and other bodies, may occur in direct succession. The best chrom. inflections in the dom.-7th chord are the lowering of the 3rd, and raising of the root. The dim.-yth chords connect with each other very flexibly. EXERCISE FIFTY. 7 ob A. Make two tables, exhibitmg the progression, ist, irom the I of C major {in any form) into the V or Vn (as dim. 7th) of all other major keys; and 2nd, from the I of a minor ( = VI of C) into the V or Vq of all the other keys. Thus : Table I C-G C-D ^W ^ J- J g^ SE f=r*^ K^ etc. ^^m Table II < a-C a-F ^^ 5tE^ ii f—r-rt ^ j- -i J f r T ' f I r I etc. i B. Basses with chromatic modulations. To be analyzed, as usual. ^ i ^mm^ fe a=ff: ^ ^ t=i=t^ ni Be as 07 67 43 It ' lHR=i S =9^ ll2p IE 3^g=F S b f ^ ^ J I ' ^ -^— ^ ^^ *=3 be e- § as a StI7 b 87 67 t «— 6- II nf a a 6 B 6 Vr^ngJ^Tm yt>r 1 !»* ii ^fc ^3 b7 ?i* " fbS t f f nS''! 15 « 87 J a- as 7 6[|S at *K» 5S 158 THE MATERIAL USED IN MUSICAL COMPOSITION. /•+3 P t* ! * »- ^ f^ r "^f-f-- ^ ^ Par. 328. 88 +7 ^^E| w =!e=* ^ ^^ b7 b5 bs P3 7 ba ba b7 na "^ bt S* D as Be b7e 7- J it ii 3 a as 3 43 a 8 6 5 7 « 5 1^ ,, I. , 4-a +8 a -5 \ D'7 Da it H? 5 u? L§ '''' 93 e as b7 ah a eps be 7 p* b7 b4 a 7 7 s 57 as 6 as bs bs 4^ 4,5 5 48 4 J 54 B3 bs bs a b ^ ^^^ ^ ^^S| m A h>7 A A a if VA ^cr #a h a f « Ba f a4 „B a tl7 , a 84 6 JUS bs 5 a C. Add a large number of Original phrases. 57 ,8 a J xe '^a #6 a pa bs— bs S7 B b3 »« S J J4 X J5 J l]5 31,5 BS- tf3 3— SECTION 4. ENHARMONIC MODULATION. 328. A progression is enharmonic when the next higher or lower letter is so inflected as to agree in sound with the original tone, thus: gb^#; g# — ob; / — e#; cb — b; g—fx and obb; etc. 329. a. It is usually called the enharmonic "exchange" or "change", upon the universal assumption that it is not a "progression"; and this assumption is practically justified by the location of the tones on the pianoforte, where both enhar- monic tones are produced with the same white or black key, and therefore are made to correspond exactly in pitch. Still, there is an actual difference, and, consequently, it is theoretically proper to call it a progression. b. The actual difference in pitch equals twelve harmonic degrees: (/# = 6 sharps, and gb = 6 flats. Compare par. 3186). Ex. 220 exhibits the actual enharmonic difference, at the keynotes i'ft and Gb; and the dotted Unes there indicate the manner in which it appears at other points in the modulatory circle also. 330. The enh. change involves an inevitable change of key, and therefore it is a modulatory factor. Thus, gS is the leading-tone of A and tends towards the "sharp" keys; but ab, which is practically identical in sound with g#, is the 6th scale-step of c minor and tends towards the "flat" keys. 331. Enharmonic chord-progressions, like the chromatic ones, are distinguished as simple or compound: simple, when the chord undergoes no other change than the enh. inflection; compound, when a diatonic or chromatic progression is made simultaneously with the enh. change. For example: a. Simple b. Compound *i) The enharm. change is divided between tenor and soprano; as it creates no cross-relation, it is allowed. And the progression in bass does not make the chord-progression compound, because it does not alter the soimd of the chord. — *2) Here, on the contrary, there are diatonic progressions in alto and bass which produce an .entirely new chord-effect,. — At '''3) all three species of melodic succession are simultaneously represented: diatonic in bass, chromatic in tenor, and en- harmonic in alto.' See Ex. 243, Note *7). Par. 332. SIMPLE ENHARMONIC CHANGES, WITH THE DIM. 7TH. IS9 332. Compound enharm. chord-progressions are the most common, because the change of letter is so apt to destroy the chord-formation, and render readjustment necessary by other progressions at the same time. Simple Enharmonic Changes, with the Dim. 7TH. 333. The best chord for simple enharm. changes is the chord of the diminished seventh, the prop- erties of which in this particxdar are so remarkable and manifold that it is often called the "enharmonic chord." Its susceptibility of enharm. transformation is owing to its peculiarity of structure, — explained in par. 2396, c, and d. As the chord always sounds the same in every shape (whether the leading-tone appears at the bottom, or not), and as there is, consequently, no distinction whatever in sound between the intervals of the chord, it follows that any (and each) of the four tones of which the chord con- sists, may be regarded as a leading-tone. This, of course, involves a successive change of key, and, consequently, of notation; and this change of notation is "enharmonic." Applied to the dim. seventh on b, the result will be the four minor keys — and also the four major keys; see Ex. 198, Note *3) — of which the tones b, d,f, and aV (or g#) are respectively the leading- tones. Thus: Leading-tone ^ Keys: A, a. Leading-tone 6 Leading-tone <{ Leading-tone / or e# Keys: C, c. Keys: EV, ei>. Keys: Gb, F#,/#. *i) All of these examples in enh. modulation must be studied at the piano. *2) These 4 chords correspond exactly, in sound, to those in Ex. 173 (which see). The modulatory distinctions ob- tained by making each one a separate and independent chord of the seventh upon the separate tones of the original chord, are apparent in the different resolutions. While all 4 chords of Ex. 173 resolve alike into the I of c minor, they each re- solve, here, into a different key, according to their notation. The enh. changes are foimd by comparing the chords with each other. 334. It is evident, then, that wherever the dim. seventh occurs, in any of the above 8 keys (in the notation corre- sponding to its key), it may enharmonically change its notation to that of any other of the 8 keys,, and so effect an enharm. modulation. For illustration: I. c--a 2. f#— A 3. Eb— C 4. G|>— eb ^^^^^m I i (At the piano) *i) etc. •a) =F Ex. 249." etc. (At the piano) *i) etc. Wfvrrrj^ pg cl VoaVo I I I I . I f#I SB Eb I i eb 9b eb e Gbl VoebVo I *i) This is an exchange of No. i and No. 4 of Ex. 248. It is not usual to make the enharm. change thus within one beat. — *2) The change from beat to beat is better, as the ear has more time to apprehend it.— *3) The enharm. change is made from one part to another (sopr. to tenor). — *4) The awkward bass-progression , (cb to dt)) is correct because it is chord-repetition in sound. i6o THE MA TERIAL USED IN MUSICAL COMPOSITION. Par. 335. 336. There are only three chords of the diminished seventh in music which differ in sound ; for, as just seen, those which represent four of the 12 minor keys, though differing in notation, sound exactly alike; in other words, one chord of the dim. seventh answers {in sound, though not in notation) to eight different keys, and therefore three different chords of the dim. seventh cover all 24 keys. There are, of course, 12 of these chords in different notations, and there would be 24 but for the fact that the nota- tion is silnilar in minor and major. The dominant seventh, on the contrary, actually occurs in 12 different sounds, as well as notations, because in no two keys (excepting each opposite mode) is it exactly alike. Besides the dim. seventh on the note 6, treated in Ex. 248, there are two others, then, which lie respectively a half- step above and below the former. Their enharmonic ambiguity is determined in the same manner. Thus: A. I. 2. 3. 40. ^b. i^egu Leading-tone o^ Keys : B,b. la. I i. Ldt. fS Keys : D, d. 2. Ldt. e Keys: F,f. Ldt. ^ or/x Keys: A\,,f^. , 4- i5 &=(^^pi J)^^(S^Ea)EiJE^ ^P^^<^^^^ -&- D\,, " Cf^,4- " -£.«• G,g. B\>,b'v. 336. When the keys are remote (and, in fact, in any case) the enh. chord should be prolonged as far as the rhythm will permit. The longer it is dwelt upon, the less perceptible will the change of key be. Comp. par. 312. For illustra- tion: *i) ^^^hm^ ^^ ^^^^^ Ex. 251. ' Q ? r*2) J^l --^w- r f#Vo- 9b -EbVo r Schubert Beethoven If o u y o *i) The enharm. chord lasts a whole measure. — '2) These enharm. changes correspond to Ex. 248, No. 36 to No. 2. — *3) Ex. 248, No. I to No. 36. — *4) The moment a dim. seventh becomes a complete V^ (by the addition of tiie root) its identity is fixed, and it ceases to be enharmonic. — *s) The enharm. chord extends through 6 measures. — *6) Ex. 2SoA, No. 3 into No. 2. — *i) The effect of this change can be properly understood only by first striking the tonic chord of c minor. — *8) First strike the I of / minor. Pm- 337- OTHER Resolutions of the chord of the dim. seventh i6i EXERCISE FIFTY-ONE. *l)j +s «a) ^ t is Kt hT I AV I ^ ° b! egs bs bs 1,7 bB br b7 .' 57 :^^ ,rs ^s n \> f r « — •- f=^ TT 7 #3 Vfb7b5^~^ Q3 bs « tl TF »f +8 o o ^ ^ i* ^ ^la i fcfe Bt-fc ±: Sr*' X- 6jt6 4J8 ' bs t)3 as 4» t|3 «a *a |a %l t3 is *i) The student may be at a loss to understand why, in several of the above changes of key, the modulation is not made ehromatically, instead of enharmonically, since the former process is simpler than the latter. It will be observed that each dim. seventh (before its enharm. change) is introduced in its legitimate capacity as incompl. dom.-gth of the foregoing key, and this is the only really correct way. If, as at *2), the dim. seventh does not belong to the foregoing key, then, of course, the chromatic introduction is unavoidable. It is the common practice, however, even among classic composers, to ignore the confusing enharm. change, and progress, chromatically, directly into that form of the dim. seventh which is vaUd for the desired key. Thus, in Ex. 249-1, no composer would write the a\> and g§ together on one beat, but would use g# alone. Similarly, in Ex. 249-2, the e# on the 3rd beat would commonly be written /I] at once, as chromatic- alteration of the preceding /tf. The enharm. change in some of these examples only serves to exhibit the actual nature of the modulation; in other examples, however, where the actual nature is most conspicuous (as in Ex. 251), the enharm. change is obligatory. Add Original phrases. Other Resolutions of the Chord of the Dim. Seventh. 337. The modulatory utility of the chord of the dim. seventh is by no means exhausted in. the above connections, because this most ambiguous and flexible of all chords is not limited to its original signification as incomplete dom.-ninth, and to Us original location upon the leading-tone. These are its legitimate signification and location; but, as altered chord, it occurs in several other locations, in both the major and minor modes. These may be found by reference to the tables of altered chords, and are as follows: a. In Ex. 199c, a dim. seventh is found, as altered II of the major mode, with raised 2nd and 4th steps. Its characteristic features are, that it contains the tonic note of its key, and resolves into the I. b. In Ex. 200c, a dim. seventh appears, as altered VI of the major mode, with raised ist and 6th 7 steps. It contains the dominant note of its key, and resolves into the V. c. In Ex. 204a, a dim. seventh is found, as altered IV of the minor mode, with raised 4th and 6th steps. It contains the tonic note of its key, and resolves into the I. d. To these should be added, in order to complete the table, the two original locations of the dim. seventh, as they are ^ven in the foregoing examples. They are found, originally, in Ex. 173 (the legitimate oV° of minor), and in Ex. 197 (the altered qV* of major, with lowered 6th step). They both cont^ the leading-tone of their key, and resolve into the I (or first into the V and then the I). l62 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 338. Applied to the ch. of the dim. seventh upon d^ (for exainple) the results, without enharmonic changes, are as follows: As Vq of minor ,1. »D 7J( 7jtJt As Vq of major As II of major As VI of major 2. 3. 4. As IV of minor ^^^^^P F*l) i) F major, according to 337J; but/ minor may also be taken, in consequence of the V, which resolves into both modes. 338. The principles of enh. transformation explained in par. 333 (which review) apply, self-evidently, to the ch. of the dim. seventh in all of its possible significations. Therefore, the chord at Ex. 252, No. 3 wiU be found not only as II in C major (whose tonic note it contains) but as 11^ in all the four major keys of which its four tones are the tonics, 1%% namely, C,A,F'^ (or Gb), and Z># (or rather, E\>). Similarly, Ex. 252, No. 4 will be found as VI in all the four major keys of which its tones are the dominants (337J). And Ex. 252, No. 5 belongs as IV to the four minor keys whose tonics it embraces (337c). In each of these four keys the dim. seventh has a different notation; i.e., is enharmonically changed, of course; but it retains the same chord-name throughout. 339. Summing up these possibilities, it appears, then, that any one single chord of the dom. seventh will occur, in some notation or other, 9 m the 4 minor keys (as Vq) ) . , , sb (- of which it contains the leading-tones; and 4 major keys (as Vq) ) in the 4 minor keys (as IV) ) 7jtjt ^ of which it contains the tonics; and 4 major keys (as II ) J , 7tJt and in the 4 major keys (as VI) of which it contains the dominants. In this manner it is easy to determine the keys to which the chord will belong, and the notation then simply agrees with the key (and chord) in question. The resolution of each chord is also very simple: excepting the altered VI , they all progress directly into their I. See par. 337a-) in the 20 lieys in which they may occur (par. 339), and add the introductions and progressions as at A. C Basses, to be worked out and analyzed as usual. ^* f=± s ¥^ bi 8l)7 Hens 4 3 « bf bf I »i ^« b3 b7 x b7 be „7 bs 2 t|3 03 #3 b. ^m iE ^ aS! f—w ^ =P=i ^m bs b7 157 f3 « § 8 fe., P5 US b7 1,3 ^ Pj X4 4 as " bs 03 3 b7 3 67 S 3 ^m I =^ & ±2: S M ^^^^ it s bs bs bs b* Bs — C V b IV I3 7« 7X#n> blVBII I3 7 Bb V 7S a IV Schubert Mendelssohn Beethoven i66 THE MATERIAL USED IN MUSICAL COMPOSITION. Compound enharmonic changes. 345. The distinction between simple and compound enharm. progressions is explained in pars. 331, 332 (which re- view). Compound changes are the most intelligible, because the diatonic or chrom. progressions which in that case ac- company the enharm. change, assist the ear in following the modulation. This is impossible in simple enharm. chord- progressions, because there is no change in sound, and hence the intention of modulating is not perceptible until it has actually taken place. The following example contains only a few illustrations of the almost endless variety of compound enharm. chord-progressions: -*i)- i ^f^H4^fl^^lH *2) ^ij^ ^Ui f— v^ ^ — ^ D I G bla Eb eb A *8) m j»M •^ Fi Ei, E V e Adaeio A A[,_ Wagner ^ ^^^TtrT^ Elt^si f=«f f- *4) *6) *6) Cad. *7) J. ^ ji ^d fe^l. ^^¥¥=1^ ^m if- -b_^ ^ -A i i a= ^ C Gb Cad. *7) -/T\- ^^} £# AI„ abV F# Chopin Andante Chopin ^XTftJUtHt^^^i-^; I J i i # i la 1^ s^'bt'i ^ *8) «9) fe ^^^i^ff^ r^ f ^ 7 E V EI Gb , Ab Vol f V GbV EbV A V d V c IV e V f V Par. 346. PIVOTAL MODULATIONS. 167 i TOP^^g=rl g r FVo a^ >^ Schubert i? i rTi> a"=~ i^ aV Abl *i) These two measures, in both cases, are actually aUke. The enharm. change in one of the measures is due merely to the transition from sharps to flats. — *2) The tonic, in bass, becomes a leading-tone. Comp. Ex. 235, Note *3). — *3) This chord may be not only in A major, but also in D, d, £# and E, according to the manner of its introduction. This principle, which greatly multiphes the modulatory possibilities, applies to some extent to every chord, — especially to the concords. Comp. the first measure of Ex. 240, in which the various meanings of the chords are given. — *4) This chord may progress into the keys of e, £, C, a and F (Ex. 252). — *s) Ex. 243, last measiure. — *6) The opposite mode, with change of notation. — •7) Cadence-modulations. — *8) First strike the tonic chord of / minor. — *9) This example closely resembles Ex. 243. — *io) Comp. Ex. 244, Note *4). EXERCISE FIFTY-THREE. S .58 .e Qe D6 6 |]6t]5 be «| 4 P4 * B i bs 3 b B tfa b7 n bbs b fe ^^ '\ \ ^ Q^ ill Add a large number of short Original phrases. b7 bs R bi 8b7 a as— 1,5 n i Pivotal Modulations. 346. The most prolific of all modulatory processes is, finally, that which is made through some tone that is common to the two keys. At any such point of contact, — at any tone of the first key which belongs to the next key in any conceivable harmonic capacity, -^ the first key may swing over into the next, as on a pivot. Hence the term "pivotal" modulations. This process has been observed in some of the foregoing examples, but the pivotal change of key was there the result of- some other modulatory purpose, rather than the direct incentive to the act. 347. A very common group of these pivotal changes is based upon some coincidence with the mediant (3rd scale-step) of either key. Thus, the tonic of a key may be transformed into a mediant — with consequent change of key; or the mediant may become a tonic. 1 68 THE MATERIAL USED IN MUSICAL COMPOSITION. Between major and minor keys the relation is close; between major keys it is remote. For example: tonic — med. Par. 348. Next-related med. — tonic Remotely related tonic — med. med. — tonic Ex. 258. ^ and reversed. C a F C A|j C E 348. As both the tonic and the mediant belong to tonic chords, it is necessary to close the first key on its I (very 7 7 rarely on the VI), and progress directly into the I {IV, or II) of the next key. The connecting tone usually remains in the same part. I. tonic — ^med. med. — tonic tonic — med. med. — tonic Ex. 259. c I 2. Allegro Al,I s- C I -Tg- EI ©- ='S~ -ig- IZ7- EI C IV Abl Si — 7b CII -ggr- Sr- ScHUBERT 3. Lento Chopin m fe ^ m 3^ Y> I - 1 X -^ 'M t^ ton. — med. #: ^ m % -(=Z-- med. r I ^i ■^ffS S -tS>-^ ■iS'-i Db = Cs A IV B1,I BbVI sr DI These pivotal modulations, though possible at any point in a phrase, like No. 3, above, are much more likely to occiu: at cadences or "joints." This is illustrated in Ex. 235-1; the tonic V9, at the cadence, becomes the mediant of Gb. Also Ex. 235-2, tonic o becomes mediant a. Ex. 236-5 may also be explained as pivotal mediant modulations, in the course of a phrase: the mediant g in £1> becomes tonic in g minor; the mediant of g minor becomes the tonic of 5I>; the mediant of the latter becomes the tonic of i. 349. Other significant coincidences are: a. The dominant transformed into a mediant; h. The tonic transformed into a leading-tone; c. The dominant transformed into a leading-tone. Chopin, op. 61 dom. — med. dom. — med. med. — dom. tonic — Idg.-tone dom. — Idg.-tone Adagio |^^ ^^ and w Ex. 260. =^ ^ -(9- 'S'sr- Eb -s>- C ■iSt- A C Ab eb Gb Db Fb(E) Par 350. PIVOTAL MODULATIONS. 169 These are illustrated in Ex. 235-4; the mediant a, at the cadence, becomes the dominant of i minor. Also Ex. 235-5; the dominant c becomes the mediant of AV major. In Ex. 235-3, , Vv, Ai>, a, G, g, F, f, E\>, e, I>|>, d\> (or, as S#, in c# minor). Besides these, it may be the lowered 6th scale- step (in E major), the lowered 7th step (in d, D), the lowered 2nd step (in b minor); as BS, it may be the raised tonic (in B major), the raised and step (in A), the raised 4th step (in 2?# and/#), the raised 5th step (in E), the raised 6th step (in D, and d# minor). This one tone C (or S#) may, then, be used as modulatory medium between any of these 26 keys, in either direction. And the same applies, of coiuse, to every tone in music. 351. There is only one important limitation to this sweeping principle, and that is that it is far more natural to transform an inactive tone into an active one, than the reverse; best to change a tone as tonic, 3rd or sth step, into a 4th, 6th, 7th step, or any other active tone. Hence, par. 349J and c are very common, but the reverse very rare. For example: step J 2# an Ex. 261. PC =g= m l__^gj^i_b^ ^±g%=tt^ C ZiS>- El, zr tf- e G T>\, Bl, E g bb e Additional illustrations: i Adagii *i) i Beethoven bi- t^ Chopin *2) Wagner Largo BE i S>4-» rrtr fii =i§-^ P3| *3) S^ ^^ w Ex. 262. W fafed^^ i gi^ S ' 7 b.V Bb A cl 7« IV i Mo^erato ^^ ^ ^ Debussy ^ *4) m ?^P^« X X j» *s) X r^r I ^ etc. n 1^^^ ^5^ ^==^ ^Sz w X y -» »- Gbl 7 G V J 70 THE MATERIAL USED IN MUSICAL COMPOSITION. Lento .ento *7) X ^ IM^ Par. 351. G. Faure ±t =^ I ^ ^3 =^ ■•-^ 9ffl common tone ^ *8) ^-^ iifl„;i^ ^;^ijt rf| , ESE bl o C Vo- 9 c V CI Jos. SUK "i) The sth step, g, becomes a 6th step of 6 minor; an inactive tone transformed into an active one. Par. 351. — *2) The pivotal tone d is the 3rd step, becoming a 4th step. — *$) The common tones are /# and e\> = ii#. — *4) From "Irfz plus que lente," given here slightly simplified. — *s) The notes marked x are embelUshments. — *6) The pivotal tone is gb = fi/l, — ist step, then 6th, then 7th step. — *7) The lowered 7th step. — *8) The common tone is At|, through- out; first as inactive tonic of b, then as active leading-tone of C. Observe that the second measure is all chord-repetition; also the change of mode from major to minor and back. — *g) This sth step (/#) becomes a leading-tone. — *io) The miusual substitution of g minor (for the expiected major) is due to the coincidence of b\> and o#, — a mediant becoming a leading-tone (at the beginning of the next measure). These illustrations might be multiplied indefinitely. It is left to the student, who, if he will observe what he sees in the literature he uses, can be at no loss for confirmation of this principle, — and all the others, — of modulation. EXERCISE ErFTY-FOUR. A. Work out these basses, and mark every pivotal tone. ^i St J-g- ip= 6 7 6 - b7 ,6 F e ^ jcde ^ ^ bt bo _ 6 .7 4 *5 Qs a B -a ^^^ s rrr^T-^ r ' r r ^ * ,70 95- 0? ans ^1 83 J. 7 Par. 352. if=^ MELODIES WITH INDICATED MODULATIONS. +« 8 171 -^tir' \-\^ ip=» ij r *i B4 a #s bs Da US Q B7 4 7 t! B. A large number of brief Original phrases. SECTION 5. THE HARMONIZING OF MELODIES, WITH MODULATIONS. 352. a. Harmonizing a melody with modulations is, as jar as each separate key extends, precisely the same process as before. Review Ex. 178. h. The only new thing that presents itself here, is to determine what changes of key are necessary, dnd where the changes take place. From the point where a key begins, until it is exchanged for an- other, the melody-notes are harmonized in the usual manner, according to the scale-steps of that key. 353. The changes of key, or the points where modulations are to occur in the harmony, may be defined: ist, by accidentals in the melody itself; 2nd, by the general construction of the melody, which afiEords more or less distinct evidence of inten- tional modulations; and 3rd, by option, at any point in the phrase where the melody will admit of a change of key. 1ST. Melodies with Indicated Modulations. 354. Accidentals in the course of a melody indicate either altered chords, or changes of key. (The former may be set aside for the present.) This is exhibited in the following example, in which the keys are indicated below the notes at the points where they m *i) *a) »3) ii^=d^^i=iJ: *a) Ex. 263.^^5 ^ ^^^ D *i) a minor, — not major. The keys should maintain near relationship, as much as possible. — *2) These ap- parently superfluous accidentals are necessary, as contradiction of the preceding key. — *3) D major, not minor. Applying the fundamental rule of modulation (par. 302, pars. 298, 300) to this melody, the result is: D- ^^ j^ nrjtt^f^M^ I ^ ^ ^ rf"=frtf r^r Ex. 264- gag? U-i-^U^ J 1 J: U= h i i i 1 ^ i JV i r ' [ ' r r [ ' r-rV GVIaV IGV I eVn I ^ ±±: 7 I D V b Vn IGV 172 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 355- 355. a. In the above example, the accidentals proved to be the leading-tones of the required keys, with the single exception of ct| in the 6th measure, which merely served to indicate that the preceding key had been cancelled. Such "negative'' modulations as the latter generally leave a choice between the two relative keys. For instance, the ctj in the above example indicates that the two-sharp key (b minor) has been reduced to a one-sharp key; but there is nothing in the del, °or in the tones which immediately follow, to define which of the one-sharp keys (G or e) is intended. Consequently, either G maj. or e min. may be taken. Thus: Ex. 265. w=f^^^i^^ 9 1 i f -w b. This choice between the two relative keys (those with the same signature) is possible at other points also, and usually depends only upon the succeeding melody-notes. For example, the/# in the 2nd measure of Ex. 264 might also be regarded as an indication of e minor; but the two slurred notes which follow {g-d) prove that G major is intended. The same applies to c# in the 4th measure, which might also be 6 minor, but for the following d-a. Compare par. 242, rule I. — This point is illustrated in the following melody: *3) »6) *l) **) »5) *a) Ex. 266. i 2 s \ m =s i F d ^^ iS, n. n * & ^i^^ptL I G c (a) F (d) C (a) *i) a minor is not possible, on account of the next measure. — *2) d minor is impossible, because of the clj which is slurred with the b\>. — *3) Must be C major, on account of the cadence. — For these reasons it is best to take d minor at *4), and a minor at *s); at *6) G major, because of the two preceding minor keys. Thus: Oj-j^CuA&J S=^ pi r ' f ir r f 'r rr ' f f f 7> ^^ Ex. 267. 3^ j=ff J I J J I J -^^ I ^^ I i ^m dV„ 9 aVo 7 G V C V 7 F V 7 C V 2ND. Melodies with Intimated Modulations. 366. There are certain features in the construction of a melody which a£ford almost, if not quite, as unmistakable signs of a necessary change of key, as accidentals do. The strongest intimations of this kind are found, ist, at the cadences; and 2nd, in the arrangement and treatment of certain scale-steps, — especially the leading-tone. In the first of the following melodies there are no accidentals to indicate positively that the original key (C) is any- where abandoned. But it is nevertheless probable that the semi-cadence is made in G, and certain that the perfect cadence is in a minor. And it is also certain that the 3rd measiu-e does not continue in G major, because the arrangement of tones does not conform to that key; especially the /|J (3rd beat) which indicates either a return to the original key (C), or the point of transition into the ultimate a minor. Par. 356. MELODIES WITH INTIMATED MODULATIONS. 173 Ex. 268. ^=^^^ semi-cad. ^^^ i (C)- Ex. 26s also illustrates this principle: the modulation from e minor back to G major is only intimated by the cadence note. If the last note were e instead of g, as it might easily be, it would continue e minor to the end. In the following melody: i ^ 4 tt*- isSii I the key of C maj. evidently ceases at the end of the first measure, because the 6 in the next measure cannot he the leading- tone of C, and progress as it does, downward to e. It is therefore obvious that a minor (indicated by g#) extends back to this b. — The final cadence must be made in C, of course. How far "back" such intimated modulations reach, or, in other words, at exactly what beat the new key will 1 depends upon circumstances, and will generally be determined by experiment. Comp. par. 242, rule 4. The above melodies will then be harmonized about as follows: C G C a C a C Ex. 269. ' 4 Jli -J- J i i i^ P^ ^ffmr^'=^^^^ ^ ^^ ^^^^ ^ A I C IV a II C II loV, EXERCISE FIFTY-FIVE. Melodies with indicated and intimated modulations. a. [ pi,\i ^-jxu=^^i^i\,i 'r \ ^=mf^fr^ h^^^fn^-fr=^^ ^#r^,^J4 gQ:^3EEa ^iMj^^^ 13 »2) *l) *3) *s) m ^=j^ Bb ■^ *7) Bg 1174 fV-ni^ THE MATERIAL USED IN MUSICAL COMPOSITION. I »8) .^ _ nr *• Par. 357. ^^^^^i^ ^ n ,. *9) , pi cad. I I I I *19) ^ .-> _ ■^^^ i ii *ii) m=i ^^ ^g _ *13) *13) »^ ^%^^j£ pi Sz n^ 5^ ^^ ^i^^44j 5^ =i=^ Z. »14:) *16) irrjc *ia) -J— vl I 1 - X ^ ^ ^ *i) Ex. 146, Note *2). — *2) d min. follows e inki. directly, despite the lack of relation, because of the sequence. Comp. Ex. 263, Note *i). — *3) £1? or c; the former is better, for variety. — *4) ^41? or /. — *s) g min. begins at this (2nd) beat, because o cannot, in this case, be harmonized as leading-tone. — *6) Here the \oiD major should be used, as V of g minor. — *i) IIi of Sb. — *8) G or e. — *9) I of ^b, as V of Db. — *io) Lowered 6th step. — *ri) Evident from the following slur, that this is the raised 2nd step of E. — *I2) E or c#. — *I3) Probably /#, on account of the follow- ing slur. — *i4) C major. — *is) a minor begins on this beat, — bass note d. — *i6) Best to use A major here, as V of the coming d. 3ED. Melodies with Optional Modulations. 357. The possibility of modulating, in the harmony to a given melody, is by no means limited to those points at which the melody itself demands a change of key. Transient modulations may be made at almost any accent, and even upon some unaccented beats, by simply intensifying the triads, at those .places, into the keys which they respectively represent. 358. The rule for these optional modulations is as follows: Every major or minor triad *i) which occupies an accented beat, may become a tonic triad (of the corresponding key, of course), provided the preceding melody-note can be harmonized with any dominant chord of that key. *i) This modulatory principle is limited to major and minor triads, these being the only chords which represent major and mmor keys. Four-tone chords, and discords, do not represent keys. The triads are first defined according to the scale-steps of the original key, upon the usual assmnption that each melody-note may be a root, a third, or f^jifth of some chord of the key. This ensures the necessary next-relationship, and decides which keys are represented. For illustration: C major Ex. 270, ^ *l) X :t=t ^ ^ 3)1 1 I II I IV V VI V IV VI II III IV III «3) III VI *l) Par. 359. MELODIES WITH OPTIONAL MODULATIONS. 175 *i) The first and last accents must, of course, be excepted. -^ *2) This melody-note c (the ist step of the scale) may, according to former rules, be harmonized with the I, VI or IV and inversions: in other words, it may be a root, a third, or a fifth. — *3) Here, only two triads are available, those on d and /. The triad on iti, being a diminished chord, does not represent any key. 359. a. These major and minor triads of the original key may, as stated in par. 358, be regarded as representatives of their corresponding maj. and min. keys, upon the conditions mentioned. Thus: *i) Ex. 271, ^ i c G e d F C a e F d G e *i) The triads I, VI and IV of the original key (C major) are the tonic triads of C major, o minor and F major re- spectively. And the keys at the other accents are foxmd in the same way. b. In order to intensify these simple "chords" into the complete impression of "keys," they must be associated with the respective leading-tones, or, more exactly, must be preceded by the necessary modulatory (dominant) chord. // the preceding melody-tone will admit of this, the key In question is possible; otherwise not. Applying this test to the above melody, the result will be: *l) *2) Ex. 272. 'M J u *3 ^ ^E -1^ c I C V— I 7 a V— I 8 FVo— I GV— I 7 e V— I 7 d V — I FY — I CV— I FV - 9 7 a Vo— (d V?) I GV — I — I CV- 9 eV, (e V^) (a V^) "i) e minor is not possible, because it has no /1|. And a minor is a little doubtful on accoimt of the gl] which follows; from which it appears that, as usual, some consideration must be taken of the following tone, also. — ■ *2) In d minor, the g 7 in soprano would be an ascending seventh (of the V), and is therefore doubtful. But see par. 218a. — a minor is impos- sible, as it has no gl(. — *3) e minor is doubtful, because of the dlf^ in the next measure. c. This melody may be harmonized, then, ist, in C major throughout; or, 2nd, any one of the above keys may be in- troduced as single passing modulation; or, 3rd, several or all of them may be utilized, in a great variety of successions. The following modulatory lines are possible: i. C major throughout, -.i. C — C — G — C — C — F — C ; 3. C — a — e — d—C—C~G—C; 4. C—a—G—F—a—C ; 5. C—F—C—d—a—C—G—C; 6. C—F—G—C—C—F—G—C; and so forth. For example, No. 3: Ex. 273. ^p frffl^tmq^^ iiE i^ j:iti.jj J J.J i-y-^:^ J j- r f f r i ^FHpfr^ r rr ^ p 360. Melodies in triple rhythm often admit of such optional modulations at unaccented beats also. The following period, which may be harmonized in e minor throughout (as there are no positive contradictions of the original key any- where in its course), evinces a strong inclination towards D major at the semi-cadence, and admits of other passing modu- lations, as follows: 176 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 360. Ex. 274. i »l) *2) *3) *4) a: ^ G e ■ D G- e ■ (a-) e *i) The indications of a minor are so strong through this whole measure (the first two tones representing its V, and the last tone its I), that the unaccented (3rd) beat suffices for the mod. — *2) The slurred 2nd beat suggests G major, although unaccented. — *3) Could not very well be the relative, h minor. — *4) There are the same indications of a minor here, as at Note *i); but there is hardly time to make the mod., except by taking the £ major I on the first beat (as V oi a, minor). The result is: % ^^^ ^^ WB ^ Ex. 275. I r ^^-f^.r- i rr^ an ^ r..) j- i W^ r77> r r^ iS-VoaV elo GV aV GV DI, 9 eVn 7 CV H 'r) Ex. 274, Note "4). The only difference between E major and minor is the g# in bass, which is preferable to gl], on account of the following a minor. Compare par. 313. — *2) This melody may, of course, as already stated, also be harmonized in e minor throughout, without the optional passing modulations. EXERCISE FIFTY-SIX. A. Harmonize Ex. 272 (perhaps at the piano, — the hass alone in the left hand) in the 6 ways shown in par. 3S9C (ex- cepting No. 3, which is given in Ex. 273). — And also Ex. 274, first in e minor throughout, and afterwards with G major in the sth measure and a minor in the 6th measure. B. Harmonize the following melodies; each in ai least two ways. a. *1) *2) *3) «4) *5) ^^u^i4^^^n:riOJiJ_J^i jJ ^ S=3 *a) * S *7) »7) «8) C. /TV «8) *B) *10) *11) »1S) ^gS ^^■ Tirr^ m ^ '=f=i- s ttittw U I '■j.^ i j ^Jf.rpJ^j]j7Jy-r^^4ftfr ll *''^ J ^-^tn^r^ttm m w «ia) «17) *18) /. -^ — r Par. 360. i Itefe MELODIES WITH OPTIONAL MODULATIONS. «ie) g. ^ 177 ^ pg^^^^^ s s *=-.zz^ J I * ^^ , *80) «2l) ^^ IK- II i »14) ^ ^^ H ^ HjN ;j i j n ^3 ^a *i) /# minor. — *2) 4 maj. — *3) D ot b. — *4) E major, — not c#. — *5) A maj. probably begins at this beat 7 (as I), because E aids on the preceding beat. It might, also, be the V of b, in view of the following tones. — *6) 51? or g. — *7) C or a at each of these accents; probably C first. — *8) A}> or/. — *9) D]? or b\>. — *io) E\?, — not c. — *ii) / minor, — not A\?. — *i2) Not D\f, xmless the following slur is ignored, — which is possible. — "13) See Ex. 144. — "14) P major. — *i5) Might be F major. — *i6) D maj. I2. — *i7) From this point the melodies also contain indicated modu- lations. — '18) The following slur (6 and d) is so suggestive of G major, that this a# might easily be a raised 2nd step of G. But 6 minor is also possible. — *ig) These slurred notes must be the I2 of F#, therefore the preceding 6i is a raised 4th step. — ""20) This oS may be a raised 4th step. — *2i) A strong intimation of a minor. C. To this exercise may be added some, or all, of the preceding exercises in melody harmonization. See the final Note to Exercise 36. PART IV. THE INHARMONIC (NON-HARMONIC) INTERVALS. 361. a. When 3, 4 or 5 tones are combined in thirds, they mutually accord, and constitute a harmonic body which affects the ear agreeably. Such tone-combinations are called chords, and the separate tones are harmonic intervals, or cAorii-intervals. b. A body of tones, united in intervals which do not conform to this rule for the construction of chords, is called an inhannonic combination, and the tone or tones which disagree with the structure of thirds are Inharmonic intervals. Par. 46c. c. The inharmonic tones are those which lie between, or beside, the chord-intervals, and, con- sequently, do not belong to the chord. For illustration, in the I of C major the tones c~e-g are har- monic, but all the other (intermediate) tones, diatonic and chromatic, are inharmonic, in connection with that chord. Thus: Ex. 276. Har. inh._ har. inh._ har. inh.. iE ^|:^^tK-i»3 ^^=«=tf ':J'-^— t'.:^'^^'^^'- i^l *l) *l) «l) *i) B\> might be a seventh, and d\> or dA a ninth of this chord, as dominant chord of F maj. or minor. But they are inharmonic in the chord as I of C major. 362. It is evident that the quality "inharmonic" is merely relative, and depends upon the ruling chord. Therefore, before it can be decided whether a tone is inharmonic or not, the identity of the chord in connection with which it ap- pears, must be established. This may be done by the accompanying parts, or it may be obviously deduced from the co«- nections with the preceding and {chiefly) with the following chords. Thus (the inharmonic notes are marked o): IV, 7 V IV, 3^^ r »3) ^ i^S *3) I *4) O r »5) CI 7 - 4 a 7 C V *i) The duration of the tones in the bass clef, compared with the brevity of the upper tones, sufficiently defines both the harmonic and inharmonic notes. — *2) The peculiar bass figuring, \, shows that the tones are combined in a non- harmonic way. Whether the J is a distortion of |, or | or |, depends chiefly upon the chord which follows. At *2) it is 7 evidently the Ig of C; at *3), the V; and at "4), the IV^. — *s) The d in soprano cannot be a "ninth," because there is no seventh with it. 363. Inharmonic tones are of the utmost importance and value in music, as they constitute practically the entire embellishing equipment of the composer. They animate the simple chords, add melodic significance to the several parts, and are an almost unlimited resource of ingenuity and effectiveness. The manner and extent of their use is so decidedly individual, that the distinctive style of every great writer is characterized chiefly by his treatment of the inharmonic em- bellishments. 178 Par. 364. THE ORGAN-POINT. 179 364. As stated above, every inharmonic tone is, strictly speaking, a neighboring-note. But it is customary to speak of four kinds of inharmonic tones: the organ-point, the suspension, the antici- pation, and the passing-note or neighboring-note, which are distinguished according to the man- ner in which they enter and progress. They may also be divided into three groups, as follows: the organ-point is a heavy Oong) embellishment, the neighboring-note a light (short) embellishment, and the suspension and anticipation result from partial mixture of a chord with those which precede or follow it. SECTION I. THE ORGAN-POINT. 365. a. The organ-point (also called "pedal-point") consists in sustaining a certain scale-tone dur- ing a section of the phrase or period (or throughout), almost or quite irrespective of the harmonic pro- gressions in the other parts. As the latter progress from one chord to another, and perhaps even modulate into other keys, the sustained note must necessarily disagree from time to time with their harmonies, and become inharmonic. b. The organ-point differs materially from the other inharmonic elements, and constitutes therefore a distinct phase of "inharmonics " by itself. As a general principle, inharmonic notes demand resolution more urgently than sevenths^ ninths and other active tones, which, though dissonances, are at least harmonic. The organ-point, on the contrary, is a heavy, impassive tone, which effects its "resolution" by simply remaining imtil the other intervals return to mutual con- sonance. 366. On accoimt of its weight, the organ-point must be a tone of such quality as will endure pro- longation without endangering the harmony, namely: as a rule, either the tonic or the dominant note of the principal key. The prolongation of the tonic or dominant notes as organ-points is justifiable on the grounds that these are naturally the dominating tones of the key, and whether they are merely retained in the mind, as ideal prolongation of those factors from which all the relations of the key must be determined, or are actually held and kept soimding in the ear, is not a matter of great difference. The following is an example of the tonic organ-point in bass: Legato i«-^^J | J j^jg Zj ^J. JJN"h^ J JJ I i , I ^ B C maj. »3) I 1^ » « « « («) * I I v^ o- . * * I 1 I J I I » « ' Ex. 278, *l) C maj. S -f^ P f^P ^^P f^ *s)i Tonic org.-pt.. *i) This, and the following examples, are continuous, — not single measures. — *2) These asterisks indicate the points at which the sustained tonic in bass is inharmonic. — *i) Throughout this meas. the c in bass might be regarded as a harmonic seventh of the chord; but it does not impart that impression. — *4) Here, also, the c in bass appears to be harmonic (fifth of the chord); but its identity as organ-point is already fully established. — *$) The student will obtain a correct impression of the organ-point, at the piano, only by striking, — not holding, — the tone at each beat. i8o THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 367. The following is an example of the dominant organ-point in bass: Andante Wagner Ex. 279. ^^^^^ ^=^ Pi=^ ^^^ Fjf maj.— ^ r =#t ^^^ ^J -^ ^W r I Dom. org.-pt.. HINTS AND DIRECTIONS. 367. The organ-point possibly owes its origin to the "organ,"' upon which it is easily produced by simply holding the corresponding bass-pedal, while the hands continue the harmonic progression on the manuals. Hence the terms "organ-point" or "pedal-point." It is, however, obviously not limited to this, or any other, instrument. The following details must be borne in mind: a. Being a tone that enriches rather than embeUishes the harmony, that aids in holding the chords firmly together, it is essentially fimdamental in character and therefore appears most appropriate in the bass, — i.e., below the other parts. It may, however, appear in an inner part, especially as dupUca- tion of the bass organ-point, and is even possible in soprano, though very rare. In the latter case it is sometimes called an inverted organ-point. b. The organ-point should, as a very general rule, begin and end as harmonic tone (i.e., as legitimate chord-interval). c. As stated in par. 365a, the organ-point is sustained irrespective of the chords in the other parts, but there is natu- rally a limit to this rule. If the sustained tone becomes harshly discordant for several successive beats, or if the modula- tions extend into remote keys, the result is disagreeable. This limit will be most easily determined by the ear. There is least objection when the other parts move smoothly; when the harmonies are simple; and when care is taken to make the organ-point harmonic from time to time. Still, it is a prerogative of the organ-point to conflict sometimes almost fiercely with the other parts, and its persistency seems to be a sufficient justification. The following example, however, is palpably doubtful. (Comp. par. 426.) Ex. 280. ' i^^4r^ ife I ^ ^ etc. I d. The length of organ-points is optional; sometimes they extend through a whole piece, or through large sections; and sometimes, on the contrary, they are quite short. The difference between ordinary (long) organ-points and short ones is very great, and will be considered later. Long organ-points should, according to the law of rhythm, commence on a^^accented beat. Par. 367. THE ORGAN-POINT. 181 e. The organ-point may be hdi, or it may be reiterated, — perhaps in alternation with the upper or lower octave, or with the interposition of another harmonic interval. This will depend largely upon the instrument for which the com- position is written, and upon the desired effect. See Ex. 282, and 285, No. 3. /. It will be well to remember that the tonic note becomes an organ-point in connection with dom- inant (ist Class) chords: and the dominant note in connection with suMominant (or and Class) chords. And both become organ-points during next-related modulations. Thus: C V 7 V Tonic_ u=Mi 4it ^ ^ B V II 8^ I I g. The accompan3dng parts should move as smoothly as possible. The following example illustrates different varieties of the tonic and dominant organ-points. I. Allegro * t§Mr»rfffi ^ 4^ Beethoven I , I -I- I II f=^ * I — :i^ ±3ti3t w Ex. 282.^ -*pi 1% ^UJi ^ ^ etc. J 3*^ J, Ji^ ^i etc. ^X- *1) *2) ^m £££ 2. Presto i^^ ^Zlf =W w ^ »3) 1/ ii ± ■^ -»- -^ £ D maj. ^^cLj Ld d/ai^^^ r r rj -» i \^M' -A I82 i feE^E^ THE MATERIAL USED IN MUSICAL COMPOSITION. Schumann 3. Allegro Schumann 4. Lento * , Par. 367. Chopin * « ^-^ s ^^ 5ft *z«i fir ^ I I r i^ I r « » » » T '-3- -J- 1 J -^ i -^i -J^i -J^. .etc. ^*^g V'^ y ^ * ^ i ^ ^ 5. Moderato »2) «8) Mendelssohn FlVfl^ ^^ S^-fel ^iiE ^ T-* g :S=4 ra-^" :K=±^ ■^r ■f^-^ D major 1^ *5) etc. gi -STl-,*!' ±L *l) 6. Allegro Beethoven i ffl ^* J j iiJ i j p^ -i 1- i =5S r=f f==r r r Bt; maj. etc ii^E rt3: :;=p :1=i: ^ ^^^ r 1 T -^ — =t- ^"^^) ^ 7. Larghetto Schumann i ^ffi p!r^^.^- j =^sE^ i i' i;-,^-j-^i-tj=;ii:i^ ¥=5^^=— s s »- Tonic -^ --I Faisst *7X J^. ■ -.L-O- rr^'M" i Mendelssohn r f u^ Par. 368. 10. Allegretto »io) THE PASTORAL ORGAN-POINT. 183 »io i J lJ jT? ii 3= i i ^^ Schumann H4^^j^y -¥g^^M=^yF^^ E|7 maj. etc. i^fcl te= # te^ I ^ i :^=^ a 7 Eb V II. Allegretto -t fe -#-•■ I -^- Beethoven s ^^^^^^s p GI 7 V ^jr^j^ i jnjnjj^ ^ffgjgj^^ ♦11) *i) Dominant organ-point in bass. — *■£) Tonic organ-point in bass. — *3) This is the manner in which the organ- point in No. I is reproduced later in the composition. — *4) Tonic org.-pt. in bass, and doubled, in alto. — *5) The org.-pt. is transferred from bass to tenor. — *6) The lowered 6th and 2nd steps in 51?; the d'9 is a passing-note, and suggests el? minor. See par. 400c. — *7) The tonic organ-point which occurs at first in bass, is transferred to the tenor by simply inverting the lower parts during the repetition of the phrase. — *8) Doubled org.-pt. in bass and alto. — *9) Doubled org.-pt. in soprano and tenor, and then in soprano and bass. — *io) An unusual example of the org.-pt. in soprano. The harmony is a chromatic succession of 6ths (par. 3260). — *ii) An organ-point, especially when in bass, is often thus »«- terrupted by the intermediate intervals of the broken chord. See Mendelssohn, Songs without Words, No. 12, first 10 measures (/# in bass); No. 31, beginning of 2nd measure, and last s measures; No. 37, last 12 measures (/ in bass). — *i2) E and c# are neighboring-notes. — See also the following general examples: Beethoven, Sonata op. 28, first movement, measures 1-24, d in bass; " " " " first movement, the last 24 measures, d in bass; " " " " second movement, measures 9-15, a in bass; " " " " last movement, measures 1-16, d i(i bass; the same movement, measures 25-34 /row the end, a in bass; and also the last 18 measures, d in bass. — Beethoven, Sonata op. 49, No. I, the last 12 measures, g in bass. — Mendelssohn, Sonata op. 6, first movement, measures 18-26; last mov't, measures 44-25 from the end. — Mendelssohn, Overture "Meeresstille," measures 20-36, d in soprano. The Pastoral Organ-point. 368. Sometimes the tonic and dominant notes are sustained together, as double organ-point, in the interval of a 5th (tonic bdow the dominant), and usually in the lowest parts. This is called the "pastoral" org.-pt., probably because the upper parts are necessarily limited to such simple chords and modulations as can be associated with both sustained tones, without producing too harsh a dissonance. 1 84 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 368. For illustration: I. Grazioso B -4=±j-j rn iji ■jj-?^ 2. Moderate fe^ j^jfe ^e= § r~r~g ' 2j 'c -L:[-:i 'fejf >^ • — ^ I yrj > ^Sffi^^^^ D maj. ^ -p - teiJ: t g 1^ «i) Mendelssohn 3. Alio. mod. 6. Andante ^m # ii Brahms i =#«■ ^^Ti^f'rflr^ 3=3= s«=^= D maj. *a) §4e I d ^ ^£^ -^ I ^ J d - *i) Tonic and dominant sustained together in the lower parts, as pastoral organ-point. — *2) Here the pastoral organ-point is presented by - i s. E I no 7 Vi s. *i) Again separate measures. — *2) S. signifies "suspension." — *3) The first measure is the given chord-progression. In the next measure, the soprano note d of the first chord, — which may become a suspension because it moves step-wise, thus assuring its quality as neighboring-note, — is held over into the second chord, where it becomes the upper neighbor of the harmonic tone c. During the second chord it makes its resolution by progressing to this c, which its prolongation had displaced, or "suspended." — In the third measure there is a suspension in alto, — /, the upper neighbor of e. — In the 4th measure there is a double suspension in soprano and alto; in the sth, in soprano and bass, — the latter a lower neighbor, with upward resolution. From the above it is obvious that the suspension does not alter the original melodic progression in the part or parts involved, but merely changes the rhythmic form. Instead of moving in imiform rh3rthm with the other parts, it limps after them (comp. Ex. 287, measures i and 2), and the perpendic- ular lines are thus bent into an oblique form. Par. S75- THE SUSPENSION. 189 HINTS AND DIRECTIONS. 375. a. Suspensions may occur in any part, but are perhaps most common in the soprano. They are also excellent in either inner part, but somewhat less so in bass. h. The length of a suspension is optional; generally it is just hcdj the value of the chord into which it extends. It may be more, but rarely less than this. Thus: s. Ex. 288. i ffizsis' g - ItP — g-^l 4« p I gl : W ^ a^ & l -zgjg- g -i^^-U^- F^^ (?), The c. The suspension may be tied to Its preparing-tone (as in Ex. 287), or it may be re-struck, as in Ex. 288, No. 3. struck suspension is more emphatic and effective. In organ music it is usually tied. d. It is apparent that the suspension must always appear upon the first {accented) fraction of its beat, — usually upon the accented beat. It may stand on the 2nd beat in triple measure, — Ex. 289^. The resolution is always less accented. e. The suspension is subject to the general rule of neigl)iboring-notes, that it should not appear simultaneously with its resolving-tone (in different parts, of course). But this depends wholly upon the quality of the principal tone involved; if a strong scale-step, the duplication is good; if the leading- tone, 3rd or 6th step, it had best be avoided. It is always wrong in the same register. For example: s. s. s. s. C V I *i) It is palpably incorrect to place the suspension / and its resolving-tone e close together in this way. — *2) Not as bad as the preceding, because the conflicting tones are farther apart. But it is scarcely admissible, as the tone involved is the weak 3rd step, which is not duplicable anyway (comp. par. 59). — *3) The above error is the inconsistency of defer- ring a tone in one part, and neglecting to do so in another. Therefore the simplest remedy for the blunder is, either not to double the tone, or to defer it in both parts, as here, — from above and below, as double suspension. — '4) Good, be- cause the tonic is duplicable under all conditions. — *5) The same. — *6) Good, as the dominant is suspended. Additional illustrations of the suspension: 1. Allegretto S_^ s. S. -FVi s. Beethoven S. S. ^etto 5. s. S. S. '-^ S. S. *2) *a) *2) *a) »3) f T 1 % i j i^ \ lA\ ^ I p j FI Va Ii 7t la BbVa I, F V, X 11, W^ 7 I9 V igo THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 376. 2. Allegro Beethoven 3. Lento S. S. S. . , ,«*| s, ^^ Schumann S. ,. r^S.r*U^p-. %^ ^S. 4- Allegro S. -t- •y-y S=^ rr e min. I etc. S. S. etc. ^ ± ■-^n Emaj.V g^^ fr^=f= ^^^ :IL y- -gz. ^ t r !-'—«- dl ' 7 Eb V„ Bb V^oli El, IVi f Vo I Org.-pt. ^^i s. s. Schubert S. fei^a^ Jl 5. Allegro Mozart S. S. ^ ^W ^ :iK: at*: ^1 -^. -J- ^ s. a i 5 i^azs: ^ P^^ I I ^ CIV I r a IV rr 12 V fl Vo I GVo I *i) Again continuous examples. — *2) At each of these places the rule given in par. 3756 is persistently disregarded. This is correct, because the intention is evident; comp. par. 6sc. Harmonic Suspensions. 376. It is not absolutely necessary that the tone which is prolonged in this manner, from one chord over into the next, should become an inharmonic dissonance. Sometimes the prolonged note agrees with the intervals of the following chord, so that they together assume the appearance, at least, of a harmonic body. When this is the case the prolonged note is called a "harmonic" suspension; and it will nevertheless produce the efect of an ordinary inharm. susp., if the apparent "chord" does not conform to the harmonic progression which is expected or required. For illustration: m Ex. 291. A-l js.h "n^ - n ^'" j^-j-i^i i J ii ■J- ^ e^ ^m w^ ^ 7 Vo se II a Be V Ii IVi as IV I as II VI 98 78 7 V I VIi VI Ij III "■i) The 2nd soprano-note 6 appears to be a fifth of the triad III; but, this chord, besides being unusual in any con- nection, is out of the question here, where the I is required, as resolution of the preceding V . This b must therefore, al- though not inharmonic, be regarded as a suspension; i.e., as a tone which is prolonged beyond the first chord for the sole Par. 377. SUSPENSION-CHORDS. 191 purpose of deferring or suspending the next note, c. — *2) This appears to be a III; but see Ex. 190, Note *i). — *3) Ap- 1 pears to be a VI, and is therefore more plausible than *2); but it sounds more like a double-susp. than like a chord. — *4) *s) Appear to be chords of the 6th. — *6) All 6-4 chords, when used in this connection, partake very largely of the s o nature of suspensions. — *7) Looks like a I, — an impossible "chord." — *8) Looks like a IV; also impossible. — ' *g) On the contrary, these soprano notes (g and c) are not suspensions, because they represent chords of undoubted identity. Suspension-chords. 377. a. Analogously, a whole chord may be prolonged from an unaccented beat to the following accent, in such a manner that the expected (accented) chord is obviously deferred for a beat or so. This causes a violation of the rhythmic principle given in par. 85 (which review). But it must be remembered that this rule refers, strictly, only to the bass tone (par. 166); and, like all other irregularities, it is entirely permissible when so ex- ecuted that the intention is obvious. b. Any misconception of the rhythm, which may result from such an irregular repetition of the bass tone and chord, should be averted by such means as serve to denote, clearly, the location of the accents, — for instance, by strong metric or dynamic accentuations; or by symmetrical recurrence, as in se- quences and the like. For these chord-repetitions the term "suspension-chords" seems appropriate. For example: I. Moderate Mendelssohn n. Allegretto Mendelssohn *3) I *— a S.ch. S.ch. S.ch. — '„ , ^_ai 1 S.ch. Ex. 292. < gs -i-n^ T Ljr i ^ 'j *^ *=!= ft p^ppa *i) ztOrg.-pt. ^ 3. Adagio a _ fa Beethoven sf sf sf sf sf ^^^^^^ *i) A "susp.-chord," repeated from the preceding measure. The correct rhythm is so clearly defined in the preced- ing measure that all danger of misconception disappears. — *i) The stagnating effect of the ties is counteracted by the Strong accentuations in bass. — *3) Here the location of the beats is marked by the dynamic accentuations (y/), and also by the slurs, which indicate which tones together constitute a beat. — See also Ex. 217, No. i; and Ex. 228, No: 8, 192 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 377. Schumann, as a rule, takes but little pains to preserve the fundamental rhjrthm, as the following extracts prove: Schumann idem. op. 99, No. 12 ^^ 1 i Ex. 293. < ^ (etc., during 40 meas.) ias H S. S. ^ etc. See, to the contrary: Schumann, "Bunte Blatter," op. 99, No. 11, Trio; and No. 12, measures 5-7; 9-11; 16; 20, FUNDAMENTAL PRINCIPLES. The suspension is a prepared neighboring-note, — held over from one chord into the next, and re- solved diatonically. Suspensions appear on accented beats, or accented fractions. A suspension should not clash with its resolving-tone in another part, unless the latter is a strong tone which may be doubled in any case. Rhythmic irregularities are corrected by strong accentuations, or by sjmmietrical arrangement. EXERCISE FIFTY-OTNE. A. Basses, to be worked out and analyzed as usual. The student is recommended to tie every susp. to its pre- paring-tone (par. 375^). a. ^, — ^ 7 5 7 ^ ^ Faisst f^aRj r ir r i T- fKR. ' ^ #1) 7- 65 a- 11 7- 4:8 ^^ 3=t :fep= ^ i m^ -^ b7 6— 4- 33 6- 43 bo as = 8- 6— 54 -P •- i^^ I *s) % a- Da- a- 4« 86 ti 6- 45 3- 87 -«-• 65 08 43 78 43 d. Bach =9^ ^ ^- « — p- li P- 1? n IS 78 P43 li I 87 3- ^%^ ^ =1^ 6- 76 b7„- 5 J- e- f78 a6 6P6 jBg |g *66 e ^6 Us 98 6„- 6- 4Q3 4- 6-B7 4t36 Par. 378. IRREGULAR RESOLUTIONS OF THE SUSPENSION. 193 ^95^ i i lii: ^ # * d 7a .08 08- b4 bs bis .34 gW * I *i)s a Us 8- e- S4 gf^^^ ^ ^ 98 08 a- 8- 86 % b7 b7 J? «ii of « ^■?- ^=t I *i) These slurs before the bass figures signify that the first bass note is a susp., and therefore the upper parts are to take, at once, the chord indicated by the foUoiaing figures. — *2) Rhythm f t or fr f ; the latter is the best. B. The following plain chord-progressions are to be modified with suspensions on the first beat of each measure, as follows: (i) in soprano alone; (2) in tenor alone; (3) in alto alone; (4) in any two parts together; (s) in all three upper parts; (6), (7) and (8) in alternating (single) parts, occasionally including the bass. First review Ex. 287, Note *3). — This exercise may be first written out and then played; or it may be done at sight at the piano. M i h^J'li:^tj^=i pi *8) I g^^T^=^rf=T^T- ^r^^T ^^ ^ ^ t^i J .J i m ^ I Efe 4=f= ^ r r -^-r "i) These unequal sths are divested of their disagreeable effect when a susp. is used in any of the parts. — "2) In this measure a susp. may be made at each beat, as ^ note. C. Play the following chord-progressions, at sight, with a variety of suspensions, using every major and minor key: I-V II I- Vj II Vi-I I! V3-I. II I-IV II IV-I II I- Vo II V-VI II. D. A large number of Original phrases. Ieeegulas Resolutions of the Suspension. 378. In order to be strict, the suspension should resolve itself at once, before the harmony can change, — as above. But this strict treatment is by no means obligatory. Very ingenious effects may be obtained by changing the chord at the moment that the suspension resolves. This simply involves a pro- gression in one or more of the other parts, simultaneously with the progression of the suspension into its resolving-tone. 194 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 379. 379. The rules for this "delayed" (or "compound") resolution are as follows: a. The suspension can not evade its resolution, but must progress diatonically into its resolving- tone. Hence, b. The other parts must progress into some chord which contains this resolving-tone. This may be any chord, of the same key, or of another key, — but it is most likely to be merely a new form (or inversion) of the proper chord itself. Thus: 3. (New chord.) *3) I a, (Same chord.) =- ■ J- rh^ C. (New key.) S. -■^^^ 1^^ Ex. 294, *4) (Ex. 287.) I K^R^ S. -3) S. ,/ \| - J--J>j -J---JNJ -J- Ji s. *s) «7) J~J^J J-J . J J.J , J Ui I Ij. V V V Vo S. I VI I II C G i C G e C Ab *i) The bass and alto make a progression at the same time thaft the suspension in soprano makes its resolution, so 7 that the chord changes its inversion. — *2) The bass moves, and changes the concord V into the discord V, during the res. of the S. — In the following meas. it is changed into a dim. 7th. — *3) Here, the arrangement of the chord is simply altered, by exchanging tenor and soprano. — *4) In this meas. the progressions in bass and tenor result in a change of the original chord (I) into its relative (the VI); but the res. of the S. in soprano is not interfered with. — *5) The resolving-tone of the S. in alto becomes a seventh. This is unique, but perfectly justifiable. The parallel fifths in the inner parts are not wrong, because the first one embraces a suspension, and is therefore not harmonic. The rule applies only to fifths which are per- fect and harmonic. — *6) The progressions in tenor and bass change the key; this is allowed if effected smoothly and 7 7 without interfering with the res. of the suspension. This last beat might also be the I of F, the V of F, the V of Sb, the 7 e dim.-7th of 6t> or of e or of g, the V of G, the Vq of £1?, or the I of 4b, as at Note "f). Write out each of these, — and others, if possible. 380. Two other licences may be mentioned in connection with the above "delayed" resolution, namely: a. The prolonged suspension. In this case the suspension is held (precisely like the short organ-point) beyond the beat upon which its resolution is due, so that the other parts move before the susp. is resolved. b. The passive resolution. Here, the suspension is extended, as at a, but the other parts progress in such a manner as to meet the susp. and make it harmonic. It is, in reality, merely a more systematic variety of the short organ-point. N.B. — In all of these cases the suspension (as neighboring-note) must make its proper diatonic resolution. For example: b. (Passive res.) a. (Prolonged S.) J=ipi s. iE r^T=F=r f= f= ^f Ex. 295. *l) S.- S. *2) -J- -J-^J J- i-J^ J ^ ^#^=i: ^i: igi I (aV) f^^ Ii VI 7 V aV CV (I) 7 V Par. 381. IRREGULAR RESOLUTIONS OF THE SUSPENSION. 195 s.- J I J J J |J I J":J^ j I J I J- J-^-^ I J I / ' i ;j — J I ^ I -I — ^ — • — - I I i 1 J . J J J: r^ r^ 7 a V 7b (CII) S. S. *4) C V Schubert -J J i J J 7 (11 S.ch. V) Beethoven i S8= «r=^^^^ ■f- S. - «s) S.ch. ^ J *i i . .A- 1 ^e I 7 V 7 (V) 7 ob CIV GVo 7b# CII 7 V *i) The susp. d in soprano is prolonged past its own beat into the 2nd beat, and resolved on the 3rd beat. — *2) The susp. c in tenor is extended into the 2nd beat, and becomes harmonic at that point (root of the I) by the progression in the soprano. — "3) This is a mode of embellishing the perf. cadence, which is quite common in older classic music. — *4) This c in soprano is really an organ-point; but its preparation and resolution confirm the nature of the suspen- sion. — *s) The bass makes two progressions before the susp.-chord is resolved. 381. a. The resolution of a suspension may, furthermore, be deferred, exactly like that of the domi- nant dissonances (Ex. 1560), by interposing any convenient interval of the resolving-chord between the susp. and its resolving-tone, or its repetition. Ex. 296(1. b. The suspension, being a neighboring-note, is entitled to that licence of the latter which consists in passing over into the other neighbor, before the principal tone follows both. See par. 409, 410. This may be done while the chord remains the same (Ex. 2966); or the other neighbor may have its own chord (Ex. 296c). In either case, the principal (resolving) tone skoidd follow. c. The suspension may be transferred to another part, when the chord remains the same. And double- or triple-suspen- sions may exchange parts. Ex. 2g6 a%^ ^^^ 3 37 ■#-=- 7 07— »,s 5 — a 3- a .8 S58 a 5 7 es 70 3b7 798 in 05 10 a 087 *S) 453 S 23 bS 3 4 43 3r- 5— 6 S ^ Pu. 383. »4) IRREGULAR INTRODUCTION OF THE SUSPENSION. 7 i +38 ■97 it g^ S i i -ez- -^ =t /• Ei5s 754: 57 a s S-> -fS 5 117 J.0 10- ,.65 06 07 59 8 07 5— III s e loi *a) -87 Qas 4« Hewison X ^ ?^:^ 75<- P^ X f±t •^ 43 it 77 2 78 7a lJ'7 sUeos 7 7- b - 6 ^g4 3- i-l ' 6- |6 I - *i) Exerdse sg Note *i). — *2) Rhythm f C/. — *3) D in soprano. — *4) Rhythm in these measures, exception- ally J* J) see Exerdse 24, Note *3). — *s) The groups of figures whidi belong to one single bass note denote exactly the course of the parts, as usual. B. The following period is to be completed, by filling in the and beat of each measure, according to Ex. 2^4; i.e., one or more of the parts must make a progression at the same time that the susp. (on the ist beat) is being resolved diaton- ically downward. i ^=S¥J :P=i I m^^ iE:4 f^^?^ rrr rr ^^ ^t^ T r ^ '^ f= C. Add a number of Original phrases, or periods. Irregular Introduction or the Suspension. 382, Although the suspension is defined as a prepared dissonance, it is not necessary to prepare it in the same register. As neighboring-note, it has a right to enter in any rational manner, and it fully asserts its place among those tones of its class which have the advantage of "preparation," if it has a place anywhere in the preceding chord, — perhaps as possible seventh, or even ninth, understood. This irregular introduction is best in soprano, but admissible in any part. For example: (7) 7 IV V *i) The suspension d in soprano is not "prepared" where it appears, but in the alto, on the preceding beat. The small note in brackets is not to be played, as it is placed there merely to show that the suspension is actually harmonic in the foregoing chord. — *2) The suspension / does not appear in the preceding chord at all; but is understood, as very prob- 198 THE MA TERIAL USED IN MUSICAL COMPOSITION, Par. 383. able seventh. — *3) The suspension is an imderstood ninth. — *4) Understood 7th, entering diatonically (as passing- note). — *s) The suspension i, in tenor, is prepared in the soprano, — *5) An understood 7th of the preceding II. — *7) Understood 7th of the IV. This is somewhat far fetched, but defensible. — *8) Very doubtful, because of the clash on the 3rd step in the outer parts. 383. Sometimes the suspension is properly prepared, in the same part, but intercepted, by some other interval of the same chord. Thus: Lento Mozart ar'j-.j „».„ ^^H .^ jaJa iB^ i r-^^ 17^ -a- ^ ^ i p ^ bVn (7) V Additional illustration: Allegro fei s. filatLi^ A Beethoven ^ I P^E^^^^3 ^ ii Ex. 299. r *i) 'PA- *3) «3) m — ■• — »- — ■■ ^ '^^^ * r DII GI II « 7 VI D V I *i) The resolution of the susp. b (in sopr.) is deferred by the interposition of c. — *2) The susp. g is a possible 7th of the preceding chord (II). — *3) These suspensions are also 7tlis of the foregoing dom. chords. See Mendelssohn, Songs without Words, No. 2, measures 33, 37, 39; No. 4, measures 7, 8, 14, 15; No. 18, measure 4; No. 19, measure s; No. 20, measures 3, 11, 18, 19; No. 26, measures 6, 10, 11. EXERCISE SIXTY-ONE. *l) *l) gg HR^ m b. _3 *i) -*- ? as -•- S~ 3 =iai 5 — 4«3 6- 6 4*3 76 06 3- 6 baa 3- .-%% *3) *3) ^ b*i) 1 S ::?e=Ht: gr a J I II * ^4.^^-1-*— ^^^ 6 6- ••-•-6 6 .5- 98 7(6 b7 -•-• ^^ *3 ^ 2 « i bts 6- i.21 4- S 6 6 6 4 *4) te «6) d.~ ^ & ^ a s 5r=^ — e 7- 43 bI xa 6 es bT *s) 7 a il ia Par. 384. THE HARMONIZING OF MELODIES, WITH SUSPENSIONS. 199 a cb*l) ^ ^ ^ dE ? "Si IS lia "li 78 4- li I; *i) The suspensions may be introduced strictly, as before, or irregularly, as shown in Ex. 297. The choice is left to the student, but preference is to be given to the/ree introduction. — *2) Suspensions strict. — *3) Suspensions all irregu- lar, and chiefly in soprano. — *4) Exercise 59, Note *i). — *s) The chord of the 7th falls on the JJrri beat. — *6) It is not unusual for a phrase to end thus in the pos. of the third. Such perf. cadences are called "Incomplete." — *i) These letters indicate the soprano notes. Add a number of Original phrases or periods. The Harmonizing of Melodies, with Suspensions. 384. The treatment of certain tones of a given melody as suspensions may be obKgatory or optional, according to circvmistances. The rules are as follows: a. Only accented beats (or the accented fractions), and ^ h. Only sudi tones as progress diatonically (as resolutions), may be regarded as suspensions (par. c. K the accented tone which progresses thus is tied to, or repeated from, the preceding tone, there is every reason to suppose it to be a suspension, with regular preparation; but, d. Even when such a tone enters with a skip, it may be a suspension, with irregular introduction (as above). e. The principal guides will be the natural' or necessary order of chords, and the character of the melody. exercise sixty-two. I Melodies, to be harmonized with occasional suspensions in the given soprano, or in any other part. i te^ ^^ ^ *—^ dA ^4-*^ -^HV ^Bi *-+•-# f # «l) m cad. Faisst * i *i) »3) IV *7) »7) A f \fj^ ffrfi^Ui^r-m-^^^n^ *b) S »6) *e) . |j.J-.Ulj-J-|fe II »9) »9) *10) ^ :JJ | J-J|JJJ J * -^ 200 THE MATERIAL USED IN MUSICAL COMPOSITION. P«r. 385. i t. Tj J n /■ s. IS % S ^ ^ ^ts P ^ id: '*— ir 11, 7 s. *is) •-— *\ s ¥ h. *9) ^^a^^^^^ *13) pi i ?=s r f I I'l l P ^^T^ i ps ^f^ s segue lLpju^j i j ^- I *14) s^ ^^ * "i) Each of these tied notes may be a suspension (par. 3840, i, c). In order to become such, it must be ignored (as inharmonic tone) and the following tone must be harmonized in its place, as if the melody were simply thus: a. I ^b. ^ etc., — and P »^ ^-1--^^ etc. — The pupil may. if he chooses, first harmonize the whole melody in this simple form, and introduce the suspensions afterward. — *2) This tone becomes a susp. on the 3rd beat. It is clear that this measure differs from the others only in notation. — *3) This must be again the V, because the preceding leading-tone (c#) leaps downward. — *4) May be a minor, or a mixed chord of d minor. — *s) It does not matter, of course, whether the tone is tied or re-struck, at the accent. — *6) G major. — "■7) Modulations at option. — *8) Melody originally: #^^ etc. — *9) At these (and other) points the suspensions may be irregularly introduced. See par. 384^^, and review par. 382. The 2nd note of the slurred group is harmonized on the ist beat, and the ist note must belong to the foregoing chord, whose choice it therefore deter- mines. The ist two measuresof this (sth) melody were then, originally: ^ I g etc. — *io) b minor I. — *ii) /S min. IV. — "12) Altered II of A major. The I2 follows. — '13) Mixed IV of 6 minor. The I2 follows. — *i4) £1? maj. ot Ab maj. or / minor. Harmonize, also, melody e of Exercise 27; and melody a of Exercise 36. SECTION 3, THE ANTICIPATION. 385. The anticipation is exactly the opposite of the suspension, and consists, as the term implies, in a tone which does not belong (legitimately) to the momentary chord, but to the following one. It is much less common than ihe suspension, because it is diflScult and lumatural to accept a tone before its time. Therefore, it is limited in its uses. It occurs most frequently: ist, at cadences; and 2nd, in sequences and the like, where one anticipation appears to confirm and justify the other. For example: Par. 386. THE ANTICIPATION. ZQi\ »i) Ant. A. A. u j i j -.^!Ld=ii ''j i J J •' h ^ '^ ^ 1 i c . Allegro S I ■ J i J r rr Ex. 287-1. -Ei- ^ Ji «3) *4) 4=A W ^ ^fe -(=- S tJ A. !g- g |-l f=^F=f^ Good c. Anticipations differ from suspensions in their rhythmic location, being always found upon un- accented beats, or weak fractions of beats, whereas suspensions occupy accented beats, or accented fractions (par. 3754^). d. Anticipations are generally re-struck; seldom tied to the anticipated note. Ex. 300, Note *4). e. An anticipation may be introduced from any lower or highet tone. As it pertains exclusively to the tone ^hich. follows, the manner of its introduction is of no consequence. 202 THE MA TERIAL USED IN MUSICAL COMPOSITION. Par. 387. Harmonic Anticipations. 387. Anticipations may be harmonic as well as suspensions. If a tone bears a closer and more legitimate relation to the following chord than to its own, and, especially, if it is comparatively short, it will produce the impression of an ant., whether it is inharmonic or not. And, on the same principle, the whoU folltming chord may be anticipated. Re- view pars. 376, 377. Harmonic anticipations are preferable to inharmonic ones, because they sound better, and disturb the harmonic sense less than the latter. For example: A.(?) .A. rlJ i ^ b. A llegro Mendelssohn ^ ^ ^PE E j J J J ,-J- ii3= -W. Ant. Ant. Ant. ^^^ i # EE ^ T— f- c. Andante Haydn i «rf ii :^ ^H __aiJ^p^ aEi ^ U 1 =1 e P i is -=1 =1- S V Tj l TT~C j'-T 1*^ I «3) A.ch. A. A. *3) P ' ' A.ch. i ts *i) This c might represent the IV, and almost surely would, if it were not so hriej. — *2) The /, as half-beat, is prob- ably a legitimate seventh; but its relation to the following tone gives it the appearance of an anticipation. — *3) Antici- pating-chord. In these two phrases, the 2nd chord of each beat is an ant. of the following beat. 388. When, as here, a chord is repeated over the bar (or accent) in violation of the rule of rhjrthm in par. 85, it may be difficult, or even impossible, to determine accurately whether the first chord is an anticipation of the second one, or the second a prolongation (as suspension) of the first. (The tied notes, in the right hand alone, in Ex. 292, No. 2, might be analyzed in either way.) In cases where there is the least doubt, it does not matter how they are conslrtied. The main (and essential) requirement is, to define the fundamental beats so clearly that no confusion of rhythm can possibly result. This matter is explained in par. 3776, which review. The following is an interesting and simple example of both cases in succession: Par. 389. SYNCOPATION. 203 389. There is no doubt of the following examples being antidpating-chords, prindpally on account of their brevity. They might aptly be termed "rhythmic antidpations," as they do not affect the fundamental harmony in the least. I. Allegro Beethoven. Op. 31, No. i. ( throughout the ist mov' t\ 't) 2. Adagio Beethoven tr 3. Moderato A Wagner -tr "n — y' I L J L J I I ^ Ant. _— - ■ Ant. Ant. u br-ftPl j-j.-r^ttn l^^g GVo # 7 -II- See Ex. 309, Mozart, measure 3. Syncopation. 390. Syncopation is the term applied to that kind of irregular rhythm in which the longer tones, occupy comparatively weaker beats, or, more specifically, fall between the beats. It is simply a violation of the metrical accentuation (see par. 4, and Ex. 5,/, g, h, i,), and results from tying an unaccented beatj or fraction of a beat, to the following accented beat, or fvll heat. It is the most perspicuous example of "oblique rhythm" (par. 374, last clause), because the sjmcopated part or parts; are literally bent forward or backward so as to differ (by a beat, or fraction of a beat) from the other parts, which mark \ the regular rhythm. 391. Whether the sjoicopated notes, when they fall exactly between the beats, are suspensions or antidpations, de- pends of course upon which way they were "bent;" that is, whether they belong to the following or preceding chord. Some- times, as stated in 388, they can be accounted for in either way, and, as a rule, it is quite unnecessary to consider this ^ doubtful question at all. The notes can be produced, and defined, simply as "oblique rhythm," or "s3Ticopation.'n In | the following example the distinction is very plain at a and b: Faiss t 6. ,and Ex. 305. ' S. S. S. S. 6. Ant. Ant. Ant. A. J— 4 i 4J ii J=I=£ I V I I I V I ' 204 THE MA TERIAL USED IN MUSICAL COMPOSITION. Par. 392. Beethoven.»4) ^^ «3)r s.| s.p jj :^ rrr^ i gfe G maj. instead ^ -p- -t- of ' I [ i^ S. stmtle U etc. *i) These syncopated soprano notes, which fall exactly between the beats, belong in each case to the chord which pre- cedes, and therefore become suspensions. — "2) Here the very same notes, owing to an alteration in the location of the chords, are anticipations of the following beat. The direction of the oblique rhythms is indicated by the slanting lines. Such double treatment is possible only when the melody moves diatonically (i.e., stepwise), — as this is necessary in order to resolve the tones when suspensions. — *3) The syncopated notes in the "left hand," being struck after their beat, be- come suspensions. — *4) PianoSonata, op. ii, No. 3, ist movement; see also measures 11, 12 (bass); a\sa from the double- bar, measures 26, 27; 30, 31; 34-37; 58-65- 392. Upon this principle of oblique rhythm in one or more parts of the harmony, very unique effects may be produced. For instance, any two parts of the harmony (the two hands in piano mu- sic and the like; or one voice against the other three; or the. melody against the accompaniment, etc.) may appear successively, instead of simultaneously (Ex. 306 a, b, c). Or the chords may be "broken" ("arpeggiated" — as in Figuration) across two beats or rhythmic groups: i.e., partly in one and partly in the next. For illustration: a. Presto b. MENDELSSOHN.*a) 8ves. c. Prest0 *3) *3) Mendelssohn . P ^tPS «4) Allegro fiflj^ ttoMn e. Presto Schumann. Op. 9 te ^§« ^^f^m i rr\ \. \ etc. *fi) / ^m ±^ f^ i M^rjt^-r-^ i^ Ant. Ant. simile Par. 393. /. Presto *6) ^■Z/Ow-.^ •& i SYNCOPATION. ^i^:^'"'"^"-^ loco 205 Mendelssohn. Op. 29 Ant. Ant. fl5 Ant. i etc. ^W^ ^ 8 8 *i) At a, b and c the harmony is divided between the two hands, which strike alternately, instead of together. This does not affect the harmony at all, but simply the rhythm, which it makes "oblique,'' as indicated by the slanting lines. — *2) Variations serieuses, op. S4, Finale; see also Var. s, 11, 15. — *3) These rests remove the appearance of sjmcopa- tion, but it is clear that they merely take the place of ties. Thus: i =F it etc. See also Mendelssohn, op. 72 No. 6, measure 3-5, 11-13, etc. And Ex. 325, No. 3. — *4) These eighth-notes, with con- nected stems, should occupy a beat together, instead of Isnng across the bars (or beat-lines). The heavier bass tones define the rhythm. — *s) The left hand here, is like the right hand at *4). This example is from Schumann's "Cameval" ("Paganini"). See also his "Fabel," op. 12. — *6) The connected stems define the "broken" chord; the brackets de- fine the half-measure groups. Their disagreement is somewhat similar to *4). — See further: Schumann, Phantasie op. 17, ist movement, measures 95, 96; 105-118 (bass); 2nd movement, measures 22-25 (soprano); 62-65 (bass); also the last 28 measures of the same movement; 3rd movement, measures 27, 28. — Schumann, op. 6, No. 4. N.B. — These oblique rhythms are intelligible and effective only in rapid tempi, where the conflicting 'harmonies are of but short duration. 393. The anticipation sometimes serves merely to prepare a suspension. In such cases the ant. is generally harmonic, but not necessarily so. For example: a. Allegr etto Beetho ven 'a. S. ' A. S. A. S. A. S . b. Andante Schubert Compare Ex. 297, measures i, 2 (parenthesized notes). FUNDAMENTAL PRINCIPLES. The anticipation is a tone, usually inharmonic but possibly harmonic, which belongs to the JoUm- ing chord. Anticipations are always imaccented, and generally very short. Syncopation is a violation of the metric accentuation, and usually represents the location of a tone betveen beats, mstead of upon the beat (or rhythmic group). 206 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 393- EXERCISE SIXTY-THREE. A. The following chord-series (in period-form): LA^ ^ ' I \\ \ I ^-j^ s. i w r r r r r ' r r c ^^ Ex. 308. §fe 4-i-^ r T" *i) f iEi ^^ r i, b to be elaborated with anticipations (either at the piano, at sight, or as written exercise) in the following ways: a. Andante b. Lento ^ d. e. f. g. c. Allegro *a) I r 1*3) I \) *2) etc. — .. '"2^ ♦4) *5) *6) Ek^ # ^ fc^ §!be :^^ T='=r ^. Presto i. j. k. *7) «7) ^^ * t4= fc «7) if *i) It is by no means unusual to add supplementary notes here and there, as in these last two chords, and the student may hereafter practice this Ucence of altering the volume of the harmony (either by additions or by omissions), wherever his taste and judgment suggest. See par. 462. — *2) Ex. 302, measure i. — *3) Ex. 302^. — *4) Ex. 300c. — *s) Ex. 306J. — *6) The 3 upper parts may be written in a group upon the upper staff, as here, wherever desirable. — *i) Ex. yiM. B. Melodies, with anticipations, to be harmonized as usual. a. Andantino b. ^ -^ I„ «3) *l) '-*' «4) «4) THE IRREGULAR ANTICIPATION 207 f. Vivace i ^ ^ m ^3 ^^^^m ^ ?c:r«: =«F *=^ t=t V-J-U- »a) *6) g. Allegro '^^^¥^^^^¥=F^- ^ n X — ^"^ "^v- y .y s. ^ g ^ ^ iE v^ =fC=p: =P± :t^ (III VI) segue I. Allegro 2. Andante (anticipation-chords) A ^ A ^ Bass. iii=a ;J J^fejf^ p » ^ ^ B7 *i) All of these short notes must be harmonized as anticipations; that is, they are simpty ignored altogether, because they do not belong to the beat in which they occur, but to the following one. — *2) D maj. or 6 minor. — *3) Compare Exer- cise 22, melody/. — *4) Par. 393. — *s) Single anticipations, or, better, anticipation-chords at each i6th-note. — *6) These two melodies, consisting of stepwise progressions, are to be harmonized in two ways: (i) so that the syncopated notes will be suspensions (on the accented fraction of the beats); and (2) so that they will be anticipations (on the weak fraction), as shown in Ex. 305, a and b. Melody e will be thus reduced to its primary form: I. For suspensions: 2. For anticipations : ^ i, M^-U ^^=^ etc. etc. *7) The weak fraction of nearly every beat is to be an anticipation, or ant-chord. The three upper parts may be placed together on the upper staff, as at Ex. 3o8g, Note *6). C. A nimiber of Original phrases and periods. The Irregulak Anxicipation. 394. The irregular anticipation is the counterpart of the irregular suspension, and is so called because it progresses with a skip, instead of remaining upon the note which it anticipates. The an- ticipated note appears in some other part, or it is understood, as possible seventh (ninth?) of the next chord. Comp. par. 382. 208 THE MATERIAL USED IN MUSICAL COMPOSITION. P«r. 394. a. This licence is most effective in the soprano. 6. As a rule, the irregular anticipation skips downward. For example Ant. b. Andante . ^ Ant, Ant. Mozart a. Ant. Ant. ___ L Ex. 309. *l) \\ ^=4 i if -^ .^ Ant. ijjii -F— *• Ant. Ant. a 9^ ?=^ ia e V i f. Allegro ^^^ *==: Schumann A. Mendelssohn ^ Mendelssohn A. ch. ^m ii ^^ 3^^S£ « i;i ^ fcfl^ 7 V asss Pt ai fr=4^ F IV V 7 aV _/\ Exceptional it=FF^-M Schubert ■iS- *2) r s^ gf=^ I i i aV- 1 Ant. I *3) §3 ^ t^^ S^= 1^1 Ant. "i) This mode of txeating the antidpation, although a Ucence, is preferable to the strict treatment. In almost all of the above illustrations, the irreg. antidpation (in soprano) reappears in the next diord in the tenor. — *2) The skip upward- from the irreg. ant. is exceptional. — *3) The irreg. ant. in hass is very unusual and difl&cult to justify. EXERCISE SrXTY-FOim. Melodies, with irregular antidpations. a. Molto mod. A. A. A. *2) i fe^^^ ^ rrv^.i.-. ,. r - ^ r'^tj i r'Cj^ i ^ n ^ r^tJ- « *l) ^. Allegretto f Vo bbVo <>. Alie^etto '-' *3) ■■" :;: ^ - f d =E=* o Vo P^> IV I, — ^^ Par. 395. c. Moderato A. THE NEIGHBORING-NOTES. A. A. A. 209 m A. E^ d. Andante ^^ ^ l>* ■ 1^ I # # »4) g yr^jj i cfg S E^^g^ *4) V i * A. A ^ 9'^ ! Lj. ^ S^ ^^ fJ^ l i-J^ # -' X + + + ^^ m ± =^=^ *3) ?? *3) I I ii I ii I ^ + + + c. Andante i ^. a Schubert ^ I ^ ^ TT ^ * tr— y il *5) fc i. I TJ ■*- f *i) The combination of a chord-tone and its chromatic inflection (as passing- or neighboring-note) is possible, as here. But it is just as well to avoid it, if convenient. — *2) Descending chromatic pass.-note. — *3) In such ornamenting groups as these, the larger internals come first in the group, as a rule, — as in the preceding group. — ""4) The notation of chromatic tones must conform to the principles of next-relationship (to the prevailing key), and will be found to coincide exactly with the altered steps. Therefore, not all ascending tones are written with sharps, nor all descending ones with flats. In this case/# is the only correct notation, irrespective of direction; g\> would be absolutely wrong, as it is too foreign to the 7 key (G or O- — *S) This might be a chord, — the IV of £# minor. Embellished Melody, and Running Parts. 402. Neighboring- and passing-notes may be employed in embellishing any single part, in uniform rhythm, — as a so-called running part. The following melody, and its embellishments, appears in op. 74 of Beethoven: Andante Ex. 316. Par. 403. EMBELLISHED MELODY, AND RUNNING PARTS. 213 ^^^^"^^ta^h f -" cij'N^'^- "f^^ir"rp' S^^fiS p P p * * ^ c. All^i^o s. i H * r i=»= ^ b p I J J J j=^ N^ P=P= :5=P= ^ i=P= Accompanied by the bass, in 3rds. ^ ^P^ J: S. S. i4 .i-^i rr^r f li i ||.u^^ Also Beethoven, Sonata op. .i. No. 2, last movement; compare measure 3 with measure 13 from the end. 403. Ampler forms of embellishment (i.e., larger groups of notes, and in more rapid rhythm) usimlly develop out of the simplest original figures, by adding neighb.-notes. Thus: Ex. i SBSEES m^-n -^— =- ^ 3'"^-re=t =L_£: m --^f^r=^ i=p: S^ ^H FUNDAMENTAL PRINCIPLES. One, or more, of the four adjoining tones of any harmonic interval may be used in connection with the latter, as simple neighboring-note, or as passing-note. The neighboring-note enters from, and returns to, its principal tone. The passing-nott, or notes, coimects two different principal tones, diatonically, — more rarely chromatically. The upper neighbors, and all passing-notes, agree with the momentary scale. The lower neighbor is usually a half-step, excepting at the leading-tone. EXERCISE SDCTY-FIVE. A. The following melodies are to be embellished alone, in a uniform rhythm of 2, 3 and 4 notes to a beat, successively (see models, and rules below) : 2. ^ ^ I I f, I J ^ | J ^ J | J i J | .J. M Jff t^^^^ 4 — #■ PE III 7 V I Vi Ii IV III la V I 214 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 403. m iE^ ^ 7 bV I 7 V * Models (No. i) (Rule 3) ^Tf^^frf ta ^ ^ 1 + X X 2 notes to a beat I + + 3 notes # M ^=± ^TT^ri"^^^"^'-^ (Rule 2) "o + X o " 4 notes Rules: (i) The running rhythm must not be changed imtil the cadence-note is reached. The latter is not embellished. (2) The given melody may, occasionally, be modified by adding other principal tones of the momentary chord; es- pecially an intermediate interval, when the skip is large. (3) As a rule, the original location of the given melody-tones in the measure should be retained. But this is not al- wajrs possible, and it is effective to place an accented passing-note before the given tone, — as in the above model, first measure, beats 2 and 3; 4th measure, beats 2 and 3. See also Ex. 314&. (4) The embellished part must run smoothly; repeated tones, in quick succession, should be avoided, (s) Play the given chords with the left hand. Review pars. 399, 401. B. The following period is to be supplied, first, with a running bass; then with a running alto; then with alternating bass and tenor, or alto and tenor (in successive measures, — or whenever convenient). In each case in a continuous rhythm of first three, and then four, notes to each beat. See models, and rules below. ^i=;=t cad. Models : ^ ^ ^^m ^ ^ Wf^ ^^ =^^ T r Rule I Rule I i^ ^t?7nrr^'- r rr ! frr'rrrirJ a ^r~rp- r i a 6 2 6 . 4 D5 a B B ^6 a 6 a,6 s bs Rules: (i) The adopted rhythm must not be interrupted at the semi-cadence; and even at the perfect cadence it should continue for one beat past the final note in soprano. (2) The inner parts may be first filled in, and then embellished (hke the given bass); or the running rhythm may it- self determine the principal tones, — at least partially. The given bass, and the chords, may be changed, if necessary. (3) The compass of the parts, and their distance apart, is optional. (4) The embellishing part must nm smoothly (rule 4, above). Sequences, and general uniformity of figures, are ex- tremely important in running parts. See also: Mendelssohn, op. 54, Var. I; op. 82, Var. n. — Beethoven, op. 120, Var. 25. — Cramer, Etudes 41, 80, 16, 32 (original complete edition). C. Construct a few Original phrases, with running parts. Par. 404. EMBELLISHED HARMONY. 215 Embellished Harmony. 404. Instead of limiting the neighboring- and passing-notes to the embellishment of one sin^e part, as above, they may be employed in aU of the parts, in alternation, for the purpose of filling. out the spaces between the harmonic intervals. This makes the harmonic impression smoother, creates a more ani- mated rhythmic effect, and adds greatly to the melodic significance of the parts. 405. Hints and directions. a. All embellishing notes progress stepwise, — usually diatonically. b. Unaccented passing-notes are almost everjrwhere good. Accented ones are apt to clash too harshly with the other parts; but they are often very effective, and should not be avoided. A test by ear is all that is required. c. When embellishing tones occiu: simultaneously in two different parts (as they may), they should generally harmonize with each other. For this reason they are most likely to run in parallel jrds or 6ths (comp. par. 66) ; or, if they move in opposite directions, they should meet (cross) on the same tone. Inharmonic tones in three or four parts at once (which is possible, but rare) should represent passing-chords, or ndgh- horing-chords. For example: I. Lento ^m iSizpS ir S. Bach *^sc ^^^^f •iE Org.-pt, 8ves. 4. Allegro *i) i and and Beethoven ^^ ^B5^ 2l6 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 405. 5. Allegro *i) In such rapid tempo these are simply neighb.- and passing-chords. — "2) These groups of neighb.-notes do not harmonize with each other as chords, but their identity is clear, and they sound effective. With neighb.-notes, almost any combination is admissible, — as will be seen. — *3) The "neighbors" are chromatically opposed to each other. — *4) Fourfold neighbors. See Ex. 217, No. s, Notes *i) *2). See also: Mendelssohn, op. 83, Var. II. — Bach, "Well- tempered Clavichord," Book I, Prelude 22; "St. Matthew" Passion, Introduction. d. Parallel fifths, which are likely to result from filling out the harmonic spaces with unessential notes in this manner, are to be judged according to the quality of the second fifth. If the second one of the two 5ths is harmonic and perfect, the parallels are wrong; but if inharmonic or imperfect, they need not be avoided. Ex. 294, Note *5), illustrates this principle. Parallel octaves, made in embellishing the harmony, are, on the contrary, always wrong. These rules are also applicable to parallel octaves and fifths which are interrupted by a passing-note. See also Ex. 120, Note *i). For example: Ex. 319. i I .good I good i!E^ good ^^T I I I good ^ S X IV V e. The rhythm which is adopted for the embellishment at the start, must be carried along from part to part throughout the piece (or section), with as few interruptions as possible. And when such inter- ruptions are deemed necessary, they can take place only at the accented beats, and must be slight. Thus: Ex. 320. m w^ *l) *l) I r f^^sp^^ffir ^^ i i g# k^^ good . *2) ^ ^^^ - notes, are slight. ^ o + o + *i) These cessations of rhythm are wrong, as they occur at the weak beats, and are too positive (from i6ths to quarter- i). — *2) Here the tenor part takes up the adopted rhythm. — *3) These interruptions are in the proper place, and Par. 405. EMBELLISHED HARMONY 217 /. The rhythm of the soprano, as most conspicuous part, should always be as regular as possible {i.e., the rapid notes should fall on the weaker beats). Therefore, the first measure of Ex. 3206 would be better thus: S. or Ex. S21, i ^^^ ^3 f ^ ^ ■4=ii6 =t=il I g. Regular anticipations, and quick repetitions generally, should be avoided, as they jar the movement. Repetitions, however, are usually good, no matter how abrupt, when the second tone is a sitspension (Ex. 322-2), — and when they occur in sequences (Ex. 322-3). For example: Ex. 322. ^EpE I I" Ant.-f: ^ g S* I I ! i i s. Bach I a= fct m=r ^^ I ^ 4z ^ s 3=5: seq. £ seq. In other words, calculate the group of tones so that it will run into the next harm, interval at pre- cisely the right moment; not before its time, as in Ex. 322-1. h. Short rests constitute a very valuable resource of hajmonic embellishment, and may be freely used. As a rule, a rest may be substituted for the first stroke of any group, excepting after an inharmonic note, or after a very short note. Ties are still more valuable, but must be used with caution. The principal rule is, that it is unwise to tie a short note; in general it is best to tie nothing shorter than a beat, or a half-beat in moderate tempo. But exactly the same exceptions are valid as in 4051:, — for quick repetitions. Thus: Rests I a= .rr^n J- ^ ^ =p ^T f i^^ Ex. 323. all good i -J^.-TT^ ^^^ ^ m -t-t5^ 2l8 THE MATERIAL USED IN MUSICAL COMPOSITION. Pai. 406. I ^^g. good 1 4 better J: - ^ « * r i i. The embellishment should not continue in any one part too long, but should pass from part to part; not in such regular intervals of time as to incur monotony, nor so irregularly as to destroy the rhythmic unity of the whole. It will usually be taken up in that part in which, ist, the convenient "space" is foimd; and 2nd, where it conduces most to the melodic quality of the part. A glance at Bach, " WeU-tempered Clavichord," Book I, Fugue 11 and Prelude 12; and Book II, Fugues 2 and 4, etc., will suflSce to show how the parts generally alternate and reciprocate, in keeping up the adopted rhythni. ]. That, from time to time, more than one part may be engaged with the embellishment, has already been seen (Ex. 318); and particular attention is directed to the possibiUty of different parts embel- lishing simultaneously in different rhythms (for instance, in 8th- and i6th-notes). N.B. The student will find very thorough illustration of this style of writing in the author's Ele- mentary Counterpoint, Chap. 24. 406. The most of these rules must be applied with discretion, for they are merely general principles, which are sub- ject to modification ih the multitude of changing conditions. The student who has mastered the laws of legitimate har- mony, who has trained his ear to discriminate rationally between consonance and dissonance, and has made a conscien- tious study of the masterworks to which reference has been made, may now confidently trust his ear in detecting harsh passages. He is again warned of the utter futility of working out his exercises at the piano. The piano should be used, first, while studying the given examples; and, second, in testing the effect of the written work, after it has been completed at the writing-desk to the best of the student's ability. EXERCISE SIXTY-SIX. Andante ^,^2 4 J ^^ ^n T "-4—1^ A. *i) i -J- r i^^ w^ f^^t 1*2)1 Allegretto r J|J, ^' | J J ^ t=t i w^^ rr-^^^-^-MSrr^Vr^ff B. •s) i* ^—U-hL..^ f^ P£ m # ^^^^ W ^H: =f^ ^r^^ I Par. 407. M IRREGULAR NEIGHBORING-NOTES. THE APPOGGIATURA. Moderato 219 ^ ± i J iJ J J ,^J J * 5a ^ Pi f=^1^T xp: C. *4) *S) ^m hlTT^ r. r r r ^:^ ii .^ ^ -- ^ ;«U .m 2^ ? ^ s? =f=f= r *i) To be embellished three times, throughout, in alternating parts, m a continuous rhythm of first 2 notes/ then 3, and then 4, to each beat. Ex. 3206 will serve as a model for the 4-tone rhythm. — *2) The bass carries the adopted rhythm on into the second beat. — *3) Precisely like A. — *4) To be embellished tvpice, in rhythms of 3, and then 4, notes to each beat. — *$) This brief preliminary beat is riot to be embellished. Irregular Neighboring-notes. The Appoggiatura. 407. Either the upper or the lower neighb.-note may. be simply placed before its principal tone, without regard to what precedes — either with a skip, or after a rest, or at the very beginning of the phrase, or in the strict diatonic manner already seen. Because, similar to the anticipation, a neighb.-tone pertains exclusivdy to its own prin. tone, into which it must be re- solved, but /rom which it is not obliged to enter. 408. a. When the neighb.-note enters with a skip it is called an Appoggiatura (or, if very brief, an Acciaccalura). b. It may stand upon the strong fraction oiits own heat (like the accented pass.-note),- or upon-theweak fraction of ihe preceding beat. For illustration: I. Ex. 324. FgM ^ ^^^ . ^p^fHfj=^ ^^ mm$m ^ 000 m 5^ X 0_ X 2. Allegro mod. ^^^^^_,^^ ^ ^, ^ m 000 060 w=T=fmii=^ ^ W -i^l^r^^ & N.B. J 4 94iO ' ' i N.B. 5: N.B. i- J N.B. J. N.B. N.B. N.B. N.B. N.B. i i i 4 -*- e HS>-=- m. r- r- r ^ r r> Bkahms. Sym. No. a 3. Mendelssohn 4. Allegro N.B. n N.B. -S:^ m A o N.B. N.B. N.B. Beethoven N.B. N.B. ^=^h^H^ \'^ 'HiSl % -^'S- IM -^■ r o aVo Eb V 7 V 220 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 4og. *i) At each beat marked N.B. the neighb.-tone enters with a skip. This whole passage from Brahms is a curious (and intentional) exception to the general rule that a sensitive tone should not be doubled in embellished form. The embellished melody is doubled in the tenor, in intentional octaves. — See also: Beethoven, Sonata op. 14, No. 2, first 4 measures; Chopin, Etude op. 25, No. 5, first section. The Double-neighbor. 409. a. Analogously, both neighb.-notes may be set before their prin. tone, jn. either order, and, as indicated in par. 4086, so that both occur in the beat, or both, before the beat, or one before and the other upon the beat. b. This is a double-appoggiatura, and the irregularity consists in the first neighb.-tone progressing with a skip (into the other one). Thus: _o *3) o o. Ex. 325. i :2-i= iSE ^ :^ i: i *4)o- m M f^^ ^ «ii~*"*«i ^ *l) I ^ -r HI =*^^ S- Allegro ^ ^ i^^s .ase °'^°, ° o^ o o CT"! I r— ; i Mozart , .„ n ri — I r-r-^ Vi-l ° ^ o 6- A llegro Chopin ^=^ I 1 f ^it'- r r I i ^^ •F V- Par. 410. THE DOUBLE-NEIGHBOR. 221 *i) Strike the I with the left hand, at each accent. — *2) Par. 3996 must be respected in all cases. — *3) This order of tones is not as smooth as the preceding figures. The choice of upper or lower neighb.-tone, as defined in par. 3990, refers to the last one in the group. — *4) When the neighb.-tones are shifted back in this manner, it is simply an example of "oblique rhythm." — *s) In rare cases, the first neighb.-note returns, as here, before the prin. tone appears. — See also: Weber, "Rondo brillant" in Ev major. 410. This is a species of "deferred resolution" very often applied to suspensions (which are always "neighb.-tones"). This, and other interesting deferred resolutions, are exhibited in the following example. See par. 381J. Ex. 326. EXERCISE SIXTY-SEVEN. ^^ Moderate ^^^^-i $^4 ^r-7 J_ J -i. I J l 'J l J! 1'^ - ♦« »■ *-s ' *-i o- i 1 n I *i) The npelody alone of this phrase is to be embellished; first, in 8th-notes, as in Ex. 324-1; second, with 3 notes to a beat, as in Ex.32S-r; and third, with 4 notes as in Ex. 325-2, and Ex. 324-4. The harmony is placed in the left hand, for convenience. — Besides this, the student may take any short melodies of former exercises, and elaborate them in the same. three ways. B. The following period (an excerpt from the pianoforte works of C . . . ) is to be embellished in alternating parts, as in the preceding exercise: first, with 4 notes to each beat; and second, with 3 notes to a beat (as i measure) . Any neces- sary or suitable licences (chiefly those of par. 407, 409) may be applied. I fiif r \j \ ',^ ^^ ^^ 3^^ :y--A i i J. tz. — T^ T 222 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 411. seq. -Z^ se ^^^=S '^m i t^ =i^c ±:t ^ k -X -i- 1 y -i ii ite e^ ^^^ :^ i tr ^ In ^ measure I I -I li =P=3t li ^^ P ■^^H -^r-.H«- f^-^-r- trv '^ i'-^i r f -^bj- ^fH^ i i# I J-. J I etc. gl^felE? ^:i 3i ^ rf I C. To this exercise may be added a similar elaboration of some former simple phrases and periods, either original, or given in Parts II and III. Or the student may write a number of Original phrases, with direct application of the given material. Haemonic Embellishment (continued). 411. The emplojTnent of passing-notes and suspensions, in embellishing the harmony in alternating parts, may be- come more elaborate and significant by adopting a small melodic figure as "motive." This imparts that equality and melodic uniformity to the several parts which is a distinctive trait of the so-called polyphonic (or contrapuntal) style. 412. Polyphony is the highest grade of musical technique, and demands great skill in the treatment of musical ma- terial. Hence its practice by comparative beginners is out of the question. Nevertheless, a harmonic phrase, em- bellished with an adopted motive, approaches the idea and resembles the effect of the contrapuntal process, and is well worth the student's attention at this point. 413. Thus, any succession of simple chords, — for example: may be embellished in many ways, with a variety of motives, as follows: i 1. Motive: * J J 2. Motive : a i Si m *a) ns3L i s f=f= i > • ujj r f^y- r^ f^\ =p:^ Ex. 327. *l) i3 ^1 I n n*: *2) i *3), ^ ^ 8 Par. 413. HARMONIC EMBELLISHMENT. 223 3. Motive : =^ i J- — -M j 4. Motive: -f ^^ ^Eji :i ^ i i ps^ j TfiT- r f r-^ -f=¥- *i) ^i I J- ifSE B^ ?^ ^ *4)IVa »3) m m zizii! i ^s m a* j^ M A* ,*s) i ^-^^ ^^ ^ -ii. etc. ii^ a 7. Allegretto i fc i^ ^ PSEl ZIM. =#t zUr p p STf -^-r ^^^474 I^^ ^ jikllSlfaJ =ail te :»e): -<=- =*=?= f r u -•- p r -^ Beethoven «a) -^-J BU^L^-).j_,^.^-i : -J--'~"J- _J I \ \ 1 etc. S? ;*7)zz: ^ r *i) "Progressive" embellishment, with passing-notes, is more dignified and eflfective in this semi-pol3T)honic style. — ■*2) "Local" embellishment, on the contrary, while necessary at times, does not contribute to the life and melodic signifi- cance of the partSi as the "progressive" does. — *3) The direction of the motive may be reversed, as here, at any point. It is called imitation in contrary motion, and is always valid. — *4) A slight change of the given harmony, for the sake of the motive. — *s) A "harmonic" motive, obtained by merely breaking the chord: It becomes the basis of the ampler motive in No. 6, — after the manner of par. 403. — *6) Motive. — *7) Motive. — *8) Op. 74; same as Ex. 316. 224 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 413. For further illustration of this style of contrapuntal embeUishment, see Beethoven, op. 120, Variations 11, 14. — Mendelssohn, op. 54, Variation 2; op. 83, Var. 2. — Bach, Well-tempered Clavichord, Book I, Preludes 12, 22, 23; Book II, Preludes s, 11, 19. In working out the following exercise, the pupil is to use moderately simple chords (and next-related modulations), and then embellish this harmony in a continuous rhythm of iwo notes to each beai, in alternating parts as usual. It is by no means necessary that a motive be adopted, as in Ex. 327, although he may experiment in that fashion; the chief object is, to impart to each voice a definite melodic character, — to make each part a significant line in the design (par. 7). Before harmonizing the given chorale melodies, the pupil will do well to make a very careful study of the chorale harmonizations of Bach (to be found in Vol. VI of his organ music, Schirmer edition (edited by Widor and Schweitzer), or Vol. V of the Peters edition; and in the chorale numbers in his "St. Matthew" Passion). See also Mendelssohn, " St. Paul," No. 3, No. 16. EXERCISE SIXTY-EIGHT. Rules: (i) Review par. 4050, c, h, and 407. — (2) The given melody is not to be changed, as a rule, but an occasional suspension or passing-note may be introduced in the soprano. — (3) The embelhshment may be added after the chords have been found; or the harmony may be determined at once in its embellished form. — (4) The use of regular suspensions (with ties), and of ties generally, is commended. I. Moderate ^ , 2. Adagio i m PT^ni^^ i Sg^ te 3EEE3 ^ *3) i s t:& Chorale 3. Adagio 1=^ lE^ W— TT^ • — f P i ^\ S Wi «4: JtiSziL zit^t i=» it P^ »a) II ^ H r r S Chorale ^S ^S #=i= t=t -*-+^ oe ?=tt •3) 7 II 4. Adagio le i ^ zt=t »3) *4) ^ Chorale A ^^^ ^^^^^^^m^^ ^^ ^-•—^ ithi 1- *— •- »s) ^S#;ppi^^*^ rtTfr fTil^ ^^P #— ♦ ¥ t=^ DI EV # WM 3tj-itt^ •5)^ ^ ^TT^ and f ^ fl= »a) Itjt m *&) II Par. 414. ,6. Moderato OTHER LICENCES. 225 ge a= isEfc Faisst -(2- ±Z:9l If ;^ "F <- Pqi:: »7) *i) Besides this melody, add the similar manipulation of some of the melodies given in Exerdses 16, 17, 22, 55, and others. — *2) The end of each Ijne (marked "> ) must be a strong Iriad, and the rhythm is interrupted. — *3) The pauses ( ("JN ) in this chorale are to be ignored. — '4) The repetition must be written out, with dififerent harmony. — *5) Sequences should be treated as symmetrically as fwssible. — *6) In this and the following melody the student may work with the utmost freedom, and depend somewhat upran his ear. — *i) This last melody may be elaborated in several different ways (but only in 8th-notes). Other Licences. 414. The upper neighbor may evade its resolution by leaping down a third, — not only in passing to the opposite neighbor (Ex. 325, No. 3), but in any case, without ultimate return to its principal tone. The chief excuse for this is, that the upper neighbor is so frequently an anticipation of the following chord (as in Ex. 309). Another justification would be its occurrence in sequential figures. For example: I. Ant. o f Ant, 2. Seq. o Ant. '^ ™ -*^ Ant. o Chopin r f '^ r *i) , ' ^ m Ex. 328. -r- f -Ki- E^^ ^m Jzfi: f==\W^ ^ t- 4. Allegretto Ant. I C V„ I *a) o Eb V- Beethoven Ant. SS I : I __j.i_ *^ I 5 i-H I ^ I I I I I ^ e *2)o n^ {. Sequences ^' i^^ au =^-^=^j -f-Ci^^r^ 5. Allegro *^_ Beethoven ^i ^^m I i #3) i—- S. o o o "' *3) r- 1 00 3. O s F~p~r"^ IS -II V— -IV- (Ex. 316) «4) 226 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 415. 5. Presto _*_ A J J. J i ^J . I + °. °. ° i te I — I o o x^ Beethoven w ^ ME W-F^ -»-#- I r r Dbl- 7 V- *i) The d in soprano is the upper neighbor of c, and leaps down a 3rd; but it is also explainable as an irregular antici- pation of the i in bass on the next beat. — *2) These unresolved upper neighbors are sequences of the preceding antici- pation i. — *3) In each of these cases the upper neighbor leaps down a 3rd into the lower neighbor, — but their conunon principal tone does not follow. — '4) Compare this with Ex. 316, from which it is derived. — *$) These imusual sequences are imaginable only in such rapid tempo. — See also, Beethoven, Sonata op. 31, No. 3, first movement, measures 10-9 from the end. 415. During the regular local embellishment of a chord-tone, the other parts may make a progression into a new chord, so that the prin. tone in the meantime changes its harmonic quality, or becomes itself inharmonic (comp. par. 378). Thus: I. Andante Beethoven 2. Moderato Schubert ^^^^ ^^ ^ Ai s s ^ r r «3) ^1 ^=e etc. feJM g g F^ ^ *3) i %- n ^ T ^ 4. A ndante | 1 Ant. -S >«_ + Bach X fe :?=*::* =#« J f 'W^- *s) *4)^ 'i^ *5) f=[f I fii ^ -I — r 7 c V 7JII IV IV *i) During its embellishment, the tone c ia soprano changes its quality from fifth to root. — *2) The prin. tone al> becomes, upon its reappearance, an accented passing-note. — *3) These measures prove that this irregularity is but one of the many phases of "oblique rhythm." — *4) Like Note *2). — *s) This descending 6th step has to appear in its raised form (contrary to par. 279), because the 7th step was not altered. See par. 400c, of which this is a good illustration; ob- serve that the "prevailing scale" on this beat is that of G major, — that is, it is the "G-major chord," as V of c. 416. The neighboring-note is such a simple factor of embellishment, and its application is so comprehensive and easy, that it may even be employed in ornamenting certain inharmonic tones, — when the latter are obviously legitimate, and sufficiently prominent to carry the embellishment without losing their identity. This is frequently appHed to an organ- point. For example: Par. 416. I. Allegro OTHER LICENCES. Beethoven 2. Allegro 227 & ^ fes ii=4J -'^Hg- * ^ ^ Ex. 330. *l) etc. I ;7^ i f p ^ i ^pp^y^yyyTt^^ ^ ± *: Tonic org.-pt. Dom. org.-pt.» ^ Mendelssohn ^ s. i ^ i Sz fc -*—* W o etc. cvfri — ^ — &=£* 1*2) W-Ut4 i £ =F 4. Allegro Mozart o o 5. Andante M end. 6. Allegro Clementi o o o o 7. Allegro tnolto B I- /-„„„,„ 8. Presto Chopin 00 00 00 i w ^ s s l=fe£Erk^3.^^= H P^ ^ T^ « ^ * J -Ffa *s) i etc. it * + + *6) i^ I ^E Db I- CI- *i) An embellished tonic org.-pt. The upper neighbor is, curiously, a half-step (representing the lowered 2nd step of the scale). — *■£) An embellished suspension. — *3) The upper neighbor is embellished (very quickly) with its upper neighbor. — *4) Embellished diatonic passing-notes. — *s) Like Note *3). — *6) Embellished chromatic passing-notes. See also: Beethoven, Sonata op. 14, No. 2, ist movement, measures 15 and 17; Sonata op. loi, last 15 measures. — Mendelssohn, S. w. W. No. 35, Introduction (tenor); No. 45, last 12 measures (org.-pt. in bass). — Schumann, Sym- phony No. 3, third movement, measures 11-5 from the end. — Beethoven, Symphony No. 4, 3rd mov't, Trio, measures SO-S9- 228 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 417. 417. Under normal conditions, a neighboring-note is brief, — not longer than the tone it embellishes. Sometimes, however, unusual prominence (length) is given to the inharmonic tone. This is extremely effective, and safe as long as the chord remains vmchanged. Thus: Rfftho I. Allegro ^ ^ B ^^ =^ *^5^ Ex. 331. "*i) -#- -251- *l) »1) ^ ife ^ 7 1% (or V IV V) *i) These neighb.-notes are accented, and much heavier than their prin. tones. — "■£) The dim.-seventh of E\> major (d-/-al7-ct>), with proportionately heavier appoggiaturas on each 8th-note. — *3) A long, heavy passing-note between /# and i. — *4) A similar heavy neighb.-note of a. See Beethoven, op. 120, Variation No. i (bass). — Quartet op. 18, No. 2, last 8 measures of the "Trio"' (3rd mov't), in the bass. —Also, op. 120, Variations 12, 28 (neighboring-chords), 8, 9, 27. — Also Ex. 3506. 418. Passing-notes, and also neighboring-notes, may be repeated. For example: 1. Allegro Chopin 2. Presto Chopin Par. 4ig. OTHER LICENCES. 229 3. Agitato Chopin 419. The most unique efifects are produced by intercepting, or deferring the resolution of a neighboring-note or passing- note, similar to previous examples (Ex. 156, Ex. 296, Ex. 326). Usually only harmonic intervals intervene, but it is even possible to interpose other inharmonic tones; and the resolution may be deferred as long as it is possible to retain the correct chord-impression firmly. For example: I. Bach 2. Allegro molto Chopin i fc^ ^ ^ n ..^^ m a ^Pe ^ ^ U LTJLTJ L [ J xn Ex. 333. *a) etc. P %=rr^ *l) i ^^ ^ww^ ^ bA: ^ ^ — ' ' — I A V- Eb I- 3. Allegretto Ed. ScHiJTT Saint-Sajsns El, I 6 . Chop in 0000 7. Moderate ^^ ±ii P ^ I i^^J^^e^ •• — •■ F4= atiatzhi i±3t r *4) etc. ^ *5) u s sS Comp. Ex. 262—4. B : f _ :g: ^ >g IS. m^ ? ^ Bl, V 7 Gb V Gbl- 230 THE MA TERIAL USED IN MUSICAL COMPOSITION. Par. 4ig, ^U^^ p p o*a) -J-.-JrJ^ + o i o o o o o o ^FT m n M" d^d ' +V (bb I)«7) sJt^S-T^ sWrTjp *^ etc. h h^ fe ^ s i 5^ U 1 R X X J f ^ =3= Gb I- T IV lrf^rr-f- | g ^ gb minor I Debussy 8. Allegro Balakirew 1 ^^M ^i O 0+ ++ o i^ i: ^ it^ ?f=±=4 Gbl- I el- *i) The passing-notes a (and cjf) are intercepted briefly by the e below. — *2) The uppermost tones are intercepted passing-notes. The example is from Chopin, Prelude op. 28, No. 19, which abounds in similar interceptions. — *3) Re- peated and intercepted. — *4) The simple double-neighbor; in the next measure increased to three tones (as seen in Ex. 325, No. 4); and, in the next, to Jour tones. *S) In this extraordinary example of Debussy ("La plus que lente") the melody-tones / and ob change their com- plexion with wonderful effect. They are given here not in the same order as in the original, but in a manner which ex- hibits their progressive changes. At first (at 7a) as harmonic tones; then, (at 76) as double-neighbor, with extreme repe- tition, — up to Note *6), where they finally resolve ftito their principal tone g\>. — *7) It is of course possible to regard this as a "chord" (the I of Jb); but it is more rational analysis to call it still the I of Gb, with the / everywhere as lower neighbor. — *8) The Jbb makes it gb minor. It is possible, however, that it is at], as lower neighbor of b\> (which ulti- mately follows), in which case the major mode is maintained. — *9) This continues 4 measures and resolves exactly as at Note *6). — '10) The / is the first of a line of passing-notes, doubled in the lower octave, and resolving on the final d\>. It appears to enter without preparation, but it comes from gb, which is amply " understood," as root of the chord. These licences are more common in modem than in older music. They do not defy analysis, and are therefore per- fectly legitimate. They represent merely a more free and extended application of the simple principles of embellishment known to earlier masters, but used by them with greater caution and moderation. See par. 426. EXERCISE SIXTY-NINE. A. The following melody is to be harmonized according to par. 415. i fe -•— p- ^ ^i=p= fe r^-f-f^^i i^=gL^tfi^ j=^ simile I f r , i r *rn^^g=f ¥^^ m D maj. fi Par. 420. THE HARMONIZING OF EMBELLISHED MELODIES AND BASSES. orig. form 231 i =#F= ^ I *: It X Use four chords in each measure, in uniform quarter-notes. The 3rd note of each group may be a passing-note, or may be harmonic; but in either case the chord must change. See Ex. 329, No. 3. B. Original phrases, with application of the various licences given above. The Hakmonizing of Embellished Melodies and Basses. 420. When a florid (embellished) melody is to be harmonized, it is first necessary to reduce it to its original simple harmonic tones by setting aside all such brief ornamental tones as are certainly, or apparently, unessential notes. The melodic outline thus obtained may then be harmonized more or less simply, according to the character and tempo of the melody. The more animated and ornate the melody is, the more smooth and quiet should its harmonic accompaniment be. 421. In reducing a florid melody to its simplest elements, the following points must be borne in mind: a. Every note which progresses with a skip is ahnost certain to be harmonic. (See par. 4050!; but comp. Ex. 296, Ex. 309, Ex. 325, Ex. 328.) b. Notes with accidentals will be inharmonic, excepting when they are unmistakable indications of a legitimate and natural modulation. c. The longer notes are likely to be harmonic. d. The natural order (and rhythm) of the chords, and the fundamental principles of modulation, define the nature of most of the notes, especially those which occupy accented beats. The following melody, for example: ^^mM\^^r^^t^mi £x. 334. reduced according to these principles, becomes as in Ex. 335. 422. The tempo of the melody is a consideration of such moment, that it will usually precede all others in defining the order and rhythm of the accompanying chords. For the more rapidly a melody moves, the more emb.-tones it is naturally likely to embrace, and vice versa. Comp. par. 169. Tte foregoing melody would be harmonized about as follows, in different grades of tempo: ^^^^ n^ ^ ^ '''^1^ Ex. 335. m a. b. c. _V_ II, VL 7 -V, I,_ GoVi _V I 7 C V 9b II V3_ Ii VI II_ _v I3VV VI IViGqVi I C 0V3 IjdViV ICVjV I IilgV At a. Allegro vivace, an average of one chord to 2 or 3 beats of the melody; at b. Allegretto, one chord to i or 2 beats of the melody; at c. Andante, one chord to each beat, on an average. And finally, if the tempo were Largo or Adagio, the original melody would not be regarded as "florid" at all, but each single tone, as essential constituent of the harmony, would demand its own chord. 232 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 423. 423. Florid basses are easier to reduce to their simple harmonic groundwork than florid melodies, because their con- struction is generally more regular, the accented notes are almost invariably harmonic, and they suggest their harmony more than melodies do. See Ex. ig6B. EXERCISE SEVENTY. A. Florid melodies. a. Maestoso b. Allegretto IE *i) " — \jr^ *a)^ 1 w *4) c. Allegrojnoderato fa ^ s #-7-^^^,-f-4r^ f^-8» — F — I ' P » J 1 ^—P- b » P m — ' f=t **) *4) i ^ -l»— r t^ fe^^ Pg^^ f=p: -• — F- #^ fcr IS J — U ntt "JT1it73^ ritard. Faisst •^ — I II ^^ :fi i -^^-^"^^^ d. Allegro «5) ^ ; i^^^ e «. 1. Andantes 2. Allegroj 3. Adagio S « j y^^t^" Lfit &^HH-- ir rrf fc^ e «3) g!^ja.S3^7^U.ll^te.^^^ I, /. Moaerato u ««.Jtrr«k«u w^^^ *«)q *" P«r. 483. THE HARMONIZING OF EMBELLISHED MELODIES AND BASSES. 233 *i) The first four melodies are supplied with slurs which indicate the rhythm Of the harmony (lower parts). — *2) May be a neighboring-note. — *3) Suspensions. — *4) The predominating tone in a group is the principal tone. — *S) In melodies of this kind, with rapid figures and large compass, the three lower parts may be written together on the lower staff. And the volume of tones may be altered at will, to represent fewer or more than four parts. See par. 462. — *6) To be harmonized in each of the 3 given grades of tempo, according to par. 422. B. Florid basses. a. 1. Allegro; 2. Andante cantabile o?) ^%^rffS* «10) j^ *"^ ^ i^s ^ ^^^i^ * — 7:4 » 7 bb V -Bbl-eb V EI- 7* ■ IV IV— (IV) 7 -V C. Franck ^ ^ jj wp^ f"Tf»f f ^E^ e VI C V FV E V FSI 70 *14) 7 V (G V)-F# I Par. 435. WANDERING HARMONIES. 237 Fritz Kreisler 12. Lento f E. HUMPERDINCK r^^^ ^^ ^ Bir^ns?iii iprnk^ m^ _b minor u pm ^^mm^i^^m w w 7 .bV 13. Lento »ia) HUMPERDINCK 8— y 1 I' ^=iit=gj=l|^ I -=1— =1- + + + + i# s t s 4^H 4^ f^ ■^ -- r^^^- GI 7 E V F#V EI Eb V 7 '^ V GM 14. Tranquillo 238 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 435. I S- Largo Db V VI E V I c IV I3 *i) Observe the uniform soprano figure, and the chromatically descending bass. — '2) It is probable that this e|j should be written i'is. That would simplify the analysis. The student will often encounter similar cases of uncertain notation, and must remember that if the analysis of a passage is quite baffing, it may be because the composer wrote hastily, with transient disregard of the true notation. In such cases, the student may test the result hy altering the no- tation judiciously. Comp. par. 285. — *3) The "chord-form" on this 3rd beat' is obvious, but its "name" is doubtful. 7b *4) Almost all legitimate chords. Observe the bass line. — *s) Or, with a\> in alto (for five beats, — then g#) : C II — a III. Comp. Note "2). — *6) Note the pivotal tones. — *^) Continuous chromatic line in soprano. — *8) The /, which is the mediant of the first key, becomes an upper neighbor (or suspension) of e. At the same time, the former tonic becomes a leading-tone. — *9) Similarly, the mediant, /#, becomes an upper neighbor; and tonic becomes leading-tone. — *io) This tone-body is almost identical with the first chord, — but the gth (,cS) has become an upper neighbor, with fine effect. — *ii) Similarly, the gth (gb) becomes the upper neighbor of /. — *I2) Observe the sequences in both outer parts. — *I3) The tones ai] and clj have precisely the effect of lower neighbors of the chord-tones before and after. -^■*i4) This bass con- stitutes the descending minor form (lowered 7th and 6th steps, — par. 272/) of F# major. The upper parts adjust them- selves smoothly, though rather grotesquely, to it. — *is) In the violin-part, a scale in successive whole steps. The first five tones follow the lingering impression of the preceding key; the rest follow the track of / minor. The second measure is a sequence, harmonically identical with the first. — *i6) The h in soprano is a pivotal tone, first as 3rd, then as sth, 7th, Par. 426. ANALYSIS. 239 '19) A and finally gth. Note the sequences in bass. — "17) Note the pivotal 4ones. — '18) Note the soprano line. • fine illustration of wandering harmony; it baffles exact chord-analysis, but is smooth and wholly plausible. See also Grieg, Ballade, op. 24, Theme (note the descending bass); and Nocturne, op. 54, No. 4, measures 5-14; 49-S4 (consecutive dom.-7ths). WARNING NOTE. 426. These extraordinary examples have been incorporated in the book because the author beUeves that it would be unscientific to disregard them. But the student is earnestly reminded that such combinations contribute to the interest only, — not to the durabilitjt^ — of' a composition; and that they serve an important purpose only when used in great moderation. The student should thoroughly absorb the following esthetic principles: On the one hand, — avoid too great simplicity, too great regularity, monotony, and lack of ingenuity; On the other hand, — amid extravagance, lawlessness, eccentricity, and grotesqueness. In a word, — cultivate moderation in every respect. An occasional unique effect is very valuable and necessary; but the value of any object is increased by its rarity; — abundance deprives it of its value, makes it "cheap." The un- conquerable power of the music of Beethoven (also of Mozart, Bach, Brahms, Schubert, and other classic masters) lies in the moderation he constantly exercises; in the unwavering loyalty to the natural laws of tone-association, the nor- mal conditions and relations of chord-movement, properly blended with an occasional irregularity that matches the most consummate ingenuity of any modem writer. Cultivate moderation; all defect lies in exaggeration. EXERCISE SEVENTY-ONE. The student may experiment with the above material, in Original phrases and periods, wisely, defer this exercise vmtil he shall engage in the study of Counterpoint. Or he may, perhaps more Analysis. 427. In conclusion, the student is recommended to analyze the following compositions from time to time during the study of Part V, in the given order, defining the chords, the modulations, and all inharmonic intervals. Ex. 337 will serve as a model, though more knotty passages than these will rarely be found. Always consider the tempo, and direct the at- tention constantly forward to the following chord or two. Mendelssohn: Songs w. Words, Nos. 15; 12; 30; 6; 48; 41; 28; 35; 27; 11; 40. Cramer: Etudes, Nos. 75; 84. Mozart: Sonata in D major (Schirmer edition. No. 14), complete. Beethoven: Sonata op. 14, No. 2, ist mov't; op. 27, No. i, ist and last movements. Schubert: Sonata No. 8 (C minor), ist mov't; No. 5, op. 143, complete. Mendelssohn: Scherzo a capriccio in Fi/f minor. Bach: Well-tempered Clavichord, Preludes (Book II) 12; 16; 19; and Fugues (Book I) 5; (Book II) 7; 21. Chopin: Nocturne, op. 37, No. 2; Preludes op. 28, Nos. 7; 9; 17; (14), and others. Beethoven: Variations op. 120, complete; Sonata op. loi, complete. Schumann: op. 15, complete. "Humoreske" op. 20, complete. Wagner: "Lohengrin," Introduction to Acts I and III. Also portions of "Tristan und Isolde." Brahms: Piano-pieces, op. 76, Nos. 7; 6; 4; 1; 2; 3. Op. 116, Nos. 2; 5; 6. Op. 119 complete. I i I 1 Mozart a. Andante S. o ^ S. o jz. ^ — ^S. o . ^ :^s. o 240 THE MA TERIAL USED IN MUSICAL COMPOSITION. Pu. 437. b. Andantino ^^:z Chopin t; I Ant. ^^m^mn^ ^^^ p%=^ ^^ 7 9 G V I (V)- -r- m c. Allegro ^ all X V I Schumann. Op. 21, No. 8 i ^^ ^ ^ ^^^^A^-^^ ^^^ f ¥=f 324* 271a zyxa etc. 'i» ^ ^ ^ Si ^ BbV- 7 7 V GbV- 7 V IV DbV lEbV I FV PART V. VOCAL AND INSTRUMENTAL HARMONY WITH AN IRREGULAR NUMBER OF PARTS (FEWER OR MORE THAN FOUR) STYLE. SECTION I. VOCAL HARMONY. 428. The general distinction between vocal and instrumental harmony is, that the former is the more strict, more quiet, and more limited in compass. In vocal music there is a definite number of "voices" or tone-lines, which are ad- hered to, and are treated with more equal consideration than instrumental "parts," which often sacrifice their individ- uality, partly or completely, in the variable volume of tone. Three-part Harmony. 429. When the number of parts is decreased from four to three (or even to two), the omission of certain chord-inter- vals is unavoidable, and duplications are less common than in regular four-part harmony. 430. The rules for 3-part harmony are as follows: a. In triads, the fifth may be freely omitted, and the root doubled. Or the root may occasionally be omitted, and the fifth or third doubled. The chord-third, on the contrary, should not be omitted — in triads. b. In chords of the seventh, the fifth is more generally omitted than the third, though much depends upon the quality of the chord. The root may occasionally be doubled, and both third and fifth omitted. c. In chords of the ninth (which are naturally rare), third and fifth, or root and fifth are to be omitted. No intervals are doubled. Thus: Soprano, alto and tenor .a. Ill Ex. 338. i ? ? ? I r ^ £££irr-r | ,p^ h h— H s a 4 *i) See par. 58. It is possible to lead adjacent voices more than an octave apart, but wise to avoid it, — especially in the two upper parts. 431. a. The perfect cadence may consist of the open tonic octave (I, with third and fifth omitted); or the Ii may be substituted for the I itself. But in the latter case the fifth is generally omitted and the root doubled, m order to im- part greater emphasis to the tonic note. ,j b. An inversion may also be substituted for the V or V at the cadence; and the lower parts may cross, if the cadence can thereby be made smoother or stronger. Thus: Two sopranos and alto f==r^=r=S=rrTr ^~:jr Ex. 339. Ii (?) V„ ^m Vi ^ i J. I I j,^ i j ^j, jw *« See the Terzet for female voices in "Elijah"; and Ex. 227-1 (tenor, alto, soprano). 241 242 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 433. EXERCISE SEyENTY-TWO. A. Exercise 31, basses a, c, d, f (and the others, at option) are to be transposed a fifth higher, and se;t for tenor, alto and soprano. The given bass figuring may be retained, or the pupil may treat the basses as unfigured, and choose his own chords and modulations. First complete the soprano melody (regardless of the given positions) and add the inner part last. B. Any of the melodies given in Exercises 16, 17, 22, 27, 32, 36, and 55, — to be set for soprano, alto and tenor. No regard need be paid to the given slurs. The student is advised to use a separate stajff for each part, as in Ex. 340. C The melodies of Exercises 16, 17 and 22 are to be transposed an octave lower (or a little less, according to circum- stances), and used as alto part, accompanied by one upper and one lower part. For example: Soprano Ex. 340. Tonnr ^ " 5 -•- Tenor -f- ^-^Ff^ ^^B F *i) Given melody. Exercise 22, g. — "2) Ex. 338, Note *i). — *i) The lower parts may occasionally cross. — *4) Passing-notes may be used at discretion, but according to the rules of rhythm; i.e., chiefly on unaccented beats. And perfect freedom may be exercised in modulating. Two-part Harmony. 432. Two-part harmony is, properly speaking, no more than a succession of intervals; for the fundamental suc- cession of chords, when expressed by two parts alone, is necessarily vague. Nevertheless, even two parts must cooperate in obedience to the laws of harmonic progression as far as their application is possible; and, for this reason, the only ab- solutely imquestionable intervals are the yds (or loths) and their inversions, the 6ths, — the fundamental intervals of chord-formation. A distinction is made between the/«K beats and Hht fractions of beats, as follows: 433. Rules for full beats. a. A third (or tenth) or a sixth can be used without any other hmitation than that indicated in par. 4350, upon full beats, accented or unaccented, and in any duration. Whether the 3rd or the 6th be chosen, depends upon the chord it evidently represents, and upon the melodic tendency of the parts. b. The octave is admissible. c. A perfect fifth represents a triad with omitted third, and is therefore to be avoided. It is allowed, exceptionally, in the V. The perfect fourth represents a 6-4 chord without its third, and ;is strictly prohibited. The diminished fifth and augmented fourth represent the Vq with omitted fifth, and are therefore admissible. d. The minor seventh (or major second) is allowed, but the quality of the chord which it represents must be considered. Major sevenths (or minor seconds) are to be avoided. The diminished seventh {augmented second) is allowed. See also paragraph 42. For illustration: Par. 434. TWO-PART HARMONY: 243 10 » = 6 ^ Good * 1 7 P ^ ^ ^ C I II V Vo C V II VI III I v„ Ex. 341, C I C 1 t ' ' r fti* ■ ■? T T T T *T C I II V 434. Rules for fractions of beats. a. Upon fractions (accented or unaccented) of beats any interval may be used, either as harmonic combination, or as suspension, neighb.-note or passing-note. b. All exceptional intervals (7th, 2nd, 9th, 4th, 5th) must appear as modifications of the unobjection- able 3rd, 6th or 8th. Thus: Sevenths and seconds Fourths and fifths ^— ~ ri ! , . . , I J 87 'rs I 89 1 a 3 3 34 ' Se eS 43 4: s Ex. 342. 87 "73 I iBQ 12 3 3 34 ' ' 66 eS 43 4 '8 436. o. Intervals of the third or sixth should not occur too often in direct succession; as a rule, not more than three (or four) times. b. It is objectionable to use weak or harsh intervals in succession. c. The part-progressions must be as melodious as possible. d. The rules of rhjrthm must be strictiy regarded. Ex. 340, Note *4). For example: (a.) Monotonous Good J J J ^.-,— J — I . J , J M ^^=fa ^ ^^-W-^ iJ_^^ -^ =j I Ex. 343. ^^m ^^ ^ ' r r r r ^^ T r r (*•) i ^ (^.) Rhythm ^=m i ^ H., ^T J J ^ 15 ^ (?) r 1^ * ^ ^1 r> I I Ex. s, i t^r The rules of two-part harmony, as here enunciated, are the essence of the laws of two-part counterpoint. EXERCISE SEVENTY-THREE. A. A number of melodies from former exercises are to be supplied with an accompan3Tng alto part, according to the above rules. It is not necessary that the added part should have the same rhjiim as the given part; on the contrary, diversity of rhs^thm is very desirable. But see par. 43 sii, and be careful that the heavier notes occupy accented beats. The utmost freedom in modulating is allowed. B. The same, or other, melodies, to be transferred an octave lower, as aito {or tenor) part, and supplied with an ac- companying soprano. For example: a. (Exercise 36, a.) # ^ 1 '■ ■ ^ \ i'{ ':- \ '7' ^1 M ^ 1 1. > ■^i'7 ^1 ni^ i .i fl Ex. 344. frrtiT^^''^' TTjrzrn cttt r'rrCrf (Given melody) 244 b. (Exercise 22, »'.) ± THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 436. (Given melody) Five- to Eight-part Harmony. 436. When five, six, seven or eight parts are employed, it is important to keep the parts well balanced, in regard to their distance from each other, and in regard to the duplicalion of the chord-intervals. It is particularly unfavorable in copious harmony when the lower parts lie too close together; but even the upper parts should avoid too close proximity. For instance: 6 parts Ex. 345. ■ 8 parts I I I I ^ ^ ^ J- fe 1^ I'll 437. Hints and directions. a. The inner parts may cross without scruple. But an inner part should not cross either the soprano or bass. b. Almost any tone may be doubled; but only the principal tones should be tripled. c. Interrupted 8ves and sths, and unequal 8ves, are allowed between any but the two outermost parts. d. The two or three lowermost parts must be kept wider apart than the higher ones (excepting when any two ad- jacent parts have the same tone in unison), as small intervals sound dense in the low register. Ex. 345, measure 3. c. Wide skips are often unavoidable, particularly where the parts cross and re-cross; but awkward leaps should be avoided. /. When a larger number of parts are employed, chords of the seventh should be freely used, as they afford more tone-material than simple three-tone chords. See also Ex. 169, measures 3 to S- g. The harmonic progressions should be very simple. The difficulty of connecting certain chords in four-part harmony is greatly increased with each additional part. This applies particularly to foreign chord-progressions, and chromatic successions. The combination of related chords, and especially repetitions, give but little trouble. 438. a. In five-part harmony (the usual foiu- voices with an additional soprano or mezzo soprano, or tenor), sen- sitive tones need not be doubled. The principal tones of the scale and chord are generally tripled. See Mendelssohn, "St. Paul," Choruses Nos. 23 and 36. — Bach, B-minor Mass, Choruses Nos. 1, 4, 11, 12, 15, etc. b. In six-part harmony (doubled soprano and tenor) the principal tones of the scale are tripled, as a rule, and the next best interval of the chord doubled. But, as strict observance of this rule would needlessly enchance the difficulties which attend the manipulation of a large number of distinct parts, it must be applied only as a general principle. See Bach, S-minor Mass, Chorus No. 20. c. Seven-part harmony is comparatively rare in vocal music. The original four parts are usually doubled, as in eight- part harmony, with the exception of the alto or bass. 1 See HSndel, "Alexander's Feast," Chorus No. 6. — Beethoven, "Fidelio," Act 1,. Finale, Chorus of prisoners (also eight-part). . , ; ^ Par. 438. FIVEr- TO EIGHT-PART HARMONY. 24s d. In eight-part harmony (each of the four original parts doubled) every licence, in reference to the' duplication of sensitive tones, and irregular part-progressions, may be freely employed. See Bach, jB-minor Mass, Chorus No. 21. And' the following illustration (German chorale): SopR. I Adagio , , , ^ -J J J J i iE i ^N ^^ g ^ sopR.11 r r Alto I ^E^fe? =P T f- i le -t- ^ ^rfi i^t -al-a^ Ex. / 346. \ Alto II I Tenor I 1 r r^-n l7 fWr^ UA i J a^E :i? Vi/ a^ r^:rrT ssl Tenor II Bass I feEfe U^^^4^^^i W-^ ^=J^ feJ^i * Bass Other examples of Six, Seven and Eight-part choruses may be found in Handel's "Israel in Egypt" (e.g., Nos. 12, 13, 16, 19, 23, 25, etc.). i a. Adagio For 5 parts »i) $: EXERCISE SEVENTY-FOUR. *3) P :^=t=*: ■iS—'S- -^ iS>—(^ F=tt=F =^=JS-^■ -<2--lS'. - ;s 454. The rhythm of the figural part must not be interrupted or changed at rests, at the cadences, nor in the course of the period. 455. As a rule, the broken chords (figural groups) should succeed each other just as the unbroken chords would. This is chiefly important in the lower (bass) register, where the rule of par. 28 is imperative; that is, the figure may continue in one direction only as far as the chord extends; when the chord changes, the figure (in bass) should change, at least briefly, its direction (Ex. 3556)- For example: a. ^ I ^ s ^ E good (')* »: ' OJ OJ i rf^^ ^ Par. 456. HARMONIC FIGURATION. 251 466. The registers, o. When the figuration is in the middle register, the outer parts may, if necessary, be trans- ferred to a higher and lower octave, so as to avoid embarrassing the figural part. This may occur during any complete metnber of the melody, — not at single tones. b. When the figuration is in the lower register, embracing the original bass part, care must be taken to preserve the effect of the latter, by using each separate bass tone as lowest note of its figural group, and generally, though not necessarily, as first note also. c. When the figuration is in the upper register, embracing the original melody, each separate tone of the melody must be distinctly heard as uppermost (and almost always as first) note of its figural group; and their connection with each other as continuous "melody" must be made conspicuous by isolating them as much as convenient from the other (lower) tones of the figural motive; thus: not Ex. 356. i ^^^ ^ ^ ■3^ J=3^ ■#:^#- d. If, on the contrary, the figuration is in the uppermost register and does not embrace the melody, it must be kept so subordinate in its melodic character that it does not detract from the necessary prominence of the melody proper. See Ex. 350^. 457. It is important to recollect that whatever movements take place within the' motive, being probably only "chord-repetition," are not subject to any other regulation than that of par. 451. The critical moment is, always, where the chord changes, i.e., generally from the last tone of one group to the first tone of the next. At this moment the same rules apply, and the same care must be taken, as in ordinary progressions, — especially in bass (par. 455). EXERCISE SEVENTY-FIVE. Melodies, with given bass, to be elaborated with harmonic figuration as indicated below. No. I. Andante ^ ^ =i^=J=i^ ^ »3)V ■^ ^ »l) «2) feE V §^ fil f^^^ i ^^ «4) ¥■ a=ii ^ Sa:3bz=i ¥ ^ ^ f^ r=w- *i) This first melody-note is not to be accompanied. — *2) The seventh may be added to the dominant chord, if neces- •sary. In general, the given bass (harmony) is not insisted upon. — *3) Indicates the semicadence. — *4) The figural part runs on to the 4th beat. 252 THE MATERIAL USED IN MUSICAL COMPOSITION. Par. 457. This melody is to be supplied with a figural part (3-part harmony) in the middle, lower and upper register, in succession^ in rhythms of i, 2, 3 and 4 notes" to a beat (J*, ^, ,^, ^) successively, with the following motives (each model to be worked out complete) : A. I. 2. -I. 4. 3^ ■ ■ ^^ =t 51 3 w w^ T- *i) T TtL ^? Ex. 367. i^ i* ^ i 5. I. li ^U H^ f *3) t f ^^1 ^ r^ ^ c. iE 3- -J- »3) I P f= f *i) Contrary motion of the adopted 3-tone motive. — *2) The motive may embrace any number of notes, in the adopted rhythm. — *3) The object of the inner part is, principally to assist in completing the harmony Its progres- sions are quite optional, but should be as quiet as possible. — *4) The original melody-notes as highest, but as second, note of the figural groups. No. 2. Andante cantabile m 4- ■^ i J i >i J -^*— ^^- •--z^ ■&-^ *l) p^ t==:=4: r^^pff^^ 7 -&-' ttt=* "^ ■ O It 6 4 n 6 6 7 * # $a Qs P»r. 457. HARMONIC FIGURATION. 253 P I J-^ J J , J -^ \ ^4-^ \ ^ J ir^^ I I3 III V »2) afe S F Sa 6 *6 4 oi 07 « »t a org-pt. r *i) The figural part must not stop (par. 454). — "2) The figural part stops at the second beat. To be elaborated similar to No. i, with original motives: o. in the middle register (figural rhythm either 8ths, 8th-triplets, i6ths, or i6th-sextolets). b. in the lower register, rhythm of 2, 3, 4 or 6 notes, at option. c. in the upper register, rhythm optional. d. in alternating registers in ^notes, transferring the figural part at discretion: say first after 4 measures, then again 4, then 2, and 2, and finally at each single measure. e. in the uppermost register as accompaniment, thie melody in tenor, as follows: etc. (Motive of one whole rneasure.) No. 3. Andante ^E X 3 T r/j 1 .^ ±:t* ia ^ m I 8 I 2 I b7 I 'a 8 7 8 7 W^^ J..l j J j Beethoven. El? maj. Concerto m f- wr w S p • i»- I -s- par. 454 ^s;fc?^ ^ i 4 » «=:(^) m 8 7 4 3 To be elaborated similar to No. i, in the middle, lower, and upper registers, and in alternating registers, in rhythms of 3, and 4, notes to a beat. 254 THE MATERIAL USED IN MUSICAL COMPOSITION. No. 4. Moderato Par. 458. g I -ztf- -I J 1 ^ J J V -(2- ai ^ I VI Ij IV oVi Vi I 7 V3 Ii IVi IV V i fe^ ^^^ 7 7 Vi I I DIIj Bach (adapted) i 7 DV„ IV oVi I V VjVo I GIVj V '3 Ii I Similar to No. 3, in rhythms of 3, and 4, notes to a beat. 7 V, Ii VI III V V The following simple period: No. 5. Moderato ^^±J=^J3tq^ E^ i tat — #< nSJr^ I I all 6 ta6f|7 05 f ab7 7 ■•-; ^^ ^^ ^ -zh^J i f; I r i F ^sa g j^j' i j -^ or an octave lower is to be elaborated with harmonic figuration at the piano, at sight, in the following modes, siiccessively: I. 2. 3. 4. 5. 6. 7. 8. 4— '"'^^r' ^^ffl^f^ ^^ i R.H. ! !- I I *i) The left hand retains the given bass. Melodic (or Mixed) Figuration. 458. a. Inharmonic notes may be interspersed between the harmonic tones, either casually, to facilitate the movement of the figural part, or essentially, as a feature of the motive itself. h. It is most convenient to use simple neighboring-notes (local embelUshment of any of the principal tones of the original motive). Passing-notes are more smooth, and more valuable, but embarrassing, because their use is dependent upon the size of the interval. AppUed to Ex. 347, No. 2, the result might be: It S g T^^^^^^: ^ Ex. 359. -± 4_ °^ iS^ ^ '«• 459. TWO-PART FIGURATION. 2SS ^ u. aa ^ S ^J-iL + x _irVi .T^m etc. See Chopin, Prelude, op. 28, No. 13. EXERCISE SEVENTY-SIX. A. Melody No. i of Exercise 75, to be elaborated with mdodic figuration, according to the following models: 1. 2. 3. 4. S. _^ U-^ ^^ U&^ i ^ifii 1^^ And finally, two or three times in aUernaUng registers, in rhythms of 3 and 4 notes to a beat, with original motives. B. Melody No. 2 of Exercise. 75, to be elaborated successively in the middle, lower and upper registers, and finally in alternating registers, in optional rhythms, with original motive, as above. Two-part Figuration. 459. In the absence of an inner part, the number of parts is reduced to two. In order to avoid meagre efifects, the motives are generalljj more copious, and more rapid, than in 3-part figuration. For example: Andante Mendelssohn. No. 37 Allegro 2S6 THE MATERIAL USED IN MUSICAL COMPOSITION. Par,, 460. Beethoven See also: Mendelssohn, S. w. W. Nos. 11 (measures 1-8), 25, 31, 37; Prelude op. 35, No. i. Cramer, Etudes 21, 24, 27, 31, 46, 62, 77. Schumann, "Albumblatter," op. 124, Nos. 6 and 16. Chopin, Prelude op. 28, No. 24; Nocturnes: op. 9, Nos. i and 3; op. 27, Nos. i and 2; op. 48, No. 2; op. ss> No. 2> EXERCISE SEVENTY-SEVEN. A. Melody No. i of Exercise 75, to be elaborated as follows: I. m l¥z :>-i-i- T^ ,j. ^-v i etc. ^i: t£r B. Melody No. 2 of Exercise 75, to be elaborated in different varieties of 2-part figuration, harmonic or melodic at option, in rhythms of (3) 4 and 6 (8) notes to a beat. C. Melody No. 4 of Exercise 75, to be elaborated in two-part harmonic &gata.tion, in either register, and in alternating registers, with 4 and 6 notes to a beat. One-part Figuration. 460. Finally, all the parts together may be merged in one figural part, embracing the original melody and bass as highest and lowest notes (but not necessarily as first notes) of each group. Par. 460. ONE-PART FIGURATION. 257 The motives are almost always copious and rapid. The figuration is apparently thrown from one register to another uninterruptedly; or it consists of continuous groups, extending throughout the space included between the melody and bass. For example: " ■ " CzERNY. Op. 740, No. 6 Ex. 361. i Allegro iPP s -X=f^ ^ ::p=tq= ■n^ ^^^^^^f ^^r^—^^ U: # ff "^-f-t Ji d ! i See also No. 18 of this collection of Czemy I See Mendelssohn, Caprice op. 33, Kb. i, measures 1-6. Cramer, Etude 33. No. I I EXERCISE SEVENTY-EIGHT. J- | J-J. | J.J- | J.J.|J- ^ m d. * -0-^ Si tM- -* I ff^ryv p^ a 7 5 bt ,f b4 83 93 i -•-^ -«»-=- g%±tif^ft^ atE^ *±bt ba hU a D7 ^ 7 * 117 To be elaborated with one-part figuration, as follows: i m i»i)= ffi :*i): & !r^ =?=t *i) -^J- ! 1 S ! S— 4 ^.^ ^i n,"~^ if 1 p^a =g^ *i) The characteristic features of these motives must be strictly adhered to. . 258 THE MATERIAL USED IN MUSICAL COMPOSITION. No. 2. Allegro Par. 461. i -gj- *3) ^ T^ r r »i 1)5 r s a , a Handel i ^ I g W- «a) *3) g^ r^- Mr r r I I 7 a bs r \ 'i) Continue in the manner indicated in the first half of the measure. — "2) The 2nd half of the motive, twice. "3) End figural rhythm on 3rd beat. — This exercise may also be made at the piano, with other (original) motives. No. 3. The sth melody of Exercise 75 is to be elaborated at the piano, in the following ways : 1. 2. 3. 461. On the other hand, the figural part may be accompanied by three or even more harmonic parts; in this case the motive is likely to be shorter and more narrow than in three-part figuration. See Cramer: Etudes 10, 18, 25, 28, 36, 40, 56, 80, 82. Mendelssohn: S. w. W. No. n, second Part (i.e., after the 2nd double-bar); No. 21. Irregular Part-writing. 462. In music that is designed for the keyboard, rather than for a definite number of vocal or in- strumental parts, the volume of harmony may be increased or decreased with the utmost freedom, at single points, or during certain members of the phrase. Such alterations in the volume of harmony should be made with some regard to the principle of tone-b'nes, and not in such a way as to produce an uneven and formless result. Therefore, when a fundamental part is temporarily omitted, it is usually necessary to introduce rests in its place, especially when the omissions are brief. Additions generally result from the octave-duplication of a fundamental part (most commonly the soprano or bass); though the increase in volume Par. 463. FIGURAL MOTIVES WITH SUPPLEMENTARY TONES. 259 may also occur at single points, as if an inner part had separated into two or more, for the moment. When the time-values are dike, any number of notes may be placed upon one stem, — never, however, when the time-values differ. For illus- tration: I. Allegro vivace i m Beethoven ^ ^s - 1 X -■^ Ex. 362. •1) ^ft W T-^^ S i? ^^^ I r r 2. Allegro ^^ iT^n. Beethoven 3. Adagio Q>0 " ^^=^ f^4.^ J . I j: jiiBtef^J^;^ ^ W ■•»- r»a) rr f =^, -^^ ^ J etc. M-^H^ £ljl feB* 1*3) ^E ¥=*: :t=*: S"^ f^ Beethoven 4. Allegretto Mendelssohn :a^ ^^^^ ^Tf *4) I ^«5) ' '«Jt". ^ J--