CORNELL UNIVERSITY LIBRARY MUSIC Cornell University Library MT 50.N85 V.1 Practical harmony on a French basis,. 3 1924 022 305 274 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/cu31924022305274 PRACTICAL HARMONY ON A FRENCH BASIS HOMER A. NORRIS PART I BOSTON H. B. STEVENS COMPANY Copyright, 1894, by H. B. STEVifcNS Company Boston Copyright secured m Englana PREFACE. The author has endeavored to prepare a text-book on harmony, based on the principles of the most eminent French theorists and composers, which shall enable the student to analyze with ease and clearness the most complex musical compositions of the modern school, and which shall also stiinulate the musical instincts of those who are endowed with the gift for composition. It is justly urged against the average text-book on harmony, that it is either too eleinentary or too scientific. If too elementary, it leaves the pupil uninformed regarding much that he will meet in the works of the masters, and it usually contains detail which fatigues and discourages. If, on the other hand, the book sets out with details of the laws of acoustics, it appeals more to the mathe- matician than to the musician : the theoretical is developed at the expense of the practical, and neither artistic intelligence nor mu- sical sentiment is quickened. Whatever inay be proved by such mathematical calculation, it has little or nothing to do with aes- thetics which is constantly changing. Our modern musical system is based on what is both natural and artificial ; it has been accepted, and our musical habits, so to speak, and much that we call musical instinct, ai'e the result. New musical effects come, we suspect, as a spontaneous discovery, rather than as a result of patient scientific investigation. For this reason, in all matters having to do with tho artistic and the aesthetic, practice should precede theory. The study of harmony can be made, and should be "nade, not a drudgery, but a delight ; and the French methods have been chosen as a basis for this book, because they present theories in an attrac- tive, as well as in a practical manner. The Frenchman is instinctively an artist. The beautiful appeals to him irresistibly, and his feeling for the narrow line that separates the commonplace from the purely artistic is sensitively keen. One proof of this may be found in the many beautiful examples by eminent French composers and theorists, written expressly for this (iii) iv PREFACE. book, and which appear in Part II. If one were not told, one would not suspect that they were "harmony-exercises." The laws governing key-relationship and all that should be understood by tonality — that element of modern music which is of the very first importance — have been emphasized. A text-book of to-day should make it clear that Wagner, Brahms, Leoncavallo, and Bruneau are as truly in key as is Mozart. It is believed that this can be most speedily and most safely accomplished by first demonstrating all possible uses of the diatonic triads. So far as the author knows, there is no book published in this ■country which reduces the so-called "Augmented Sixth" chords, the stumbling block of all harmony students, to altered Dominant Seventh chords. He feels certain that with this system they will be readily recognized, and what is of the greatest importance, that their tonal relationship will be apparent. Moreover, by this method the works of the masters can be analyzed much more easily and clearly. The system of a figured bass has been adhered to in the opening chapters, in order that the pupil, before being thrown wholly on his own resources, may gain a certain facility in correct writing. Terms in common usage have been employed wherever possible. The chapters are divided in keeping with the subjects discussed ; the length of the lessons must be left to the discretion of the student or of the teacher. A small pamphlet, intended for teachers, and containing all the exercises, with the harmonies of the composers, is issued separately. The author desires to express his appreciation of the warm words of encouragement, and of the suggestions sent from time to time during the writing of this book, by his Paris teachers : Messieurs Theodore Dubois, Eugene Gigout, Alexandre Guilmant and Benjamin Godard. He also acknowledges his indebtedness to the various text-books used at the Paris Conservatory, and notably to the Treatise by Reber, with the accompanying "Notes et Etudes" by Theodore Dubois. The author claims little or nothing that is new ; the book is rather a compilation or condensation of that which he believes to be the best. It is hoped that among the really good books on this subject it will find a welcome place and add something which may be of use to the modern student. Boston., August., i8g4. THE AUTHOR. PRACTICAL HARMONY. PART CONSONANCE. CHAPTER I. Note. The only eleinentary knowledge of music presupposed is that necessary to sing or to play, unaided, a written melody of the simplest order. INTERVALS. <- The distance from one note to another is called an interval. Intervals are reckoned upwards, and are measured by the number of degrees they occupy. By degrees is understood the lines and spaces of the staff'. The interval at a, in example i, is a fourth; from C to F, inclu- sive, there are four degrees. The interval at b is a sixth, and that at c a ninth. Ex. 1. lUili^ An intei'val is harmonic when two tones are heard simultane- ously, melodic when heard successively. Ex.2. Harmonic. V Melodic. j Intervals are named either perfect, major, minor, augmented, or diminished; they may also be doubly-augmented, or doubly-dimin- ished. The interval from the first note of any major scale to any note of the same scale is said to be major, excepting the fourth, fifth, and (I) PRACTICAL HARMONY. The diminished second, having more the cliaracter of an enhar- monic interval, is not included. Diminished primes and octaves occur in melodic progressions, but are not used in the construction of chords in elementarj'^ harmony. A diminished interval made one half-step smaller becomes doubly- diminished ; an augmented interval made one half-step larger be- comes doubly-augmented. These intervals are not often found nr the writings of the older masters, but are of frequent occurrence in modern chromatic hariiiony. Ex. 10. Doubly-aug. fourth. Doubly-dim. sixth. i W-r. ;s^ :bfe "i-"s-- g It will be noticed that intei'vals may contain the same number of steps., and sound the same when played on a piano or organ, and yet bear different names. Ex. 11. Aug. second. V Minor third. =I=S3: I If in naming an interval the lower note is impracticable for the beginning of a scale, as Fb, BJ, DJt, etc., move both notes either up or down one half-step -without changing the letters., as at b and d in example i 2 ; this will give the same relative distance. Ex. 12. i 'vr d. w -s^ =1^- 5^ :tJ^ la^t^^B INVERSION OF INTERVALS. An interval is said to be inverted when the position of the notes is so changed that the one which was the lower becomes the higher. Ex. 13. i^ -G>- I Third. Inversion of third. CONTENTS. PART I. CONSONANCE. Chapter I. page i Note, — Intervals, — Inversion of Intervals, — Classification o£ Inter- vals, — Exercises, — Suggestions. Chapter II. page 8 The Major Mode, — Chords, — Triads, — Part-writing, — Melodic Progression, — Harmonic Progression, — Consecutive Octaves and Fifths, — The Tritone, — Sequence, — Rules for harmonizing Basses, — Suggestions, — Exercises, — Additional Exercises. Chapter III. page 23 The Minor Mode, — Melodic and Harmonic Progression in the Minor Mode, — The Augmented Second,; — Suggestions, — Exercises, — Addi- tional Exercises. Chapter IV. page 29 Chord-relation, — Harmonizing Melodies in the Major Mode, — Sug- gestions, — Harmonizing Melodies in the Minor Mode. Chapter V. page 34 Figuring of the Bass, — Open Harmony, — Exercises. CHAFfER VI. page 39 Chords, — The First Inversion, — Exercises, — Note concerning the Study of Counterpoint. Chapter VII. page 44 Chords, — The Second Inversion, — Observations concerning the Terms Consonance, and Dissonance. (v) VI CON'TE.,ic. Chapter VIII. page 54 Form, — The Phrase, — The Period, — Cadence, — Exercises. Chapter IX. page 59 Modulation, — Tonal Relation, — Modulations of the First Order, — Exercises, — Modulations of the Second Order, — Modulations to Re- mote Keys, — Passing Modulations, — Exercises, — Harmonic Se- quence, — Exercises, — Tonal Sequence, — Exercises. Chapter X. page 78 Resume. Notation, — Chromatic Scale, — The Ecclesiastical Scales, — Chords, — Triads, — Melodic Progression, — Omission of Voices, — Consecutive Fifths and Octaves,— Hidden Fifths,— The Tritone,— The Augmented Second, — Tonality, — Form, — The First Inver- sion, — Modulation, PRACTICAL HARMONY. 5 All intervals, except those called perfect, change their character by inversion : major intervals become minor, and vice versa; the diminished become augmented, and vice versa. The perfect fourth and perfect fifth are the only intervals that remain the same when inverted, and this is one reason why they are called perfect. The unison by inversion becomes a perfect octave, and is also classed a perfect interval. A few theorists name the perfect intervals major. As they stand in the regular order of the major scale they are certainly major, but they alone remain unchanged by inversion, arid for this reason, as well as for others that will appear later, it is better to give them a more specific name. Moreover, these inter- vals are termed perfect by the more prominent theorists, and it is always best to follow tradition unless some great advantage is gained by a change. CLASSIFICATION OF INTERVALS. There are certain intervals which at once please the ear and give a sense of repose or finality. The most important are the fifth and octave which are termed in musical t\\eo\y the perfect consonances . The next in importance are the major and minor thirds and sixths ; these are termed the imperfect consonances. The interval of the fourth is classed by the best theorists a tnixed or neiitral'wAe.xv&X ; it is sometimes consonant, sometimes dissonant, according to the position it holds. Theoretically it may be con- sidered a perfect consonance, but musically never, because few intervals give a less sense of repose or finality than the fourth. At one time it was considered one of the most perfect of intervals, later as a dissonance. This suggested that it might be either one or the other according to conditions, and so it is now named a mixed interval. This will be more fully explained in the chapter on the inversion of chords. In writing ascending passages of half-steps it is correct, as a gen. eral rule, to use sharps, as at a in example 14; in descending pas- sages it is correct, as a general rule, to use flats, as at b. Ex. 14 Ef^^^^llEOdE^Ji^^^B PRACTICAL HARMONY. Played on a piano or organ the CJ at a gives precisely the same sound as the Dl? at b ; but played on a violin or any instrument that gives a pure scale, the Cjf is higher. For this reason sharps natu- rally ascend and flats descend. From C to Cjf is called a large half- step, from C to Dl? a small half-step. In other words, a chromatic semitone forms a large half-step, a diatonic semitone a small half- step. EXERCISES. Copy the following notes on a staff and above each write the in- terval called for. Chromatic Diatonic Enharmonic Small Large Unison. Aug. prime, semitone, semitone, interval, half-step, half-step. S^^d^5EEl^5EEEl^:iE^l^teZzl^^LEl= Major second. Minor second. Aug. second. Major third. Minor third. i I^H p Aug. third. Diminished third. Perfect fourth. Aug. fourth. Dim. fourth. "tJZS"" Doubly-aug. fourth. Perfect fifth. Dim. fifth. Aug. fifth. Doubly-dim. fifth. i mmm w =i«i Major sixth. Minor sixth. Aug. sixth. Dim. sixth. Major seventh El^H^H^pi^ e; g Minor seventh. Dim. seventh. Perfect octave. Dim. octave. IE ii«z =#s: Aug. octave. Major ninth. Minor ninth. Aug. ninth. a Wi PRACTICAL HARMONY. 7 Note. The diminished fourth and fifth are often called imper- jfect intervals, to distinguish them from the perfect. The terms imperfect and diminished are synonymous in speaking of the fourth, fifth, and octave. SUGGESTIONS. The student is urged at this point to name the intervals in any standard piece of music. For this exercise nothing could be more exhaustive than the overture to Wagner's Tristan and Isolda, which may be found in inexpensive edition at any music store. This exercise is for the eye only, and it is the teacher's duty to see that the ear is likewise trained, for it is of the greatest impor- tance that the student realize at the beginning that he should hear as well as sec. One of the most practical exercises is for the teacher to play or sing a melody which the pupil should notate on black-board or music paper. It is best to play or singthe melody slowly, and with as little accent as possible ; in this way it becomes a valuable exer- cise in rhythm. Unless the pupil has absolute pitch, it will be found necessary at first to name the key in which the melody is played or sung. It is best to play a short phrase three times, with a slight pause between the first two hearings, but connecting the phrase the third time to the succeeding phrase. The pupil should notate all of the phrase he can hear before the third repetition. After the whole has been notated, the teacher should play it through slowly, the pupil correcting the errors as best he can. With a few exceptions this exercise w^ill be found discouraging to the student at the beginning ; a few lessons will show surprising results, and later he will realize the great advantage of such an acquisition. Another useful exercise is for the student to write any intervals he may choose. The teacher may play them either correctly or not, and the student must decide whether or not they are played as written. For all work of this character the black-board is more useful than music-paper. The pupil will save much time if he will acquire the following method of notating : In making a whole note draw the upper half from right to left: ''~^, then add the lower half from right to left: 8 PRACTICAL HARMONY. O. In making a half note a stem only need be added : ^. This method not only insures greater facility of execution but elegance of notation. Whenever a single note stands above the third line the stem should extend dovvrnw^ards : — p — . Whenever a note stands :±= =1= below the third )ine the stem should extend upwards : — ^ — CHAPTER II. SCALES. THE MAJOR MODE. TRIADS. PART-WRITING. MELODIC PROGRESSION. HARMONIC PROGRESSION. CONSECUTIVE OCTAVES AND FIFTHS. THE TRITONE. SEQUENCE. The form of the major scale as used to-day has remained fixed for about two centuries. It consists of a succession of major and minor seconds, the latter coming only between the third and fourth, and the seventh and eighth degrees of the scale. A scale with the above succession of intervals is said to be in the major mode, and diatonic. Ex. 15. I ;7^=^-^=^ E^g=fJ I ' 3 4 5 Unless the student is thoroughly familiar with all the major scales he should now write one from each of the following notes : C, G, D, A, E, B, F#, C5, Cb, Gb, Dt?, A\> Eb, Bb, and F. Place no sharps or flats at the beginning of any scale, but insert them wherever necessary, preserving the same order of intervals as is given in Ex. 15. CHORDS. By the word chord is meant the simultaneous sounding of diflier- ent tones. / Chords are built by taking any note and adding above it a succes- \ sion of thirds. The lowest note is called the root or fundamental. PRACTICAL HARMONY. In example i6, G being the lowest note, and those above formed in a series of thirds, G is the root or fundamental of each chord. Ex. 16. i -s- -'Sr- I To find the root of any chord, arrange the notes so that they be- come a succession of thirds ; the lowest note will always be the root or fundamental. In example 17, E is not the root of the chord at a, because the intei'val from the second note of the chord, Gi to the next, C, is not a third but a fovn-th. Rearrange these notes, as at i5, in a series of thirds, and the root is found to be C. a. b. Ex. 17 ^^ii^Hi Chords are reckoned in this way containing three, four, and five notes ; those of more than five notes, or aggregations that cannot be readjusted in thirds, will be explained later. EXERCISES. Name the roots of the following chords : Ex. 18. ^^SSSHHIPI^B S \ W^3. -j- :f^_=Eg=l:l «- S=^ 1 * I ^- TRIADS. A chord formed of three notes is named a triad. This chord forms the basis of all musical composition, and for that reason will be used exclusively in Part I. of this book. Triads, like intervals, are either major, minor, diminished, or aug- mented. A triad may be formed on any degree of the scale. lO PRACTICAL HARMONY. Each triad is formed by adding a third and a fifth to any note taken as a root ; the distance of these upper notes from the root de- termines the character of the triad; i.e., whether it be major, minor, diminished, or augmented. ' A major third and perfect fifth form a major triad. A minor third and perfect fifth form a minor triad. A minor third and diminished fifth form a diminished triad. A major third and augmented fifth form an augmented triad. Roman numei'als beneath chords show upon w^hich degree of the scale they are founded. The different kinds of triads are usually dis- tinguished in this way : large numerals denote major triads, small numerals denote minor triads. A zero (o) by the side of a small numeral denotes a diminished triad, and the plus sign (x) denotes an augmented triad. The different kinds of triads found in the major scale would be distinguished by Roman numerals as follows : Ex. 19. i Major. Minor. Minor. Major. Major. Minor. Dim. w s- I II i IV vn^ For convenience in speaking, and also partly to indicate the rela- tive importance of chords, special names have been given to each note of the scale. The following is the order preferred by many theorists : Tonic — Super-tonic- Mediant Sub-dominant- Dominant— -ist degree of scale. -2d degree of scale. -3d degree of scale. -4th degree of scale. - 5th degree of scale. Sub-inediant 6th degree of scale. Leading-tone 7th degree of scale. The major chords are the most important and are called the fri- tnary or principal triads There are but three, those built on the tonic ( I ), aominant (V), and sub-dominant ( IV ). In this book the terms super-tonic, mediant, and sub-mediant, will not be used ; those degrees will be called respectively the second., third, and sixth. A musician rarely speaks of them in any other way, this PRACTICAL HARMONY. II distinction making prominent the more important triads. The term leading-tone will be used in speaking of the seventh degree of the scale. The triads on the second, third, and sixth, to distinguish them from the primary triads, are called the secondary triads. Both the primary and secondary triads are consonant ; the triad on the lead- ing-tone, including the diminished fifth, will be classed later. PART-WRITING. DOUBLING OF VOICES. In the study of harmony the student should always write for voices, unless otherwise directed, and usually for a mixed chorus of four parts, — soprano, alto, tenor, and bass. These voices should rarely exceed the limits given below. Soprano. -JSi Ex. 20. (f): Alto. Tenor. "^A 1. \ Bass -<9-/-*- ©r m "^^^^m^ 5)-5-- In writing four-part harmony, as there are but three notes In a triad, one of these notes must be doubled or used twice. Any note of a triad may be doubled, but it is better to double the root than the fifth, and better to double the fifth than the third. The third of a chord, especially if it be major, is particularly conspicuous, and in certain registers so overweights the chord that little else is heard. This is particularly true in a low register. Ex. 21. fe—lEi^EiEz-J 9z:z^=E| =gJzrE| E Doubled in a higher register between soprano and alto, or alto and tenor, the effect is often vei'}- agreeable. Ex. 22. iiiHiB '^ i 12 PRACTICAL HARMONY. As the doubling of the tonic, dominant, or sub-dominant strength- ens the tonality or key, it is often well to double these notes when they appear as either the root, third, or fifth of a choi'd. Tonic doubled as Tonic doubled as Tonic doubled as root of a chord, third of a chord. fifth of a chord. Ex. 23. St la ll~% :i3 -f^-^ I But as a rule it is best to double the root of a chord. Play and note the comparative effects of the following : Ex. 24. i Root doubled. VFifth doubled VThird doubled. T^s: - -&- -e>- J 0,. ^ 1 ■D \ " ° 25 1 1 !• I 1 1 ^ ^ ■ 1 1 1 v 1 1 1 1 Many popular hymns and patriotic songs contain good examples of natural, expressive melody. In the following illustrations it will be noticed that nearly all of the intervals are small, and that they progress mostly in the scale. H PRACTICAL HARMONY. GOD SAVE THE QUEEN, :4=t: *—P~ -t^-n- X- '*^-p- pzqr: -vrX- m ■<=Z-. ^1 -^-^-fi-r^— •- i=r=t EEEEEEJE p=r^ :^-f= ^^i0 =tp r-^s^ t=t AUSTRIAN HYMN. ^g: EEgi£^gE^ ^.^iSSbt* ^S^^i^zfiig: ^- ^iis ^ ^^••l Jt5zp^,:^-^z pr #-» r^ • #-^^ ^^=&^ ■^-*z~3t:P^' :^i 1 RUSSIAN HYMN. tfEffiTr^jf ^gsgg ^^ #E^ a -N--^rP-»- I 3E P^i&— •- *Tt ;5:=^ DANISH NATIONAL HYMN. -^- H- :?--H=+ -r-ff p= -iS"- _f2_ =^ "d^^p^V^ Ttt (n) t / jV- c^fJ- It ^-^ -P- -^-P SE^r-?f:tp 1^^-^- i: t?SE:i=^ ::^= =^1 ifct i^±=F ::^P -*-i- 1=^:^-« •— F:i=^-- -•-|L» LJi!^ Ttat "P=»= tt ^itrf =^ ■4Z— «■ :?— «- THE WATCH ON THE RHINE. H:?— !"-*^ eE^::rf^^=3 E? i»-^- E JCp:^: tJ- r=5:i-=Ei :^=F=^t=^2ti-t=S!- ^y|afeSg^grEf^_E^^gE±fEE s^ £ =F^cp^ ^^ # #1 ifrf: -g-X- PRACTICAL HARMONY. 15 It is a mistake to think, as many do, that all the beautiful melo- dies of the great composers came to them suddenly, as inspiration, and that they were written as first conceived and never changed. Nearly all of Beethoven's melodies are rhythmical, simple, and nat- ural in intervals and modulation, yet no oonriposer spent more time in changing, polishing, and perfecting his melodies than did he. HARMONIC PROGRESSION. Here, as in the rules for melodic progression, all that can be done is to point out as clearly as possible those harmonic progres- sions which are repugnant to the ear and have been avoided by all the masters. If striking exceptions are found in the works of these great composers, one may be sure that these masters first knew the value of the rule before they disregarded it. Those who know most about such matters agree that the best way to study any form of art is by absorption. The student will save much time and labor if he will follow the advice of his teacher, taking a great deal for granted. It is not -wise to experiment on matters already solved by others. He will later fully appreciate and understand present restrictions. But the teacher should explain as clearly as possible, and es- pecially by appealing to the musical instinct., why one progression is forbidden, another permitted. In connecting the different triads in a satisfactory succession, either of three movements may be used. When voices rise or fall simultaneously, as at «, example 2S, the motion is said to be parallel., or similar. Whenone voice rises while another falls, aS at b, the motion is said to be contrary. When one voice remains stationary while another rises or falls, as at c, the motion is said to be oblique. b.\ I I Ex. 28. Contrary motion is preferable to either oblique or parallel. By its use the parts gain individuality, and many pi-ogressions which are considered faulty are avoided. i6 PRACTICAL HARMONY. CONSECUTIVE FIFTHS AND OCTAVES. If the student will play the following melody with an added part five notes below, he will find it most disagreeable. Ex. 29. m itt» V^tL — »-^— - — j-K- — —r- ^\ fTpftff^i i4:iti ■rr ^^- ■ntriM. ~^^t-^ vrr I Nor will he find it more acceptable, but rather worse, if the mel- ody be doubled one octave lower. etc. Consecutive fifths or octaves like the above, either by parallel or contrary motion, are forbidden. Fifths by Fifths by Octaves by Octaves by parallel motion, contrary motion, parallel motion, contrary motion. Ex. 31 -«=i — ai ll2- I S- i 2=c=f=|=^=F=i=f| There are other successions which taken alone are nearly as un- satisfactory as fifths, as, for example, a succession of fourths : Ex. 32 =8 w -G>- i But the preceding may be made very musical by the addition of another interval : Ex. 33. i w -St- 1 While the bad effect of consecutive fifths is rarely bettered by any arrangement of the voices. Consecutive unisons., either by parallel or contrary motion, are forbidden : . 34. ^ ^^ PRACTICAL HARMONY. Parallel motion. Contrary motion. 17 ^^r^^ -~. — H W-^— - "^ — e© — H -ts- Rt — 5> - ^ H ^^^ — g — II r^ II THE TRITONE. A tritone is an interval of three ^vhole steps. Ex. 35. i EI: This succession, when heard under certain conditions, produces ■one of the worst possible effects, and for this reason w^as called the diabolus in musica by the old school of Italian musicians. When the chords of the dominant and sub-dominant are heard in succession, w^ith the leading-tone in the soprano followed by tonic, the two notes of the tritone are heard, first in the soprano, then in the bass. Ex.36. V II ■fi^ giS^ g H ^ •S','***!*,^ s^ H kJ ^ ^^^ r»' ^ ^^"^r' II 11 II This harsh effect is called the false relation of the tritone., and should be avoided by placing the leading-tone in an intermediate ■voice. Ex. 37. SEQUENCE. A sequence is a s^'mmetrical repetition of a melodic or harmonic figure. Melodic. i^. Ex. 38. ^fe SB i8 PRACTICAL HARMONY. Harmonic. Ex. 39. b^3t:* _r__ ^ ^ gr^E^IS.^ I I I .^-p 3 -zS- ^: !±i:i:l W^M *i -f=^ =F ^h =^p: =t SI In the above harmonic sequences the same bass is harmonized three ways. In each all voices move regularly in exact sequence. But this is not always necessary, nor need the responsive figure always be exactly reproduced. In sequence, the ear being gratified by a regularly recurring rhythmic figure, certain progressions which would otherwise be considered faulty are permissible. Note. It is not expected that the student will memorize or even , understand all the rules and accompanying illustrations in this chap- ter. They are placed here more for future reference than present study, and he will better appreciate them after wi'iting the succeed- ing exercises. The foregoing illustrations are condensed for convenient reference into the following . RULES FOR HARMONIZING BASSES. MAJOR MODE. I. If no figure stands over the first bass note, begin the exer- cise with the octave of that note in soprano, placing the other notes of the triad in the nearest position underneath. A 3 or 5 signifies that the soprano is to begin with the interval indicated. This ap- plies to the first chord only. II. If a chord contains notes that were in the preceding chord, they should be retained in the same voices. This rule may be disregarded under the following conditions : When the bass moves from the second note of the scale to the dominant, as at a ; when the second chord is a repetition of the pre- ceding chord, as at b ; and in sequence, as at c. b. 15- =g= m^^mm Ex. 40. I m i PRACTICAL HARMONY. ip III. If there are no notes alike in consecutive chords, move the soprano, alto, and tenor in contrary motion to the bass. IV. Consecutive fifths and octaves are forbidden. V. Allows no voice to. progress any augmented or diminished interval except the augmented prime — chromatic interval— and the diminished fifth, as in example 26. VI. In the succession V, IV, do not allov^r the relation of the tritone between soprano and bass. ( See examples 36 and 37.) VIT. Double the leading-tone rarely except in sequence. ' SUGGESTIONS. Choose positions neither too high nor too low. — Do not pass the limits in example 20 ; the extremes should be of short duration As a rule, double the root in preference to any other interval. — Con- ti-ary motion is stronger than either parallel or oblique. — With a bass moving sequentially, seek a corresponding symmetry in the other voices. — Although not invariably to be observed, it is usually best to close an exeixise with the sopr'ano ending on tonic, pre- ceded by leading- tone. Note. Particular attention is called to the fact that when the bass moves from the second degree of the scale up to the dominant, it is often best to move the three upper voices in contrary motion to the bass. See first exception to Rule II. Also when the bass moves from the dominant to the sixth, it is often best to double the third of the chord on the sixth degree. This is especially true if the chord on the dominant has its thii'd — leading-tone — in soprano. Not. Ex.41. P^^g^i^p^P^^ A careful observance of the preceding suggestions will save the student much labor and needless confusion when he comes to exer- cises in the minor mode. In the following exercises a soprano, alto, and tenor are to be added to the given bass, according to foregoing rules. In harmo- nizing these basses no instrument shvuld be used. The key- board should not be touched until the exercises are finished. PRACTICAL HARMONY. Z*. '■i* i A\>. '^^ -p2=:q: '^' — F— '-«'■ m I V ii aJ - =F= ^t^E^. I 3. ^-Sp^i=F -P2- £=F -S—\-(^ EEEb^^~ :^t 11 H |fi- r*z=t:= ■gi — '^ - :q=3= F. mm^?:^^:^. ^--=^= -j:; s.- I 6. 3 ^. ^'«fer U-- =r= -&— -i — -«■— X — 1— -1 — n^z: ^H ^\^^ w fc^-I ^t?. ■f^ — " ■f^' E=^= i ^^^^E^. n- 8. «■— (2- ^■f£r=^^ ^- ^i3li^:^ig •-[-1=— g-T-«'-=-r-H- EiE^E=Pi5 3^ G. 10. =iS^s?BE3^3 fcEzt -«.— h^- egii 1 1, 12 ^9%$=^ /: fc^-=t ^^^i=iE^a fiii^^: ^~ A^. X — ^- b:^=,^= I^B ■i is.E^iiir ^r^ElEF^Jj c?. EEEEt ■^==tF=:rr ist:'*— 2^- P PRACTICAL HARMONY. 21 After these basses have been harmonized they should be played ; whenever a succession is unsatisfactory it is possible that a rule has been violated. If a passage could be written in either of two ways, each apparently correct, write the form preferred in large notes, and the other possible disposition in small notes. After the exer- cises have been corrected in this way by the student, with the aid of an instrument, he should listen to them while played by another. Without looking either at the keyboard or the music he should name the major — principal — triads whenever they occur. As soon as these can be readily distinguished the minor chords should be named in like manner. This exercise stimulates the musical in- stinct and should be followed throughout the book. It is recommended that the preceding exercises be corrected be- fore the following additional basses are harmonized. The lessons should all be written in ink, and the pupil should come to his les- son prepared to play them in the key in which they are written, and also to transpose and play them in the keys indicated by a capital letter at the right of each bass. This practice of transposing the lessons should be continued in keys selected by the teacher. ADDITIONAL EXERCISES. The following basses are to be harmonized according to previous rules. The repetition of notes, in-egular rhythms, and generally light character of these exercises are purposely introduced ; it is one one of the aims of this book to lead the student beyond the writing of monotonous psalm-tunes. Although the succeeding exercises are instrumental rather than vocal, all previous rules regarding the tieing over of notes common to consecutive chords should be strictly fol- lowed. Whenever rests occur, as in exercise 5, the voices should move to the next chord in as strict accordance to rule as though there were no rests. As a general thing it is best to tie over a note which will bring contrary motion ; this rule may often be disre- garded in progressions like the following, when the outside voices move in thirds. Ex. 42. i I i^ "S ■3-- i 9-f: =f== ^ PRACTICAL HARMONY. EXERCISES. Allegretto. -0-0- -0- -iS>- :iir-ffl?Ef$E^rES Et£t rw-'Y-ir'S- § =B ^:q-" ma -§3f!t-^ »'^-\-0- titlt li — c^ ^^ '^^A ::^=i=:^=P= =P=P=S= «=4E EEEE^ m- I -f2_ t^^i^p-- =t=^t :td::s: P-^- r^-r»- ^9^fc|=§ i.ws= =F=t 't^ -0 — f- ;9^.fe elEEz Allegretto. 3 Lightly. ?=i<=i:^ e£2^ pp li^EiE^ Si inzzt i93 ^^E^^iiZ^ ^= -^— ^ — -s^- -sl-i PRACTICAL HARMONY. 23 CHAPTER III. SCALES. THE MINOR MODE. MELODIC AND HARMONIC PROGRESSIONS IN THE MINOR MODE. THE AUGMENTED SECOND. The two scales employed in modern inusic are the major and minor. Eacli major scale has an accompanying or related minor scale, called its relative minor. It is customary to use capital letters in designating the major keys ; small letters the minor. C (Major). a (Minor). Ex. 43. llz i I The relative minor of any major scale has for its starting-point, or tonic, the third note of the descending major scale, and its sig- nature is the same as the major to which it is so closely related. The relative minor of C would be a : that of G, e ; and that of F, d. A major and its relative minor are said to be related., because they look and sound much alike. The major scale of C is formed as at I. in example 44; one of the earliest forms of its relative minor, a, stood as at II. : ir. Ex. 44. S =ri: f 1=4= ^ -0- _^_,_ iiii This form was in use long before our major scale. It has under- gone various transformations, which would here be confusing and valueless. The form used to-day in elementary harmony, and for that reason called the harmonic minor scale., stands as at II. in the preceding example, with its seventh note chromatically raised. Harmonic Minor Scale of a. Ex. 45. l^E^EE^^^^E^E^l 24 PRACTICAL HARMONY. The harmonic minor scale, then, is found by taking the third note of the descending major scale for a tonic, and chromatically raising its seventh note. This seventh was raised to gain a leading-tone and to secure a dominant chord in minor the same as in major. A chord on the fifth degree in any minor key without this leading-tone vyould be dis- appointing and produce no satisfying close. Ex. 46. -^- i^i i^riii: -z5i- -s ^ I 5z=3z =1= j= -s<- -t- 1^1 At a, the closing chords are vague and unfinished ; at b, the same chords with the seventh raised give a satisfying close. In the major scale, example 44, the half-steps come between the third and fourth, and seventh and eighth degrees. In the minor scale the order is quite different, and it is this different disposition of intervals which gives to each scale its character. Ex. 47, ESI ---t- --X -M i ^ 4__:^ ' — - It will be noticed that there are three half-steps in the minor scale. Between the sixth and seventh degrees of the minor scale there occurs the interval of an augmented second. See X in example 47. This interval does not occur in the major scale, and following the general rule that no augmented intervals are to be written, this aug- mented second must not be used in elementary harmony. In the rules for harmonizing basses in the major mode, the rule for retaining notes in the same voice could be disregarded when the bass moved from the second degree to the fifth. It is necessary to do this when the succession comes in the minor key, in order to avoid the augmented second. Augmented second. Ex. 48. ji -■4-- S ISI i asEi -1=2- V PRACTICAL HARMONY. 25 In the major mode it is often well to double the third on the sixth degree. In the minor mode the third on the sixth degree must al- ways be doubled when preceded by the fifth degree, to avoid the augmented second. Not. Ex. 49. r r ' ' '^ -^ 1 1 — — 1— ■-■ / -^-^ =1" ~g — ~sr 1— s^j d- t^H f^ 1 ^7 S "^ ^ SS ■ ,! »^~ ^ -i- -g: % ^ ^ -«^ ""-«!- f f^T 1 75- «■ 1 i ^5^ — © 1 1 ^^ -^-w 1 3-—^ f- 1 J ^ 1 1 (^ — 11 \ sJ \ /^ 1 A—^ — 1 1 1.1 V VI V VI V VI The third doubled in the octave, as at a in preceding example, is always preferable to the unison, as at i5. This unison between soprano and alto weaken^ the harmony, and should not be used when another disposition is possible, unless coming on an unaccented part of a measure, as at a in following example, or at the close of a musical phrase, as at b. Even in the latter it is generally better to allow the leading-tone to descend, as at c, in order to gain a fiall chord at the close. Ex. 50. J- m%Em BE :Se i i The unison is least objectionable between inside voices, and is best introduced on the weak part of the measure. The different kinds of triads in the minor mode are as follows : Minor. Dim. Aug. Minor. Major. Major. Dim. Ex. 51. 3gz Ilix i V VI For the present the diminished chord on the leading-tone, and the augmented triad on the third degree will not be u-sed. Reasons for this will be given later. The diminished triad on the second degree will be of frequent use. The principal chords of the minor mode are the same as those of the major, and all that is written regarding them there is equally applicable here. 26 PRACTICAL HARMONY. Whene\er a sharp, flat, or natural, stands over a bass note luith- out a figure by its side, as at a, example 52, it signifies that the third note from the bass is to be chromatically changed. A figure by the side of a chromatic sign calls for the corresponding intei-val from its bass to be altered. See l>. a. b. $ Ex. 52. 3i^ -^ -M- ^-W- :B #s ^^ 1)3 i A chromatic sign once used to change a note, will effect all other notes in that measui'e that are on the same degree. ADDITIONAL RULES FOR HARMONIZING BASSES. MINOR MODE. I. Whenever the bass moves from the fifth to the sixth degree of the scale, or vice versa., double the third of the chord on the sixth degree. II. Whenever the bass moves from the second degree of the scale up to the fifth degree, move the three upper voices in contrary motion. Note. The early musicians, as a rule, made the final chord of any piece of music major, even though the mode were minor. Such concluding chords should not be looked upon as changes of key or modulations, but rather as a change oifor?n from the minor triad to the major. Palsstrina. Ex. 53. "ST -IS- I L-i =ig= ;b These early writers looked upon the minor third in a triad as an imperfect or artificial interval, and consequently rarely used it in a concluding chord. This concluding optional major third will oc- casionally be found in the succeeding exercises ; it will be designated by the necessary sharp or flat enclosed in parenthesis, as in examples 2 and 3 in Additional Exercises. PRACTICAL HARMONY. 27 SUGGESTIONS. Carefully reread the rules and accompanying Suggestions at close of Chapter II. The student will do well to look the basses through before hannonizing them, noting those places where the bass moves either from V to VI, or VI to V, or from ii to V. After marking the places where these successions occur, again read the two additional rules for harmonizing: basses in the minor mode. —-=4=^ — F EXERCISES. % I « , l <3 i 'i- 2. i^iSTfe _f2 1 : :^— p- (2 ^ ^ -^—rxf U 1 ^ 7^ — ^ 3- Ei^ffi^-ib -s)- 4. :i^5:g-r /• TS»- -gi-a^ 'mi-m-- TE±EE ?2--^F^ 6. ^9^=g=?-g=f ^^%±. -^-•-^=-^: f=^t ■e^;^.- -fi'T H I ;9i.tel l±|pE3=F E^f= I©— :^=p: t: 8. :i^iS^g E^E =t== /. 9. ii^g^gE^EE ^^-^==^-4-r^J- i^i ii -pq^» I 10. ^ §ftg$E _^ i2_ -^ i2- I 28 PRACTICAL HARMONY. B ^-. ^ n__ 1 1 . EBiEfca3^eE.-=pF=p=# s— -*=F ti:^ I 12. 13. '^^i^t ^ iS= -gi— - m^- f t=^ it'. i =t 4: -I — «'- ADDITIONAL EXERCISES. The following exercises, corresponding to the Additional Exercises in Chapter II., should be harmonized after the preceding exercises have been corrected. "l*"". n r — pT r1"*»^ r. ,f--f-. , ^ ^ m-'- 1 II P'^^^^ -•- — 1 i_L^- :F=?=E?:F^£f^= tF*^H a It 2. atSEST EESE P=fe -• — p- -s- /s ^^=^: / ^m i-\--i--& — 0- ±atati:=fc J PP EEEE i:J=:t:s--:d=:qd=p Tt=ti± « («) I ■5 « • » • a c»'«n ^ ^ ^ f 1 * i.tt I) » s. ^ v» 1 « N* >.* N> , S< 3/ O "^ J •*' f R i ' K ^ K 1/ ■K T ,. .a ^ ._ .* . -U , 1 igiii^p i^-t-S: -=!^S^^ I -^-i/-» H-«-='-* EXERCISES. The student should now compose several short basses in both the major and minor modes. The arrangement of all like work must be left to the discretion of the teacher. T/tt's original work is of the greatest importance., and should be insisted on at each lesson. fRACTICAL HARMONY. 29 CHAPTER IV. CHORD RELATION. HARMONIZING MELODIES. The relative good or bad effect of a chord depends much vipon preceding and succeeding chords. The same chord, placed under different conditions, produces wholly opposite effects. This is so true that a triad heard under changed conditions so changes in char- acter, that to the inexperienced ear it is unrecognizable. A chord which, preceded by certain other chords sounds very disagreeable, may become under other conditions one of the most agreeable. The truth of this may be in a measure realized by playing the following illustrations, which contain precisely the same chords : Ex. 54. That at a is almost intolerable, while that at b is acceptable. The chord on the leading-tone, marked x, is unpleasant at the best when coming in the major key with its root doubled, and for that reason has not been used. This same chord in the minor mode is full of character and beauty. Ex. 55. i ^=^= i 30 PRACTICAL HARMONY. When one hears an isolated consonant chord, the ear immedi- ately accepts it as a tonic. If thei'e are several chords in succession the ear is not satisfied until the tonic is again heard. Ex. 56. i w dl -s- :^ =^= I At a, example 56, there is no satisfactory close ; at b, the same suc- cession with the tonic added is complete and satisfies the ear. For this reason it is generally best to begin and close a piece of music with the chord of the tonic. In a series of chords there are three chords which must be more frequently heard than others in order to make the tonality and mode decisive. These are the tonic, doiminant, and sub-dominant. A suc- cession which did not contain more of these principal triads than the secondary triads, would be indecisive and lack tonal force. Their excessive use produces monotony ; their good effect is height- ened by the judicious intermixture of chords on the other degrees. Composers give as delicate attention to chord-succession as paint- ers do to the mixing of colors. The chords of the tonic, dominant, and sub-dominant have the strongest tonal force ; next to these in tonal force are the chords formed on the sixth and second degrees ; the latter should neither be too frequent nor too prolonged. The chord on the- third degree in the major mode is weak, tonally, and should be more rarely in- troduced. The augmented triad on the third degree of the minor mode, as well as the diminished on the leading-ton6 of either mode, are not to be used. HARMONIZING MELODIES. THE MAJOR MODE. In the following exercises a soprano is given, to which alto, tenor, and bass are to be added. The rules given for chord progression in the harmonizing of basses apply here. A soprano note could be harmonized as either the root. PRACTICAL HARMONY 3^ third, or fifth of a chord. For example, C could be either the root of a chord, as at a, the third of a chord, as at /5, or the fifth, as at c. Ex. 57. rsr ~s~ i m SUGGESTIONS. Begin each exercise with tonic and close with same The inter- vening chords should consist largely of the three principal triads. — The chords on the second and sixth are of frequent occurrence.^ The chord on the third degree should rarely be used except when followed either by the sub-dominant or the sixth. Ex. 58. i i i A chord may be built on any note of the scale except the leading- tone. — It will be found best to first compose a bass, then add the in- termediate parts. — The harmony should change with each soprano note, and the root of each chord must be in the bass. — Never move from the fourth degree to the third degree. — (See note Ex. 59.) Never move from the fifth degree to the fourth degree, with the soprano moving from leading-tone to tonic. Note. The progression from the fourth degree to the third degree produces the false relation of the tritone. Ex. 59. 32 PRACTICAL HARMONY. Note. When first attempted, the harmonizing of jtnelodies is exceedingly difficult. The following exercises should here written till satisfactory to the teajcher. With the average pupil, two or three or perhaps more lessons should be spent on this chapter. Not more than eight melodies should be harmonized before the teacher corrects them. The practice of transposing should be con- tinued. MELODIES. THE MAJOR MODE. feg J^=^^: B. t=t=F '•-4- m-*\ 'S-\f-T-^-f :tt=t:;: ^^m A. S^B ■(=-#-^- :t=t=t -s>—si- <=-«? i i--X- E]>. t "frfrr^p^ ^=SEEEtEEEE^ i^i £=t=tt Si^gSg I EMEEEEE^i^ ^=i 'jt^ l=i4 t=^b*i-^±^=» ^^ =f;^^t: i ^i=«^^^ ^- #p ^^ ^fe^#=g^^ tedijv iiH-i^ itJ-d: SI -*vi- ^T-|^-*-h ^T^T|- ^T^-* -| '^•-,1- l-^^-g^ 8. i ;fc«i=flz«=-« ^.- ^^EE=g=e=i=i^ littfc PRACTICAL HARMONY. 9. 10. 1 1, 33 B. IllBJipi-^i^g^gE^^Ei^i :fc^-l A. ^ i^T^-S^^^^-^-S— j-fc-^3"-3^Efg-^-[=i: :B ^^- =F=F=t^=F ■t=f -sHi5: £tJ. I.-Zl5=5= ssa I •S'— '-- &— l~2y- 12. i i=5^ lr6=B3tzt=*=?= :^ 1=q--1= ^^=i i 13. 14. pfc0=g=g :p=:p= ■i2— «- t=-\--- A\!. ■:h-^z=tz-^. P?=|=^=£zEt=f=^=^: §tE?ErfE^E^^ I ' ^- ^fe f=r=FJ g ^^^^^^fe^g Gt^. w eB MELODIES. THE MINOR MODE. i=^=:j: I S -»i — 4- -4 — ^rzziL -gsh iilfc M ~bi^ i g^ ^='=J E I P 1 2^ -(&-=- :(»2:^ 5-=^E3E :^= ^t>. a iI^S^if=±±t v»-=-»^ -imp:; itj* i I g-R^f^-a^-p- ifez :ff— f2- fe: :t=t 34 PRACTICAL HARMONY. i :i2= ^-ts. f%- m i-z^^=i=t:z^f:^ f^—n- ^^^^^^^l^E^^^^^l -='-5'-L^ ^-^tl^ ,fc&^ (S.)c. teFSg:^=^E^l^^E^^^S^B -^-^- -w-5- CHAPTER V. FIGURING OF THE BASS. OPEN HARMONY. In order to indicate as clearly as possible the position which the notes forming a harmony are to occupy, figures are placed either above or below the bass. The figures indicate the relative position of the upper three voices above the bass. The figures | would signify that an octave of the bass should be in the soprano, a fifth from the bass should be in the alto, and a third from the bass should be in the tenor. (See a, example 60.) It must be understood that these three upper voices may occupy any octave above the bass, pi'ovided the voices do not pass the limits given in Chapter II. The figures 5 would signify that a third from the bass should be in the soprano, a fifth from the. bass in the alto, and an octave from the bass in the tenor. (See b.) Ex. 60. i -6>- 3 a 8 I I It is often desirable to move one voice of a chord while the others remain stationary. This may be indicated by changing the figures according to the interval desired, and by drawing a horizontal line after those figui^es, the corresponding notes of which are to remain, stationary. PRACTICAL HARMONY. 35 Ex.61 Such changes are often made to gain rhythmic or melodic variety, or both. A horizontal line over different bass notes signifies that the harmony over the first bass note is to be continued. In such a case the upper three notes may remain stationary, as at a in the following illustration, or \h& position — not the harmony — maybe changed, as at b. Ex. 62. fe i m -J- ^m^^^m A horizontal line drawn through a figure signifies that the cor- responding interval should be diminished. Ex. 63. m — ^^ i W ibsr ^i: I ^1^1:1 Consecutive octaves and fifths which result from a change of posi- tion of a chord, are permissible. Ex. 64. 36 PRACTICAL HARMONY. It often occurs that a change of position does not correct what would otherwise be consecutive octaves or fifths. d. ,/ k.. Ex. 65. fc^^^iiiiiii^ r 3^*^ ^^s^^m^^^m The consecutive octaves at a and c are hardly more disagreeable than those at d and d. The change of position, coming on the weak part of the measure, does not destroy the effect of the octaves. The same is relatively true of the fifths at e and_/", and of the octaves and fifths at ^ and A. Experience and instinct are the best guides regarding progressions like the preceding, because the part of measure on which the chord occurs, as well as the relative length of the different positions, greatly influence the character of the successions. OPEN HARMONY. When the soprano, alto, and tenor lie close together, as at a, example 66, the harmony is said to be in close position. When the voices are so disposed that the soprano, transposed one octave lower, comes between the alto and tenor, or the tenor, placed one octave higher, comes between the soprano and alto, as at b, the harmony is said to be in open position or open harmony. Ex. 66. u. n b. <3 f \j in <-i I ^ - III I /\ '^ a % \ 1^ e^ 11 1 ifh ^ n II 1 V'-' rn ' ^ "^ ■■ -IS- :^" 1 t ^ II 1 •"i. 1 1 1 \ ^ ^j ^ - F«^ I =T 46 PRACTICAL HARMONY. The six-four chord, although constantly used by modern musi- cians, is subject to peculiar conditions. No other chord demands more delicate handling, nor is there one that is more abused. The laws governing its use are among the most important in musical composition. In every six-four chord in a major key — except that of which the root is the leading-Xxme. — there will be found the interval of a per- fect fourth between the bass and one of the upper notes. Whenever a six-four chord is introduced on any note except a. tonic, one of the notes foi-ming this perfect fourth must have appeared in the preceding chord. When a note has thus appeared in the pre- ceding chord it is said to be prepared. If a six-four chord were to be written on C it should enter in one of the following ways : ^ 6. Ex. 79. i W-- I gtz In a six-four chord, on C, the two notes forming the perfect fourth are C and F. One of these notes is prepared in each of the above examples ; at a the F is prepared, at d the C is prepared. In the chaxA following the six-four chord, one of the notes form- ing the perfect fourth should remain stationary ; the other should descend. This is called its resolution. b. i Ex. 80. -^ I 9*: I At a, in the preceding example, the fourth is prepared in the bass and resolved in the soprano ; at b the fourth is prepared and resolved in the tenor. It should be clearly understood that either one of the notes form- ing a perfect fourth maybe prepared, and that this preparation need PRACTICAL HARMONY. 47 occur only when the fourth is formed between the bass and an upper voice, and may be dispensed with entirely when the root of the chord is a tonic. In harmonizing a six-four chord it is best to double the fifth of the chord, — that is, the bass note. Ex. 81, %^ 9fc i The fundamental, when doubled, produces a good effect in pas- sages like the following, where the fundamental forms a part of the succeeding chord. Ex. 82. I ^i: ^^=P"^=i M--=i; -<&- -Sh -&- i :^=f:: If, however, the fundamental of the six-four chord does not appear in the choi-d_/b//oW2«^ the six-four chord, it is better not to double the fundamental. Ex. 83. 1 ri iS ::^= -ei- I i As was stated at the beginning of this chapter, any chord in its second inversion, entering without preparation of its fourth, will produce a modulation. From this it will be understood why the second inversion on a tonic needs no preparation in either major or minor. A six-four chord on a tonic only strengthens its own 48 PRACTICAL HARMONY. tonality. This chord on a tonic should always be attacked on the strongly accented part of the measure. Ex. 84. i -j- -^- 91: Wz I i When a six-four chord is preceded by another position of the same chord it needs no preparation, as at « ; when succeeded by another position of the same chord it needs no resolution, as at ^ : Ex. 85 I Successive six-four chords are permissible only when one is built on a diminished triad ; this fourth needs no preparation. The fol- lowing would be practicable in the minor mode. Ex. 86. S^; ==ii P=i-I ZL^^ Hi^H -6> -(&- -g- ,-<9- -g- 6 4 3E=^= PI I I Whenever a six-four chord is built on the second degree of a minor scale, as at example 86, the bass note should not be doubled. Although the second inversion is best when used on the principal triads, it may occasionally be introduced on other degrees on the un- accented part of the measure. Here it will not have too great tonal PRACTICAL HARMONY. 49 importance, ing chord. Ex. 87. In such instances it has more the character of a pass- On sec ond d egree. On third degre e. On sixth deg ree. -^ 4 6 I T?.^ -li- =1= =r= X i In each of tlie six-four chords in example 87, one of the notes fonning the perfect fourtir is both prepared and resolved, as explained in examples 79 and 80. OBSERVATIONS. When musicians speak of a dissonance they do not necessarily mean a discordant, inharmonious combination of sounds. A dis- sonance is a chord that is not accepted by the ear as final ; it must be followed by another chord. Dissonances may resolve into other dissonances, and indeed, it is a marked characteristic of the modern school of chromatic harmony that they do so resolve ; but, unless they eventually arrive and repose on a consonance there is no satis- fying close. The following successions, although harmonious and agreeable, are dissonances. No ear with the slightest musical instinct could be content with an ending on any one of them. Ex.88. Sp=^»^Eqg=EpEE^EES3jeUlteteii-ll -ffl-r-SiZ- WW- d2^ ^d dfc i Ex. 89. % =1= 3t ~-Ml. ^ -^- Wagner. -S *=gi -ffsi so PRACTICAL HARMONY. The following, on the contrary, are consonances, and any one heard alone would be accepted by the ear as final. a. Ex. 90. i il^=b: S- (i tt^ i EilE I i :t!5i JE ^- The difference, then, between a dissonance and a consonance is this : a dissonance, though oftentlines more harmonious and satisfying than a consonance, must be followed by another chord, while a consonance, taken as an isolated chord., will be accepted by the ear as final. The best effects are those in which there is a judicious u«e both of consonances and dissonances. Wagner. Ex.91. g^"^ ^ =^ 4.l£=lfe-_J?b^: 9-tfe -1^' ItSi: $fez^i :g=$bj=c— i -<-&|g'- J:^^ :?J P^ lSt > f ?^ < gS* X ^: fe^5i: fto*- ^fi%i =«t *1S— jft^ — i^^- I He =jfe rr -"^-i^- y-^- 'M- -A-A m^^^ ^^m <&«- ■53-- *«^ PRACTICAL HARMONY. 51 The chord following a dissonance is called its resolution. When dealing with dissonances as explained in Part II., it will be found that the school resolution of any dissonance, demands that the dissonant note shall progress down to the next degree of the scale. The six-four chord, although not properly a dissonance, has this characteristic of all dissonances : it will not be accepted by the ear as final. The regular resolution of the dissonant note, the fourth — espe- cially if it be used on a tonic where it has the most character — follovvs that of all dissonances and should descend to the next degree of the scale. Ex. 92. a I 9i I All that was written in Chapter I. regarding the interval of the fourth as having, at certain times, the character of a consonance, at other times that of a dissonance, for which reason it is called a mixed, or neutral intei"val, will now be better understood : when the intei'val of the fourth comes between two of the three higher voices, as at a in example 93, it is consonant ; but when it comes between the bass and any higher voice, as at b, it is dissonant. b. Ex. 93. 1 IS5Z -g3- I f- A clear understanding of the preceding will be of great service to the student when he begins to write strict counterpoint. The most frequent exceptions to the preceding rules regarding the six-four chord, are included under the following irregular resolutions. I. Either one of the two notes forming a perfect fourth, instead 52 PRACTICAL HARMONY. of descending, may remain stationary and form a part of tlie succeed- ing chord : Ex. 94. ll-%- ^-s>- ^^ -&- 6 -G)- -w — |~g~ :t:gi= e i II. A fourtli, instead of descending, may ascend chromatically : Ex. 95. i ff^ i^ =«s= I A chromatic change of the fourth, like the above, always im- plies a change of key. The resolution of the fourth is often dispensed with by the best writers, when coming on a tonic in successions like the following : Ex. 96. i ~:^. y] But all such progressions are usually followed by harmonies which may follow the six-four chord ; and they should be looked upon as interrupted resolutions of this first chord. Many of these " observations" will not find their application till later. It is not expected that they shall be fully understood at this period, but if they have been carefully read the student will be well-prepared for the study of dissonances as they are treated in Chapter XI. The figures % followed by a 3 or a 5, or either of the chrom.atic PRACTICAL HARMONY. 53 signs tj, if, signify that two cliords should be written over the same bass note ; the bass note is always the root of the second chord. Ex. 97. i P= ^- -M ■V /■ — ■1-. s= -J- =B=2= 1^ &:it I I EXERCISES. 1. §±$E =^EE -si — r- 3 f) 6 8 4 6 6 2. 3M- 3 8 5 3 6 6 8 5 4 3. 43 -•=fC =i«=i; I it=F ^9^fi^f *=4=zt :a=i E» -^-•- =3:: -a^- "I K m^ -X=-- I ;iS- EEfc 3 5 6 6 6 8 4 , 6 4 3 5. =Ft ipzf: :t?r: =^-£t =Me 4 Jt :^: 1- =F=f :^= -i^=t I2Sl- 54 PRACTICAL HARMONY. m It ■iiz^z izt H ^=^- WM 4f I ;i^eE3 =i= :^z "-!=>- 3 • ^ 43 63 1 , %3S e 6 43 |3 «- 2=3 the 3 :Bi-iiif= ' r ^ 1 1 > a III 1 1 P J ^J^ "P P-TcJBi 1 II ■^ fill t ' J_ ^ * m f 1 h ^['-•t'* SJ i' -\ l-l l/i4- f LM_ L'—U t J &I • LJJJ CHAPTER VIII. FORM. THE PHRASE. THE PERIOD. CADENCE. Form, in music, is the means by which the composer gains unity and symmetrical proportions ; it is the frame in which the inusical picture is placed. Music without rhythmic order, melodic and harmonic relationship — without form — ■ would be unintelligible and monotonous. As form is the outward expression of the thought, there can be as many forms as there are varying thoughts. There are certain orders of musical form which are more symmetrical and gratifying than others : these have been so perfected by the great masters that they are almost universally accepted as the best mode of expression. The best examples of form are to be found in what is called " abso- lute " or "abstract" music, in contradistinction to what is known as "programme" music. The smallest succession of notes, which, taken alone, forms a satis- -fying musical thought is called a Phrase. The length of the phrase varies according to the length of the thought to be expressed ; but the most commonly used is that of four measures. fe iEfa .=1= &- 1=f: Beethoven. Ex. 98. PRACTICAL HARMONY. 55 It should be noticed that in the preceding example the rhythrei of the "third and fourth measures differs from that of the first and second, and that the four measures are necessary to complete the full thought. A passage of four measures, in which the third and fourth ai-e but repetitions of the first and second, does not form a four- measure phrase, but is called a Double Section. If the third and fourth measures are but rhythmical repetitions of the first and second measures, the passage is still called a Double Section. Ex. 99. i Si 5 r^-i Ex.lOO. ■v^ il = r"j3--i:r» ?-j=j=^=r»^?r^8^ The distinguishing characteristic, then, of a four-measure phrase is, that the four measures are indispensable for the expression of a musical thought. The Period consists of two phrases of equal length. As a rule there is enough similarity in the two phrases to show that the second is responsive to the first, although the second is usuallj' more emphatic and final. Beethoven. Ex. 101. i ai P^=^ 3^ V- -ili=¥ i When one speaks of a period one means the period of eight measures, similar in construction to the pieceding. There should be 56 PRACTICAL HARMONY. enough melodic and harmonic order in the period to form by itself a complete musical sentence. There are other periods of different Isngths but they are nearly always qualified, as, for example, " six- measure period, " " seven-measure period, " " ten-measure period." Without such qualification the period of eight measures is under- stood. CADENCES. A cadence is the close, more or less definite, of a inusical thought. It is to music what punctuation is to prosody ; it divides the thought and gives the proper emphasis. The Authentic Cadence is the strongest. It is forined by the chord of the dominant followed by the tonic ; the latter chord must always fall on the accented part of the measure. The following are forms of the authentic cadence : Ex. 102, Illustrations I and II, with the root of each chord in the bass and with the soprano ending on the tonic, are termed the Perfect Authentic Cadence. The same harmony, but with either the soprano ending on a not^ other than the tonic, or either or both chords inverted, are termed the Imperfect Authentic Cadence. See III, IV, V, VI, and VII in preceding example. The Plagal Cadence., consisting of the subdominant followed by the tonic is particularly agreeable when following the Authentic. Ex. 103. Authentic Cadence. Plagal Cadence. ■ I 1- n ''J II IftV » ... rv 1 1 S S 11 I pv. e> I rj m ■^ 1 1 The Plagal Cadence may be used without being preceded by the Authentic. PRACTICAL HARMONY. 57 The Half Cadence., as its name suggests, marks a short rest; it usually comes between the members of a phrase or period. The half cadence is usually made on the dominant, preceded by any other chord. Ex. 104. Et 4- Et X I The Deceptive Cadence — sometimes called the false, intev rupted, or broken cadence — consists of the dominant followed by any degree of the scale except the tonic. It is often followed by another degree of the same scale, sometimes by a change of key. N /' s .' N r s Ex. 105. I_,5ZE_^_|_«,_r_^_]_^ F_s2 I: 9^ fe- vt vi> p-c:Sg= i=g=r g?- n y V^ V Vljj The character of a cadence depends largely upon what has preceded it. The authentic cadence is most frequently preceded by a six- four chord on the tonic. This use of the six-four chord is the most common and the best. Ex. 106. ^i* ^^3 p-» S* -«'-©'- :^iSi -S,+f4^ -•- -s>- m -SI -^ 1^ :&=- I EXERCISES. 1. Compose a short bass in C, ending with Perfect Authentic Cadence. 2. Compose a short bass in_^, ending with Imperfect Authentic Cadence. 58 PRACTICAL HARMONY. 3. Compose a short bass in A, ending with Plagal Cadence. 4. Compose a bass, longer than the preceding, in A b, dividing it with the Half Cadence, and closing it with the Perfect Authentic followed by the Plagal. 5. Compose a bass in d according to the formula in No. 4. Before harmonizing the succeeding melodies, the student should read again all that was written in Chapter II. regarding melodic and harmonic progressions, as well as the " suggestions" at the close of Chapter IV. The chapter on the second inversion should also be re-read. This done the student should divide the following melodies into phrases, seeking that cadence for the close of a phrase which his musical instinct tells him is best adapted to its character. After the cadences have been decided, the other harmonies of the phrase will more naturally suggest themselves- The second inversion is a most important factor in the cadences ; it makes them emphatic and final. (See Ex. 106.) Although it is not absolutely indispensable, it should be employed whenever the nature of the phrase permits it. As its use is somewhat diffi- cult, it should be seldom introduced except in cadences, and then under the conditions recommended in this and the preceding chapters. Whenever the nature of the melody permits, change the harmony with each note. Sometimes it will be best to retain one harmony during two, or perhaps three notes. In this the pupil must follow his musical instinct. EXERCISES. .^=zt 1=5=:^:^ :e=^-: -sJ- n- :tjt 2. i^iiS - ^ — m^^^^ -\-( ^ — •- -•— f» -^- :^r E^ I ^■^ EEE£ =^^ -•-h- F-"^ IH 4 i 6Ss^ _ffl G>- I^ i PRACTICAL HARMONY. 59 -gg-d -?^ & ^i i i&fce ^T^=i I ^^ :j=1: 6. -| g — g- - gi — 1& -j^'g-^- Andante. ii -L , — I — I — I— — -^^^■ CHAPTER IX. MODULATION, TONAL RELATION. MODULATIONS OF THE FIRST ORDER. EXERCISES. MODULATIONS OF THE SECOND ORDER. MODULATIONS TO REMOTE KEYS. PASSING MODULATIONS, HAR- MONIC SEQUENCE. Modulation is the art of moving from one key to another. If a composition of more than a few phrases in length were to remain in one key the monotony w^ould be wearisome. Digressions from the original key are made, to gain variety. The possibilities in modula- tion are probably limitless. From Mozart to Brahms there has been a constantly widening latitude. Art is progressive ; that which to-day seems impossible, may to-morrow be accepted. Hence, it is wiser to say what one may do, I'ather than what one may not do. The most helpful theory is that which enables one to analyze, imder- stand, and better appreciate the compositions of acknowledged masters. The question ought not to be " Is this passage in Bach, Beethoven, Schumann, or Wagner, wrong.?" but rather, "Should not the old system, which cannot account for the new effect, be modi- fied } " Practice should precede theory, and one function of a new text-book is to adapt the old rule so that it shall include the latest discovery of a great composer. It should be understood clearly that modulation is the method we ,"^p!oy to get to a new key ; it is the process and not the result ; it is the means by which the change is effected and not the key into which we pass. A sudden change of key does not necessarily 6o PRACTICAL HARMONY. include a modulation. If the chords of C and Gb were heard suc- cessively : 5=f= Ex. 107.< ES =§5-- ^ ^5- :2e: ^i there would be no modulation, only a brusque, unsatisfactory leap from one key to another. If the two keys were united by a succession of chords having one or more notes in common, the progression could legitimately be called a modulation : --^=^ fe- is: ^^=A- ■b-S- 15= V-i> Ex. 108.< =^=l J_ b^^ =15= T =65= ^ It will be seen, later, that it is not always necessary to have a note common to successive chords. One should realize that the same rules apply to harmonies in different keys, as to harmonies remaining in one key, and that sat- isfying modulations are governed by intelligible melodic movement of the different voices. With a clear appreciation of the principles of tonal relation, it will nearly always be possible to understand the effects of agreeable modulations, even of those which seem intricate and remote. Whatever means one may employ to effect a modulation, there is really but one principle to be kept in mind: destroy the tonality of the old key, and prepare the ear to receive the new. Whether the modulation shall be brusque and startling, or well-prepared and gradual, depends wholly upon the effect desired. TONAL RELATION. CLOSELY RELATED KEYS. Keys are said to be related when they look and sound alike. PRACTICAL HARMONY. 6l The keys most nearly related are those whose signatures are the same, and those whose signatm-es contain one shai'p or one flat more, or less. The nearest related keys to C are its minor, a; its dominant, G; and the relative minor of G, e; its subdominant, F; and the relative minor of F, d. They may be represented by the next five ascending notes of the scale : ,- X Nearest related keys to C. d. e. F. G. a. Ex. 109. : •i Wz i=± ij^ji i This is relatively true of all major scales. Minor keys have equally five related keys which are represented by reversing the order and descending" five notes of the scale : Nearest related keys to a. G. F. e. d. C. Ex. 1 10. i --i—X E3^^ The nearest keys, then, to any major, are its dominant, its sub- dominant, and the relative minors of these three keys. The nearest related keys to any minor are its dominant and sub- dominant ininors, and the relative majors of these three keys. The tonal relation existing between more remote keys will be explained later. MODULATION. Continued. A modulation is effected by introducing notes characteristic of the key to which we are going, but foreign to the key we are leaving. Two chords at least are indispensable to determine a key. The phrase at a in the succeeding example, is presumably in C ; by the introduction of gjf, as at b, the key is probably in a : Ex. 1 11, v II /k' 1 '' ^c '-' w-g— -f— — « — :Sg — — n rr J. -sr '■-%- ^ -TSr i^ r\" 1 II ' - i i 4th 5tli 3cl 4th In art there are many things which cannot be explained. Any attempt to explain the tritone is useless and illogical ; it is suffi- cient to realize that one progression sounds good, another, bad. To modulate from C to F, the modulation can be effected by introducing any chord — except the chord on the leading-tone — ■which contains bt*, the characteristic note of the key of F, and following this by another chord or other chords defining the key. Note. In the following exercises the modulations are to be made in the fewest possible number of chords. The modulating chords are to be considered as parts of a phrase. GENERAL RULE. The old key may be quitted from a chord formed on any degree of the scale — except the seventh — and the new key entered on any degree of the scale — except the seventh — containing the charac- teristic note. To the rules for melodic progression given in Chap- ter II. should be added the progressions in example 116. PRACTICAL HARMONY. EXERCISES. I. To modulate from any major key to its dominant. Leave the key of C from a chord formed on the first degree in root posi- tion and inversions, entering the .key of G on its. dominant. The following example shows the gertei'al order to be observed : Ex. 130, r\ r ^ ^ ^, ^ ^ I I I i> f-i I <^ o ^ I o 1 i /si j*^ 1 ' — & — r, N ^ ^ y r' 1 ^•s 1 1 — « a — -1 i^-g — ~ W, —IS % — > -S % :(g — r^-— II *j -tS>- "c^ n -S>- SJ c/ -&' "CJ a tr- e^ "-J. ^ 1 1 -.' 1 11 II Leaving C from root position, entering G on inversions of the dominant. II. Leave the key of C from chords built on each degree of the scale — except the seventh — i.e., the second, third, fourth, fifth, and sixth degrees, entering the key of G on its dominant. Inversions of chords may be used, and as many examples as possible of each progression should be made. The rules given for the six-four chord in Chapter VII. should be observed. III. To modulate from any major key to its subdominant. Leave the key of C from each degree of the scale — except the sev- enth ■ — entering the key of F on the _/bz 1 -^ r3 '^ ej -a :_«2 ; a : 11° lio This will be more fully explained in " Harmonic Sequence. " Leave the key of C from chords built on each degree of the scale — except the seventh — entering a on the dominant. V. To modulate from any m.inor key to its relative m.ajor. Leave a and return to C on the fifth, the third, and the first degrees. The entrance to the new key on the dominant will be found the most decisive. For convenience, the relatives are condensed here : Each major key has five closely related keys, three of which are of the first order and two of the second order. For example, C has for relatives of the first order a minor, G major, and F major, and for relatives of the second order d minor and e minor. Each minor key has five closely related keys, only one of which is of the first order. A minor has for relative of first order, C major, and for relatives of second order G major, F major, e minor, and d minor. If the teacher think best, he should now arrange modulations of the second order. OBSERVATIONS. CONCERNING MODULATIONS TO REMOTE KEYS. It is of great importance that the chord or chords forming a lemote modulation be of sufficient duration to prepare the new key ; and as a rule, it is best for the more important chords to be placed on the strongly-accented part of a measure. A succession of chords containing material for an effective modu- lation may be made thoroughly ineffective, either by introducing 70 PRACTICAL HARMONY. the chords on the weak part of the measure, or by giving them so little time and emphasis that the modulation is indecisive. In general, a modulation is as much more satisfactory as there are notes coinmon to the modulating chords. Among other ways, satisfactory modulations to remote keys may be effected by the following means : I. Major chords may succeed each other with good effect, provided they have one note in common : Ex. 132. ■ ^i: "^ ibsi i II. By the use of chords which alone dp not pi-oduce a definite modulation but are common to several keys. In the following succession : Ex. 133. i i=i=il The second chord may be considered as if in the key of F, and thus leading to that key : Ex. 1 34. 3^-'— r— p — F — F- — i-i ^6,Lg|_gLs,L .1 -«- -«>- -%- -19- „ iy, s s- j 1 or as if in the key of a, and leading to that key : Ex. 135. i eEiE -ig— ^i: PRACTICAL HARMONY. 71 or as if in the key of B b ov iJb, and leading to either one of these keys : Bl^ or b\) Ex. 136.< Pi= =5i eISeH ^ lii III. By enharmonic change : Ex. 137.< i =ttsz i5i ^: ^63= :EE*E IV. By several modulations into closely related keys, leading gradually to a remote key : Ex. 138.< ie=te =t :b3zl^E=tE 1=S# i^- =5^- :6^ :&^ i Note. The early masters rarely used modulations to keys other than the five which are called the nearest related. If keys were used not closely related to each other — as F and G — it was only in cases where these two would be closely related to the principal key of the piece. For example, F and G would be closely related to C. One must not suppose that the preceding examples exhaust the 1 es3urces of modulation. The possibilities are too numerous to catalogue. PASSING MODULATIONS. It was stated at the beginning of this chapter, that a modulation cannot be determined by one chord, even though this chord contain a note or notes foreign to the principal key. A phrase may contain chords having notes foreign to the key and yet not destroy the unity of the principal ke}'. Such are termed "passing modula- 72 PRACTICAL HARMONY. tions," "transitive modulations," or "borrowed chords." Anew key is, in general, rarely determined except by the aid of a cadence. In the following : Ex. 139.< Wz^. -t^ J-^ i)i=E:3:t: -i=- !?-fe: i i^^iipS -^- 3^ 3=FiEsiE= -'&— z^- --g-- 1 ^:^:^^ =3^ Although here are notes foreign to the key of C, there is no mod- ulation. It is best to look upon those chords containing the foreign notes as borrowed from other keys. Note. When the prevailing mode of a piece is major, chords are often borrowed from minor keys. When the prevailing mode is minor, chords are rarely borrowed from major keys, because the major chords imply too strongly, a modulation. From this point the student should unite in one note all those notes which may be repeated in a measure. The few exceptions should be explained bv the teacher, as the}' occur. -4— f— J— J— „ ,., a^^a^ Ex. 140. i-=^^^=r='^l instead of ^1^ i -:ir^- I EXERCISES. MODULATIONS OF FIRST ORDER, AND BORROWED CHORDS. Allegretto. 5. 1 % , -•- -G>- — S,.6 _ 6 X --^^Vr^ EF-'F '■w=i=-Jm- ;i^ffi t^l-rp :EeS -F=r= PRACTICAL HARMONY. 73 9^^ %_ 6, 8 6 t 36 \ — 6 ^ -g'-Fzg— Fl — t'g+f-r-^ 6, 4)( -(=- EEEE ;Ee Ti- K=tz^ =t -b^- :p=Sp=|?:3jEq 1^ 8 - ,48 be - '-W=W- I =95 15" ! — z?~ Adagio.^ % 6 I 8$ 6 4* a 6 J. 6 6 , 4 4 # 2. 9^-fi a-Tig-i Lire -4 — d- -(2-^«J ^tf :^C-i2-» t=t=t:=f :fi - '^— «^ -5*—' :9^ 8 6 6 6 6 3 4 6 .43 34345 :?- ,^.- t« eB :^ ■G>- „ Cantabile. 1 . c. i y 1 J_ 1 a -J 1 ■ y t,4- « f a _^ J a f-^ «M^ a /(■\''/i J i' r 1 ^ • ** J 1 ~^ t \ ^^ V-^ 4 *^ 1 ^ "* * • 1 • u ^-V- F. Vd.SeeEx. lairJF. 15: =F- :^tf5P=J=P=:^: -i^-i^- -■^-ti SECOND ORDER. Allegretto. 6 6 6 4 ^^ b c\- n 1 fO -1^ *-). fi • ^ 1 n 1 -^ A a 1 1 - -4 ^ • b ^^- -b.-r^ :t=^: -sJ— 6 6 5j 6 -1- 6 4 <5 . f r^- r3 . • (-S 1 PT • 1 — f^ i (S • 1 ^ 1 1 6 :^==Ft: 5: 74 PRACTICAL HARMONY. ^D r«'-»+f2-^ -(S-: ;^EE^EEtt Andante. REMOTE MODULATIONS. tsb b eljsb 6 3— .^_^^,^i,_. * « S$ 6 5* 6# 5* 5b be J i ^ * J* » b p Ei? i:^ i?»^ -(S>- be sb sb b4 3 , b =§i- 5* ■^ 9^=6* :£ ^ 6 % 2 :9i: (2 — 1 —f^- -& — -p_^^ -«■— rtT- ^ -"^^'"1 ^1 -P— - 1 . _l 1 1 1 1 ^ * ^1 HARMONIC SEQUENCE. In sequences, the ear being gratified by a regularly recurring responsive figure, certain harmonic or melodic successions may be introduced which would otherwise be disagreeable. The most pronounced of these are the use of the triad built on the leading-tone, which we have not used before, and the freer use of the six-four chord. The triad built on the leading-tone when heard alone : Ex. 141. ^m m^z is weak and disagreeable, but when heard in sequence : I 1 - >^ . 142.<' ¥ m I it becomes more agreeable. PRACTICAL HARMONY. 75 The six-four chord may be vised on any degree of the scale ; provided the fourth is prepared and resolved according to the rule in Chapter VII. Ex. 143. The chord of the sixth is much used in sequence: Ex. 144. r=^r zSr ;g= sz. I Hr=P^ The melodic intervals prohibited in Chapter II. under "Melodic Progression" ai^e permissible in sequence. It is best not to use these intervals in the first measures, which form the model., as they would there be difficult of intonation. After the figure has been announced, any of these intervals may be used. The model should contain as many of the principal triads as possi- ble, and must conclude with one of them. The perfect symmetry of the sequence may be broken at, or near the close, in order to gain a more melodious or more tuneful pro- gression of the parts, or to gain a more satisfactoiy close in any way. See seventh measure in example 143. Sequences are said to be tonal or diatonic, when intervals are re- peated in the same key without regard to differences in the quality of the intervals : Ex. 145. ■g-a- f ■^ EdE :^=S; Fi^-F^ s-^g: f-pr ^: -4 /S 1- ■Z^-2^- e „ 6 6 i W- -J IS — * — ' — \- I 76 PRACTICAL HARMONY. Sequences are said to be real or modulatory, when the quality of the intervals represented by the model is exactly repeated : Ex. 146. * b -S- J- =ii- --^^-- ^i-=ii W- Wl -fe^- :^ te-l i^ I 1I22: -&«t i S=P^ dJe: 5= :feii fc^=55 -^^■ :l=z :b^ :&gr IB ii rg^Et -H 1 1' It is recommended that the pupil play the following exercises from the figured bass, instead of writing out the other voices as he has done heretofore. The position of these voices in the first chord has been omitted purposely. As the greater number of these basses may be harmonized in two or more positions, the pupil should choose that position which seems to him the most desirable. EXERCISES. TONAL SEQUENCE. IB 1. m^^l rw -1©- 2. ^— r-l— f=- ;i5^«^^tEEEt -«— (2— f=t -25l- I 3. '■^t^^^^M^ I PRACTICAL HARMONY. 11 m:mESEE^. Ei^EE^E^l -S> 1=2- 4 1 1 = -s< — =911231^ \i-t-- -is—P- ■F=t -is>—a- ■F=t 6 4 6 6 -© «2- i 3L—A. — *_ -^-S- 6 4 3 5. -n—»- =F=F= :r=[=E X=f- i §i« -^sj-o- -Sl-|2- ■f2— «i- t=^±p^t: 6 4,3 i -,(=-*-- ;i»g -f2- ;Eig| -P2_s.- ^F 6 6 6_ -f2- -%- -^=F^ (=^#- ;iiESL=tE -p — ^■ E^E ;i 8. E?-:^^: - si— -s- (^ ^ ^ 6 6, 6 6 r:» • h 1 ■ 1^ 1 ^ r-' ,^ ■ 1 1 -^ ti O 1 1 1 P ! 1 "^^ P ;J "25 H « r _ 9 ^ >- |Z^ L — L_|:_ -' U ■iri iSi . |- io.PiLSSE^^- 666666 66 -f2- ::1; i ^ ,1^ — g — g — p- :t=t=s 11, i9i:a 3486 6 6 6 6 -»S'-. 343 343 343 343 343 6- i -^—\—i9- 6 6 6 6 — ^ 6 4 6^646 6. 4 6, 43 1 2|gWgEtE^af^l&|f^g -S'-y^-Si- i3jg± r^-=^ te 6 . 6 , 6 f-F^=-^h^- i 78 PRACTICAL HARMONY. EXERCISES, REAL OR MODULATORY SEQUENCE, kI, eb sb eb sb 5b sb eb ebsb sb ^'^ b 5b 5b, b b b , b b ibb b H ;i±fi =F:t :^ :b^ fefcfe =t= =t ?«■■ 5t) SQ SQ 51] SQ 50 5Q l^li^fe^S ^^s^ -gy--g^= -a- ^= §5- ;i±$^ :^= 5« « E^E 5J 5$ 5« iSf5)t *, t it 4* J =»*- :J^ -%^ ^m -!^- 5b sb 5$ b b sbbfl B :r5- ^-^nm-lX. b 5b H ife sb sj 6 SS Sjtt 5S =C*=1= -85^ :ife: i 6B ;iis^=S t^= a 60 sQ sn a sdeO 40 50 so ft?- i =5^ - si-gg- djs 6b 5 4 lb «n 6.^i^= =g^ sb 6 5b eb eb sb sb 5 40 4b SO 4b 4b b =tt^ ±^. :t=l^ I The student should now compose several short sequences, both tonal and modulatory, following the suggestions given on pages 74 and 75. CHAPTER X. RESUME. Note. In this concluding chapter of Part I., subjects which were purposely treated as briefly as possible in the prieceding chapters, will PRACTICAL HARMONY. 19 be discussed more fully. Matter which would have there been cum- brous and confusing, will here be useful and more readily under- stood. CHAPTER I. At example 14 it was stated that it is correct, as a general rule, to use sharps in ascending passages and flats in descending passages. Modern writers usually choose accidentals which are nearest in tonal relationship to the key in which the phi'ase occurs. A descending passage like the following : Ex. 147, i IE :q= :d=ji I would be much better notated thus : Ex. 148. li=&=!Sfi=S^ 11 because the FJt is nearer the tonality of C than is the Gl?. The same would be relatively true of the following : Better notation. Ex. 149, iE= Itj^ SeI^ ;^ II In our musical notation we recognize no interval smaller than a semitone. For reasons which have to do with the inatter of temper- atnent, the whole step is theoretically divided into nine equal parts called the Pythagorean Commas. The comma is supposed to be the smallest appreciable interval between two sounds. Note. The terms half-step, and semitone, are purposely used as synonyms. Of the nine commas dividing any whole step, that portion of them representing the diatonic semitone is the smaller, and receives but four commas, or four-ninths of the whole step. The chromatic semitone is the larger and receives five ninths of the whole step. A comma, then, or one-ninth of a whole step, is the interval that separates the diatonic semitone from the chromatic semitone ; i.e., it is the difference between the flat and the sharp which may separate a whole step. So PRACTICAL HARMONY. ILLUSTRATION. f/if/e COMMAS of/£y//ioie FIVE COMMAS, dHnontflTic fuve) nfiLF-srei;^ **J DIfirofllC (Simll) ft/ILF-SnP. ,c^ COMMA I COMMA 2 COMMA ? '^"""^ 4commaF°mmaP u Fl are identical. On instruments where the sound is formed by the executant, like the violin or the violincello, the musician is governed by melodic in- stinct and submits involuntarily to the fine difference existing between the flat and the sharp, making use, ordinarily, of the large half-step in ascending passages and the small half-step in descending passages. If this is understood, the student will realize that an instrument like the piano or the organ is never perfectly in tune when played with stringed instruments. The difference is slight, but sufficiently marked for the piano to sound colorless and unsympathetic, when entering alone after a full passage b}' the strings. CHAPTER II. SCALES. The chromatic scale is composed entirely of chromatic and dia- tonic semitones. Any major or minor scale may be transformed into a chromatic scal& by the use of the intermediate semitones which separate the whole steps. These intermediate sounds in noway imply a change of key, and the supreme characteristic of the chromatic scale may be said to lie in the fact that sharps, flats, or naturals, foreign to the key, may be freely introduced, and cause no sense of modulation. Ex, PRACTICAL HARMONY. CHROMATIC SCALE OF C. 150.<^ ^IjJij^EJl. i 8i Musicians differ as to the best notation of the chromatic scale. Composers are often inconsistent, at one time writing the ascending series with sharps, at another time with flats. As a note sharped is nearer the semi-tone above than the note quitted, it would seem to be the better notation to use sharps in the ascending major scale and flats in the descending scale. An important exception is made in the flatted seventh in ascending, and the raised fourth in descending. Ex. 151 ■tis The chromatic scale in minor is usually written as follows : Ex. 152. ^ ggg^ggg^g^jgg^a i The question of the notation of the chromatic scale is one on which there is great diversity of opinion. Conditions have so much to do in determining which shall be written, sharps or flats, that it would seem wiser to attempt no inflexible rule. No further proof of the inconsistency of musicians as regards the 82 PRACTICAL HARMONY. notation of the chromatic scale, need be given, than the follow- ing example b)' Beethoven : Ex. 153. ^^^^ itt fA-^' :t=|: $: i About the only thing on which composers seem to agree, is in writing the fourth note sharped in the ascending major scale, and the seventh note flatted in the descending scale. ( For an expla- nation of this, see examples 147 and 149.) This done, they evidently think of the convenience of the performer. It should be understood that we are now discussing chromatic melody. Chromatic harmony will be considered later. THE ECCLESIASTICAL SCALES. The " Gregorian Tones.," " Church Modes" or '■'•Ecclesias- tical Scales," as they are variously named, are of Greek origin. If the student will play a scale from each note of the scale of C, using white keys only, he will obtain the seven different forms of these Church Modes, or scales, as they would now be called. Each mode has a different order for its steps and half-steps. As many pupils have a desire to know something about these scales, we add the following typical list : The Dorian, or First Mode. F. D. The Hypo-Dorian, or Second Mode. F. D. i -al— g S =3^ i i The Phrygian, or Third Mode. F. D. id=^r Jti±: Hi The Hypo-Phrygian, or Fourth Mode. F. D. !ET=1 i The Lydian, or Fifth Mode. J^ ._}y iiHi^ The Hypo-Lydian, or Sixth Mode. F. D. ^- t= The Mixo-Lydian, or Seventh Mode. The Hypo-Mixo-Lydian, or Eighth Mode. F. D. F. D. l¥. -d—* -^m^m -g—m- M PRACTICAL HARMONY. 83 It will be seen that the Ecclesiastical Modes are formed of the notes of our scale of C, each starting from a different degree. These scales are grouped in pairs, so to speak. The first, third, fifth, and seventh modes are termed Authentic. Each of these has a collateral mode at the interval of a fourth below ; they are distin- guished by the prefix Hypo ( under ) . The Hypo modes are termed Plagal. It would seem, at first glance, that if harmonies were formed on these different modes, without the use of accidentals, the general tonal effect would be the same as bur key of C major. These modes are characterized, however, not only by the difTerent order of intervals in each, but by the constant recurrence of two chords, called the Final and Dominant, corresponding to our Tonic and Dominant. It is the insistence of these two choi-ds which makes each mode distinct. These chords are designated by a whole note in the preceding list of scales. The Final, or Tonic, is marked with an F, the Dominant is marked with a D. It will be noticed, that although the order of intervals in the Hypo-Lydian corresponds to our major scale, the points of repose coming on F and A remove it farther from our idea of key, or tonality, than either the Lydian or the Mixo-Lydian. In order to avoid the relation of the tritone, the B is sometimes flatted. If B were flatted in harmonies in the Lydian Mode, the tonal effect would be much like our major mode. This system was later extended to fourteen modes. Modern composere have at times employed these scales with good efTect. Handel has made frequent use of them in his ora- torios. Saint-Saens and Brahms have employed them with charm- ing results. CHORDS. The terms chord and triad have been intentionally used as synonyms in the preceding chapters. A triad is always a chord, but, as will be seen in Part II., a chord may be larger than a triad. TRIADS. The triad, or chord of three sounds, forms the essential and indispensable element of harmony. Until the close of the sixteenth century, this chord, united to certain effects known as 84 PRACTICAL HARMONY. "artifices of composition, " to be explained later, was the only one used. The triad on the leading-tone, although classed by some theorists as an independent triad, is classed by the greater number, and by all the modern French theorists, as an incomplete dominant 7th chord. This will be fully explained in Part II. A triad formed on any note of the major scale, except the leading-tone, is consonant, and may be used as a tonic. For example, any triad in the key of C when standing alone will be accepted by the ear as a tonic, either major or minor, according to the degree on which it is formed. In other words, they all are consonant chords ; they give a sense of repose, requiring nothing to follovi^ them. The triad on the leading-tone, on the contrary, is, with its diminished fifth, distinctly dissonant : — i I and in no sense gives the feeling of repose or finality : something must follow it. This triad in its first inversion., was classed among the concords of the so-called ancient strict style : Ex. 154.< i 15: a I i This inverted chord was often written by early composers in preference to the dominant chord. This will be understood when the true generator of the chord has been discussed. This leading-tone triad in its first inversion seems to be the con- necting link between the strict style and the free ; the bridge over which one passes from the old to the new. It contains no diminished nor augmented interval from the bass, nor the interval of a fourth from the bass, yet it possesses all the distin- guishing characteristics of a dissonance as explained in Chapter VII. PRACTICAL HARMCNY. 8S OMISSION OF VOICES. The third of the dominant chord is often omitted. As the third of this chord is always major in either mode, its suppression causes no ambiguity. Passages like the following are of frequent occur- rence and entirely satisfy the ear : Ex. 155. The omission of the third of any chord other than the dominant, by very reason of its ambiguity and strangeness, has a j^articularly pungent effect. This is especially true of a tonic : String Quartette. Haydn. Ex. 156. ^-«= -e- -rr^- -4 ~w- :^: •-^-» ->»- -> ggg^H MELODIC PROGRESSION. Students often ask why the apparently easy interval of the major sixth is forbidden. Experience proves that this interval is difficult of correct intonation unless another voice has anticipated it in the preceding chord : Ex. 157.< m m or unless the progression is from the tonic to the sixth degree : Ex. 158. ii: I S6 PRACTICAL HARMONY. CONSECUTIVE FIFTHS AND OCTAVES. As little as possible has been said about these so-called forbidden intei'vals, for the reason that so much attention is given to them in the average text-book on harmony that the student imagines an octave or fifth in every possible progression. Consecutive fifths, and octaves by contrary motion, are found in the compositions of the best composers : Pastoral Symphony. Beethoven. Ex. 159. as|H -X-- s^i i Passages like the preceding should not be imitated, but they prove that after one has gained sufficient technique he may make a good effect out of material which, in the hands of the inexperi- enced, is crude and distasteful. HIDDEN FIFTHS. When two notes move in similar motion to a fifth, as at a and b, Ex. 1 60, the voices pass over notes which, if written out, would jiroduce consecutive fifths : b. I Ex. 160. ii A- ^^. r i Such progressions are called hidden fifths. They are oftentimes as disagreeable as the consecutive fifths which they suggest. Like all other questionable progressions, they are most disagreeable be. tween outside voices. Hidden fifths or hidden octaves are usually unobjectionable between outside voices if the upper voice moves diatonically and the lower voice by a skip. Hidden fifths. Hidden octaves. . 161. < ^^i^^a ^^^ ::s=c FiH PRACTICAL HARMONY. THE TRITONE. 87 If what was written under Ex. 129 concerning the tritone, is thought too sweeping, one need onl}' consult the various text-books on harmony and counterpoint to find the most obscure and contra- dictory rules. The essential thing is to understand how to gain the good effect and avoid the bad. The following is sufficient. Avoid the relation of the tritone between outside voices., in the progression from the fifth degree to the fourth degree. The progression from the fourth degree to the third degree also contains the tritone, but this progression is disagreeable under any comlitions and should be avoided. CHAPTER III. SCALES. THE MINOR MODE. In addition to the harmonic minor scale as given in Chapter III., there are other forms, the most used of which is the one called the melodic 7ninor. It is formed as follows : Ex. 162. i -g g-ftg^^-ftg -gg- t^ This form of the minor scale with its seventh flatted in descend- ing, permits the use of the melodic progression from the seventh degree to the sixth degree, which is objectionable in the harmonic minor scale, on account of the augmented second : Mendelssohn. Ex. 163. pl:^ -j-T SE I THE AUGMENTED SECOND. The interval of the augmented second is musical, and one of the most expressive in the whole category of intervals. It is used by composers as an expression of strong emotion, and is so frequently and freely used by modern composers, that it seems unwise to 88 PRACTICAL HARMONY. forbid its use unconditionally. Unless carefully introduced it is difficult of intonation, and for that reason it has been forbidden by the majority of theorists. It is much easier to sing as an ascend- ing interval than as a descending, and may be used occasionally when the second note is leading-tone moving to tonic : Ex. 164. t"^—- — -t:^ =^H -a- This interval should be introduced rarely and then confined almost wholly to solo voices. In the minor mode the melodic interval of an imperfect fourth is permitted when the second note is leading-tone moving to tonic : -J .- Ex. 165. '^m. i± This same interval, moving from the leading-tone to the third degree, is often found in the writings of Bach : Ex. 166. w. i ^ --U- I Note. (See note and Ex. 53, page 26.) The aversion of the early composers to an ending with a minor third was so strong, that the third of a final chord was often altogether omitted, and a close made as follows : iiipi Ex. 167. zbisi*: PRACTICAL HARMONY. 89 This close is found in modern compositions where there is a wish to suggest the archaic character of these earlier writers. CHAPTER IV. CHORD-RELATION. TONALITY. By tonality is meant a succession of tones, either melodic or harmonic, sufficiently long to clearly establish a certain key. When one hears such a succession the, musical sense instinctively clusters these tones around one principal tone, or point of repose, which we call tonic. Taking all the tones which affirm, so to speak, this tonic, and we have a scale ; taking the chords found on the different degrees of the scale, and we define or make clear the tonality of a key. An appreciation of the laws of tonality is of the greatest impor- tance. Without it many of the great works of the modern school seem obscure and keyless. The student will remember that "the supreme characteristic of the chromatic scale lies in the fact that sharps, flats, or naturals foreign to the key may be freely introduced and cause no sense of modulation. " That which is true of chromatic melodic passages, is equally true of chromatic harmonic passages. Here will be found one clue to an understanding of the modern school. CHAPTER VI. THE FIRST INVERSION. The first inversion is so agreeable, that when moving to it many hidden fifths and octaves, which would be forbidden if the chord stood in its fundamental position, are unobjectionable : Ex. 168. ;i 91: i* -6 1 — 6 1 — 6 1 — 6 H go PRACTICAL HARMONY. CHAPTER VIII. FORM. The study of form is most necessary. It is a branch by itself, and no attempt was made in Chapter VIII. to do more than barely define it. Musical compositions are divided into two principal forms, each essentially distinct from the other ; one is the Fugal or Canonic, the other is the Metrical. The fugal, on account of the irregularity of its members and development of its periods, together with various artifices of composition which do not permit the regular return of the cadences, may be compared to prose ; it appeals to the more cultured mind. The metrical, by its frequent and regular return of cadences and corresponding members, approaches nearer verse ; it impresses itself more readily on the memory than the fugal. Since the beginning of the eighteenth cen- tury the greatest composers have united both the fugal and the metrical in their more important works. This combination is found in all its splendor in the works of Bach. The student cannot become too familiar with the compositions of this unparalleled genius- Charles Gounod said : ' ' Bach is in music a star of the first magni- tude : like Dante, Shakespeare, and Michael Angelo he marks one of those summits reached but once in the history of one art ; he alone has laid the foundations of the music of the future. His work already dates more than two centuries ; time cannot alter it, and far from being surpassed no one has equalled its bold invention or its dignity of style. His language has a biblical grandeur recalling that of the prophets. "But that which cannot be too strongly emphasized is that his incomparable audacity is a direct result of his severe discipline, and that there is not a caprice of his marvelous fantasy which may not be resolved to the most simple elements and be explained by the most rigid principles. " We cannot too strongly recommend the young musician to read and re-read the works of Bach ; more than that, we urge him to learn some of the most remarkable passages by heart. " The young musician generally underestimates the importance of having constantly before him models of the great masters. If he fears that in memorizing their works he will lose his individuality, he does not reflect that the study of a inaster always brings us into the presence of two elements, — that which the master knows, and PRACTTCAL HARMONY. oi that which he zV, and that of these two elements' — united in the master — the first only is communicable and can be assimilated. "Art is subject not only to grammatical rules, to principles of correction without which there would be a fault, but also to princi- ples of beauty, to laws of aesthetics, which, although they may not, like the former, be reduced to rules, are no less sure and positive, and which constitute the chain by which all the great masters are united ; grand laws by virtue of which Dante, Shakespeare, Michael Angelo, Bach, and Palestrina are all one family." Cherubini also urges the student "to read, and also carefully and thoughtfully to copy as much as possible the works of classic composers. By this practice the student will train the ear by the eye, and his taste, sentiment, and style will be progressively formed." CHAPTER IX. MODULATION. Modulation will form an important feature of Part IT. The examples contained in Chapter IX. are not sufficient to enable one to analyze modern music. The tei-m "closely-related keys" is inisleading. Examples are numerous in works by modern masters, in which beautiful modulations are made to keys supposed to be the most remote from the original tonic. As these modulations neither shock the ear nor destroy the sense of unity, it must be admitted that there is a relationship existing between all keys. A theory may claiin that there is no relationship existing between keys of which the tonics are dissonant, and yet the student will find countless examples in which melodic and harmonic material is used in keys said to be unrelated, and used in a way which proves that there is a relationship. The question is one of aesthetics, and not one that can be settled by laws of acoustics, or explained by the so-called "harmonic series" or "overtones." "The exactitudes of science and Art ideals have nothing in common." Part I. closes here. As consonant harmony is the basis of all harmony whatsoever, it is important that it should be well mastered before taking up dissonance. The teacher must be the judge as to whether or not certain lessons should be reviewed. END OF PART I. "NAIN" A SACRED CANTATA FOR MIXED CHORUS, TENOR AND MEZZO-SOPRANO SOLOIST, BY HOMER A. NORRIS. PRESS NOTICES. The music shows talent, undoubted talent. Some of the choruses are exceed- ingly effective. The angel's chorus, " Benedictus, qui venit in nomine Domine, " contains some exquisite harmony. The two most brilliant choruses are the " Praise ye the Lord "and the concluding "Who shall ascend" which is a triumphant movement with a vigorous march rhythm. The most effective solos are the melo- dious responsive recitatives and choruses, " Art thou weary? " the powerful aria, " Out of the depths, " and the plaintive tenor solo, " Seek ye the Lord. "... The orchestration is brilliant throughout . . . The individual parts are so good that it is a thoroughly enjoyable work. — Sprmgfield Republican. The orchestral score of " Nain " is full of beauty and strength. — The Home- steady Springfield. Homer A. Norris, a young musician of great promise, has added to the dis- tinction he already enjoys by the compilation and composition of a sacred cantata called " Nain. " The argument opens with the passing of Christ and his followers between Capernaum and Nain, and the singing of the heavenly choirs. Then comes the first meeting between Mary Magdalen and the Christ, and the opening of her heart to the new feeling of her own unworthiness. This is followed by her questioning of the disciples as to what it will profit her if she follows the Saviour, and her cry of joy on knowing she will not be rejected, and the cantata ends with Christ's proclamation of pardon and peace to all the world. Mr. Norris' long ac- quaintance with sacred music has enabled him to bring to this work that religious atmosphere, that pathetic fervor which is always so convincing, and his music is characterized by straightforward simplicity, fine harmony, and dignity. Mr. Norris is especially to be commended for recognizing the necessary co-operation of the human voice, and has kept his music singable and within that range of the voice that is capable of the heartfelt expression needed for the best interpretation of such music as his. — Boston Home Journal. This work is a good addition to melodious cantatas of the modern school. It does not strain after contrapuntal devices, or extremely complex effects, yet on the other hand, it does not descend to anything like trashy or merely catchy melody. There is a spice of motive treatment in it, and the phrase attached to Christ is espe- cially sweet. . . The Saviour is here a tenor part, in contrast to preceding bass and baritone treatments. There is considerable antiphonal effect in the opening of the work between male and female choruses, and the effect is a good one. The arioso, " Yea, though I walk," is an example of Gallic tenderness of musical treatment, it is graceful, yet one might demand more of breadth and power in the general por- trayal of the character. Of the popular success of the number there can, however, be no manner of doubt. The same comment, only intensiiied, can be applied to the second scene, "Art thou weary?" and a few touches of imitative treatment here are effective. The leading of the voices all through the work is easy and un- forced. The Lord's Prayer is given chiefly a capella and is not very different from many German maennerchore, but it is eminently singable. . . All in all, the work, although it belongs to the popular, rather than to the strictly classical school, must be classed as one of the best of its kind. — Louis C. Elson. There is apparent in it a serious attempt to write truly and to write in a real vocal style. The success attained in both the difficult aims reflects much credit upon the composer, at the same time the work is thoroughly original, sometimes delightfully so, and modern in spirit. — Boston Musical Herald. But the chief interest was in the cantata " Nain " which received its first performance here. (^Richmond Indiana.) A new and meritorious production, and for church concerts there is perhaps nothing written that is better adapted. The sentiment and music are in perfect keeping with this class of entertainment. The work is in some respects a remarkable one. Some of the choruses, particu- larly the opening one, and the last, " Who shall ascend, " are noble compositions. The cantata is not only musical, but ennobling. N. B. Arrangements for the use of the orchestral score may be made with the publishers. H. B. STEVENS COMPANY, 212 BOYLSTON STREET, - - BOSTON.