fvRIC'W' MA NUAIiP^MRMONi ■gg Si[ J. C.D PARKER. i^H QJarnell Unluecattg ffiibtary atljata. Nem fork FROM THE BENNO LOEWY LIBRARY COLLECTED BY BENNO LOEWY 1854-1919 BEQUEATHED TO CORNELL UNIVERSITY MUSIC •IT rr, r,^?";" University Library MT 50.R53 1873 ''ichter's Maniial of harmonyia practical 3 1924 021 633 429 A Cornell University J Library The original of tiiis bool< is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924021633429 RICHTER'S MANUAL OE HAEMONY: PRACTICAL GUIDE TO ITS STUDY: EXPRESSLY PEEPAKED FOK THE CONSERVATORY OF MUSIO AT LBIPSIC ERNST FRIEDRICH RKKHTER. TKANSLATED TROM THE EIGHTH GERMAU BDITIOIJ J. C. T>. PARKER. BOSTON: PUBLISHED BY OLIVER DITSON & COMPANY., low YORK : 0. H. DITSON & CO.-OHIOAGO : LYON & HEAIY. Eutered, accorOi^ to Act of Oo^^e.. ^^^e^^e.rim..y^^^o. * Co.. in the Office of the librarian ^ U' PREFACE TO THE FIRST EDITION. The cMef motive for the publication of this system of Harmony is given on the title-page. It was to furnish pupils through their course of study in musical theory with some aid iu illustrating and reviewing the principles brought before them. The essential qualities of such a book the author believed to be these : that it contain the substance and fundamental features of musical theory in as condensed and complete form as possible ; that it present these outlines together with practical directions and hints, to prepare the way for later attempts in composition. The book comprises, scientifically speaking, no theoretical treatise upon Harmonics, but although, like every system of Harmony it rests upon a firm foundation, it is devoted only to practical ends, which with the scanty means now accessible it might be difficult to reach upon abstractly scientific prin- ciples. There has indeed been hitherto an eager inquiry for mathematical preci- sion in musical rules, especially among the young, who, naturally opposed to an authoritative creed, would fain have everything so clear as to be beyond a doubt ; while on the other hand they are ever fearful of learning to know and comprehend the blooming life of art by the anatomical knife ; nor is it to be denied," that in this regard there is a gap in musical literature, which no one has yet been able completely to fill. All attempts of this kind have thus far failed to produce a really tenable scientifically musical system, in accordance with which all phenomena within the domain of music shall be constantly regarded as necessary deductions from a single fundamen- tal principle ; and all that the philosophers, mathematicians and physicists have achieved in the matter is indeed worthy of notice, but has been on the one hand too disjointed to form a complete whole, and on the other too abstract, less serviceable for music than for other purposes, and whatever >V P E E P A C E. comprehension of musical matters it may have displayed, having but littlo reference 'to the essentially musical, which for the musician is the chief point in 'question. But all that has been laid down in musical manuals as a scien- tific basis has thus far failed to hold good, partly because as the result of individual and learned research it was also unable to form a complete system with infallible deductions, and partly because as a fanciful structure it was wholly wanting in scientific support. (It may be permitted here to call attention to a work which may be able to fill an evident gap ; The Nature of Harmonic and Metrical Laws, by M. Hauptmann.) Yet rightly considered, this want is felt only by the riper and cultivated musician, who loves to busy himself with theory; but for the less advanced scholar is not so detrimental as to affect his immediate progress ; and the skepticism above alluded to is to a certain extent no more to be heeded, than that childish disposition, which from overweening curiosity would fain come at the primal cause of everything by questions that can seldom be answered intelligibly enough to conform to the precise stage of his progress. In his early course the musician has to direct all his energies to his technical for- mation, as it will cost him time and trouble enough to reach the point whence he may with greater ease meet his peculiar position as artist. It concerns not here to ask Why, but more nearly How ; to learn from experience and from the best models the necessity of certain principles, not to calculate it ; afterwards, when culture, knowledge, capacity and calling demand, it will be time to search out the why, and all the knowledge acquired by experience will be an assistance not to be despised in discovering the musical laws of nature. With this practical object in view, the author has endeavom-ed to give in a simple and clear manner an explanation of Harmony, and of the results of observation and experience ; and as he intended the book for study, to let the truths contained in it work for themselves, without wishing to procure for them by a very learned garb or winning form, a large circle of readers. PREFACE. V It comprises the whole doctrine of Harmony with hints of a rational method of making exercises for its more thorough knowledge, and for the skillful use of all the fundamental principles. These exercises extend as far as the beginning of contrapuntal studies; the science of counterpoint itself will follow in a later volume. A word in conclusion to the young student, serious indeed, but well-meant. A far distant goal is to be reached ; it is really this, that art has to achieve. For this is needed an intense, untiring activity to grasp the funda- mental principles of music, and to give vital shape to what is acquired and recognized. They will be bitterly deceived, who, filled with the works of our great masters, endowed with poetic minds, suppose they can pluck the blossoms, without learning thoroughly to know and test technical means ; who adhere to the idea that the sacred charm of beauty which overhangs a work of art must suffer by the analysis of material, or that the natural forms of the latter could never be developed into that essential beauty. No talent has ever reached that height at which alone artistic efforts are successful, without thorough knowledge (which for it indeed was easier to attain than for the less gifted.) Practice without theoretical intelligence is not the mark of the artist, it is merely the working of instinct, which will make the want of a thorough culture continually perceptible. An ingenious thought cannot dispense with form, and this it is which must be recognized and learned. If this indeed comes often of itself with the inventron, it is impor- tant in music more than elsewhere, to analyze the thought logically as it were, to remodel it into new shapes, and to change it in the most varied manner. The knowledge of these things and skill in their use the man of talent must acquire, and it can only be done when one is at pains to recog. nise musical laws and what others have already discovered long before, and seeks to imitate and further develope it. Earnest, persevering effort, and above all a rational method for unfolding to maturity and for the creation of vital works of art, will with musical capacity surely lead to the goal. PREFACE TO THE SEVENTH EDITION. The methodical arrangement of subjects has been retained in the former editions of the Manual. I have been the less induced to make any altera- tion from the fact that, apart from my own experience, the book has been found useful in more enlarged circles, as is proved by the editions so quickly following each other. Having endeavoured, however, in each new edition, to introduce improvements and additions in the exercises and explanations, I have bestowed much care in revising the present one also. It contains, nevertheless, no essential changes, so that with the exception of the first three, all the previous editions, specially the sixth, can well be used with this — a great advantage in schools where the book is introduced. PREFACE TO THE EIGHTH EDITION. This edition also contains no important alteration, only that I have endeavoured here and there by improvements of style to contribute to the better understanding of single passages. For the friendly recognition of my labours, as is best shown by the rapid succession and marked increase of editions, affording me a pledge of the utility of my unpretending book, I have to express my special gratitude. ERNST FRIEDRICH RICHTER. Leipzig, February, 1870. TABLE OF CONTENTS. PACE, tNTEODUCTION.— System of Intekvals, . 13 SECTION I THE PRINCIPAL HARMONIES AND CHORDS DERIVED FROM THEM. CHAPTER FIRST.— The Triads of the Majok Scale, . . . .21 CHAPTER SECOND.— The Tkiads op the Mihok Scale, ... 40 CHAPTER THIRD.— Inveksioxs of Triads, 47 CHAPTER FOURTH.— Seventh-harhojiies. Chords of Eour Tones, . 54 CHAPTER FIFTH.— Inversions of the Seventh-Chord, .... 59 CHAPTER SIXTH.— Collateral Sevesth-Harmonies 64 CHAPTER SEVENTH.— Inversion of the Collateral Sbvesth-Choeds, . 78 CH-^PTER EIGHTH.— Seventh Chords in Connection tvith Chords of OTHER Degrees 81 CHAlPTER ninth. — Chords op the Ninth, Eleventh and Thirteenth, . 88 CHAPTER TENTH. — Chromatic Alteration op the Principal Harmo- nies. Altered Chords, 91 C:iAPTER ELEVENTH.— On MoDnLATioN, 102 SECTION II. INCIDENTAL CHORD-FORMATIONS. TONES FOREIGN TO THE HARMONY. CHAPTER TWELFTH.— Suspensions 105 CHAPTER THIRTEENTH.— Organ Point.— Sustained Parts, . . 123 CHAPTER FOURTEENTH.— Passing Notes.— Appoggiatubas, . . .128 CHAPTER FIFTEENTH.— Passing Chords, 138 CHAPTER SIXTEENTH.— Means op Modulation, 141 Vm CONTENTS. SECTION III. PEAOTICAL APPLICATION OF HARMONIES. EXBECISES FOR THEIE USB IN PURE PART-WEITING. PAGE / CHAPTER SEVENTEENTH.— Simple Harmonic AccoMPANorEST to a oiTEK Fast, 151 CHAPTER EIGHTEENTH.— Extension op the Harmonic Accompani- / MENT 173 CHAPTER NINETEENTH.— FoEMATioN or Melody 176 CHAPTER TWENTIETH.— Formation op the Accompanying Parts, . 183 CHAPTER TWENTY-FIRST.— Exercises in Thrke-part Movement, . 187 CHAPTER TWENTY-SECOND.— Two-Pakt Movement, . . . .1193 CHAPTER TWENTY-THIRD.— Harmonic Treatment of a given part I IN Melodic Form I 193 CHAPTER TWENTY-FOURTH.— Five-part Movement, . . . .202 CHAPTER TWENTY-FIFTH. — Six-, Seven-, and Eight-part Move- 1 UENT 206 CHAPTER TWENTY-SIXTH.— Forms o» Musical Eudisos, . . .213 INDEX OF SUBJECTS, .816 INDEX OF SUBJECTS. Accompaniment, figured page 183; harmonic ncc. to a given part, Isl, 173, 195. Afterslriking of harmonic tones, 121. Alto, 23 ; Alto notes, Alto clef, 1 13. Antecedent, 177. Anticipation, 121. Appoggiaturas, 128, 129, 134. Arsis, 107, 138, 174. Boss, 23 ; movement, progression of the same, .'54, 36, l.'jS, 205. Cadence, 55, 81 ; whole, half, 178, 214; perfect, imperfect, 62, 214 ; in modulation, 148. Cadence-formtdce, 149, 150. ' Cantus firmus, 196. C-def, 113. Chorals as exercises, 175, 205. Chtyrd, 21. Chord-formations, incidental, 105. Chord of four tones, 54 ; see Seventh-chord. Chord of the eleventh, 88, 90. Chord of the Fourth-and-Third, 59, 61, 62; augmented, 96. Chord of the Second, 59, 61, 63. Chord of the Sixth, 47 ; augmented, 94. Chord of the Sixth-and-Fiflh, 59, 60, 62 ; as Suspension, 189 ; augmented, 97 ; in modula- tion, 147. Chard of the Sixth-and-Fourth, 4S; in forming cadence?, 53; in modulation, 143; as passing chord, 139 ; use of the same, 153 ; of the augmented triad, 92, 198 ; of the diminished triad, 155, 188. Chord of the Sixth-Fourth-and-Second, see chord of the Second. Chord of the Sixth-Fourth-and-Third, see ch. of the Fourth-and-Third. Chord of the ITiirteenth, 88, 90. Chords, altered, 43, 91, 101 ; passing, 138 ; view of the same, 93. See also Triads, Seventh- chords. Chromatic alteration, 91. Close, -32 ; authentic, plagal, 32, 213. See also Cadence, Whole cadence. Half cadence, False cadence. Closeformation, 40, 53, 55, 213. Closing cadence, 55, 81 . Closing formidce, 40, 41, 149. Collateral seventh-chords, 64, 78, 86. Collateral tones, harmonic, 128. Collateral triads, in major 33 ; in minor 42. Compass of parts, 113. 9 10 MANUAL OF HARMONY. Cmrnedim, 25, 73, 81 ; local, inward, 35. Consequent, 177. Consonance, 17, perfect, imperfect, 17. Contrary motion, 26, 135, 201. Cross relation, unharmonic, 166. Degrees, diatonic, 13 Dissonance, 17. Dominant-harmony, see Triad, Seventli-cliord. in modulation, 144. Doubling of intervals, 25, 39, 48, 58, 70, 94, 109, HI, 132, 203, 206. Eleventh, 14. Exercises for practice in harmonizing (principal triads in major) 30, (all the triads in major) 37, triads in minor) 45, (inversions of the triads) 49, dominant seventh chord) 58, (inversions of the same) 63, (collateral seventh chords) 73, (connection of seventh chords,) 74, (collateral seventh chords in minorj 77, ("inversions of the same) 80, (false cadence) 85, ("collateral seventh choi'ds in connection with chords of other dcgi'ces or keys) 87, (augmented triadj 94, (other altered chords) 98, (study of mod- nlations) 103, (suspensionsj 112, 119, (harmonic accompaniment to a given melody) 151, 152, 157, 163, 164, 165, 170, 171, 172, 173, (formation of melody) 177, (three- part movement) 187, 188, 191, (two-part movement^ 193, (harmonic treatment of n given part in melodic form) 195, 199^, (five-part movement) 202, 205. Extreme parts, 23. False cadence, 81, 214. Fijleenth, 14. Fifth, 13, 22; perfect, 15, 16 ; augmented, 15, 16, 7u ; diminished, 15, 16, 38, 60 ; fifth in the seventh-chord, 57, 70. Fifth-progressions (parallel fifths), 26, 28, 51, 79, 97 ; open, 30, 79; concealed, 30, 37, 99, 158, 204; in passing notes and appoggiaturas, 133 ; in contrary motion, 201. Fourteenth, 14. Fourth, 13 ; perfect, augmented, diminished, 15, 16; preparation of the perfect fourth, 155 ; the same as chord, 189, 196. Fourth-progressions (parallel fourths) in passing, 134, 136. Fundamental harmonies, 21 ; chromatic alterations of the same, 91. Fundamental tone, 21 ; in seventh chord 57. Half cadence, 178, 213. Harmony, System of, 21. IntercJuxnging, 47 ; see inversion. Interval, 13; major, perfect, 14; minor, augmented, diminished, 15. Intervals, division of, 17; view of, 16, 19; transposition (inversion) of same, 18. See also Omission, Doubling. Intervals, doctrine of, 13. Interval, steps and skips, augmented and diminished, 156. Inversion, 47 ; of triads, 47 ; of seventh-chords, 59, 62, 78 ; sec also Intervals. Inverted intervals, 18. leading tone, 37, 39, 56, 76, 116, 159, 203. Major triad, 22, 64. Melody, formation of, 176; rhythmical formation, 177. Middle parts, 23. Minor triad, 22, 33, 64. Modulation, 102 ; means of, 141 ; extension and completion of the same, 148. MANUAL OF BARMONY. H Motion, direct, contrary, oblique, 26. Mtmment, one-part, 185; two-part, 1 93 ; throe-part, 187; four-part, 23; iive-part, 202; six, seven, eight-part, 20G. Ninth, 14; major, minor, 15, 10. Ninth-chord, 88, 118, 127. Ninth-suspension, 118. Numbering, 34, 48, 53, 55, 59, 63, 111, 104. Oblique motion, 26. Octave, 13 ; perfect, augmented, diminished, 15, 16. Octave progressions (parallel octaves), 26, 28; open, 30, 110, 133 ; concealed, 30, 36, 52, 84, 158, 204 ; in contrary motion, 201. Omission of intervals, 57, 73, 188, 193. Organ-point, 123. Part-management, 24. Part-moaement, 26. Parts, extreme, 23 ; middle, 23 ; formation of accompanying parts, 183. Part-writing, pure, strict, free, 24 ; pure, 137. Passing, passing notes, 128, 134. Passing chords, 138. Period, 177. Plagal cadence, 33, 41, 213. Position of the chord, close, open, dispersed, 31, 32, 114. Preparation of seventh, 70; of suspension, 107. Prime, 13 ; perfect, augmented, 15 , 16, Principal seventh chord, 54, 64. Principal triads in major, 23, 33 ; in minor, 40. Progression, melodious, unmelodious, 155, 156 ; of collateral seven th-chord.-!, 65, 73, 81. Relation of parts, 173. Resolution of the dominant seventh chord, 55, 61 ; of collateral seventh-chords (in major) 65; (in minor) 74 ; of suspensions, 106, 109, 116, 120. Scale. See Triads. Second, 13; major, minor, augmented, 15, 16. Second progressions (parallel seconds^ in passing, 134 ; with appoggiaturas, 136. Second step, augmented, 44. Sequence, 37. Seventh, 13 ; major, minor, diminished, 15, 16 ; passing, 72, 173 ; preparation of, 70 ; same without preparation, 72, 77, 158, 164. Seuenth-chord, 21, 54 ; Dominant-seventh-chovd, 54, 57, 61, 82, 144 ; fundamental, 64 ; same in passing, 139. of the seventh degree in major, 68, 78, 90, 199. diminished, 76, 79, 87, 90 ; same in modulation, 146 ; same in movement of several parts, 206. Seventh-chords, connection of, 73; same in connection with chords u'cJic., d:;gr'.c5, 81, 86, view of the same, 100. Seventh-progressions (parallel sevenths) in passing, 134 ; with apj)^z=.^-i=i^-=-5r==^ An exact, thorough knowledge of this essential transposition of intervals is not only important for exercises in double counterpoint, but facilitates a comprehension of, and insight into, simple hai'monic structure, wherefore the study of it is strongly to be recommended. A few remarks may follow here. The reason why in the first table of intervals (p. 16) all diminished miev- vals were formed by raising the lower tone a half degree, and not by lower- ing the upper, can be clearly seen from the above table of inversions. Since diminished intervals result from augmented by transposing an octave, this formation comes of itself. For instance : the augmented fourth =fe ■sz must necessarily produce the following diminished fifth : -¥- 20 MANUAL OF HARMONJ. Likewise the perfect fourth belongs ■ originally to the consonances, since by transposition it is changed to the perfect fifth, just as the perfect fifth can produce only the perfect fourth ; and in general, a dissonance can never result from a consonance by transposition. Mention is here made of this, because in special cases, which will be noticed hereafter, the fourth has to be regarded like some of the dissonances, which in former times induced many theorists to pronounce it merely a dissonance. Likewise it becomes clear that the augmented octave, as well as the ninths, cannot be transposed, as they can never fall below. Other kinds of transposition, as into the Tenth and Twelfth, which pro- duce entirely different results, may be passed over here, as they have no influence upon our immediate studies. Since a complete and thorough knowledge of all the intervals is indispen- sable for the studies in harmony which follow, written exercises in them, as well as oral solution of given intervals, will greatly facilitate a proper con- ception of them, and should be repeated again and again. SYSTEM OF HARMONY. Combinations of tones, sounded simultaneously, and composed of difier- ent intervals according to certain fundamental principles, are called in gen- eral terms : Harmonies, chords. The science of Harmony points out the nature and kinds of chords, and teaches their natural treatment. This consists in the proper, natural con- nection of chords one with another, i. e. in the transition, resolution, blend- ing of a chord in and with the following. SECTION I. THE PRIMITIVE HARMONIES AND THE CHORDS DERIVED PROM THEM. Among the different chords which may serve as the harmonic groundwork of a composition, we may easily distinguish such as appear independent without a determinate relation to others, from those which clearly point to a connection with other chords, consequently are not independent. Consonant and dissonant chords. To the former belong most of the Triads, to the latter the Seventh-chords. Both kinds form the primitive harmonies from which all the remaining chords are derived. CHAPTER I The Triads of the Major Scale. A Triad is formed by a combination of three difierent tones. The lowest of these is called fundamental tone, to which are added its Third and Fifth, ' for example: 21 22 MANUAL OF BABMONT. But these triads, formed from c, g and a, exhibit another difference in their intervals. While the triads of c and g are formed here with major Thirds and perfect Fifilu, the triad of a contains a minor Third and perfect Fifth. A triad with a major third and perfect fifth is called a Majok Triad, oue with a minor third and perfect fifth a Minok Triad. Remark. — The explanation of other sorts of triads cannot follow until later. As the diatonic scale makes up the substance of a key, and forms the groundwork of the melodic series, so also the triads, which are built upon the different degrees of the scale, wUl form the essential part of the har- monic substance. Natural connection of tlie triads of a key. The triad based on the first degree of a key must indeed be the most in»- portant, as fixing the key ; with it, however, stand others in the closest rela- tion, serving to explain its position. Viewing the triad in its natural form as third above third, the Prime ap- pears as the fundamental tone, the Fifth as the highest tone, the summit as it were. 2. $ ■.Fifth. Prime. Bemarh. — Any further addition of a new interval would either alter the chord or double tones already present. The chord which stands in the closest relation to this must indeed as an independent chord lie wholly outside of it, but yet rest upon one of its tones. This tone can be found only in the extreme limits of the chord, namely c and g. Therefore G, which is here the fifth, wUl become the root of the nearest related triad, while c in like manner wUl form the summit, the fifth of the other, whose root would be F. The connection of these three chords can be best seen in this form : In these three chords, standing in the closest connection, it is especially to be remarked that their tones include the entire scale ; that they form the outlines of the key, and that they are and must be the most frequently used in practice, if the key itself is to be clearly and distinctly represented. MANUAL OF MABMONY. 23 On account of their importance, special names have been assigned them. The first chord) resting on the first degree of the scale, is called : T-HE TONIC TEIAD, the second, on the fifth degree : THE DOMINANT TRIAD, the third, on the fourth degree : THE SUB-DOMINANT TRIAD. Let these three chords be ranged in their order in the scale, and they wiU appear thus, without showing their inward connection : i ^#r- -»- ^ rv. and they are also seen to be all major triads. Application of the above Harmonies. In applying these three chords, we will use here, as also with chords to be treated of later, four-part harmony. I Eemarlc. — The theoretical connection of chords can be, it is true, well represented in its manifold relations, with three parts. It would however keep us longer from our prac- tical object, and may therefore be left for special treatment. Four-part harmony will ever maintain its importance as the foundation of all kinds of composition. Every harmony is regarded not as a mere mass of tones, as often appears in Piano-forte compositions, but we divide its ingredients into four special parts. The upper part is called Soprano, the lowest Bass, the two together the extreme parts; that next below the Soprano is termed Alto, that .over the Bass, Tenor, both together the middle parts. The following is an arrangement of these parts in score, and the triad appears thus : 5. SOPKASO. Basb. ZSl ~Sr :3= 3ZI zsz ■:21CL 24 MANUAL OF HAS.M0N7. For the three upper voices special clefs are used, which are better adapted to their compass than the Violin clef employed above, and of which we shall speak hereafter. To obtain an easier survey of the parts, we will adopt in our next exer- cises the Piano-Forte arrangement of parts, and not take a separate staff for each voice. The distribution of parts in No. 5 will stand thus : These different parts will be considered in a double relation: first in reference to the progression of each part by itself, then in its relations to the other parts, both of which must be fure and well-constructed. The result of these two conditions constitutes pure ■part-management. This purity of harmony and progression is attained by seeking and prac- tising what is natural and in accordance with law in the connection of har- monies. Hence arises what we term 'pure part-writing or severe style, which im- poses rules and laws resulting from the nature of music itself, and whose observance will afford the surest basis for a subsequent free use of the materials of composition. Exercises in this style render the judgment heen, cultivate the sense of what is true and correct, and enlighten the taste. Remark. — So far as every composition should be the result of a right use of all availa- ble means and of thepun'ily (that is, natural expression) wrought thereby, the term pure part-writing in the general sense would as a matter of courser equire no farther explana- tion. In the narrower sense, however, something more is implied, which might be more closely and better indicated by the synonymous expression: strict composition, strict style, in contrast with the free style, which in its real meaning, as opposed to the pure, is not to be understood as impure writing; for this, however often it may occur, is in all cases to bo indicated ss false, whereas the free could in the main be founded upon what is legal in the pure. As was hinted above, by the term pure part-writing in the narrower sense is understood MAJfUAZ OF HARMONY. 25 Bach as in the natural development of all the relations of toiies allows the fewest deviations from what is legal, and only such as do not affect what is essential and fundamental. If the idea of pure part-writing is thus in general determined, yet its limits are not yet drawn ; and it is precisely this that creates all the more difficulties for the beginner, since the limits are very differently fixed by theorists themselves. This difficulty has induced many of them, especially some of the more modern, to say no more of pure part-writing or strict style, but generally to commence at once with the free style and learn the harmo- niclaws incidentally. Whether this compliance with youthful impatience, which does not love to busy itself with the abstract, this tendency to premature living creation, before the organic is developed into a creative faculty, can bring anything to real maturity, is not to be farther investigated here. It is to be hoped that those who follow the views of this book and let their studies con- form thereto, as well as all who have to go through a strict school, will be convinced that their freedom for future work will by no means be lost by what is forbidden them, but, based on natural principles, will develop all the more fully and powerfully. Real master- ship has ever learned to reach the greatest intellectual strength when under restraint, whereas the wildest fancies frequently give evidence of mental disease and weakness. On the other hand the scholar cannot be warranted, where rules are at stake, in making use of principles based upon exceptions, such as may perhaps be found in the best masters, or in general in wishing to produce compositions, when his business is to perform exercises theoretically well. The three chords thus far found, when applied in four-part harmony, will lead to remarks and observations, from which certain principles and rules are to be established. Since triads contain but three tones, one part (interval) must be doubled, when four are to be used. Each interval of the triad may be doubled, but in most cases the root is the best adapted for this purpose, more seldom the fifth and third, and the last, in many cases to be pointed out later, not at all. All doubling is to depend on a good and correct progression of parts. To accomplish the connection of two triads, the following rule is to be observed : "" When there is a tone common to two chords that are to be connected, it it retained m the same voice. 7. i zsz zsz 26 MANUAL OF BABMONY. In example a we find c common to both triads ; the Soprano, which had the first c, retains it also as fifth in the next chord. So in example 6, where g in the alto makes the connection. The other parts move to the nearest tone, as in a the Alto from ^r to o, the Tenor from e to /, &c. When no tone is found common to two chords, the parts must be moved independenlly in such a way, that no one shall appear in Parallel Fifths or Octaves with another. In order to explain this faulty progression more fully, we shall first premise what is necessary concerning the movement of parts relatively to each other. The movement of parts with, respect to each other. One part can progress with another in direct motion (moius rectus'), contrary motion {motus contrarius) and oblique motion (motus obliquus). Direct motion takes place, when two parts ascend or descend simulta- neously, e. g. i ^i^E -zy i^ ZSr ~&1 T 1 Two parts move in contrary motion, when one ascends, and the other descends, e. g. •i _se: is: -isiz [^ Oblique motion occurs, ,when one of two parts remains upon the same tone, while the other moves, e. g. 10, 1^ ZJIZI A-.. ISZ 1 7^1^ 'T ~sn. % ^ -«)- ::ffiz ?^ MANXfAL OF HARMONY. 27 These three kinds of movement occur promiscuously in chord connections. Thus in example No. 7 h. the direct motion appears between Soprano and Tenor, contrary motion between Soprano, Tenor and Baas, and oblique motion between the Alto and the rest of the parts. The above-mentioned /aM% progression in parallel Octaves and Fifths can only appear in direct motion, as for instance when two parts move thus by steps or skips : U. IZ22 CS2I I This is equally a fault with all the parts : The following harmonic progressions contaai both errors : 12. ■x^.^. :>^^ ■nz^. E^Em^mm^^m In example a. there are parallel octave movements between Spprano and Bass, in example b. between Altb and Bass, and in example c. between Tenor and Bass. Parallel Fifths appear in a. between Alto and Bass, in h, between Tenor and 'Bass, and in c. between Soprano and Tenor, as well as between Soprano and Bass. The mechanical means of avoiding these and similar erroneous progres- sions, is, for cases like the above, the employment of contrary and oblique ^notion in the parts, i. e. the voice which already stands an octave or fifth from another, must either move in contrary motion thereto, or, if the follow- ing chord contains the same tone, remain stationary. The other voices then pass to the tones nearest them in the new harmony. Thus in example 12 a. three voices must move, one remaining still ; in b. and c. contrary motion of all the parts • to the Bass is to be employed, foi instance : 13. zzzz ^S- 5£ rs; ISC ^ i 28 MANUAL OF HARMONY. Kamrk. — The reason for this prohibition of the octave (that of the unison is included) can be easily found in the necessary independence of the parts. To discover the reason for prohibiting the progression by fifths is not so easy, however much one is convinced of its necessity, and great pains have ever been taken to express it clearly and definitely. Let the following view of this subject be examined. If every chord-formation presents for itself an independent whole, which, however else it may be shaped, yet in respect to its root and fifth principally, unites itself as it were into a circle (the Seventh as an addition is here out of the question), and if harmonic connec- tions are only produced when two chords become in a manner merged into and identified with one another, it is obvious that two chords with their extremes, fifth following fifth, do not become thus merged, but, when placed side by side, appear without any relation to each other. Tliis is easily seen by comparing the following formations : 14. i ^ ^IS- Sevenths form essentially no new chord, nor can they be conceived of as outside the circle of the primitive chord ; they only serve to mark more definitely the relations of two chords, and to render the harmonic connections closer and firmer. Now wherever the perfect fifth appears, it will carry in itself its character of demarca- tion, and whether the other component parts of the chord (the contents as it were of the fifth) or an added interval like the seventh, lie above or below it, the unpleasant effect of the succession of two pet feet fifths will always be traceable to the lack of connection, to their isolated nature. "While speaking of the fifths of triads, it may be observed further, that in the case of perfect fifths which arise from added sevenths, the law of preparation partly indeed of itself prevents parallel fifths ; but in the case of the progression of such a seventh, forming a perfect fifth with another voice, to a succeeding perfect fifth, the unpleasantness and want of connection will be equally perceptible, just because this lies only in the second fifth, which appears without connection, for example : But as far as the diminished fifth is concerned, which in the Dominant Seventh chord under certain conditions can appear even unprepared, its entrance without preparation even in parallel fifths perfectly justifies the views above expressed, since whenever it foUoua the perfect fifth, its connecting character is maiutttined, but when it precedes it, the latter, MANUAL OF BABMONY. 29 to say nothing of farther laws of progression, at once departs from the uniting circle of both harmonies. Compare the following passages : 16. Though passages like the following are often found in compositions of the stricter style : 17. J ^ It is to be understood that the doubling of the diminished fifth (the/) requires a double progression of the same, and the consecutive fifths are justified as lying in the middle parts, but that the following progressions could not be called pure: 18. fe -J^^r^ I IZfc J^^ __ J^^- partly because they are too conspicuous in the upper part, partly because the above con- dition of a necessary double progression is wanting, although passages like that in No. 16 c, are often met with. It becomes clear here also, why parallel fifths resulting from passing notes in manf cases do not sound as disagreeably as those discussed above, wherefore many theorists allow them as faultless ; this however is not to be admitted unconditionally, since many of them are based upon other false progressions (for example, upon concealed fifths) and it is not to be denied that, when widely dispersed and of sufficiently long duration, their unpleasant effect is obvious. This is not the place to treat further of these relations, and much might be said upon many points, as for instance the progression of the fifth in the augmented chord of the Fifth and Sixth, which would lead us now too far away. We shall be led back to this point in our practical exercises by individual matters. 30 MANUAL OF BABMONY. If the meaning of the above explanation be too obscure for the beginner, it will never- theless with his advance in knowledge and practice and his necessarily ofwepeated study of the whole harmonic system, be soon understood. The faulty progression of parts thus far mentioned, we call open fifth and octave progression. When in direct motion between two parts the «ecorac?. interval forms a, fifth or octave, it is concealed, e. g. : 19. idi^a- r«- Open parallel fifths and octaves are never admissible for harmonic connec- tions ; respecting the value or futility of concealed fifths and octaves we shall speak hereafter (chap. 17) ; for the present this must be left for oral instruction, as, in general, with a proper conception of the exercises, there will be no immediate opportunity for errors of this kind. Remark. — The beginner will do well in writing his first exercises to pay no attention whatever to concealed fifths and octaves, because, by too anxiously avoiding them, the first principles of chord connection are violated, and other errors, much worse, may easily arise. Many things will in the sequel bring us back to this point, and be especially examined and discussed. * Exercises. The use of the three principal triads musically in connection, observing the rules thus far established, will be the next exercise. We wiU select for this purpose some Bass progressions like the following : 1. 2. fs ■ a ■ /"J ■ sso. r^ ' y\' fj rj a ■ ^J 0: I IT izz: 1 zs:. 131 Eemixrh, — These and all the lessons that follow, serve to indicate the manner and method to be pursued in our practical exercises. They should always be contiuned as long as the subject in hand renders needful. The disposition of the three upper parts to be added in the first chord will lead us to further important remarks. MANUAL Of HAMMOSY. 31 "We have already seen in example 5. that the disposition of the voices in a chord may vary greatly. This disposition of the voices is called the position of the chord. Close and Open Position, A chord is in cbse position, when the three upper parts lie so near each other that neither the Soprano nor Tenor, if transposed an octave, would fall between the other two, though the Bass be far removed, e. g. 12. ISI :3zz =i= 12= d. The first position of the chord a. is so changed in b., that the former e of the Tenor is given to the Soprano an octave higher ; in c. the case is the same with both tones g and « ; in rf. the c of the Soprano is reversed and put an octave lower. In all the transpositions the distribution is changed, but not the close position. It is otherwise when the chord appears in open position (also called dis- persed position,) which is the case, when either the Soprano can be placed between the Alto and Tenor, or the Tenor between Alto and Soprano, so that the close position shall result therefrom, e. g. 22. d. ~^. ZZIZ ZSEL I2ZZ zsz In a. the chord appears in open position, by placing the g between Alto and Soprano in close position, 5., likewise in c. and d. In /. the g of the Soprano in the chord e. is put an octave lower between Alto and Tenor. But thQ following disposition of the parts (No. 23) would not be an open posi tion in this sense, for by transposing the Tenor the disposition of the 32 MANUAL OF HARMONY. upper parts is not changed, 6., and only the transposition of the Soprano would give the true open position, c. I3C ISC i 23. IS= ^[1 Although the open position renders the chord fuller, yet it should not be always used, and for our first exercises is not compact enough to be clearly seen, so that at present we shall give them in close position. Remark, — It will always he better to write the examples at first in close position, and not to use the open position until later, commencing with the exercises in the second and third section, where it will be seen of itself to be needed. Beginning with the open position the scholar continu- ally stumbles upon difficulties, which it cannot be his immediate object to oTercome, and art therefore much better avoided. Usually the different positions do not appear singly, but occur promiscu- ously, according as the movement of the parts requires. When the position of ih& first chord is determined, those following are no longer so free as regards distribution that any can be taken at pleasure, but it is governed by the rules already given on pages 13 and 14 for connecting chords. This chord connection and movement of parts .in the first exercise No. 20 can proceed thus : ISZI I2ZI 24. ^^^ lai I32I m C: I IV The natural relation of these chords to each other becomes clear in the above simple example, if their connection be closely observed ; but especi- ally from the last two chords may be seen the close connection, how one completes the other. The sensation of return, of rest', of satisfaction, which lies in this combination, renders it suitable for forming the close. This form of cadence through- the dominant chord, which inclines to the triad of the tonic, is called, when the latter falls upon the rhythmical acceht or on a good place as to time, the authentic cadence. MANUAL OF BABMOITY. 33 25. :ai 1 zso Another form of cadence, which is formed through the Sub-dominan: triad, as above in No. 20, 4th example, is called the Plagal cadence. 4- r^i 23. I2ZI IV I Of these and other kinds of cadences we cannot speak at lengih until later. In order to become familiar with the succession of chords which arises, when the Bass moves by degrees (as in example 24 F — G), it will be well to write out the succession IV-V and V-IV in different positions and keys. The triads of the remaining degrees of the Major Scale. All the triads of -the remainiilg degrees of a scale belong, to be sure, to one and' the sijme key, but, do not point to it so decidedly, as e. g. the chord connection V-I. These triads are called, to distinguish them from the j)rincipal triads, COLLATERAL TRIADS. They are formed upon the second, third, sixth and seventh degrees of the scale. 27, i ^ H VI VH' The triads of the second, third, and sixth degrees are seen to be minor triads, as their thirds are minor and their Jiflhs perfect. The triad of the seventh degree is essentially different from the rest, 34 MANUAL OF HABMONT. since it has beside the minor third a diminished fifth ; it is therefore called the DIMINISHED TRIAD. As an easy mark of recognition we take for the minor triads small letters to number the degree on which each is built, to which we add an ° for the diminished triad, as above vii°, a method of numbering introduced by the theorist G. Weber. Now tte triads of the major scale collectively will stand thus : 28. ^ IV V VI Itemark. — The beginner must be very cautious -lest he regard all these chords, when they appear, as tonic triads, an error which greatly obstructs the understanding of har- monic connections. As long as C major is the prevailing key, the incidental triads of G, F, of d etc. are merely llie chords of the several degrees belonging to it (the key of C major,) aiid we are not speaking of G major, F major, d minor, since these keys do not appear independently. Hence arises an ambiguity in chords, which it is well to heed. Every triad can belong to various keys. The C major triad may be : 29. I F; T G: rv If therefore, in connection with this chord, we speak of C major (meaning, according to ordinary usage, the key,) this is true only in the first case, where the C major triad occupies the first degree, but in all other cases is incorrect. Application, In connecting these chords with each other, as well as with those previ- ously found, no new rule is immediately necessary: much that is new, however, wiU appear as we proceed. The Bass can move either by skips or by degrees. In the former case there will always be connecting tones (degrees com- mon to two successive chords;) in the latter, the parts must move in contrary motion, according to the above rule (p. 27,) in order to bring «ui the natural connection of chords. MANUAL OP HARMONY. 35 a. The Bass moves by skips. b. NB. 30. ^- ^^- =1:: I22C -t-- better. -S= ^■ ■E^^EBi^3z%z V\' 1 \ f'J w ■\ ^J ■ ri- n <-t -^ p'? 1 II IV n ^ZZ" I22Z II VI etc. Skips in the Bass, as in these examples from the second degree, can be managed similarly from all the remaining degrees, so that tones common to the two chords shall remain in the same voice. In many cases, however, there are exceptions to this rule. In example 30 at NB. there is a progression of parts formed according to the above rule, which contains a concealed octave between Tenor and Bass, and which is decidedly improved by the progression which follows. Though the local connection of tones be wanting in the latter case, yet there is still an inward connection, since the d of the Soprano in the first chord caji easily be conceived of as doubled in the lower octave, by which the connec- tion becomes at once evident, as in 31 : 31. Remark. — The reason why precisely ihis tone should be conceived of as doubled, since sucli might be the case with any other, is based upon the fact that it is the fundamental tone, tbat, in fact, which gives the entire chord its determin'ite character. The unpleasant effect of the above-mentioned concealed octave consists in this, -that the upper part moves a whole tone; and the effect is still more etartlino' when the octave is contained in the extrepie parts, as in example 32 in a. 32. :22z =^T"^ rE2Z 36 MANUAL OF BABMONY. By the contrary movement of the Bass in h. the progression can he im- proved, also hy the contrary movemenf in example c, although even here there is a succession of concealed fifths between Soprano and Tetor. (See the remarks under example 34.) neinaik. — In the cases given above, we are not speaking of absolute errors. When wo have entire liberty as to the movement of the parts, much can be avoided which wo can- not escape under other circumstances, o. g. in handling a cantm firmus, a motive; or when other reasons exist, iinportant as regards the composition. The corrections are here cited only from an absolutely theoretical standpoint. Of the concealed fifth in 32 c. we shall speak more particularly under No. 34. The unpleasant effect of the concealed octave vanibhes at once, when the vpper part moves a half toni!, e. g. 33. m^ =^^ ^i ^^ I l5E^ 9^»- X b. The Bass moves hy degrees. Here contrary motion is constantly to be employed, e. g. XD. 1. better. piSiti^lig^iiiii^g '■t- - - f_^f-rp^ — o — — «— E ^^T sr-r—^=2 — «— tf? 1 ... L_ffl=.t IV MANUAL OF EARMONY. 37 Remarks upon these Chord Connections. In all the progressions used in ISTB. 1 and similar passages which follow, it is better to double the third in the second chord, in order to avoid con- cealed fifths. Their unpleasant effect is even more prominent, if the chords appear in open position, e. g. 35. is: 22:; -s'-^^fsr -a»„ .S2Z ^sz ^1 ^ 32Z -O- =i= rsc =22= -Ml The progression in b. is preferable. If these concealed fifths occur in the middle parts, they are, under certain circumstances, sooner to be allowed, not being so prominent. 36. In NB. 2 the doubling of the third in the second chord is not always to be resorted to, since in general the doubling of the seventh degree (m example 34 the h of the second chord) is to be avoided. Of the use of this tone, called the leading tone, we shall speak more at length in the exercises which follow. Exercises to he written out. i^ :^ g 37.^15 =^ -?£ '^l s>—(^ 7iz =32: S^ -^ :^ -IS — ^- NB. 22_. i .5. ^ Z^Z l9=?Sl 1 zzsr. EE?^ 1^=3: 3z: The fourth exercise gives occasion for some remarks. The progression of the Bass here in the first four measures proceeds in a regular, consistent manner. Such a regular harmonic or melodic progression is called a Sequence. MANUAL OF HARMONY. This consistent progression of the Bass requires also an equally regular movement of the other parts. If we harmonize this passage on the above established principles of con- necting chords by means of stationary tones, e. g. 38. 2Sz ^ ^=^. &c. z^z=i- ^ this object will not be attained ; on the contrary, the progression must pro- ceed in such a manner, that the first chord in the second bar shall be in the same poaition with the first in the first bar, so that the connecting tone d Aoea n^ii remain in the same part. 39. ^ ZfZZ m NB. _ &c. =?Z= 1 So in the first exercise, on account of the sequence, concealed octaves, of which we spoke above, are allowable, if they are not in the extreme parts. In the third measure in exercise 4. we find a chord not heretofore used. The Diminished Triad. It is based upon the seventh degree of the major scale, and is less inde- pendent than the triads thus far found, as it points distinctly to one progres- sion, caused by tlie dissonance, the diminished fifth. The natural progression of diminished intervals can in general be con- ceived of thus, that either both tones approach each other one degree (a.), or that one or the other moves while the other remains still (J., c), a method of progression which only becomes plain in a real chord connection. Inversion. MANUAL OF HARMONY. 39 In the third which follows the diminished triad (d.) the triad of the first degree c appears incomplete, the fifth being omitted. Since according to the relations of intervals heretofore explained (pp. 18, 19) as regards inversion (transposition,) an augmented fourth results from a diminished fifth, so their progression must likewise appear in an inverted manner. See 40 e. The fundamental tone, upon which the diminished triad is based, is called LEADING TONE. It appears again as third in the dominant-triad, and as fifth in the triad of the third degree. 41. i -s>- ni 1 Since the leading tone is of itself very distinctly prominent, it is not DOUBLED in simple four-part harmony. So its progression should be to ascend a half degree, when the chord that follows contains this tone. The necessity of this progression lies in the melodic character of the leading tone,, preceding, as it does, the tonic of the scale by a half tone. This is particularly observable in the dominant-triad, if the leading tone be in the highest part ; thus a. in example 42 is more satisfactory than b. and c. c. d. e. 42. ;=€s; =i:i;ra= IS= This upward tendency is less decided in the middle parts, as in d. In many cases in such chord connections, skips in the upper part (in c.) are positively unendurable; and skips in the middle parts (in e.) are to be employed, when the Bass progresses by cpntrary motion. In example 39 in the third measure we have the leading tone doubled and progressing contrary to. the above rule. Both were on account of the sequence contained in the example, which allowed no change either of position or progression of the chords. On the more iComplete Formation of Cadences. The cadence by means of* the dominant chord noticed on p. 32 (the authentic cadence) appears in the last examples in a still more definite form. 40 MANUAL OF HARMONY. That is : as the natural relation of the dominant chord to the tonic triad renders the two chords suitable for the formation of the cadence, so there is observable in these examples a still further preparation of the same by means of the triad of the second degree, which stands in the same relation to the dominant chord, as the dominant chord to the tonic triad, e. g. 43. ^ zzaz ^ ^m zso =t 32= 1 Besides the triad of the second degree, that of the sub-dominant is also well adapted to this form of cadence, e. g. i^ ■ij&i * _gK ZOL g 14. 32r ZSr IV V The forms of closing (cadences) which result from this connection of chords will assume a stiU more definite shape by a use of the chords to be explained hereafter. CHAPTER II The Triads of tlie Minor Scale. a. Principal Triads. The principal triads of the major scale were found upon the first, fourth andffth degrees. O/i the same degrees we find also the principal triads of the minor scale. The relation, however, in which the dominant triad stands to the tonic chord, as it is seen with special clearness in the cadence-form above shown, necessitates the alteration of one tone of the minor scale. The seventh degree, which according to the signatures of the minor key ia always a whole tone removed from the eighth degree, is raised chromatically a half tone, so as to receive the character of the leading tone. e. g. MANUAL OF UABMONY. 41 ~az -S>—ZZZ 45. i^ — B— ^ — at. -7S - NB. i By this means the domiuant triad in minor is formed exactly like that in major, thus : A minor. A major. 46. »# a: V A: V or to speak briefly : - Tlie dominant triad, both in major and minor keys, is always major. This is plainly seen by comparing the cadence-form of both keys : C major. C minor. 47. I^I^Sfe ia= l^^^liE m That the sixth degree, however, of the minor scale is in a harmonic sense not capable of any chromatic change by raising a half tone, as is often required in a melodic relation, is proved by the plagal cadence a. (see p. 33) which cannot be conceived of at all as in b. in A minor, a. 48, -w- :^i^= gh rszT. Z3£. i The three principal triads in minor can be represented in their most natural relation, as formerly explained, thus : 49.1=^^ r. V 42 MANUAL OF HARMONY. The miuor scale, therefore, as a basis for harmonic formations, will stand thus: 1 i 1 1 i 14 i 60. p Z2ZZ Z3C Bemark. — All other forms of the minor scale, as 51, i rrsc or descending : 52. i -ti^-^ I2ZI HEZ rest upon melodic conditions, which do not admit of the intervaj of the augmented second found in No. 50 between the sixth and seventh degrees. Abstractly these forms have no influence upon harmonic formation ; yet the harmonic sub-structure reacts upon the formation of the minor scale, as the following examples show : 53. E±^ ?=!=T^ ^» ^E^g^l ^ 9^^ m ^^^i^g -^b*^-JS^ iHiA =t I ^ U=i--i=^ &c. fe The last case, where the descending scale has this very interval of an angmented second b — a flat, which in the sequel we shall carefully avoid in harmonic connections, is explained in this way, that 5 was necessary as a component part of the chord, but a\), in order not to destroy the minor character of the passage, which is strikingly the case with a, while in tlic ascending scale (in the first example) this is already perfectly preseiTed by the minor third e\). b. The Triads of the other Degrees of the Minor Scale. SECONDARY TRIADS. According to the establishment of the minor scale, the secondary iriadt appear in the following form : 54-^^ u 1-=^-= n° NB. IT V VI vn" MANUAL OF BARMONY. 43 The second degree gives a diminished triad, as formerly the seventh degree of the major scale : likewise a diminished triad is found on the seventh degree. The sixth degree forms here a major triad. The third degree brings a new form of the triad. It has a major third and an augmented fifth, and is called therefore THE AUGMENTED TRIAD. From the forced or strong connection of this chord with others of the same key, it can seldom appear as the fundamental harmony of the third degree of the minor scale. The following examples may prove this : 65. d. /. 13?: m. m^^ 122= --iar -li=i= ;g=:^ TjSZ raz isr^ TI Of these examples those under c. and e. will be the most practicable. The introduction of this chord appears still more difficult : 56. Its introduction is the most tolerable, when the augmented fifth is pre- pared, i. e. is already present in the same voice as a member of the preceding chord (in d.). Remark. There exists something peculiarly foreign in the chords of the third degree as well in the major as in the minor scale, so that this harmony, even when it appears simplv as a minor triad as it does in the major scale, can with great difficulty be connected naturally and effectively with other chords, and therefore seldom occurs. Most of the practical chord-connections indicated above will occur in other relations, and not allow the augmented triad to be recognized as the third degree of the minor scale. The augmented triad, which is very often used in . more modern music, belongs to the chromatically altered harmonies, which will hereafter be explamed under the name of Altered Chords. (See chap. 10, Altered Chords.) u MANUAL OF HARMONY. Application. The principles already developed of harmonic connection and part move- ment wUl be valid here also, and what was said above concerning the progression of the leading .tone, is eminently applicable to the connection of the principal chords in minor, since the interval of the augmented second from the sixth to the seventh degree in the minor scale, as well as from the seventh to the sixth descending, is to be avoided as unmelodious, when the two tones, which include the interval, belong to different harmonies, e. g. 57. I '-M ih ia= VI VI * m laz In connecting therefore the chords of the fifth and sixth degrees, which very often happens, the leading tone must always ascend, by which in the triad of the sixth degree the third appears doubled, e. g. 58. Hence it would be impossible to present correctly the example given under 57 I., unless an intermediate tone were used, as thus : ^ 1 59. ^i RemariC. — In certain special cases practice deviates from this rule. It will be well, however, to adopt the progression indicated above, for the reason tliat it should not be overlooked, that every deviation from rules in praclice has and should hniv a stated motive, whereas in numerous other cases the observance of them is still recognized. MANUAL OF HARMONY. 45 Exercises for Connecting the Triads of the Minor Scale. 1. 2. 60. sil^g # i 3 # # lai =«: i^iz: §i^^ 3 # 5# # ■3 # 5=a= is: 1^ i # -f2- # = # ii^S ^- 3= Renaarks upon these Exercises, A chromatic sign over a Bass note without a figure, as e. g. in the third measure of tlie first exercise, always has reference to the third of the Bass. This raising of the third in the dominant chord, as very often happens in minor, is the raising of the leading tone spoken of on p. 41. In general, when the Bass has the root, the triad is not figured in Thorough Bass writing, and there must be special reasons for figuring with 3, or 5, 8, . 8 g' or fully with 5. In the third and sixth exercises there is a reason for figuring with 5. The introduction of the triad of the third degree in minor has here been attempted, and it was necessary to indicate the elevation of the fifth, since it forms likewise the seventh degree of the minor scale. Where a 3 or is given with the first chord of some exercises, it has reference to its position. On this point see remarks under exercises (p. 50.) The principles thus far developed will be verified by filling out one exercise. We take the first for this purpose. NB. 61. ^=--:t -^^ Ei ^km mi Z(S1 zsz i The first principle of chord-connection (through connecting tones in the same voice) is observed here throughout, and therefore in the third IG MANUAL OF HARMONY. measure (at NB.) the Alto makes the erroneous progression of an atig- mented second from/ to gi^. To avoid this error (according to p. 44,) it will be necessary to let the Alto move from / to e, the Soprano from h to gi^, and the Tenor from d to 6. thus: -I- 62. (a connection of chords already explained in No. 31, where the tone-con- nection did not take place in the same voice,) or : the Soprano retains the h, the Tenor descends from d to gi^, and the Alto from / to e, by which the close position is left, and this and the following harmony appear in open position : =1 1- =S= zsz 63. ^ 32= Further remarks, rendered necessary by the difficulties of progression as regards the chords of the fourth, fifth and sixth degrees, are in special cases to be left for practical guidance. Before we pass on to the further use of triads, we shall give a synoptical view of the chords thus far found as follows. View of all the Triads of the Major and Minor Scales. Major. 64. i ^^ ^i^^^ =f= -IS- I n m IV V VI vn* Minor. |_^pgE^Efe^^ 1 vs." Ill' IV V IV vn" in maior. Major tri%ds are found ^ _ % g — '■ — ^ | >» [t IV V V VI MANUAL OF HARMONY. 47 Minor triads. Diminished triads. Augmented triads. i in Maoor : in Minor ; 5^ liz II m VI I sx in Major. in Minor. •« — IT -e- i£l ^^^:3 VII= 11° TU" in Minor. ^^ III CHAPTER III. Inversions of Triads. Chord of the Sixth, Chord of the Sixth-and- Fourth. The use of triads and of all fundamental chords generally, is not limited to tMs, that the root, as in all previous examples, shall lie in the Bass ; the Bass can also take the third or the fifth of the fundamental chord. Hence arise transformations of the fundamental chords, which we call INVERSION, TRANSPOSITION, INTERCHANGING of the chord. Remark. — It may well be observed that we are here speaking only of moving the Bass Into another interval, and that the transpositions before mentioned of the other parts into close and open positions and into various intervals by no means ehangc the chord essentially The Triad is capable of two inversions : a. When the Bass takes the third of the triad, we have the Choed of thb Sixth. 65. p Fund, chord. Chord of Sixth. =r zsn Third of fund, chord. 48 MANUAL OF BABMONY. b. When the Bass lakes the ffih of the triad, we have the Chord of the SlXTH-AND-F0UETn.~ Fund, chord. Chord of Sixth & Fourth. '■P 66. 1?^ -g_ Fifth of fund, chovd. The Cliord of the Sixth is indicated by 6 over the Bass note, the Chord C 4' of the Sixth-and-Fourth by ^ over the same, e. g. 67 m^^ zsz laz c c c 0:1 I I Hereafter to indicate the root we shall use the letter, and to indicate the degree, as formerly, the number, by which, as may be seen in example 67, only the position of the root, not the casual Bass, is to be regarded. Eemarlc. — As tlie root of the chord of the Sixlh and of the Sixlh-and-Fourth in example 67 is still C and not the Bass notes E and G, so the chord itself will not be based on the third or fifth, but still on the ^rsf degree, since these are by no means newly-farmed chords, but only by means of the Bass brought into another position, and are therefore derived choi'ds. Application. By using the inversion of chords, there results not merely a greater variety in the management of the harmony, but the movement of the parts, ©specially the Bass, becomes more flowing. According to the rules given on p. 25 respecting the doubling of one interval of the triad, it will be better in the chord of the Sixth also in four- part harmony to double the root of the primitive chord, and the doubling of the Bass tone in the chord of the Sixth (i. e. the original Third) or of the third of the Bass (i. e. the original Fifth) can only take place when the natural movement of the parts requires it, or when false progressions can be thereby avoided. In accordance with what was said on p. 39, it may be remarked further that the leadmg tone in like manner forms an exception to this doubling, when it lies in the Bass. It need barely be mentioned too, that the distribution of the tliree upper parts depends only on their movement, but has no other essential bearing upon the chord. MANUAL OF HARMONY. 49 The Chord of the Sixth can therefore occur in the following forms : 3r: 1^1 z 3ZI zsz -O- 68. Q_ &C. ^1^ S The use of the Chord of the Sixth-and-Fourth is less frequent than that of the Chord of the Sixth, and requires certain conditions, which will be mentioned later. We find it mostly in the formation of cadences. The Bass tone, the Fifth of the primitive chord, is the best adapted for doubling, and the chord will appear in the following and similar forms : ^ zsz :jzl 69. -n — -7S — :^— lar: &c. ■JSr ~sz ZJEl • For connecting these chords with others, no farther mechanical rules are needed than those already given ; in like manner we omit the mere mechan- ical combination of two and three chords, and exhibit the application of these derived chords in short pieces, which, however insignificant, contain the form of a complete whole, and admit of a better estimation of single cases in their relation to the whole. Exercises. 70. § a=^=^ =^ rzt s ^^ ^ 3 6 ^=^ ?Z= §3^ 6 6 =5=?2= iS- "S^ ZJI^ :2zi -25i — e>- 6 P^ ZJSt. =221 i Z3C ^ 4 3 -e>-^ -is>-?2- -2J) » 6. 3 6 6 ^E ^ 50 MANUAL OF HARMONY. 6 e 3 6 ^ E^ 3z: =?- =2fc # 6 # 9. 3 6 S ii$ =?z= ^ =^ ^—7i-6) ZBIZ ^ H. 6 # 10. ;»• §^ -<0 " ^ 1 Compare also Remark on p. 28. The progression of the parts in the dimmished triad takes a difierent form, when the Bass passes to any other chord than the tonic triad. A few chord connections may follow here : »o8 pure. ^32Z 76. zsz. ^JlZL I22Z ^^ =^ zsz zsz vn° in vii° IV vii= V 52 MANUAL OF HARMONY. better : iwt : =5=:^ ^^ -isar =g= =^ g^ laz Z2ZI ;:si jioi; -&- n ■ '5> « 1 ^ " ' Ar-«' ^= — e>— -« — ?5 — &— — ^ — iff— -^ J- fg) rj—^'^ - ■—up »- 1 ■ e — ^ -a »- —75 "l* 6 6 6 6 6 6 6 6 6 )■ /""*" •^ S , LL and others. The diminished triad of the second degree in minor admits of a different treatment, since its root may be doubled. See p. 50. A succession of two or more chords of ilie Sixth, when the Bass moves by degrees, as in exercise 70. No. 3 and others, will compel one or more parts to move in contrary motion to the Bass. e. g. 77. The series of chords of the Sixth in the 5th and 6th exercises in No. 70 can be harmonized indeed in different ways, but it will be best, when the regular Bass progression is retained in the other parts also, e. g. 78. il^ ^ ^^ '^^ g~ ^ =^= ■X X 6 &o. \ Concealed octaves, as in the 2d and 3d measures between Tenor and Bass, are not to be avoided in such cases. Hence we may conclude, thai to indi- vidual abnormal progressions, when placed in comparison with the CONSISTENCY OF THE WHOLE, we are not to attach that fecial importance MANUAL OF HARMONY. 58 which is otherwise their due, since the formation of details, though to be aa perfect as possible, will always be subordinate to that of the whole. Remark. — 'Without doabt the principle just laid down can be easily misunderstood by the beginner ; yet its statement was unavoidable, and, to escape all possible error, it may be added further, that a final decision on these points belongs only to a judgment fully ripened by experience and practice. The Signs used in Thorough Bass Writing. The figures aud signs in Thorough Bass are called in general. Signatures, Some of them have been already explained, as the chromatic sign so often used in minor. The figuring of the Chords of the Sixth and of the Sixth- and-Fourth was given on p. 48. A line through the figure (e. g. in exer- cises 8, 9, 10 under No. 70 through the 6:0) is used when a chromatic elevation of the interval a half degree is needed, instead of which, however, a ^ or b] by the side of the figure is often used (e. g. di^ or 6tj, St]). Other figures will be explained hereafter with their respective chords. Formation of Cadences by n\.eans of the Chord of the Sixth- and-Fourth. In the exercises 70 we find, through the inversions of the triad, an ex- tension and more determinate form of the cadence previously cited. It appears namely, that the chord of the Sixth-and-Fourth of the tonic triad before the dominant chord leads directly to the close. C: I The triad of the fourth or second degree often precedes the Chord of the Sixth-and-Fourth. 60. C: IV razi =1= 3^ =?z= 3E zsc 54 MANUAL OF HARMONY. While the chord of the Sixth-and-Fourth points so decisively to the close, and has likewise so positive an influence when a modulation into foreign keys takes place, its appearance is equally flat under other circumstances, so that its proper use is dependent upon certain conditions, which will be discussed hereafter. CHAPTER IV. Seventh-Harmonies. Chords of Four Tones. Seventh-harmonies are based upon the triads. They result from the addition of a third to the fifth of the triad, forming a seventh from the root : 7 7 81. I Beside the different kinds of triads, the different kinds of sevenths also will produce a variety of Seventh-harmonies. General Properties of Seventh-Cliords. Seventh-chords are not as independent as most of the triads, but point directly to one progression, so that they never alone, but only in connec- tion with triads, produce any effect that is complete or exclusive. On the other hand they render the relations of chords to one another closer, more intimate, and by this property become particularly useful in combiniD" chords and managing the parts. The Dominant-Seventh-Chord in Major and Minor. The most prominent of the Seventh-chords, and the one that occurs most frequently, is the DOMINANT-SEVENTH-CHORD. also called the principal Seventh-chord. Like the dominant triad it is based upon the fifth degree, and is formed exactly alike in major and minor, namely /rom the major triad and minor seventh. 82. •^ C: V V, c: V MANUAL OF BARMONY. 55 In the fundamental position it is indicated by 7 over the Bass note and in our method of indicating by V^ : 83. gi # i C; V, G: V, The relation, in which the dominant triad stands to the tonic triad, has become generally clear through the cadence formation above exhibited (sea p. 33.) The close receives a still more decided character by the use of the dominant-seventh chord. The following chord-connection wUl show the form of cadence : 84. i =a= iliJ ?gg~ §L: 7 -7S- 7 rffir C: V, • I a: V, i Remark. — It should be observed here, that the triad which follows the seventh-chord U incomplete; in both cases the fifth of the chord is wanting. The reason of this will appear from what fojlows. The inward tendency of these chords to some point of rest, and their con- sequent union with a triad, is called RESOLUTION OF THE SEVENTH-CHORD, (Cadence.) When the union of the Dominant Seventh chord with the Tonic triad takes place as in No. 84 and similar combinations, it is called a CLOSING CADENCE. As regards the movement of the parts, the progression of the intervals of the Seventh chord will furnish some important remarks. First, we regard the closing cadence as the regular resolution of the Dominant-seventh-chord especially. The Seventh as the essential interval of the chord is, from its relation to the root, forced to a determined progression. Regarding the progression of the Bass, wrdch contains the root, as given, an upward progression of the Seventh will seem impossible : 85. 56 MANUAL OF HARMONY. even if a third part be added, as in h ; whereas its movement downward is fully satisfactory : 86. =i^ ^ Since the progression of the root a fourth upwards or a fifth downwards is already determined, that of the Third and Fifth of the Seventh-chord remains to be considered. The Third of the Dominant- Seventh-chord is always the leading tone of the Scale; its natural movement is determined therefore from what has been said heretofore concerning the leading tone (p. 39 ;) its progression is to ascend a half degree, hence h. will not appear as natural as a. 87. ZJSH ^ 3< zsz In example 87 b. the Third is given to the highest part, which makes the strangeness of its progression especially palpable. This movement can be tolerated, if the Third lies in a middle part, e. g. 88. i I.. uSl =2ES: -OSm. ZSZ 1 This descent of the Third (leading tone) is therefore to be employed under the following conditions : a. When it lies, not in tlie highest part, but in one of tlie middle parts, e. g. seldcym used. =f==3Z= 89. =g= I3C 1 MANUAL OF HARMONY. b. "When the Bass progresses by contrary motion, e. g. I. not. 57 80. ^t^%J^ ^m. W ^^- The reason for the second rule is evident, if we observe the concealed fifths between the Alto and Bass in example b. The movement of the Fiflli in the Seventh-chord is free. While it for the most part is forced by the Seventh one degree downward, yet there may be reasons for allowing it also to move a step upwards, as is seen in example 88 6., where the d in the Soprano is carried to e. If we condense the substance of these remarks, we obtain the following rules for the regular resolution of the Seventh-chord, and for the cadence especially : The Seventh descends a diatonic degree, whilst The root moves up a fourth or down a fifth; The Third is carried a degree upward, contrary to the seventh, whilst The Fifth may ascend or descend orie degree. Remark. — With this progression of the Third conlranj to the Seventh may be remembered ■what was said before (p. 38) of the root and diminished fifth iu the diminished triad. Both intervals occur again in the Dominant- Seventh-chord. Application. Except in forming cadences, the Dominant-Seventh-chord, as we have thus far learned to apply it, is seldom used in the middle of a piece, and then only in such places as do not create a sense of complete termination. This happens, namely, when the Seventh of the chord lies in the upper part, forming an imperfect close, or when the Dominant-Seventh-chord falls upon the accented part of the measure (Thesis,) since in a perfect close (cadence) the tonic triad must fall there (see p. 33.) Moreover the chord often appears incomplete by the omission of an interval. This interval, however, can only be the Fifth, seldom the Third, Bince the omission of the root and the Seventh would entirely alter the chord and make it unrecognizable. 58 MANUAL OF HARMONY. 81. c. teldom: d. ^^ 'M - 1 .. q -f==g= =i-=g— =^*i — g-l-S— ...^ . — «> <» — _5 — f -rS>- ^ j-z? — 1 a \. In o., S., c?. the Fifth is omitted, in c. the Third, in place of which the root is in all cases doubled, restoring the closest connection with the following chord by sustaining the tone, and thus allowing the tonic triad again to appear complete, which in the former resolutions was not the case (see No. 84.) Concerning the omission of one interval in the chord we annex the following remark : From the movement of the ■parts a chord may appear incomplete ; the omitted interval will generally be the Fifth of the fundamental chord. Exercises. 82. ii^ 3 =^F=F= ziSz =^- -^ TS- ZSL » :; — pg ~ =2t -t g r - r i^E -?2— r- S- 6 6 7 ^ =?Z= 4 7 -7S ' |- I3ZZ ^E^E =^: =?2= 4 3 =?2= 4 7 ^ ^ IZfc I =^ 7 =PZ= fcl E3E Ep 3E =^ I "[~T~"^g" 3C MANUAL OF HARMONY. 59 These exercises need no further explanation. It has been formerly mentioned that by 7 the Seventh-chord in the position thus far known is indicated, also that the sharp under it, or in general any chromatic sign which occm-s without a number annexed, has reference to the Third from the Bass tone (see p. 55.) CHAPTER V. Inversions of the Seventh-Chord, As the form of the triad can be changed by the Bass taking another interval than the root, this can take place likewise with Seventh-chords : 2 he first inversion results, when the Bass takes the Third from the root; The second, when the Fifth of the primitive chord lies in the Bass, and 27ie third, when the original Seventh is given to the lowest part. The inversions in close position appear thus : 93. 3^~§- -<^- =^ G, G, A comparison of these inversions of the Seventh-chord with those of the triad shows clearly their analogous positions : 94. G, =35 G, z&z h\ G, 2(22) ii=p=^ G, These derived chords take their names from the order of their intervals : The_y?;-s< inversion is called: the Chord of the Sixth-and-Fifth, The second : the Chord of the Sixth-Fourfh-and- Third — or hne^j Fourth- and-Third, The third: the Chord of the Sixth-Fourth-and-Second — or briefly th« Chord of the Second. Their figuring in Thorough Bass may be seen above in example 94 60 MANUAL OF HARMONY. We need only recall the fact here, that with these inversions, as formerly with those of the triad, the only essential point is the position of the Bass or lowest part, and that the other intervals may be variously distributed among the upper parts, e. g. es. -e 1 1 € 1 f3 I ^ 1 ^so—. fS ^ ^^ — ^_ — i=:' — «■ — — & — /V^ /ii r> xF ^~^ ~J ^ 6 6 _ — 4 i — — IffiZ ia= &c. =52z: Application. The regular progression (resolution) of these derived chords is hosed upon that of the primitive chord. As the dissonance, the seventh, established the progression of that in one direction, so also with the derived chords, where the two tones, root and seventh, either appear again, or by inversion become seconds, the tendency to the same progression will exist. i E^ 96. zsa zzs^ -B^ ^:#: Progression of the Chord of the Sixtl\-and-Fifth. Since the original Seventh also forms a dissonance, a diminished ffth, with the Bass tone in the chord of the Sixth-and-Fifth, whose progression has been discussed above (p. 38,) 97 B: ^ — g^iF the resolution of the chord of the Sixth-and-Fifth will naturally be as follows : G- C MANUAL OF nARMONY. 61 The progression of the root cannot be here as it was formerly given, as the G of the upper part is sustained and becomes the fifth ; tliis, however, is only apparent, for the same progression lies at the foundation of this harmonic connection, as is shown by the figuring G7 C in example 98. Beside other causes, the chief reason why the Soprano or a middle part cannot take the progression of the fundamental tones note for note, lies in the character of these parts, which is better suited for the connection and union of harmonies, than for their foundation, which belongs to the Bass. Remark. — Irregular progressions of the root in tbese cases, sucli as might result from a freer movement of the parts in certain relatious, are not hereby excluded, only there must be an inward connectioti and relation between the cliords. Progression of the Chord of the Sixth-Fourth-and-Third. Beside the Seventh and its inversion, the diminished Fifth, or its inver- sion the augmented Fourth, again appears here : 89.^ The resolution of this chord proceeds as follows a 5. G, C G, C The Bass, the original Fifth, can move in both these ways. Progression of the Chord of the Second. This chord has this peculiarity, that the original dissonant intervals, the Seventh and the diminished Fifth, can only occur in their inversions, as Se.rond below and augmented Fourth. The progression of this chord is the following : 101. The resolution of the Ohord of the Second therefore is through the Ohord of the Sixth. It may be seen from these resolutions, that they are all based upon the natural progression of the Dominant-Seventh-Chord, called above Cadence, for throughout we find the root indicated Gj O or Vj I. 62 MANUAL OF HARMONY. These resolutions therefore will of themselves form Cadences, only not of so perfect a kind as those before mentioned, and as those are called perfect cadences, so these are distinguished by the name imperfect cadences. View of the Natural Progression of all the Inversions of the Dominant-Seventh-Chord in Various Positions. 102. i ^ggg- 3t: 3^ -(Z_ e b. The Chord of the Sixth-Fourth-and-Tliird. ^^^Is^i^g -^«*«i- i^a MANUAL OF BARMONY. 63 C. The Chord of the Second. 103. §i£^i Exercises for Using these Chords. is; i^ ?2I ZJ^ 6 8 7 i^ - I i 1-i is: -B) — e>- 3 2 6 3 ^P^ ^-F-«'- gfc 2 6 1 3 6 8 7 I^ 3 :^ -zi- I22I ::^ ii^ -751- E3E 3 :2fc J_#_ tiir=l= ._^-_^ g^ s- 2 6^ iiSziizS; U lai iii$ -<»• ;8' 3 6 -■g — s^ : F i^ i^ :Si i=? JL# I32Z Iffil §£P^ :t if 3 2 6 3 6 4 # -g - ^ -zi- lai Observation. The figures 8 7 in the last measure but one of exercises 2, 4 and 5 mean that the Seventh should not appear at once with the chord, but follow after the Octave. 64 MANUAL OF MABMONY. CHAPTER VI Collateral Seventli-Harmonies. Whilst with the triads three principal chords are necessary, in order io establish the key (the relation to the tonic triad being the central point,) with Seventh-chords only one principal chord is needed, the Dominant- Seventh Chord, the contents alone of which make the key unmistakeable, and whose natural progression to the tonic triad represents it. Remark. — In view of the fact that the Seventh of the Dominant-chorcl is at the same time the root of the Subdominant triad, the relations of the two tones ^ and / (as roots of the dominant triads) to their common centre c (as tonic triad) becomes perfectly clear (see above p. 22. 3.) Beside this Dominant-Seventh-chord, also called Principal or Fundamental Seventh-chord, Seventh-harmonies can be formed from the other triads in major and minor, whose relation to a fixed key, to be sure, is undeniable, but by no means so decided as with the former. They are termed : COLLATERAL SEVENTH-CHORDS. They are simply to be formed by adding to the triads a Seventh of the root, a. In Major : 104. 4= 1 — ^— = J= i — ^ =^i- I7 II w III, IV, 5. In Minor : NB. NB. We arrive here at the chord formations, which without connection with other chords sound more or less hard and therefore strange, because, as was said before, their relation to a fundamental key is not as decided and clear as that of the Dominant- Seventh- Chord. Their use therefore is somewhat less frequent, but none the less adapted for giving variety and especial coloring to harmonic progressions. Amongst these collateral chords, the following kinds may be distin- guished : Major, triads with major seventh. MANUAL OF HABM0N7. in Maior. 65 105. i ;f; in Minor. 1^ E£ IVj a: VI, NB. Major triads with minor seventh always form dominant chords of the seventh. iji Minor. ' b. Minor triad with - g: • ,7 \Cp ■ ^ not used as fundamental liannouy. C. Minor triads with minor seventh. I in Major : in Mino, 1^1= =g- 1 C: H, Diminished triads with a minor seventh. 7 ^7 in Ma^or : in Minor ; I C: vn°. i e. Diminished triad with a diminished seventh. f. The augmented triad with a major seventh, I in MiyioT ; i w a: Ilf, as it is found on the third degree in minor, is indeed not impracticable, but for reasons before discovered under the augmented triad, rare and ambiguous Remark. — We shall find this chord again in the tenth chapter with a different basis. . Use of the Collateral Seventh-Cliords in Major. The Seventh, or its inversion, the Second, whether major, minor, dimin- ished or augmented (the last applying to the Second only,) will always in its relation to the root as dissonance incline to a progression. This natural progression with the collateral Seventh-chords is none other than that already found with the Dominant-Seventh, namely one degree downwards towards the root, if the latter descends a fifth or ascends a fourth. Accordingly while the progression of the principal intervals of the chord is found to be the following : 106. -iff- E^ =2z: IZZI i 66 MANUAL OF HARMONY. no new rules are needed for the other intervals ; the Third will ascend one degree, whUe the Fifth can progress in either direction. a. 6. c. 107. -^ 7Z1 13= IS -v ^g; zsz lai =22= =22 H C:I, IV Bemark. — The exceptional progression of the Third in example 107 h. arose from this, that the concealed Octave, which would result from the regular ascent of the Third by one degree, e. g. 108, ^ 5^ -ff-aaa- ^^ ^^ was thus avoided. See p. 35, example 32. But whether, through the movement of the fifth, the leading tone ip the following chord «hall be doubled, as in example 107 c, or the following concealed fifths are to be preferred: 100. will depend upon circumstances, to be judged upon in practice with reference to place and position. Natural Progression {in Cadence-form) of the Collateral Seventh- Chords in Major. a. of the first degree. or : -&■ 110. '^^^^^. IS= ^ not : — Tn ^?S ;»:*= C: I, ^good ; w not : =2ZS ^ifc: ~sc. =^=;- =i= *«".». ^ ^ ^ ^^ =e: zss.: IZ2C:: 32= "25- =ffl; MANUAL OF HARMONY, leith omission of the fifth: ^; 67 E :5ffi- =SS -=g- §S^ ^Ss ^^S 5. of the second degree. ^ or; lar -iS>- rz2i nsz nsr -r C: 1I7 without fifth: not: not: =Z2£l IS^I E -^- :3c I22I not: S^ c. 0/ iAe third degree: .O- I r-#i. s^^~ \ — ^~I 1~^~ iS li: S; _Sj. ~^^- ■^- i^^; 32=i: 2aii: =23^ S^S ::^:i^ ra; 32: C: HI? not; VI - no^' »oi; d. of the fourth degree (seldom with this resolution- ) E^g 3^ rg= ~ zy !22:: not good; ^^^ -z2: ^— gs i^-s:: rjoJ; C: IVy VII " without fifth; '- — T rr«'- _ffl_ -OO- i^s C: Ti, K0<; not: not ; not ; /. of fAe jCTcntt degree. better : not : C: vn", in without fifth : SI- „ I lEZZ 122^ lE^ ^i=!^^E ■^■r^ ::S=^ no<; Remarh. —7- The progressions here given of all the Seventh-chords are neither exhaustive in their positions, nor have tliey been presented as including all thatjare possible. The difiSculty in forming such progressions lies only in the frequent occurrence of con- cealed fifths and octaves. So all the remarks above annexed, as " not," " not good," which refer mostly to the movement of the Bass, so far as it produces those faults in connection with other necessary part-movements, are in many cases to be taken only from the theoretical standpoint, whereas in practice, even in the so-called pure composition, such and similar cases must often be judged according to the principles above stated (on pp. 52 and 53-3 As theory hitherto has not. succeeded in establishing positive rules for all cases of the kind, the true and the false, the admissible and inadmissible in this respect can only be discerned by a thorough harmonic culture and a true musically formed ear. More on this subject will follow later. Of the Peculiar Progression of the Seventh.-cliord of the Seventh Degree. In the above table, under 110, of the progression of all the Seventh- chords in major, that of the seventh degree, similarly to the others, was carried to the third degree, i. e. the progression of the root, as with the other seventh-chords, was to ascend a fourth, or descend a fifth. This progression is the less frequent, and is for the most part used only where there is a MANUAL OF HARMONY. 69 ■uniform movement of the harmony (sequence.) That one occurs oftener, ou which the diminished triad, to which the Seventh is here added, is based (see pp. 38 and 50), namely to the tonic triad. lU. -&.- is::. ::iSSL =r=# -w- ~er =S- lai C: vii = ^: 1 Tliat the relation of the diminished triad to the tonic triad is not changed by the addition of the seventh, on the contrary is still more positive, is plainly seen by the above example. It is to be observed also, that when the chord appears in the above position, the Third of the following triad must be doubled (see 111 J.,) as otherwise perfect fifths would result (see 112 a.) ; 112. E^ ^1 or a skip must be made as in i., a movement of the Tenor which not infre- quently occurs, and which is very effective notwithstanding the concealed octave. It is a peculiarity of this chord, that its only satisfactory position is that in which the Seventh lies in the highest part, whilst the other positions, if not impracticable, are yet more confused. 113. i lE ifE la.- I2Z 3E 1321 zsz :j2z -JSZ 2 ZSSL 1 i Eemark. — Whether the reason of this lies in the fact, that the Seventh, with the pro- gression as above, has the character of the Ninth (as many theorists affirm that this chord with its resolution is based upon the Dominant-Seventh-chord with aNinth added,) which, although resembling that of the Seventh, is yet more comprehensive, and does not admit of a middle position, cannot here be farther investigated 70 MANUAL OF HABMON-T. The Freer Treatment of the Third and Fifth in the Seventh- Chord. Different progressions of these intervals have already been used in the above chord-connections. The Fifth moves in either direction, the Third likewise at times a degree upwards, at others three degrees downwards. This was generally m view of avoiding concealed fifths and octaves. Apart from these faulty progressions the Third especially may move differently still, whence the part-movement often becomes freer and more independent, e. g. i. not good : c. 114. It is seen in c. that this progression is possible in the middle parts also, if the position admits of it. The progression of the Soprano in h. is not good, because a sKp of an augmented fourth is produced by it. The step from the fourth to the seventh degree is called the Tritone, because it contains three whole tones. Upon this more in the sequel. Other progressions of the Fifth are only possible, when the Bass also changes its usual progression as fundamental tone, as in general still further progressions of the parts will result, when we seek for other chord-connec- tions than those hitherto employed. The Preparation of the Seventh. We have thus far spoken of the progression of the Seventh-chords, but not of their introduction. The harshness of the entrance of many dissonances and especially of most of the Sevenths in the collateral Seventh-chords renders a careful introduction of them necessary, which consists in their leing prepared. A tone is prepared, when it already exists in the preceding chord in one AND THK SAME YOiCE as a harmonic tone, so that it can be connected by a tie. MANUAL OF HARMONY. 71 Such a preparation of a tone we had previously in the first chord-connec- tions presented, e. g. 115. lar: P--=i= ZffiZ sj= "ZJ- I2ZI -zz: I 1 We may say here : that the c of the Soprano in the second chord is prepared by the c of the first chord ; also the g of the Alto in the examplQ that follows. But the necessity of the preparation of Sevenths lies not only in the harshness of their effect when they are heard without preparation, but specially in the character of the harmonic connection and union of two successive chords, which is eminently peculiar to sevenths, and would not appear without that preparation. The preparation of the Seventh can be efiected as follows : 116. fadi ggp^l^lS :g2= =g= =^: 32: 11=1 ::^: -fS^-t- 1221: C: V I^IV V I^IV IV I gr T7g~i -i^-HT^^^g J--^ J- A :t=^ W- ^ -I- J-J- i^fS m -liz 3^ ^5=^ 1-^ C: III IV J- VII = In all these examples the tone, which is connected by a tie with the same tone following, forms iih& preparation of the Seventh. In forming such a preparation the following rules are to be observed : a. The preparation falls upon the unaccented part of the measure (Arsis) and must b. At least be of equal length with the following Sepenth: it may lie longer,, but not shorter, e.g. 72 MANUAL OF HARMONY. 117. I ^h lEZ not : T =??- Remark. — Tlie preparation of the Seventh forms one of the most important parts of the harmonic system, and is to be managed and practised with great care, because upon it depenas the most essential feature of the inner, closest harmonic connection. Although exceptions on this point also may be found in practice, yet it may repeatedly be called to mind, that they are nothing else than Ktc^iions, which'Cannot disprove the im- portance of the principle of harmonic union, but can only be judged as a concrete case, caused and intended by reason of its position and relations. (Page 44. Remark.) These exceptions occur mostly with 7ninor Sevenths, as the less harsh, like that of the second and seventh degree, and are always tempered by a good progression. But the Seventh of the Dominant- Chord, also called the Fundamental Seventh, forms a special exception to the necessary preparation. It is that whose effect, by its relation to the tonic triad, to the fundamental key, is the least harsh and strange, and does not need preparation in aU cases. The following may be observed as to its farther use : The Dominant- Seventh needs, to be sure, no preparation, hut its free entrance requires the presence of the root, if the progression is to be pure and without harshness. • 118. -7S*^ ^J^ 13= -■■^g] J- %! J- '7* ^0^3^ O*— =?z: C: I ES hsz:: :zt: V, V, I Bemark. — The so-called passing Sevenths, which naturally as such cannot be prepared fere regulated according to the rules for passing notes, which are explained afterwards. Concerning passing sevenths, see Chap. 18. The Seventh of the Seventh degree, also, in major and minor (in the latter case the diminished Seventh-chord) on accotmt of its peculiar char- acter by no means requires preparation in all cases. MANUAL OF BARMONY. 73 Exercises. 119. m =^ r 7 i 7 zszrzrz 22: ^- :g=t :^^ 3C 2 6 7 4 7 E ig SB g 3: n3zz ::sz 6 4 7. iM^ ::^: I2t lai 6 6 7 -19- ~& i^: 6 7 iS i:EE ?z- 2fc The Connection of Seventli-Cliords with each other. The progression or resolution of the Seventh-chords in the previous examples was always through the triad of the fourth degree above, or, which is the rame thing, of thejifth degree below. Instead of the triad, a Sevetith- chord also of the same degree may follow. The progression of the parts undergoes no change by this, only the Third of the first Seventh-chord will in this case serve for the preparation of the following Seventh, therefore not move, but be sustained, e. g. 120. C: II zS^ =F =^ ^^ IV Here the Third of the dominant-chord, h, forms the preparation of the following Seventh. The peculiarity of this harmonic connection is, that in one of the Seventh- chords the Fifth will always be wanting. In example 120 the fifth of the first chord was omitted. When several Seventh-chords follow each other, the^i!7i will be wanting in each alternate chord. 74 MANUAL OF EABMONY. X21. feUo:^ I I 'n--4r^TUT'i J pa^E^a? fZ-fi- i r?2= ^ 132 £ ::i; =^^^=±=f^ i:^^ £ 1 C: I 117 V, I_7-I T;?- VI IV;7'Vii°7 1117 n, ii, V^ The following rule may serve for harmonic connections of this sort : When two or more Seventh-chords IN the fundamental position succeed each other, the fifth is omitted in the alternate chords. Exercises. 6 6 6 m 122. ^S ^ ISC -e>-<^ ^ =221 :t=t -+- iffi g^-g^^g^^ -7S>- »- 7 7 sB^g 4 7 3 m ^^- :g=<2: 13= 7 7 i£^ 3z: 3= Use of the Collateral Seventh-Cliords in Minor. The use of collateral Seventh-chords in minor is more limited. Many of them for Chord-connections, as used in major, prove \msuited, or indefi- nite and ambiguous ; others in their cadence-progression result in difficult and unmelodious intervals in the parts. One form of Seventh-chord, as given by the first degree, produces no progression analogous to the above, since the following combination is inconceivable. 123. MANUAL OF HARMONY. 75 Bemarlc. — Although progressions can be formed with the above combination ofinlemah, as thus : 124. ^ -§-- 7# 6 yet it would be difiBcuIt to prove that this was a progression of the Seventh-chord of the first degree in minor. The resolution of the chord of the Second degree is to the dominant, and b very frequently used : IfE -ig— »^'' 35 i m rs/gr jSZ ■^ 125. -sz a not : not ; :jsz .JSIL. 3.Qi A progression of the Seventh-chord of the third degree is not impossible ; 126. a: Iir^T- VI wA: not : it is, however, ambiguous, and might be met with in G major oftener than in A minor. (See: Altered Chords.) It may here be observed that the Jifth in this chord, as an augmented interval, will always ascend one degree. The chords of the fourth and sixth degrees are uncommon, as the progres- sion of the parts in the resolution is awkward and immelodious. S= ^ 127. ^w^ — -» 7S- ^=^- 9t=^ a: IV- vn = =r -s--a- i^ ^ ^r 76 MANUAL OF BARMONT. 128. ZSH ^ zzsz ^ ^ -i- s 1^^ i i The forced effect of most of the above progressions is undeniable, and makes them of little use. — The seventh degree in minor furnishes an important chord, which is gen- erally known by the name of the DIMINISHED SEVENTH-CHORD. A resolution of this chord like that of all the others is impossible, as it would lead to the triad of the third degree, which was found above to be doubtful and ambiguous. Instead of this, its progression, as with the Seventh-chord of the seventh degree in major (see p. 68,) is based upon the natural movement of iJw leading-tone, upon which this chord rests : 129. "i :2S= m \^- As the root of this chord (leading-tone) moves a half degree, so also the Seventh descends a half degree, while the Third and Fifth move with the same regularity as with other seventh-chords ; but the progression of the Third in many positions (130 a.) is to be carefully observed, because it easily leads to a faulty progression : not: 130. ^^ d fc # ^ ri^ f - g=^ whereas the position of the Third in J. and c. gives more freedom. Hemark. — The natural progression of this chord, as of the Seventh-chord of the seventh degree in major, to the tonic triad, has induced the older harmonists to trace its foundation to the harmony of the Dominant-Seventh. They considered a ninth (msijor or minor) to be added to this chord and the root omitted, whence resulted both chords of the sevcmb degree. MANUAL, OF BARMONY. 77 lu referring to what is said later in Chap. 9th concerning the chord of the Ninth, wa would state here as the ground of our views, that that assumption as regards Ninth-chorda is needless and far-fetched, and that the simplicity of the harmonic system for practical purposes would be preferable to any complicated theory. As to the use of the diminished Seventh-chord, the following also should be observed: The diminished Seventh, the smoothest of all, needs no preparation (see p. 72.) Exercises, 131. 1-3 6 6 7 1 • 6 # 7 # C4frt-F^ (9 — "^ =1 9^:E=:H :_s_5L — ^ A— :f-h- —[— ■ — e — — <9 ^=J [ . (i? -, 1 i_#_A# 6 2 6 ^ It ^i^i isr 12^: =1^ :^=t is: iS- 7 6 # * i^. 7 ^^^P^g g^l §i^ 7 H =?z: :t::=#^: -» 1- lai These, and all former exercises in this chapter, whose object naturally was only to learn the mechanical use of the chords explained hitherto, and test the established rules and remarks, for this very reason are in their structure somewhat gtiff and unwieldy, since the great number of seventh-chords could appear here only in the fundamental position, and because the intro- duction of many of them from our present standpoint, which did not aUow us the choice of other means, was difficult and could not but seem forced. The following may yet serve for their illustration : The root of these Seventh-chords moves throughout & fourth or fifth as in cadences, as may be seen from the Bass part, only in the third exercise of 122 and 131 there appears to be an exception. In the fourth measure of the third exercise in 122 the Bass tone remains stationary, but the progres- sion of the root is still contained in both chords according to rule: a^-D^. The sustaining of the Bass tone was possible here, because we have already become acquainted with, and may therefore use, the modifications of the Dominant- Seventh-chord. The case is the same in the fifth bar of the third 78 MAirUAL OF HARMONY. example of 131, where the progression of the root takes place ^y-e? with a sustained Bass. In the second exercise of 131 the Seventh-chord of the third degree in minor is used, and it may be admitted that with this introduction it will not Bcem unnatural and harsh. CHAPTER VII. Inversions of the Collateral Seventh.-Cliords. By the inversion of the collateral Seventh-chords are produced the same derived chords, which have already appeared with the dominant-seventh, namely: the Chord of the Sixth-and-Fifth, of the Sixth-Fourth-and-Third and of the Second. The varieties of Thirds, Fifths and Sevenths in the fundamental harmony effect no alteration in the treatment of the inversions. For although the major Seventh becomes by inversion a minor Second, the diminished an augmented (see pp. 18, 19,) yet their progression follows in the same manner described above. 132. =i= i^^ ■4- ^ ^^ ^g^^ I7 IV No new rules are needed for the progression of any of these Seventh- chords. That of the Seventh degree alone in major and minor re^quires some care, as has been already remarked, on account of the easily occurring open fifths. Something may here be added concerning their treatment. Progression of the Seventh-chord of the Seventh degree in major. 6 4 6 6 6 not: 3 6 3 4 ^^«- P^p^^l^^l^ ^z: iSfc -ig- C: V1I=, I All these transpositions of the chord are available, though the last, the chord of the Second, finds its degree with most difficulty, since the resolu- MANUAL OF HARMONY. 79 ■ tion into the chord of the Sixth-and-Fourth could seldom take place, and at best as a passing chord. We must not be deceived by the compact form, in which these chords are exhibited in 133, as to their utility ; as was mentioned above, it only depends here upon the Seventh lying above or below the root, and positions of the Chord of the Sixth-and-Fifth and of the Sixth-Fourth-and-Third like the following : -::f= 134. :2z:; no- -*- Z7K1 "S:: seem consequently more satisfactory, because the Seventh lies above the root. The diminished Seventh-chord requires a method of progression like the above, e. g. 135. ^ sz. 91 6 6 -<9- fe 91 5 6 3 ^3E^^ t^i 2# 4 zso ^m Here also the third inversion, the chord of the Second, will prove the least practicable, as is shown by the unsatisfying resolution into the Sixth- and-Fourth, a chord that always requires careful treatment, of which what is necessary will be said hereafter. That consecutive'fifths, which result from the resolution of the chord of the Sixth-and-Fifth and of the Sixth-Fourth-and-Third in this manner : 136. are to be considered faulty, has been already mentioned (p. 76.) As to consecutive fifths of this sort compare also p. 29, No. 16, 17 and 18. With this very manageable chord the position of the root relatively to the Seventh makes no such essentfal difference, as is the case with the chord of the seventh degree in major ; the seventh may lie above or below the root, the similarity of sound between the augmented second and the minor third always adding softness to the chord, and causing the former to be felt aa such only in relation to the key. 80 MANUAL OF BABMONT. Exercises. 6 6 137. §:^^ =?z: t-=t ?^ ZjS iii 1 i 3 7 3 26 77 iiffiES=!s =^: -^-+-(^ ?i :tn4::rtf i:r±4 :3Z 2 6 5 =?2: -s> — 5^- :3i 1^ l==l: 6 6 a tF^=^ :^ i^- lEZ 3 :3i±=at zsi ate Sg 6 5 7 7 t:=:2S:^: ^^E^ zzii 3 2 a^§g 6 6 7 7 _^_:zgr =^ SE 2fc iE^^^ # i. js- J8r 1 3 _1 ° # *=t;2zt -^_: ^ ^ — g: 1121 3 2 „7 fe= -fi. ^- 7 3 6 g±$ 3= =2t ^ ^^=^=i|^=^ I3ZI .7 6 7 6 6 7 7 7 #4 *^ ^^^^^ P^P^ iH^^ 10. jS- IB^S 66 73 #2 eJS" 7 =?=F=^ E}g « 4 # ^ MANUAL OF HARMONY. 81 CHAPTER Vni Seventh-Chords in connection with Chords of various De- grees, other than those before Used. False Cadences. The familiar rule, that tlie Seventh must in the resolution descend one degree, is indeed completely confirmed in the chord-connections previously shown ; it has, however, as little positive authority as other matters, which under diiferent conditions and relations, in the great variety of chord-con- nections, are subjected to necessary alterations and deviations. With the movement of the Seventh, or its inversion, the Second, all depends on the progression of the root. If this, as in all cases presented thus far, is such that without the descent of the seventh no intelligible and satisfactory result would follow, then that rule would possess full authority. The progression of tlie root, however, may entirely annul this tendency of the Seventh ; it may either remain stationary or even ascend, e. g. 138. i - TPtZr^ - ;i=aE^ 2z: This leads us to the possibility of connecting Seventh-chords with chords of other degrees than those hitherto employed. We may adduce here a few familiar kinds of chord-connections with remarks, that in trying new forma- tions of this sort we may be able to proceed on critical principles. We begin with the Dominant-Seventh-chord. It has been said before that the resolution of seventh-chords as shown thus far is called cadence, and that of the Dominant-Seventh-chord, closing cadence. When any chord but the tonic triad, which forms the closing cadence, follows the Dominant-Seventh-chord, the natural tendency towards the close is either delayed or else wholly removed. The anticipation of the natural result experiences hereby a disappointment, hence thase combinations are called FALSE CADENCES. In general, therefore, false cadences arise, where the progression of the Dominant-Seventh-chord leads, not to the tonic triad, but to different cliords. 88 MANUAL OF BABMONT. A few instances we shall now explain. 1. The connection of the Dominant- Seventh-chord with triads other than that of the tonic, where the Seventh descends one degree. a. Connection with the S^xth degree : in Maiar; in Minor: 139. " ^ ^ C : V7 VI This combination (false cadence) occurs very frequently. The effect of this progression with the inversions of the Seventh-choM is not as decided, and therefore more rare : in Maior: in Minor: 6 1 6 6 66 36 31 66 140. P ^^ ^^^^^^^ C: V, ^=^iE="=2^^ a: V, VI b. Connection with the third degree : 141. I better petition. 7 6 522= -sz ^ ^fm^^ E^=^ C: V, "75- -75- -»- -Br Bemark. — Trials with the inversions of the chord are omitted here and in the seqnel; they are easily made. This progression is more decided when modulation is employed : 142. i 7 '3SS1 ISC -s^^ ¥^ -gi-*!:gz- In minor also the connection with the triad of the third degree is possible, only the latter as a dissonant chord (through the augmented fifth) require* that something follow. 143. fei # - ^^ =fe -BL. ;f^^22= ^ a: y III' VI 2. Gonneclion with 'riads with the Seventh sustained. MANUAL OF UARMONY. a. With the second decree: 83 not: useless in Minor. 144. |d -if f'^^ r ZSZ C: V. -25- 1321 ii fi:=^ffi= 1 II' b. IFii/i the fourth degree : in Major. in Minor. 6 145. P^ 13= Ei: :3C IV f: 13; ::2z =^ -'iS — s>i a: V- The connectibn of the Dominant chord with Seventh-harmonies of other degrees, than those we have used, is also possible. A few of them here follow : &th Degree; 2 3(Z Degree: 6 S Minor; Zd Degree. 146. ^i 122.-^; ^ ^ 'm.mSI- igr^^^zizz: ^ :a; C: V- VI7 .r !.- V, III'- VI When we modulate into other keys, the possibility of new combinations is greatly increased, e. g. a. With descending Seventh : 147. C: V, d: V7 b. With sustained Seventh C: V7 6; vii°7 a.- V, F: V, a: V, G: vii = 148. i ElblE ^ ?2zntt; ■^CiV^EbiV, C:V, Bb:V, a; V, C:V, 3. Connection of chords with the Seventh descending. This case may occur in the ordinary cadence (V7-I) as well as with other progressions of the Seventhkjhord, (e. g. 1I7-V.) a. By exchanging the progression with various parts. 84 MANUAL OF BABMONY. 149. The movement of a third in the Bass renders the descent of the Seventh impossible, as the concealed octave caused thereby 150. i -«>- -r/ 1^ SI is entirely erroneous. This progression of the root is not to be used in the other parts. 151. All these instances are faulty. b. By sustaining the fundamental tone : not: 152. The root (G^) serves here as the so-called sustained part. (See later; Organ point.) But it must be remote from the Seventh, and the following progression would be wrong : 163. MANUAL OF BAEMONY. 85 C. By a chromatic change, and modulation : jar 4 3 154. 1 3 2 u4 as* m. C: V, G:V, 3_=#i iz?£:; -»- =^ =©:=; i I ^-TC^ =2?^ ^ 7 7 enharmonic; 3 -#-- 7 -iS- 1 .^a_ C: V, G: V, V, e; vii°, C: V, F^: V. 155 d. jBy contrary/ motion of the Bass in modulating into other hcys ; ■St'^^t^ n ig-"*^'=' IT » IT g 1 — ■ i^ ^ te i^ Oi»|-ffi_ sei^ PS =^5si C: V7 d.- V7 C: V7 6[,: vii"^ u; V7 rf; vii"^ C : V, F: V7 (See atiwe, No. 149.) The foregoing table of chord-connections gives only an indication of possible combinations. Its object was to call attention to the variety of harmonic progression. Of the value of these and similar combinations criticism can decide only in special cases, since their proper use becomes possible only by considering their introduction, their progression, their rhythmical imparlance, and, in brief, their whole situation. The particular character of a piece, the part-movement expressly formed with reference to the motive or idea employed, and similar causes, may lead to such harmoni(3 connections ; but to use them adventurously, for the production of new and strange formations, in general for the sake of appearing original, might in few cases so succeed that the object would not be perceptible : Exercises. 156. §^^ iS= 3ZI SC S 3 =^ 6 1 :t^±:t: =^ z^^^St: '^ zsiz 86 MANUAL OF EARMONV. 3. li^i 4 7 3 e i 7 =?== ^^^ — &-'■ —trj — jg- 7 7 iS: =?2: =^ :??= igz: 3^ :2t K 4 "• opmjjosition, 3 6 6 7 -. # ii^E 1221 =??: 2^^afc|^d:z^ 7. i3 u 6 6 6 4 4 3 JL_L# 122:: P =2^: izfcig: 2£ TS'-g' ::ffii §ipt -(2- - rJ g- :e: Remark. — The open position in the 5th exercise has reference to a part-mOTement cited on p. 84 ; it can afterwards be abandoned. The Collateral Seventh-Harrrionies connected with. Chords of other Degrees or Keys. A few chord-connections with collateral Sevenths may follow here. To cite all cases of the kind would be both impossible and inexpedient. a. With regular progression of ike Seventh. 157. ■^am C : Urn III ^^ ii=s2£: -te E^ — B -g g. ^ II, e; V, C : iii, IV in, F: V, C: IV;r G: V, i not; -^m "mw^ ^i^ better; —tsi — ^ -sz i^^ 1 w ^m a; 11°, III VI ir, V b. With free progression of the Seventh. &c. IV, V VI^-G: V,a.-vii'=,d.vn», MANUAL OF HABMONY. 87 168. I not: J — ■ ig - =i= ^- E^iE =r «- ^iP C: 11, G: V, ^ i^vjiY^ C:ii7c;Tii7 C:li7 a;V7 C: 1I7 d; vii'7 Bemark. — The reason why the last example is not good, lies in the so-called cross rehSJum, an explanation of which follows farther on. With Seventh sustained. C. 158. i. ^ d. 6 6 '-^ :s2z ^=i: '^ lez ?^- z?g=^= il ^^ C: n, IV -- VI 17 XV H7 VJL AI7 ± 117 The last succession of chords is often used. It forms a delaying of the cadence-progression of the second degree into the fifth by means of the chord of the Sixth-and-Fourth of the tonic triad introduced between them. The chord of the Sixth also of the same triad often occurs during the resolution of this chord, as in example e. The diminished Seventh chord is often used in like manner : 160. 71? 1^ _ 1 ^m§^ g: vn», C:I V Here also the natural progression is only delayed by the chord of the Sixth-and-Fourth. The mechanical combination of such successions of chords may be left to individual practice and investigation. Their use will depend upon the insight acquired into the relation and connection of chords, and therefore not be so lightly estimated, as might first appear ; in general it will stand about in the same relation to composition itself, as technical studies and preliminary exercises to the practical execution and performance of musical works. Both produce readiness and skill, cultivate the powers, and render the productions of genius possible. Only it may be further observed here, that for the criterion of such com- bination the relation of the Seventh to the root and its progression will always be found sufficient. If this is pure and the movements of the other parts commit none of the heretofore mentioned errors, the chord connection will be serviceable for particular cases. Exercises. r 6 6 161. §^ 3z: z^z =^ 88 MANUAL OF HABMOlfr. e 6 6 6 7 5 2 6 =^ ^=:i ^ =^ rsz - '^'g'-^^ 3ZI ite m k^ ^ -y^ S i i^: izS: ^ i^ il 2SZ -s>- is .i_#_^ t=^ 5 ^4 iEP £ :t ^ 7. ?2= fg-— -| g ^_#. ^ 6 6 4 2 S=^eS i^i^ 3 -fZ^ ^ ^ 4 6 3 =^ 3:: 67 Eemarh — MaTty of the cases above cited could not yet be included in these exercises, because they are based upon modulation, which is hereafter more fully explained. (The sixth exercise affords opportunity for modulation.) So too, many of these examples by the use of modulation would have been smoother and less stiff and stran- JJv, -e>- 175. fc rs: riz: -iK IffiZ PS22= ^ 321 -M -- -iSi- :JI^ C: Ir IV • C. The addition of the Seventh to the augmented triad of the fourth should be very rare : 176. C: IV;^- TII In all these combinations so far the cadence-progression of the Bass (e. g. V-I I-IV &c.) has been employed ; but a few examples may show that the chords here treated may be used with chords of other degrees and a different Bass-progression. = # 5# 6 3C 177. -22 — e>- ii^ zs^e^ 5 -gyg - i^^ f-p- ^^^ -^^-qT=g=j^ ^ is: ^5= V^a.-V C:Y, rf;vii° i C: V, jr.- vii" I i 5 S# # r 7 .5# .! 0^=:=^^- zzzz ^=^1 :M 32= 5 E 6 -J- I ^5S! gg- ffi^=a5Z_ 131 is: ^ liz: e ^ C: V, erV, i C:iii Ijd:V C:iii I^-GiV, These harmonic connections, sometimes strange and harsh in sound, acquire significance only through the position which they assume, and par- ticularly when to a certain degree they are brought about by an inward necessity. If it is the duty of a manual to point out the possibility of such harmonic 94 MANUAL OF HABMONT, formations, its duty is likewise to warn the beginner against overrating the value of such attractions, and in general to advise him, not to occupy himself purposely with such uncommon harmonic expeflients, before he is wlwlly conversant with the treatment of the simplest harmonies, of simple pure part-writing. Too early employment of them and a wilful searching for peculiar effects obstructs a clear view and insight into simple harmonic principles, even renders it impossible, and diverts the mind from essential to secondary matters. Exercises. 178. m^ 5 afj; S 6# 3 6 6_ :^- Z2t. 6 — ZBC la: B# B^ 66^ 6 2 6 4 7 i^^ ::^ ar 4: zsz 66# * 3 3 6 7 4 7 zsz i^ =^ =^ =^ e J^£Je 3C 36# 7 6 6 — g^ 3= 3^6 *=t 3z: :^ St Remark. — In the fourth exercise the augmentefl fifth was used even with the minor triad of the second degree (at NB.,) which in this connection does not sound unnaturally. This would correspond with the form/ above in example 170. Henco it is seen, that with a natural movement of parts many new chord-formations may be obtained. From the form e of example 170 : P^^F (which is also treated under the name : double diminished triad) there arises a harmony which is much used, namely : THE CHOED OF THE AUGMENTED SIXTH. The first inversion of the above chord gives ; 179. '•i ■f.- o g— f ^fer=^^^^=% From its progression, which is determined by the augmented Sixth cb-c^, the origmal chord here belongs to G minor, whose fourth degree, C minor, through the raising of the root inclines to the fifth degree. MASXTAL OF HARMONY. 95 Wherever this chord appears with its natural progression, as shown above in 179, the last chord proves itself to be the Dominant. This is verified by certain harmonies formed like the chord of the augmented Sixth, the chords of the augmented Sixth-Fourth-and-Third and of the augmented Sixth-and- Fifth, whose construction is explained farther on. Semark. — The affinity of the augmented Sixth-chord with those just mentioned, has its origin in the source of the former. The chord of the augmented Sixth has this peculiarity, that only its Third (the Fifth of the original chord) can be doubled in four-part harmony : % 180. ^ Efe f^^^^ ii2s: Of the other positions of the original chord (the so-called double dimin- ished triad,) the^rst (fundamental) may be used in three parts, though very rarely ; the third (second inversion) also in four parts, but only in widely dispersed harmony. I b. not: -^ tetter: 181. m ^^3gF ^ %%-- ZSl Remark. — The chromatic alteration of an interval of the minor triad is already included in the formations in Nos. 169 and 170, and therefore needs no further investigation. Sc the chromatic alteration of an interval of the diminished triad will result either in major or minor triads, or formations, which are to be found in the examples above_cited. Thus the form of the triad in No. 170 d. will be like the following as found in C major: 182. 1^ C; vn» hetler in open position. l=f^^P^^ is: In maily books this chord is called : major.dimimshed triad. Chords of this sort, if they may be called such, usually appear only incidentally in nassing and their progression follows relatively to their intervals, i. e. augmented intervals ascend, diminished intervals descend, one degree. The chromatic alteration of an interval of the Seventh-chord was partially 96 MANUAL OF HARMONY. noticed above, where to the triad chromatically altered the Seventh also was added (p. 92.) This was in the case of the augmented triad : Among the other collateral Seventh-chords, the chromatic alteration of one of them receives a special importance. It is the Seventh-chord of the second degree in minor, which in the following form produces chords that are often used. The chromatic elevation of its Third 183. i IF, ^ gives the following inversions : 184. Of these inversions the second is the most important, and is much nsed, the others are rare. The chord resulting from the second transposition is known as THE CHORD OF THE AUGMENTED SIXTH-FOURTH-AND-THIRD. Its progression is based upon that of the original chord, i. e. as the seventh- chord of the second- degree leads directly to the dominant, so also here it wiU be the case. 185. r EgE zfe ~a- m i If the root be omitted in this chord, we have the augmented Sixth-chord already found above, whose progression to the dominant finds here its expla- nation (see p. 94) : omitting the root; 186. ^^ -jsa ^ or as compared with 179 in G minor: Vrnidatti. citord; ch/rom. elevation chord of migm. chord of augm. , of the third: Sixth-Fourth & Third: Sixth; 187.1 :*= «"«; fr 9-- "7 nsr V ^^ MANUAL OF BABMONY. 97 Remark. — It may here be further observed, that the formation of the chord of the aug- mented Sixth-Fourth-and-Third can be reached also through the major-diminished triad mentioned on page 95, by the addition of the Seventh: only that the resolution must bo different, since that was taken on the seventh degree, while this is found on the second. Instead of the root, the Ninth of the original chord may also be added, whence arises the CHORD OF THE AUGMENTED SIXTH- AND-FIFTH. Its foundation is the followino; : Inversions: root omitted a. jS" 6- ^ original cluyrd: with ninth: Js third raided: 5 3 188. i=|=^l=i^l ^t-^ :g£- -#■ e. 2# JiSs ^ #g- pa I Of these chords, that which results from the first transposition a., the augmented Sixth-and- Fifth chord, is the most available : the others are rare. Its natural progression is likewewise to the dominant, but always produces parallel Fifths. 189. m 3c: :3Z^ This progression of fifths, not classed among the most offensive, is avoided either by a previous resolution of the fifth (the original, above-mentioned ninth as a suspension,) as in the following example (a), or by a movement of the same to the third, whence arises the augmented Sixth-chord (6), or most frequently by sustaining the third and fifth while the Sixth and Bass- tone move, whereby the chord of the Sixth-and-Fourth is inserted before the resolution (c), and can be regarded here as a prolongation of the suspension. Remark. — The addition of the ninth does not entitle this harmony to" be pronounced a Ninth-chord; the ninth has here the same character as a suspension as elsewhere, as is clearly apparent from the progression a. ; the progression in b. and c. also corresponds 98 MANUAL OF HARMONY. precisely to iho treatment of suspensions, so far as (like the fifth in the above chord) they require preparation. It would follow from this, that this harmony should have been first spoken of together with suspensior.3 themselves; yet mention of it had to be made here, because we are treating of construction, and should not with the above-mentioned views ignore a univer- sal method of naming this harmony. / #: Exercises, 6 g^a- # 2 'i. I # i«i- SfE^^E iz^: :^ :t=^ z^. 3z: 91 4 3 S=-5 # 2 11 JB-- 6 4 3 4# ii^ -zt: zsz zsz 4 3 91 h-^yt. 2 :?2=5- :?2= i± ^^ Efeil =?z^ -t=t lEz: 6 4 3 — 4 3 :rlr 1 laz; 2fc In closing this chapter, we survey once more the wide field which it opens for harmonic formations. We have discovered much that is universally known and useful, much has appeared to us unavailable and worthless ; yet nothing was manifested in its primitive state ; everything was trimmed and subjected to change, to a certain degree, embellishment. This abandonment oi original form induces us to call attention again to what was said on p. 93. It was indeed a long time before these harmonic transformations were discovered, and still longer ere they were turned to general use ; and much, that has hitherto proved useless, may still in time be brought to perfection ; only it is not advisable, from a desire for originality, to direct all effort to the invention of new harmonic forms, or to an exaggerated use of them and a departure from original principles, lest the sound inner kernel be lost. Since all these formations serve rather for the decoration and, we might say, the more elegant carrying out of simple harmonic principles, one must only use them with discrimination, or his work will be overladen and him- self consequently reputed as void of taste. MANUAL OF HARMONY. 99 In closing this representation of all the essential harmonies and their immediate use, we annex further a brief view of the same, thcii kinds and derivations. View of all the Chords belonging to a Major or Minor Key. I. FUNDAMENTAL tlAKMONIES. i . a. The triad. b. The Seventh-chord. -tS. — — i A. Kinds of triad: Maior, minor, diminiihed, a/agmented. Major triads I of the maiar scale: liE of the minor scale: c-.-r ^ r^:: IV a: V VI Minor Triads of the iimjor scale: I 38: ill C:fl" I of the minor scale: Diminished triads of the major scale; I I of the minor scale: ■\s-_ 0: vn° a: n° vn= Augmented triad of the minor scale : i a: III' • KB. The other augmented triads see under II : Altered Chords. Inversions (transpositions) of the triad. a. Chord of the Sixth. i 5. Chord of the Sixth-and-Fourth. 6 4 =?:: 100 MANUAL OF HARMONY. B. Kinds of Seventh-chord : a. Dotninant- Seventh — or Principal Seventh-chord. b. Collateral Seventh-chords. Dominant Seventh-chord (major triad with minor seventh) : in major and minor formed alike: •^ cTVt •^ c; V7 a: V7 Collateral Seventh-chords : 1. Major triad with major seventh in mxjQfyr: _ in minor: S 0: 1^ vr;r a: VI, I 2. Minor triad with minor seventh in major: _ in minor: -«- -i»- i a: IV7 C ; n^ ni7 V17 3. Diminished triad with minor seventh in mc^'or: in mint I C: vn= n=7 4. Diminished triad with diminished seventh (diminishetl Seventh-chord) i a: vii°7 6. Augmented triad with major seventh in minor: P a: III' I MANUAL OF HARMONY. Inversions (transpositions) of the seventh-chords : a. Chord of the b. Cliord of the Sixth- c. Chord of the Sixth-and-Fifth; Fourth-and-TMrd; Second: 6 6 1 5 3 2 zjs?-. ■jp9- -«- -B^- I 25" 7^ III. CHROMATICALLY ALTERED CHORDS. The augmented triad formed from the major triad: 101 »^„ S- -St- o:-r IV V b. Chord of the augmented Sixth, formed : 1. from the minor triad with the root raised (so called double diminished triad) : -Jk 2. from the Seventh-chord of the second degree in minor (see the follow- ing chords.) C. Chord oi the aicgmented Sixth-Foitrth-and-Third; d. Chord of the augmented Sixth-and-Fifth, — both formed from the Seventh-chord of the second degree in minor : Raising of Second the third: Inversion: i =k With the ninthfrom Soot omitted the root and without Chord of augm. Sixth: the latter: =te: ^ ^n Ei^ :^ A 3 jer 6 102 MANUAL OF HARMONY. CHAPTER XI. On Modulation. The term modulation has a varied meaning. Formerly it signified the method of arranging the succession of harmonies to a given melody. In the modern sense we understand by it the transition from one hey into "another. The expression : transitional modulation, which is sometimes found, would according to the original meaning of the word be no pleonasm. The meaning of the term being fixed, it next becomes important to learn to recognize and define every occurring modulation (transition into a foreign key :) later, in the sixteenth chapter, we shall treat of the means of modula- tion, whereby the capacity to recognize it will be made more complete. A modulation takes place then, when a harmony appears, which is foeeign to the previous key. The former key is then wholly abandoned, and the harmonies must be reckoned as belonging to the new key, until a harmony foreign to it appears, which effects a new modulation. Thus in the following example 182. a modulation into D minor wiU ensue in the third measure, because d^-e-g- bb belongs no longer to G major, but unmistakeably to D minor, whereas in the fourth measure it is doubtful, whether the triad of C, which is foreign to the previous key (D minor,) belongs to Q major or to the G major which follows, whilst the modulation into A minor in the fifth measure is obvious. The Dominant- Seventh — as well as the diminished Seventh-chord must ever be recognized as the chief means of modulation ; all other chords are ambiguous, i. e. they may belong to several keys. MANUAL OF HARMONY. 103 Thus the G-major triad belongs not merely to G major, but is .jlso the Dominant of C major and C minor, the Subdominant of D majoi, and the sixth degree of B minor. From this ambiguity it often happens that the modulation can only be recognized from the chords that follow, as in general the decisive modulation itself can only be formed with the Dominant-Seventh harmony and its derivatives. A musical ear can of itself very easily catch at a modulation : it always conceives of the foreign harmony as belonging to that key which is nearest allied to the prevailing one. Thus, for example, the major triad of D in 193. zai viewed independently, vrould belong to the key of D major ; but in connec- tion with C major it will at once be recognized as the Dominant of G major, and the following chords only can determine what key is to predominate. A few examples are annexed here for practice in investigating modulation ; for further discussion of this subject see chapter sixteenth. 3 Exercises. 6t|_5 ,_J[, •"■ ^^^^^^^^m =^ C : I G : Vt I C: IV V7 Id: vii° 7 i C: I m V I22Z 3 gf^E 15 2 6 7 g jg^Eg^E j 4==±=t: ia= 6 7t) gj^^^EJlgp b 61, 2 3 1 7 3 ^~ 3 ii =2^: -s^- u =2z:i S H^-.» _^ •— t -= i =^: =E=2t ^ 6 je- ±-h =» — z;) — «'- "tz: 104 MANUAL OF HARMONY. mm -j^z ^M m^^m k 3 6 87 :^ 2fc t=t 2 3 «b 6 4 6 i^^m m^ ^=(S=^- i==P iK % is z^: ra=^= E^_#^^ Efe -g— gi- 3 I" 6 3 5 S^ ^ ^ I^ :^5^- The iudication of the modulation can proceed in the manner given in the first exercise, by which the letters denote the key, and the Roman numerals, as usual, the degrees upon which the respective chords are based. MANUAL OF HARMONY. 105 SECTION II. INCIDENTAL CHORD-FORMATIONS. TONES FOREIGN TO THE HARMONY. CHAPTER XII. Suspensions. The simultaneous progression of eacli part to the following chord, especi- ally when, as in our previous examples, it proceeds without any tnetrical variety of movement, produces a certain formality and monotony in musical phrases. A new mode of linking and intertwining chords, and hence an inter- esting variety of harmonic connection results when the parts do not progress simultaneously throughout ; when one or more of them remain in their place, while others are already forming the materials of the next harmony. The best and most important method of linking chords thus together takes place through the SUSPENSION. It is effected by the delay of the movement of a part, which is expected at a fixed time or even necessary, and that too in such a manner, that thai voice which has to descend one degree in order to take its place in the fol- lowing chord, shall still linger upon the tone of the first chord, while the others move to the second, and the former shall not pass to the harmonic tone until later. In the following harmonic Combination 195. i zso 2=fi -<9- ~sz 106 MANUAL OF EABHIONY. the Soprano dunng the entrance of the second chord can remain upon e and afterwards pass to h, as follows : ^- 12- 2?5=gi ^ 196. m^^ -z>- -JSZ. ia= So by delaying the Tenor in example 195 a suspension can be formed: 197. i §Be lEZ The characteristic feature of suspensions is, that they /orwi a dissonance with the harmony with which they appear, and that they thereby effect the harmonic connection, while through the expected resolution of the dissonance they render closer the necessary relations between two chords. In this respect they bear a resemblance to Sevenths, since like these as combining intervals they are subject to preparation as well as resolution. To be sure, the dissonance in a suspension does not always consist in an interval's forming a dissonance with some one part: cases may occur, where the suspension as interval forms a dissonance with none of the other parts, but only through situation, position and progression the character of the suspension predominates, as in example 197, where the tone of the suspen- sion forms a Sixth-chord, and where only the unusual appearance, as well as the whole position of the triad of the third degree, together with the pro- gression of the Tenor, produces the character of a suspension. The above examples furnish the necessary rules for the formation of suspensions : A suspension can he formed where a part descends one degree, under thi following conditions : it must 1. be prepared ani 2. be resolved. Thus three points will have to be considered in a suspension : its prepara lion, the suspension itself and its position, and its resolution (progression.) MANUAL OF HARMONY. 107 a. The preparation. The preparation of a suspension cap happen through either interval of a triad. Also Sevenths are used for preparation, though less often ; the Dominant- Seventh the most frequently. 198. Preparation through octave of the root : ^. -TSr 321 'JSZl ^ :ifgE through the Third : issr TT^ jEI 7 6 ^ - 3 — 3ZI ZSZ -&— zsz I a.-vii°- C:I ^ :;ii through the Fiflh: ISI is= -^ 9 8 :::si 9 I 1-4 -i2_ he: 3ZI I G: V VI C: I IV I e .• vn ^ through the Domimmt Seventh. P =ai m 5 — i 3 lEZ IE; C: V, V The preparation must be upon the arsis, the suspension upon the thesis. Also the rule mentioned above (p. 71) holds good, that the preparation may- be of equal or longer duration than the suspension, but not shorter. b. The Suspension : The entrance of the suspension on the Thesis has just been spoken of, its further position shall be explained more particularly. The suspension can appear in either voice hefore an interval of the triad,—' before Sevenths only in rare cases. 108 MANUAL OF HARMONY. Smpendona before the Octme of the root : gyg- 188. S4-=,«)^. lEZ ^ zzzr. JS^ 7 6 7 6 -«■ .^-^J- ^ i MANUAL OF HARMONY. 109 In the first case the seventh will be always a passing one. c. The resolution. The resolution of the suspension, as was said before, takes place by the descent of the same part one degree. Remark. — Irregular kinds of resolution will be exhibited later. It is here further to be observed : The resolation-tone (that whicli is delayed by a suspension) must he con- tained in 710 other part; on/y the Bass or lowest part can take it without injuring the harmony. 201. not: y. 5. better: not: d. KB. I^ '^^—e>- J— i, ^=m riz^n ■S- -isz In example a. the Tenor moves from a to c, which last is suspended in the Soprano by d ; in example c. the Tenor takes g, which has the suspension a in the Alto. Both these cases of doubling are incorrect, especially because they are concerned with the third and fifth of the chord. In the example d. at NB. it is the root that is doubled. The effect in this case is better, particularly when consistency in the movement of parts requires it, as in the following phrase. Boot: TUrd: i J- Fifth: 202. -iZ_ !-• — J- J JElp 1 1 J- a -- 1 Eemark. — It may be further observed here, that the doubling of the root always pre supposes a distance of one Octave at least, and that to double in the unison is incorrect. e.g. i U 72=l± i only between Bass and Tenor or in the part lying next to the lowest the suspension may appear even in such close proximity. The.lowest part, usually the Bass, has however, as that which determines the chord, a counteracting influence against the dissonance of the suspension, 110 MANUAL OF HARMONY. SO that doubling is admissible, if it be founded on a good movement of e.g. i—a>^. i ,^^ 13: =Ei :?z=T F=r-r- incorrect: -«** ^ 203. 6-6 9 8 •«— 1=2- :t: ■BP- The incorrect progression of the Soprano and Bass in the last example ■ becomes clear, if we remove the suspension, as a mere delaying of the movement, by which open octaves result. 204. The same is the case with proffressions by fifilis, which are covered by the suspension : 206. Here, however, the same considerations will govern, as are usually taken in:© account in cases of concealed Jifths, since position, situation, and progres- ^sion will admit of such a part-movement, without the disagreeable effect of fifths being prominent. We briefly condense these observations in the following rule : Suspension does not remove parallel octaves and fifths. The following iprogression, therefore, will be erroneous : 206. m ±^ s- ':^i paralel fifths of this kind, however, are not to be rejected nnconditionally, provided the unpleasant succession be counterbalanced by the movement of ■the other parts, so as not to be too conspicuous. It is impossible to give positive difflecfcions on this point ; to reject them invariably would be too restrictive. MANUAL OF MARUONY. Ill Suspensiors in the Bass, which generally occur before the third of the cliord (or, which is the same thing, before the chords of the Sixth or of the Sixth-and-Fifth,) admit of no doubling in the other parts. 207. i not: E£ lan :S: tS- -f -JSl :a= §! e t=^ S^ :33 Suspensions before the root and the fifth in the Bass seldom prove of use. not: zSsz -JSZ 5= az ;^ =i 208. 1 - 2 — 1 ■ g-^-^.g^-^ :?z= i^zE? The figuring of suspensions in Thorough Bass writing is partially con- tained in the above examples. If the suspension lie in one of the three upper parts, the interval reckoned from the Bass is given together with the resolution, e. g. j"^ "9876- ^^ other figures determine the chord where it is necessary, e. g. the chord of the Sixth g^ the chord of the Sixth-and-Fourth \'^ or ^^• If the suspension be in the under part, the incidental intervals of the other parts are also indicated by figures, e. g. ^'Zj or ^it^i the seventh-chord 5 — 4 — the lines that follow denote that the parts retain their tones while the 2 — suspension is being resolved. A suspension in the Bass is also denoted by a cross-stroke over it, and the proper chord placed over the resolution-tone, which in respect to the latter is more distinct, e. g. 209. ■32H ^ ^1 Tn the following exercises the former method is adopted, as most in use. 112 MANUAL OF BARMONY. Exercises. 7 6 6 7 5 — 4 3 210. g^^ 32Z -(=Z- ie: zsi 3 6 9 8 I5>- m^ C: I 6 7 IV V, I II, 6 — 1 — 6 2 — ll# §i =^ 32:: r i:^ zsz ^ S - 6 3 ^2 — 7 6 7 5 ?E 6 _ 3iq 6 js- 6— 7 — 5 4 4 3 -^ m 3S;r ?=1- ■ g"-^- S^ 4. B — 4 — 2 — 9 8 ^2 6 6 2 6 5 6 '^I-Sitzfe— s^- — ^^ 1 — &- — ^ — -j — ^ — <^ — ' 1 — — M- ^y!p-^— -r-^ I.' "r : -1 1 — iS — :zfet-= ei <='-l 7_6q 6 5b m- pe S isr _fe sp^ 5 — 4 3 Iffil :^ -e>-^ 7 JB" 4 — 6 3 — 4 2 7 1=:^: 7 6 6 9 8 7 6 5-:, 443# g^>^^ E^ -«>-^- i2z:i :^ is; 3b 6 2 — 4 3- iiite _(2- 6 — 4 3 2 6 ;i^ igzzM :#^ - g* . i - 2 6 6 4 5 3 7 mtz 9 8 7 5 =F=^ 12*: O iffi2r:^:s: ^ -7!(- 7 6 6 — 4- 7 6- 3 2 6 6- 6 4 3 4 765 1, # : Cj; h ««.^i f*-^ ->y ., .. ,i ^r"* — i — !Z_-» a—^ — ?5 1^ — g>' g - L 1. %: — J 1 1 u 1 — fil-i-li In working out these and the following exercises it will be expedient to divide the parts and write each upon a separate staff. This mode of writing MANUAL OF HARMONY. lis in sconj aftbrds a better view of the movemeut of each individual part, beside being generally a useful exercise preparatory to reading from score. It is, however, necessary here to write the parts, which in pure part writing are always considered as vocal, in the clefs which have always been assigned to them, a knowledge of which is indispensable to every musician. Familiarity with these clefs may soon be acquired by attentive practice and comparison with those already known. Eemarh. — A knowledge of the Alto and Tenor clefs is essentially necessary for under- standing and reading scores, as many vocal and instrumental parts are written solely or partially in tliese clefs, and even the knowledge of the Soprano clef, which more rarely occurs, greatly facilitates reading in the case of various instruments, which have a partic- ular pitch. The clef used for the three upper parts. Soprano, Alto and Tenor, is called the G-clef. For the lowest vocal part, Bass, the F-clef or Bass-clef, which has been employed hitherto, still holds good. The position of the C-clef always indicates c of the third octave, and for the Soprano this c is placed on the lowest line, for the Alto on the third, and for the Tenor on the fourth, e. g. Soprano, r ^ Alto, m Tenor-clef. The ordinary compass of the voices in these clefs stands thus : I -zi=r^ ^-"-r - -»-H^ -•— ^- ^-^-^- -»!—<»- ii=t=zi^=t=t Soprano-clef. -•— ^ 0—^ [i-k I I I I I i-i. Mio-def -^ J }~ ^=f=l=r=4- • — ^- Tenor-elef. \ [ .i -k—f- iE^^ ■i— •■ -i-if-F- EE 114 MANUAL OF HARMONY. Eemarlc. — It is interesting to trace the origin of these differeni clefs from a very simple basis, the so-called Tablature (a staff of usually ten lines, on which the parts were all written with especial indication of those lines, upon which the three principal tones F C G were to stand,) but a further explanation would carry us here too far. The easiest method of fixing these clefs in the mind might be, to observe carefully the position of the C-triad in the different voices, by which the intermediate and adjacent tones are easily found. Thus the position of the C-triad in full, with the root doubled, will be : In the Soprano: In the Alto; In the Tenor, iest in the position of the clwrd of the sixth-and-fourth: ^ We annex here the first exercise of 210, written out in these clefs: 211. Soprano. Alto. Tenok. Bass. i -^ ^^ ^ ZSl -F=^ m^^ c I ^ '^ s 5 — 1 3 7 6 7 6 5 7 5—43 G V IV I xi; G. V„ c I To work out these examples with all due observance of the rules thus far given, requires an easy, somewhat free movement of the part in respect of position, since the necessity of a better distribution of the suspensions often demands a change in that distribution of the parts, which we have hithertb always endeavored to keep as uniform as possible. Thus it will be clear when to use the open position of parts, which must again be exchanged for the close position, whenever necessity and expediency require it. MANUAL OF HARMONY. 115 In thus shifting the positions of the parts, tliese rules must be observed : The parts, in passing from one to another (differing) chord, must never move either hj steps or skips, out of their proper place simultaneously; only in single cases, where one and the same chord is transferred to another position. Either part may leave its position, when one or more are sustained itpon one tone. The 8th exercise of 210, worlied out as follows, will make this clearer. 212 SOPKASO. / Alto. Tekob. Bass, ElHl W- 1= m m. IS?I =^-fi^ IS2I iit^ -e>--- S 7!- »t=3: '-^-t ~ezi ::^=^ NB. ;t=t 5 3 7 -"^r- q — c — 7 a°7 rf F- Bh Eb Bb C- F 7 g: I — IV— 7 ii^TBbriiiV, I IV I F: V^ IBb:V, (g - g- 7 NB. 8 _^- ■!«— «'-T-6'- It- =^=5: i :p=t: W- L^~Z_^. £ _-#^ m v=^ -ST. 7 6 5—3 7 5 6 4 gipl^l^ is: It :ai - rs—si - D, ? F7 Bb c 9- : D, I IV Bb: V- I 11 .7 I c IV VI II =7 V 7 7 I Let the following serve to explain this : The close position, in which this example begins, is in the fifth measure abandoned for the open ; this in turn continues till the close appears again ill the eleventh measure. 116 MANUAL OF HARMONY. This was effected by a freer moyement of the Soprano and Tenor. The former in the fifth measure moves away from its position to the Seventh E\) (at NB.) a skip which may take place if the root is already there and remains fixed (as F here in the Bass ;) so in the seventh measure it leaves its position by skipping to the fifth g, the rest of the chord heing sustained-. by which the suspension falls into a better place. Finally the close position is again reached by a free and better movement of the Tenor in the tenth measure. Suspensions from beloAW. Suspensions from below are to be regarded as such only in a few single cases ; most progressions of this sort have originated in the suspension from above hitherto treated, by a contraction (shortening) of the same, followed by an upward movement, e. g. 213. ^ fT^=^ from: ± I The suspension from below may take place in the progression of the leading tone: 214. ^ j: =vfil r) *a= z^sz --T and with many intervals, which ascend a half degree, especially with those altered chords, that contain augmented intervals by elevation, e. g. : I ^S=t s 22: d^^iF^^ 215. #-g- i^ -^ ZSti f^ % :i-£i^i=^=.K^^4£^ X^^L It should be observed here that, as formerly, the resolving (harmonic) tone can stand in no other fart but the Bass. Remark. — The last of the above examples gives us tie same combination of tones, which resulted above (p. 64J as the seventh-chord of the first degree in minor, and which was pronounced useless as a fundamental harmony (see p. 74). That, used as above, it i» simply to bo regarded as a suspension of the leading tone, needs no farther explanation. MANUAL OF SAItMONY. 117 Other suspensions, especially those that ascend a wliole degree, 216. i ^^ m. ^-X zst ^J-J—,^-ja:rrA.^^^.aL»r-(5'iS'- Suspensions in several Parts. Suspensions may occur in several parts at once : pensions in two voices ; in tliree voices : 218. Also the chord of the Sixth-and-Fourth often appears as a double suspen- sion, e. g. : 219. i^s :s= j_ Freer movement of Parts in Resolving Suspensions. In our previous examples the preparation, entrance and resolution of the suspension took place through two chords, since the parts not concerned remained stationary during the resolution. The same may also take place with three chords, by which the change of chord and the part-movement become yet richer and more varied. This happens when, during the resolution of the suspension, one of the parts, gene"aUy the Bass, or several at once, move and form thereby a new harmony. 118 MANUAL OF HARMONY For instance by progression of the Bass : 220. zSsz -g / j ^-" - ig=g:::iffi ei3Ei r r :?jz -«■— ?s: C: V, I — E 1 SI II, V I I IV 117 Ia:Tii°7 I By progression of several parts : 6. 221. i d: -zn. ZSEL f^&=^ -^z. M ?£Sg: =si 7 3 7 2i=z2r:-.EEE -Jr-: J- J_ 4 3 C : I II V, 1 I^ 3: IV vu° VI I V, a-V, I In all these examples the resolution of the suspension follows regularly during the progression of the other parts to a new harmony, of which the resolution-tone forms a part. Remark. — By way of illustration of the view expressed in chapter ninth concerning chords of the Ninth, it may be remarked here, that many passages, in which the Ninth occurs, and which are recognized by many as Ninth-chords, may be explained in the above manner, as in example 221 b., where the cadence-progression of the roots F-b is easily and far more simply represented as a progression of a suspended Ninth by the tise of three diords, and leads to the same result, as is likewise seen in all the following examples : Ninth suspension with two chords : with three chords : better : 222. i ^j- IffiZ :iid:tia:: -fe=^ r i Concerning the unprepared Ninth we shall speak later under Organ point. As supplement to what was said in chapter ninth it may be further added, that as an argument against independent ninth-chords may be reckoned also the impossibility o( transposing them together with the root in such a way that the latter shall be brought into immediate proximity to the Ninth, as may always bo dona in the case of seventh-chords, MANUAL OF BABMONY. 119 223. i -^ e>- .=ii. 1 — » — «. T 7^1 -g=^=i - -r^- 1 So four chords may be used with a suspension, provided it stands before i harmonic tone, which is not contained in the other parts, e. g. 224. i without 'suspension : 1 2 3 4 a- — gig- 3^= 'P= i^^ElE 32. :l3ii _— ^^^ -■-^--^ §i4: IJEZ I'az hS«- Exercises. 3 — 8 7 S 4 4 225. a^ :S: ^feE^ SE^EiE^ :^: z^-.z^: =?z: 8 2 2 pit ^^ 7 6 6 6 6 — 6 4 -,_^H_ m 6 74 7 ^iii \^ 'it^¥- =?z: c f^-Kf^ c iife 9 7 4 7 — J^E^g^E^l^f^ rs g eS£ i^i^: ;8^ 4 6 6 5 4 7 i -«■- i^ JB- 6 7b 6 — 4 Itflll^I 3e; -i» — ; »• IffiZ l!^= ^Zs>- 7 6 — 4 6 — gj^gg ^ '-?^ #7 6 6 6 4 7 7 46 824 l-^ai: -?s- =F= :i52: S?z: 4 6 :ir::: 120 MANUAL OF HABMONY. S 7 i 2 74 7 s SiteE; -Tjr- :3=:z^ #--«?- i^ife^^^; ilS 8 6 4 a iz?- :EE^E _(•_». K a 4 3 1^ :^= -^ — • ■•-#- P :t==i: m 7 6 7 — *-|i 3 2 7 9 6 4 3^ -»-^-U It ^#^ Between a suspension and its resolution other tones may be inserted in the same part. These may be : 1. Tones belonging to the chord, e. g. 226. ^■ggr * Ifl- * ^1 ^ 12^ * 3bd: fflj g_ :^::e; 4tJ -»- -»- "»- -»'~ • ST -S- 2. Tones foreign to the harmony, appoggiaturas, e. g. 227. I .z^L^J'€ £:;-^--^J , ^-7 Lj__j^. -f7-:Z2Z. 22= ia=::rsE :3i =s=:::S ac "W- A more complete explanation of these and similar passages will be given farther on under the description of passing-notes and appoggiaturas. Passages also occur, where the suspension has no resolution at all, e. g. 228, i umaUy tJmi; Z311 -f -e>- ^S W" ^ They have resulted by elision from the following phrases : MANUAL OF HARMONY. 121 r-fT^Jz^ »^ or: ^ ^5=4: IS2Z 229. Anticipation. The anticipation of a tone, which is of less frequent use than the suspeu sion, is the reverse of this, and consists iu one or more parts allowing tones of the chord next succeeding to be heard sooner than others, and before the metrical structure would lead them to be expected. "Where notes are of long duration, and in slow movements, this method of progression seldom or never occurs, since the harshness of the dissonances that appear would amount to uuintelligibility ; it is generally only in shorter divisions of the measure that anticipation takes place, e. g. Anti(Apation in the Bass: 230. i i :^*=g: in the Soprano: 1 I 1 ^T^p-p-*:«- I " a J:: 3^ f tJ-raral: in several parts: 22i2l rf- :^=S «f- 3^-: -•— S- =i- 3— ?zz:t The resemblance of this part-movement in its metrical form to that known in the general musical system as syncopation, is unmistakeable, only that the latter is formed or acquires rhythmical value, not by the anticipation of chords, but rather by their afterstriking. Here also the movement of the parts may under circumstances be freer, e. g. another harmonic tone may be anticipated beside that which was intended for the entrance of the chord, as in the familiar closbg phrase : ' 231. :sz i -w '-W- As the reverse of anticipation may further be mentioned the afterstriking of harmonic tones, which so far resembles suspensions, that here also prepara- tion and resolution take place, but differs again essentially, since its character 122 MANUAL OF HARMONY. impresses itself more upon the metrical and rhythmical movement, conse- quently it always appears also in a longer series, whereas suspensions, whether singly or in greater numbers, appear under totally different condi- tions. A series of such delayed tones would be the following in the Bass : Allegro. 232. -V^-rr-, zpz Under this head also would be classed the unison passage in Beethoven's Overture to Leonora (No. 3) : 233. i 4- -&-i- # ~4-^ -*^¥ "IS^ J^-i i uj -^-'-S>- :ffiz ^ ¥ ia a;S= --!?= I L ^^- -W- -TS^-'^—'-ii-^ t5- — -^ -'■ aziiqz -*—z)z zJj^ s ^•#=^ >— ^r_ ^^ ^r- r- :E Efe^ £J=U=:ri^?'i^=?fTrf£=_%TE^^=fe ^^=rs i ^ =£ ^teNi^ ^=^: L^fe zt: &o. S^i p^ttrzpz MANUAL OF HARMONY. 123 CHAPTER XIIi: Organ-point. Sustained parts. A PECULIAR variety of harmonies and mingling of tlie same is produced by sustaining one, and even more parts, upon one tone, and by the chorda thus incidentally formed. We often find, especially in the Bass, as well at the beginning of a piece as in the middle and at the close, where a cadence should appear, a lonir- continued tone, while the other parts, apparently without any relation to it, continue their harmonic movement. When this tone lies in the Bass, it is called ORGAN-POliSrT; when such long-continued tones occur in the other parts, we call them : SUSTAINED PARTS oe SUSTAINED TONES. Remark. — Many give to these last also the name Orgar.-point, but nofcrightly. The tones adapted for sustaining are the Tonic or Dominant ; hoik at once also occur. Remark. — Attempts, which in later times have been made with the third of the triad by many composei'S, sound unnatural and forced. The harmonic connection as also the progression of the remaining parts during the organ-point stiU takes place according to the established rules, the lowest of them acting as JUide to the harmony, and in general without regard to the sustained tone. A few examples follow first, before discussing in detail tlie mode of treat- ing organ-point. 234. a. Organrpoint on the Tonic : -I2SZ =J— 4 ^^'=^A iiEE zsz ^ 124 MANUAL OF BABMONY. I 6. ou the Dominant : J: 4=F^ '^ li- i Lj-j I ^rn^rm rg r ::si lEi: iiE srrrTT" lEI :a:: isz e?. on both at once: * ^ ^ -^— •- I -*± IE: ite I22Z :s= isz ZZIZ '^m -jar In these examples the chords to which the Bass-tone does not belong harmouically, are marked with a cross. The following remarks may serve for the treatment of organ-point : 1. The entrance of the organ-point must he at a time rhythmically marked, 2. By a chord, to which the Bass-tone harmonically belongs, 3. The last chord of the organ-point must also harmonize with the same. The first takes place at the beginning or end of a period or section thereof and upon the accent ; the second and third usually through the root of a triad, as in example 234 a. c. d., or as in h. through the chord of the Sixth- and-Fourth. It is further to be observed, that the chords foreign to the Bass-tone should not follow one another too frequently, but often alternate with chords to which the organ-point belongs harmonically. This is necessary in order to avoid digressions, which would destroy the character of the organ-point, which lies in the close union of different chord-connections. MANUAL OF nARMONY. Thus the following organ-point would be faulty in this respect 125 235. 4 4- d-l c=^ J- ffifi^E^i^^E^j^^ 32= The part lying next to the Bass, in lour-part composition the Tenor, becomes in the case of organ-point the foundation of the harmonic move- ment. Hence all the necessary progressions will depend upon this voice, even though the organ-point might accidentally belong to the harmony. Thus in example 204 a. the progression of the Bt> in the Alto (in the first measure) is determined by the movement of the other parts, and not by the fact that it is the Seventh of the Bass. If the organ-point be upon the Dominant, as is often the case at the close, there can be no plagal cadence formed upon it, as follows from the third of the rules above cited, e. g. 236. The plagal cadence may however be used, if the organ-point be upon the Tonic : 237. =s=s AZTlt. J -«*'- ZtSZ u zzm Z3C The end of the organ-point is to be heeded with fuU as much care as the entrance. In the above examples this always takes place with a cadence. In this case there is no difficulty, except in passages like that in No. 236. The organ-point, however, may pass sooner into the harmonic movement, and then the third rule must be carefully observed, e. g. 126 MAJX'UAL OF HARMONY. 238. ^=f3.i,^=P^P|J^ ?iEE 122= -fflZ To break off in this manner would not be good : I 239. iiEE 3^i: -•-^ &c. Sustained Parts. Sustained upper and middle parts upon one tone after the manner of the above-described organ-point are much less frequent than the latter, and require greater caution in their treatment. Sustained tones of this sort suit the character of these parts only when the chords not belonging to them appear very seldom, since these parts have not the power to act as a counterpoise against foreign chords, this being the peculiar property of the Bass or the lowest part as that which determines the harmony. Thus the organ-point in example 234 «., when transferred to the highest part, will sound very unpleasantly in the last measures : 240, 122= -r-r 22Z Iffil I E^ X :tiid^.-Md= =f=^^^^ ^^i^^ whereas the following, where the Dominant is the sustained tone, is better, for the reason that the last chords of the example belong to the same : 241. fe f^rr j-it- Z^sr Misp -Mm jjj. -.iLi ?3^Ff^ MANVAL OF HARMONY. 127 As an example of effective use of sustained parts and continued tones, and for the treatment of the same, may be cited a passage in the " Gloria " of Cherubini's Mass in C major, where the violins hold a long A.\), while the chorus and accompanying instruments below it carry on their peculiar melodic and harmonic progressions ; also the D of the violins in the intro- duction to the Overture " Calm sea and happy voyage" by Mendelssohn - Bartholdy. In both passages chords will seldom be fouiid, to which the sustained tone does not harmonically belong. Here also may be classed the Trio of the Scherzo of Beethoven's A-major Symphony, which is throughout based upon the A, that appears sometimes as a sustained tone in the upper and middle parts, sometimes as an organ- point in the lowest, and serves as a foundation through the entire piece. Sustained tones in the middle parts are to be treated with the same consideration as in the highest part. In instrumental compositions they are always proportionately reinforced : in four-part harmony they occur but seldom and not at too great a length, e. g. 242. i A — \- -U- ^^ I =^J^--^r_^ -J- =F=^ ?=^; f-= NB. -4— J- I .1 =?z= "I? Remark. — As supplementary to what has been said of chords of the Kinth, may be added the following. In the above example h. we find, if the sustained tone be reckoned with it, a complete Ninth-chord in inverted position with a regular resolution. It has been already said of Ninth-chords that their transpositions cannot be so used that the root and ninth shall be brought into close proximity, as with the Seventh. That they may occur simultaneously at a, greater distance, as above, affords no reason for regarding them as independent chords, when they only occur in the above relations, namely, with a sustained tone, whose character it is to support harmonies which are foreign to itself, as e. g. is the case with the following Ninth, which in reality forms no chord of the Ninth. 243. :^ -*-Til- fTT^ i=t -f—0- -& i!2- ■X=:X^ 12a MANUAL OF HARMONY. When the harmonic progression is to be indicated by figures over the organ-point, they must always have reference to the tone sustained in the Bass, so that iu many cases the usual figuring of chords becomes changed. Thus the organ-point iu No. 234 h. might be figured in this manner: 9 6-7 6 4 -» 5 3b 9 7 6 4 4 9 9 7 6 7 7 5 4 4 8 7 6 4 7 4 2 - . ^, ' /C-' ■ K4.4.. •-). This mode of figuring, being diflScult to see readily and at the same time imperfect, is only employed for special purposes, so that in scores, where figuring is used, we often find with the organ-point the words " tasto solo," indicating that in the usual organ accompaniment only the organ-point itself is to be given. CHAPTER XIV. Passing notes. Appoggiaturas. Undee tones foreign to the harmony are especially to be classed ^ossin^- notes and appoggiaturas. The former result from filling out greater or smaller harmonic intervals with the intermediate tones, e. g. 245. The notes marked x are passing, those marked are secondary harmonic tones, that is, so far as we regard the first note as belorging to the triad of C or A. e. g. MANUAL OF HABMONY. 129 246. The passing notes under a. in example 245 are called diatonic, those under b. chromatic. Passing notes Tnove from one harmonic note to another ; hence they appear not with the entrance of the chord, but after it, in subdivided parts of the measure, and can only be used by successive degrees. Appoggiaturas on the other hand, are those tones foreign to the harmony which either appear, like a suspension, with the entrance of the harmony 'that is, in this sense, on the accented part of the measure,) and be close to the harmonic note (247 a.,) or, like passing notes on the unaccented part of ;he measure, serve as a melodic ornament to two notes of the same pitch (247 h.) 247. -*-^ O-jt- zk i^^--^^--^ =J"= =t =m zzzz ^^\-tA 3t?3t:3: I -=r An appoggiatura, therefore, may enter hy skipping, hut micst he next to the harmonic note, as is seen in the examples in 247. It is further to be seen from the above examples, that appoggiaturas can be formed as well with the note immediately helow the harmonic note, as with that above. The appoggiatura below the harmonic note, especially if struck upon the accent, has this peculiarity, that it gladly forms a 'minor second to the principal note, by which chromatic tones are produced, as may be seen from 247, and phrases like the following could not be written : 248. 130 MANUAL OF HABMONT. This is especially true of appoggiaturas introduced by skips. The case is different if they follow one another by degrees, by which they at once assume the character of passing-notes. Thus the following succes- sion of appoggiaturas a. need not of necessity be written as in h. : 249. ^J^^g^-tan^, Appoggiaturas below, not falling upon the accent, need only at times the minor second. Thus example 250 a. need not necessarily be written as in b., while c. is not as good as d. 250. i r J-2--I ^i:u r This point does not admit of fixed rules, nor are they indeed essential, inasmuch as every musical ear will surely determine what is right. Eemarh, — The third of the triad suffers the appoggiatara to be a whole degree, sooner than the fifth or octavo. Since in the last case the appoggiatara may appear likewise as the seventh, decision must be made in accordance with what follows. Appoggiaturas above the harmonic note, whether they enter free (by skips) or as in 250, may form ruajor and minor Seconds to the tone of the chord, because they are always formed diatonically, and are therefore regulated according to the key or modulation. 251. "We often lind figures where appoggiaturas above and below the chord- note are used alternately, e. g. 252. MANUAL OF HARMONY. 131 This is the basis of the following embellishment, which often occurs : 253. ^^ 3fiEi r Passing'notes and appoggiaturas may occur in all the parts. If it be in one only by way of preference, this will contrast strongly with the rest, and acquire an obligato character, while they serve as an accompaniment. If this is not the case, then all the parts can be alternately made prominent by such secondary notes, and gain thereby increased importance. In general where the position and progression of a part is adapted for the introduction of such notes, it is thereby made susceptible of greater melodic significance ; but even here, unless the proper proportion be hit upon, a crowded and confused effect may be the result. , The following simple harmonic phrase 254. i zui ^ s; ;2= J. "f^ iS: =^ ■ A — h- -J -ri — :t=5^^si r.^^- ?=-'i^- I2Z T dr -^ -fSv- jl ::^ d= '^ ^=^ ^=i=fz by the use of these secondary tones might be written thus : 255. m -^ — *- m --t 3=1: ^--. Wwn & i u 132 MANUAL OF HARMONY. I ^5: N^^fe! -•— ^- ^2= r- s^ J J-:--^ 1^1 .Aii fi^ The passing notes and appoggiaturas are here marked by crosses X- It may be seen in the above example that a phrase can easily suffer from such an accumulation of tones foreign to the harmony, if it is executed in quick Tempo, whereas a slow movement is better adapted to this style of writing. As has been already remarked in the case of suspensions, care must be taken also in the use of appoggiaturas, that no part shall contain the har- monic ton^ which in another is introduced hy an appoggiatura, e. g. : 256. i ^ J- This can only happen when the harmonic tone is at least one octave removed from the foreign note, e. g. : 257. i ^ ^ -79- According to the principles of doubling, the root or fifth is better adapted than the third of the original chord for such a purpose. In case of a quicker movement, however, and longer continuance of such figures formed of appoggiaturas, there are other considerations, as the follow- ing phrase will show, which indeed cannot be conceived of as a four-part vocal passage : 258. ^£^ mMMm. 1 With regular passing notes the same considerations hold good as to prox- imity to harmonic tones, and figures like 259 a. b. are not as pure as in c. d. e. MANUAL OF HARMONY, h. 0. d. 133 ^'■^^ ¥^ =2= -a- r' i^j i ZST- -^ Here also more rapid figures sooner admit of this proximity, e. g. . 260. P '-o-^-i—m- IS^ -iSt-- I 3: -g-^- -e J_ -•-4- §i: =tirt: p: EEf ^ ' — ■I-^»- 1^ Erroneous progressions witli Passing Notes and Appog- giaturas. As it is the office of passing notes to fill out the interval where a skip is made in the harmonic progression, care must be taken in changing the harmony, that no false progressions arise, as in the following examples where concealed fifths become (ypen : 261. i d= --F -^—e- -k =t: C=f2 ^ T --^ -z^- -r^rf^ Open octaves, formed with passing tones, may not occur, as the first of them will be equally harmonic with the second : 262. ■^ -•-I 11 I On the contrary, in the following cases the passing notes do not cover the Dpen octaves, and are therefore faulty : 263. ^^^S r Bemarh. — la. instrumental composition, where strengthening and doubling is intended such octal ;s might be used. 134 MANUAL OF HAUMONY. Likewise tlie entrance or progression of an appoggiatura by direct motion is to be pronounced faulty, if it proceed as follows : 264. helter: r r — I ^^zs: r22Z =^ _JJ^J_ -A_X ^ -fS^iiU*- The last example is better, for the reason that the octave progression is covered. Passing Notes and Appoggiaturas in several parts at once. A direct motion of thirds and sixths is best adapted for passing notes in several parts at once, e. g. : 266. =.B¥ j- --^ ■i^I^p^g: :?2Z 3r^ Sf-F= -4-- ^ The free movement of parts with the aid of passing-notes may produce also parallel seconds, fourths, fifths, sevenths of all kinds ; these require, however, great, care, and on account of harshness are admissible only in single cases and under very favorable positions. Progressions of fourths are good when another part takes the third below : 266. Single fifth-progressions, formed by passing-notes, are found sometimes in good compositions, which, however, afibrds no ground for recommending MANUAL OF HARMONY. 135 them in general as faultless (see remarks upon consecutive fifths on p. 27 and elsewhere.) In like maimer the harshness of successive sevenths is alleviated only by favorable position, good progression of all the parts, and in general by Tempo, movement, etc. In contrary motion the varied intervals of passing notes often give the movement a new, peculiar coloring, and add greatly to the independence of parts, only they should not be too crowded or appear in too many parts at once. 267. Here also it will be found that those passing notes, which with others, outside of the simple fundamental harmonic structure, form as it were an inner new (passing) harmonic movement, are more natural and smoother than those whose combination cannot be shown to be harmonic. The value of such movements can only be judged of with reference to their character and Tempo. In regular diatonic progressions several parts at once td&j have passing notes, e. e. : 268. ^^ ^i^i^^ The main point in all such passages is, that at the change of harmony, which in the last example occurs at the half-bars, the parts shall be so disposed as to admit of a regular formation of their progression. Appoggiaturas can occur in different parts : a. in tv)o parts : 13G MANUAL OF HARMONY. 269. in direct motion: gStrtsd ^^^: ^¥^fe:^ in contrary/ motion; 270. i irstilz M | i i , . ^^ — a — S- i -^-'- -•-W ,, l^O rf f-r=3i=i^'E^=rp±=^Tf^^^ b. in three parts : 271 8— e— 5— « . .> . C. in /oMJ" parts: 272. -U- :2=£ fe'f it --fE^^f'f Remark. — Most of the above examples can also pass for harmonic progressions apon an organ-point. It appears from these examples that for appoggiaturas also, in a direct movement of two parts, progressions of thirds and sixths are the most natural, while parallel seconds, fourths, fifths and sevenths alwa3-s have a very- harsh effect. Thus no one cquld easily pronounce as good, appoggiaturas like the following : 273. ■=f:r- Appoggiaturas may also be of greater length than the harmonic note that immediately follows them. e. g. 274. M-ANUAL OF HARMONY. 137 As regards composition, the importance of tlie matters explained in chap- ters twelve to fourteen inclusive is sufficiently great for subjecting them to a careful examination, as a thorough knowledge of them aids essentially in understanding the inward harmonic structure of a composition. — It yet remains to speak of their relation to pure part-writing, the object of our next study. As on page 24 we spoke but generally of the term " pure part-writing," it here becomes necessary to limit the question more closely and present it somewhat thus : What application of these materials for contposition is allowed hy our next object, practice in pure part-writing ? It is undeniable that these materials especially adapt themselves to the perfection and adornment of the parts. If, however, our immediate concern be with the recognition and working out of simple harmonic formations, then indeed whatever is adapted for the perfection of the parts may properly be used, but all else, serving them merely for ornament, must be put aside ; in brief, a distinction made between the essential and non-essential. "With the non-essential must invariably be classed first of all : Whatever is affected in harmony generally, so far as there lies at the root of it no inward necessity ; unnatural introduction of harmonies little used. These readily occasion superfluity, bombastic overloading of the piece, and rather give evidence of a sickly or mentally weak condition, than of originality and a fresh, free, strong and steady action ; again : irregular employment of suspensions ; the use of sustained parts, of anti- cipated and delayed tones ; but especially : appoggiaturas abruptly used and the figures formed from them,, in short, whatever is inconsistent with simple, good four-part song. Vocal composition being generally accepted as the basis of all music, much will naturally be excluded from it which is proper in instrumental works. Although for practice in the use of harmonies and for the study of good and pure part-movement, the writing of chorals or simple movements in choral style is suggested as most serviceable, yet even this will not exclude the use of those materials, so far as they serve not only as ornamental, but also as perfecting the movement of parts. 108 MANUAL OF BARMONY. lierewitli is particularly to be reckoned the use of suspensions, regular passing notes and appoggiaturas. From what has been said may now be estimated the strictness of pure part-writing at the commencement of the study of harmony and in later contrapuntal work, which prohibits much as inexpedient, unessential and diverting from the main point, that in practice may readily be used at proper times. A complete understanding of all the subjects hitherto treated will be greatly assisted by the thorough study of good compositions : for individual experiment opportunity will be afforded in chapter nineteen in the third section of this book, in which we shall recur to these topics. CHAPTER XV. Passing Chords. Passing- chords are those which like passing notes in several parts appear in smaller subdivisions of the measure as real chord-formations, but whose entrance and treatment deviate at times from the general rules of chord-connections. One species of these has been already seen in those passing notes and appoggiaturas in three parts, which assume the form of a chord, e. g. in Kos. 271 and 272. So in one sense most chords formed upon an organ point may be called passing. There are, however, other cases of this sort, which we shall here explain. As, in the main, passing notes and appoggiaturas rest chiefly upon rhyth- mical relations, it becomes necessary also, for the explanation Of passing chords, to glance at the different divisions of time. It is known that in simple even kinds of time the natural accent falls upon the first part of the measure, whUe the second has less weight. Now if the harmonic progression be simply based upon the two divisions of the measure, so the harmonies also, which fall upon the accented part (thesis), must be regarded as the most important and as the point always to which the chords of the second part are directed : MANUAL OF RABMONY. 189 276. I ^ i^ =2^= -'g- — T— g f-- g P^!g-/v=4-— -^ ^ rirp-^: In this sense the chords in the second half of the measure may be called passing chords, although moving thus uniformly their character does not stand out so prominently. That this has been so understood in theory, though seldom plainly ex- pressed, is proved by the fact that greater care at their entrance has always been bestowed upon the chords on the thesis, and much that was inadmissible allowed to those on the arsis. The character of passing chords, however, appears more distinctly in harmonies which are assigned to the lesser divisions of the measure ; as in the following examples : 276. ^=£ P^ :^ :J- -&- ZSr ^ ^m ^ J 7b 2 7b i -id J -^- -»-(«- 2,77. =s= zzrai ^=t -tr-t- =i=i :_ — SI lai ^W I -t—^- =t:* The peculiar appearance of the chord of the Sixth-and-Fourth in example 276 a. and c, as also of the Seventh-chord in c. is to be explained only as a 140 MANUAL OF BABMONY. movement of all the parts ly degrees in the character of passing notes lo tht position aimed at (the chord on the thesis of the following measure.) These parts may appear still better in their character as passing, if one part be sustained, e. g. the Bass 277 a., or the upper parts b. (see above 277.) By the use of both methods arose the part-movement in 276 a. If this condition (the movement of parts by degrees) be fulfilled, then aU chords may enter free, and find explanation in the chord which terminates. 278. r3^"5. ^ :t=t *— al- "rf~^T^ — r " ^ f ^''' i 1 ^ -a—f- -a-ft. Eemarlc. — The free treatment of the seventh before mentioned finds its warrant also in this explanation of passing chords (sec N. B.) In the simple uneven kinds of measure the accent falls likewise upon the first part, while there are two parts of less weight. Passing chords will appear thus: 1— ^ * * ' 279. 7 6(, 9 W^r Smaller divisions of the measure may also contain passing chords, exam- ples for which are not necessary after what has been said, neither for the compound kinds of measure. Here also the study of good compositions will serve to illustrate and assist. For individual exercise the following remarks may be in place. All chords indicated as passing will either progress according to the known rules of harmonic connection or deviate therefrom. In the former case, the most frequent, no further remark is needed ; in the latter it will depend on a flowing, melodious movement of the parts, as well independently consid- NANVAL OF HARMONY. 141 ered, as in relation to one another, whether formations of this kind are to be considered correct. It can only be said in general, that here also the tnovement of the parts hy degrees will determine ike character of the passing chords, and that all such passages must be estimated with reference to the rhythm, Tempo and character of the piece. CHAPTER XVI. Means of Modulation. TiiE term ■'modulation has already been explained in chap, eleven. Having there treated of the proper method of determining all modulations, we shall now discuss the principal means of producing them. The art of 'modulation consists in discovering such harmonies as stand in relation to two or more keys, that through them we may pass from one key into another. Any modulation can be effected in different ways, and will serve various purposes. It may be first: sudden in appearing, of short duration — and passing, or second : with longer preparation, seeking the new hey as an end and acting longer as a basis, ' In the former case it will employ the simplest means, be decisire, but leave the new key speedily, and of itself even have no determined validity : in the latter, it is usually through various means prepared and carried out by degrees, seeks to impress the new key upon the ear, and itself leads to a finite conclusion. Thus in the following example 280. I Se gte -V C: F: V- ?c:ii J=j G: V, 2 £^« 4 7 C: I I2ZZ ZZ2Z 142 MANVAL OF HARMONY. the modulation is passing, changing often, without essentially leaving the main key C major. This kind of modulation is only adapted to the keys nearest allied, and though others more remote may be reached by special and absolute methods, their development must be guided by perfectly natural and organic connec- tions, or they will appear unintelligible. In the next example, however, the more remote key becomes the end, which is gradually reached ; the original key is wholly abandoned, and the aew takes its place : 281. E^ ZjZ. H- &- 7b -^^ ^_,g r_ ±^ 5 60 It 1 6b: vii°7 Bb:I /; V, Eb: V, r^lyJi^ :taz This example shows clearly how the extended modulation, having the new key as its end, makes use of the passing modulation in order to reach it ; the rather, as it was not the purpose here to pass quickly into Etj major. Unless these short phrases are employed as interludes between two pieces of different keys, or as exercises, their use in composition must be in a special manner, as upon this very formation of modulations rests in part that also of periods and their connections. This is, however, an important branch of the study of form, and has to do with the order of modulations in a com- position, consequently is foreign to our present purpose. Remarh. — An explanation of this may lie found i)v the authors work : " The principles of musical forms and their analysis." At present we take as exercises the formation of such modulations, in order by this means also to promote skill in the use of harmonies and their proper connection. In discovering the means of modulation, we pay no regard at present to the kind of modulation, as they may serve for both kinds indicated above. The first and simplest means will be itself THE TONIC TRIAD OF THE NEW KEY. If this triad, however, already forms a part of the first key, the intended modulation will only be definitely determined by what follows, particularly if it be the dominant-harmony of the new key. Thus in the following MANUAL OF HARMONY. 143 example in a. there will be no modulation perceptible, while in h. first the third harmony makes the key of G-major to be distinctly heard : lar :az — xs LI — % — X— ZISZ i 282. -§:r sr- -TS- In the case of remote keys, indeed, the effect of the irdnor triad as the tonic may be more decided, yet this also will be followed by the dominant- harmony for the sake of clearness (in cr.) ; but the Ttiajor triad is more readily received as a Dominant (b.). 283.^ ^^^^^ iffir ^ C : I /; 1 Pg i2z: ~SIZ zsz 1^^— ^ III e: I i =s= W -¥^- e&- 321 :3Z ISI C: I a: V I C: I Though the iorajc triad used as above for modulation be so unsatisfactory, yet one position of it, the chord of the Sixth-and-Fourth, has the property of rendering a modulation thoroughly decisive. For as this readily forms a part of the closing cadence (see pp. 49 and '53,) with the same effect it produces also a sense of modulation, provided it be not used like a passing chord, but enter on the thesis. But also in this case the dominant naturally follows, the modulation not being complete without it. 284. ^^^^ -.ssz: s; i^ ZSI t=t= ^ 7 :3i I G:I VIC: o: I "V, la: '^m .i_# I C: d:i 144 MANUAL OF HARMONY. On the arsis it will not indicate tlie key so decisively. 285. i Efci 6 i 7t) -g- ^ -As — ^ — M= =f: ilEz zso ISZ # :2z: 1 All the ahove examples, however, point to a still more effective means of modulation ; this is the DOMINANT HARMONY. The triad as well as the seventh-chord of the dominant appears as the most natural and best means for modulation, since by it (particularly as regards the dominant-seventh harmony) the key is paost unmistakeably fixed. The modulation through the Seventh-chord of the dominant may take place without any intermediate chord in the following manner. According to the principle that that harmonic connection is most intelligi- ble of all, which is effected through similar or sustained tones (preparation,) we may modulate from the tonic major triad through the dominant Seventh chord directly into all the other keys, except those of the minor and major third and the augmented fourth. From C major then we may pass to all other 'keys, except E Jlat, JS and F sharp (whether major or minor, need not be determined at present) in the following manner : From to d: i F: c — raz 286. i^i^iE :g.-5g.-^r _g^^r^ M |s^ - -or -TSr G — C — D\): or: W^^^^^^ G — B\): 3C=^ -^52^: WW In all these examples the similar tones, connected by a tic, effect the tran- sition to the dominant of the nest key, thus from C major to d minor the tones g and e, which become the Seventh and Fifth of the dominant-harmony, etc. MANUAL OF HARMONY. 145 Remark. — We need only hint that these modulations are attained als 3 through other positions of the chords, e. g. : C — A: 287. =^ *- JZl Eg^E 12= -a- i If we wish to modulate in the same manner into the three keys not found above, this may be done by the insertion of a chord (a triad is simplest) which supplies the desired connection, e. g. from G 288. B\}: G — E: ^P^fzr EEi=i^ig=r^ =|r±g=£-^^i=fc|^ir^i==^ ■P#-- From minor the modulation will admit of these forms : _(&_■ From a to h: — d: 289. ^^^S^f — F: Ei^^zigz -i^ zar. -^53?: -ig~Z ~o' ^ I G: B\). ia= a=-^ =^is =g i -&- - g: -*»- S:5= -»- |2g- Into the remaining keys C, Db, Eb, F:}j! and At» through a connecting chord : , From, a G; 290. M :srrrs= =ai — ■P#-- a — Zib; o Ef— iE^Ei^^^3i^^ jETj: IS5=!=^ :2: ^^3 =22= s==iEkls^i E^^=^:^i .4b: ^^^^ ^ m^sMm It is understood that this method of modulating is merely adduced as the simplest principle, and that a modulation need not invariably proceed in this manner ; also that as simple harmonic connections can be effected without a sustained tone, the same will be the case with modulations, as e. g. the follow- ing may take place without an intervening chord: 146 MANUAL OF EABMONY From G 291. to E\): C — — G. =l2^=i ■^SSI^JTJSS. |ii^i=dfcLf&8i^i: :3= -gig Sr 5= -V- Still for the connection of harmonies, and of keys especially, it will always be greatly beneficial to become thoroughly familiar with that principle, and for this purpose to write out modulations from all the keys, bringing the chords at the same time into the most varied positions, and to illustrate these connections by playing them on the Pianoforte. This mechanical practice wUl greatly promote facility in the use of all the means of composition.— There is another chord which shares with that of the dominant-seventh this aptness for modulation. This is the DIMINISHED SEVENTH-CHORD. ' This chord, which in most cases takes the place of the Dominant-harmony, will often prove better adapted for modulation than the latter, since its appearance is less harsh, especially in cases where seventh and root would have to enter simultaneously without preparation. The following examples wiU show the use of this chord. 292. This chord, beside the above application, exhibits stUl further capability from its enharmonic nature. The following chord, precisely similar in sound, but differently written : 293.: ^^^^^^ wiU belong to ^our different keys, namely : in the first form, / minor, in the second d minor, in the third h minor, in the fourth ab minor. Hence a fourfold modulation becomes possible : 294. Fro mC to f: g — d. O — b: G — ab Now as all the diminished Seventh-chords can appear in the following Hiree positions, as can be most distinctly seen on the Pianoforte : MANUAL OF HARMONY. 147 ^''' %^^^^ each of which, howover, may by enharmonic change belong to four keys, we thus have modulations for all the twelve keys in minor, to which in many cases may be added the twelve in major, as this chord may often be used in major in place of the dominant-harmony. As far as the intimate connection of all the keys is concerned, and the variety of harmonic connection, it will here also be very useful to write out diligently this method of modulation. Although in composition itself this kind of modulation proves useful iu many ways, yet it should be at the same time observed, that it ought not to be employed too often, because with its facility of application it loses in artistic value. Of similar use, that is by enharmonic change, though not in so extended a manner, is THE CHORD OF THE AUGMENTED SIXTH-AND-EIFTH. Its similarity in soilnd to the dominant-seventh chord : 296, Lte renders it well adapted, in conjunction with the latter, for modulating into certain keys through an enharmonic change, e. g. FromC to b: 1!\) 297, . ^^^^m^^^^^^^M -Tsr C: V, 6: 11° 7 I V I Eb. V7*ii°7 I V i Though we have been seeking above the means of passing quickly from one key to another, yet, as it is not always the object to effect a modulation quickly and decisively, we may to acquire readiness extend our exercises and arrange them thus : From one key to the other through the triads of different degrees : From G to d through the triad of the third degree : % 298.^^^,^^^ 148 MANUAL OF HARMONY. From C to d through the triad 299- i i of fhefowrth degree: of the fifth degree: of the nxth degree; M '^2Z -6>- -^-^^3BZ IZ2I of the seventh degree: -eg — /s — SI — ;^--u .S>- -—- —-—izz -& 25- ia= =^=^ =^» i— ^ From C major to E through the triad of the eeeond degree: of the fourth degree: of the fifth degree: 300 i of the sixth degree: of the seventh degree: 3ZI 3E 32= These liints may suffice, in order to learn to form other modulations ob the same principles. Extension of the Modulation and its conripletion through the Cadence. The above-described process of passing from one key into another, was based upon the simplest and most natural means. If we wish to extend further a digression into a new key, the above means indeed will serve this purpose likewise, only we must not apply them so abruptly and directly, but make use of the passing modulation mentioned before, aiid introduce the new key only gradually. The use of the cadence- formulas, however, will best determine the key we arrive at. For this object the following kind of exercises may be employed, e. g. Modulate from G major through d minor, a minor, G major to e minor. This woxild be performed somewhat thus : 301. J :^ ■Ei: iiiifesi^ ife ^-zj:^tl>z ¥ :^ ^ fe C: Ici-vii", «z G:V, f V, -g'-'g MANUAL OF HARMONY. 149 In adding tlie cadence the following should be observed : If the modulation take place through the chord of the Sixth-aud-Fourth of the tonic triad of the new key (see p. 1 43,) the following of the dominant chord with its natural progression is sufficient to create a cadence, e. g. 302. i i2i X -^ 1 In other cases the extended cadence or the familiar closing formulas will be requisite in order to determine the final key. As the simplest of these formulas may be used the following : 303. ) ™' »^ in other positions: J&L =Sl 1^ ■S- -^- 3ZI r^z i2g: -w % ZZIZ :2^: ;sz =??:: -^ ^^- 6 5 Igh m -^ ZSlZ ZJ2Z I in other positions: ■^ -Jsg,. 32SI -&- ?Z= I^= ::j^z :;g2— .gz-'-ig: ■^- §i=E i zst: If these cadence-forms be added according to the position of the last chord of the modulation, the latter is completed. This may be shown in some of the former examples. The modulation from G to E flat No. 288 ends there with the fifth in the Soprano. To this is added the cadence in the position corresponding to that last chord, e. g. : 150 MANUAL OF SARMONY. 304. From CiaE\,: Cadence : g^ T- 'i=l2^= f-^- -w =g=±£^i »E^ 6b % *b 7b i :^ =t22fc =te :b^ 1 The following modulation from C to a in No. 286 would require a cadenct in this position : From Cto o; 305. ^ 1^ GadeiKe. -^- :^- i J8^ 4 3 :-i Zfzz ^ The modulation from to ^, using the cadence under No. 303 J. : from G to £; Cadence: 306,.' (^ I ^^ *;^i ^y^^ ^p?^^fip= a^E :^ it. Lfe =?z= =^ or from CtoDb.' Cadence: - 13= 3Z= zsz jBI i or thus : 312, 'm^- isi The addition of the middle parts will not now be difficult : G C d G C 313, C _ZS[1 SOPBANO. Alto. Tenoe. Bass. ^^ ^■ JW S ii$^ :irsi zsc d 1^ ■zsz 221 I'lg~ 3Z= The above may serve chiefly as an illustration of the exercises them- selves. The next will furnish occasion for studying the principles of a good Bass- movement as well as a melodic part-movement in general, so far as the simplest harmonic progression requires it. Examples incorrectly written out will best serve our purpose. Exercise with fundamental tones given. (?7 814.: SE izz: c 32= d Gi G Bemark. — In working out this and subsequent exorcises, avo sliall for the sake of room use the Violin-clef, writing the parts on two staves ; most urgently recommending, how ever, for individual labors the method of notation employed in No. 313. MANUAL OF HARMONY. Let this exercise be written out thus : C F Q-i G d Gt 153 816. is ISZ zaz _a_ zsz -19- 112L =ffi;: 1 ese SL -s,- 'Jsn -T There appears in this example no violation of the rules thus far known for progression and connection of chords, and yet it is wholly objectionable from the stifihess, weakness and lack of firmness in the Bass. Excepting where there is fin organ-point, a good harmonic Bass-movement admits of sustained tones only when caused by the necessary preparation of a tone, or counterbalanced by a decisive movement in the other parts. The above example also twice contains the chord of the Sixth-and-Fourth, which may afford occasion to say more of the use of this peculiar and diiii- cult chord. Of the use of the Chord, of the Sixth-and-Fourth. The infrequent use of the second inversion of the triad, the chord of the Sixth-and-Fourth, arises from the fact, that its appearance is tied to certain conditions. In the first place, we find it oftenest in cadence formations, as the preced- ing examples show. Then it appears in the same character in viodulation (see p. 142.) It may enter abruptly too in both cases, but is not to be regarded as a passing chord ; on the contrary, it must always fall on the thesis. Beside these instances it appears most naturally as a tonic, dominant and sub-dominflnt triad under the following conditions : a. When the fourth is prepared : b. Wlien the Bass moves by degrees to the next new chord, or is sustained. The following examples show the application : 316. :z^- 6 4 zs; :ai It s :3^Sz r 154 MANUAL OF HARMONY. ^ i ^P ^m -f—r £ E^ In example a. it appears most naturally, because it is based upon the Tonic, Dominant and Sub-dominant, wbile on other degrees (i.) it readily produces a sense of modulation. Used upon the arsis, it may also appear, beside according with the above conditions, with z. ^preparation of the Bass. 317. i t^ ■^=f^ -JSl 3?- eet 4 ^= ?^e jSZ As in all these examples the chord of the Sixth-and-Fourth appears either as a passing chord (on the arsis) or as above in the character of a suspen- sion (on the thesis,) its effect on the thesis with a preparation of the Bass is much weaker : 818. igi rS= --^ zsz 1^ ^ ^^ =^ i|=tr: Often it appears also as a suspension itself, whereby the preparation of the fourth is fully vindicated. zs: ai ^^i 319. zzn /2r r zsz =p — -tst- ia= ^=1 MANUAL OF BABMONY. 155 In the second case still more decisively, as it appears in a chord that seldom occurs (that of the third degree.) That the chord of the Sixth-and-Fourth, however, where the parts move by degrees in the smaller divisions of the measure, can in passing enter without preparation even, as : 320. < m :^:? ^~ -Jen ^-^ ^ * i — li^^ will need no further explanation after what is said in chapter fifteenth con- cerning passing chords, and after examples 276, 279. Berriarh. — The frequent necessity of preparing the perfect fourtli in the chord of tha Sixth-and-Fourth has induced many theorists to class it among dissonances. In the division of intervals on page 17 of the introduction to this work it is classed with the consonatices, and the reasons for it are given on page 20. The uncertain relation of the perfect fourth and the necessity of its preparation appears only as against the Bass or lowest part, and in general only in the chord of the Sixth-and- Fourth, since even in the chord of the Sixth-Fourth-and-Third this necessity of prepara- tion does not always exist; as regards the other parts, the perfect fourth is to be treated precisely like any other consonance. With actual dissonances this is not the case, for they retain their character throughout) whether lying in the highest, lowest or middle parts. The chord of the Sixth-and-Fourth of the diminished triad can seldom be used in four parts, showing itself to be too imperfect. 321. iS: -f^~ It will occur, however, in three-part harmony, where it often supplies tha place of the chord of the Second (see later : Three-part movement.) Beside the condition of a good harmonic progression, that the Bass part shall form a good and intelligible foundation for it, the second requisite in THAT THE PROGRESSION ALSO BE MELODIOUS. Certain skips have always been properly classed as unmelodious pro- gressibns. 156 MANUAL OF HARMONY. A succession of two fourths or fifths in the same direction e. g. : i 322. ie= These skips are better thus : 323.^1 1 IZZ Even skips of a sixth are more practicable as thirds in contrary motion, if the position and compass of the parts admit of them: tetter: better: 324. :2i :si^ Skips hy aucjmented intervals are lo he avoided as unmelodious, diminished, however, are serviceable : not: better: not: fc better: 325. ZZ2.Z ZZZZ not: better: not: better: S2= lEZ ■¥-- Deviations from this rule often occur ; they find their explanation in the formation of the melody or the peculiar character of the composition gener- ally. The observance of the rule in theoretical study will always be very advantageous. A skip of a major seventh is viholly to be avoided ; hut that of a minor seventh is praciicahle only in an inversion of the same chord. not: not: 326. gi^ !ffl_ 1 lEZ IZ2I The last in some such harmonic progression as the following : not good: not: not: ^=i=g=rL-gZ Tr gj; 827. jSZ. :^ w- 3z: 321 =g= JlE 3Z= ^ 6 To- MANUAL OF HARMONY. 157 These few remarks contaiu the chief features of a good melodic progres- sion of parts, and for the next, simply harmonic, exercises particularly, will prove sufficient. It should be further observed that these rules apply not only to the movement of the Bass, but in general to all the parts. The exercises given under 314 may with an improved Bass-progressioii be written somewhat thus : 328. ^^^ 3E § 3= -&-^ -Tj- ■^r §iE^E^ ■:^z=-=3- :jsz 328 b. ^ r-~ 131 -fi- ^! -e>- zsz C — F G zzc G — F "Ty 4-gL ^= di Gt G G a d Gt G dn ^fc zsz SZII^C r Gi di G a di Gi G The next example leads us to explain an important and difficult part of harmonic connection and pai'tmovement. 329. F Exercise. 6° G dt Gi --fa=: {=a= f=:g= irsz The following incorrect solution may serve to illustrate : C F h° G a di G-i G 330.- i % -'-«- ifE^ s ZSl ^ ZSl^- ijsai 12^: C^ rS= :=l= =?2= 1 158 MANUAL OF HARMONY. The errors here consist, first, in the doubling of the third in the Bass of the second chord, which gives j;o this and the following harmony an awkward position ; secondly, in the concealed fifth indicated between the fourth and fifth measures, and lastly in the seventh introduced by a skip in the last measure but one. As to this last, it can only happen with the dominant-seventh, when the root is already present (prepared) (see p. 70.) 331. I 3E P^^^^ ss= ■zsz zsn The free entrance of Seventh and root is more endurable and less liarsh in contrary motion, -a e, „ a- 332. p =221 but in direct motion either wholly objectionable, or only to be used in speci- ally favorable progressions, when perhaps as in the first example of 333 the root g is already present in the preceding chord, although in a different part. 333. =az =a= 122= The first of the above-mentioned errors shall be corrected in the sequel. The second is more important, and leads us to speak in general or CONCEALED EIFTPI AND OCTAVE PROGRESSION. We have already spoken on p. 29 of the nature of these progressions. Concealed fifths and octaves arise, when two parts progress IK direct MOTION yVom a different interval to a fifth or an octave, e.g. I Concealed Fifths; IE 334. 3= zsz -«— ff- -•iS^ i Concealed Octames: -<9- =a= ps= •lar 38= -»-&- =i=i; TSr- MANTTAL OF HARMONY. 159 These fifths and octaves become obvious, if the skip made by one or both parts be filled up with the intermediate tones, as is indicated above by the black notes. Since in all four-part harmony certain concealed fifths and octaves may occur, without which the choice of chords as well as the movement of parts would be very limited, but others again are to be avoided, it becomes neces- sary first to examine more particularly the mode of their appearance. The attempt to furnish positive rules for their use, sufficient for all cases, has never yet been successful, nor could it easily be ; only general remarks therefore are to be made, which nevertheless for special cases will afford a standard of criticism. Concealed fifths and octaves between two parts may occur : 1. when one part moves hy step, and the other by skip ; 2. when both parts skip. In the former case : a. by degree in the upper, hy skip in the lower part ; b. by skip in the upper, hy degree in the lower ; As to the position of the parts, relatively to both cases : a. between the extreme parts, b. between the middle parts and C. between one extreme and one Tniddle part. Concealed Fifths and Octaves in the extreme parts. They are allowable, if the upper part move by step. a. Fifths. h. c. Octaves. d. e. 335. -zr- :32is5:^:?3Js-:!3z:: rsr: 'no. §±$E is: 2z: It wUl be well also, if one part at the same time move in contrary motion or be sustained, as in example 335 a., b., c. Not so if all the parts move in direct motion (d). Eemark. — Though the above rule will suffice for many cases, yet it will not hold good universally, as is seen in the above example 335 e, which is not to bo counted among those having a good part-movement, the progression from the Sixth-chord c being a very forced one. Likewise should be called to mind what has been said on pp. 35 and 36 of the cadence- forming Bass-progression, namely, that concealed octaves over the leading tone or generally over a half-degree are more tolerable than over a whole degree. 100 MANUAL OF HARMONY. In the examples above cited, the octave appears throughout as root of tlie chord ; cases where it forms the third of the chord are more doubtful, and are consequently to be used with greater caution. not: not: 336. Even as the fifth of the chord it is not to be considered good : 337. '■^^^m TJemari. — In case of a concealed fifth the hwar part will always be the root of the chord. Concealed fifths in the extreme parts are forbidden ichen the vpper par moves by skip. 338. In all cases where a seventh aids in the harmonic connection, as in b., d., e., the progression of fifths seems more concealed and less harsh. Concealed octaves in the extreme parts are not absolutely forbidden wlien the upper part moves by skip. h. not; d. not; 839. P#^ ai ^Etgz 122= Ss; lac -& — o- f 3S zsz 2?!5?e2: a= g j2_ Here also those cases, in which the Bass moves a half degree, are seen to be the most endurable. What was said in 336 and 337 holds good concern- ing d. and e. Concealed fifths and octaves in the extreme parts are forbidden, if both pa'^ts skip. MANTTAL OF HARMONY. 161 340. "When they form merely transpositions of the same chord, they are not to be regarded as errors, because they are really not then fifths and octaves progressing to other chords. -»- -y^ S2I 341. _:& zsz -s^ _g_ ZSl- Concealed Fifths and Octaves in the middle parts. Although the movement of the middle parts should be quite as pure as that of the extreme, yet their position being greatly hidden by the latter allows them also at times a greater freedom, especially with regard to con- cealed fifths. Concealed octaves should be avoided here, for the sake of a good relation between the parts, and the case of concealed fifths, beside the rules before mentioned, must principally depend upon an otherwise good harmonic connection. A few cases may be annexed : 342. Concealed Fifths and Octaves between the extreme and middle parts. Here also the points to be considered in such part-progressions are rather to be found in a good and natural harmonic connection, than to be settled by tnerelv mechanical rules. A few examples may follow : 162 MANUAL OF HARMONY. :2Z= iSte22= '-S>lS^- Sisi S-fflL. 343. ii ^- liz ^=^^TrJ2^T--i=- ::§? is= i& «ot £roo(i: no<; -"g- :^:S^ Ei?S ia -fflj - e>- -7s— One particular case of concealed octave is specially to be mentioned, that over the seventh, which in all the parts is to be avoided as erroneous. 344. zgj!?-^ , feggy^gv -g3?^a^^;:g:"q..g_„ -^-•■*. i :s= zsr. m IffiZ 22: (Seep. 84.) What was said of octaves, applies equally to concealed unisons. Between Soprano, Alto and Tenor they should be wholly avoided, between Tenor and Bass, however, according to the position of the chord and of the parts them- selves to be regarded as concealed octaves. The cases, in which concealed fifths and octaves may appear, are so mani- fold, that it would be superfluous to cite them all, if it were at all possible. We may rest satisfied with the foregoing considerations, adding thereto the following maxim, which indeed is not written for those beginners who are still occupied with the technical or the purely mechanical harmonic structure, without regard to the higher demands of art : Avoid indeed concealed fifths and octaves as far as possible, but use them without scruple in cases, where, on the one hand, by so doing, a good harmonic connection results, or, on the other, considerations of a higher nature prevail, as the melodious movetnent of parts, use of given motives, or others. After this digression we return to No. 330, in order to correct the faults already moiitioned. MANUAL OF HARMONY. 163 It will be hardly possible in this case to correct the concealed fifth found there, which belongs to that class where both parts skip, because, even if tho Bass progression be in contrary motion, the evil appears again elsewhere. e.g.: 345. All that remains therefore in this case is to change the harmony itself and denote the fundamental tones differently. The change may be made as follows. 346. ^ — d-7 ff7 i^i '^ -f- lar isz i& I22Z 347 i ^ -^- iiE$: isz a isz d'7 ff7 IZfc -6>- ' I 6 S 8 i Exercises, 347 B\> =E= B\) e= -JZZ d gi Ci F ^ fc -E= -g^— I Kf- gi 164 MANUAL OF HARMONY. he: ^P — [~ s- II 2 .jii—i:. ¥ F sb g Eb g- Ci F ?SE 3C F Let the following exercise 348. :i: |Ji^^ i)7 G gt Ci F Hi 22= — is>- be -filled out tlius : 349. The errors here are indicated by the figures. The movement by skips of all the three upper parts in direct motion in No. 1 is not good, being contrary to the first principle of all harmonic con- nection and not at all necessary. A shipping movement of one or two parts can only happen, when (lie har- vionic connection (hj sustaining a tone or by contrary motion) is preserved in a third part. No. 2 also has the same fault, which becomes here still harsher, because seventh and root appear in direct motion without preparation, and thereby arrive at an awkward position, so that one is pushed aside by the other. It has already been mentioned (p. 72 and 158) that the free entrance of the dominant-seventh cannot but have a harsh effect, unless the root be already present and can be sustained in the same voice. Thus all. the following examples exhibit an undesirable movement of parts. -/s>-. 350. MANUAL OF EABMONT. 165 A few of these and similar passages could be excused for weightier melo- dic causes. The following examples may further serve as supplementfiry to what was said on p. 158 of the allowable free introduction of root and seventh in contrary motion : The passage in example 349 No. 2 contains also another error, violating the rule before mentioned (p. 153) under the chord of the Sixth-and-Fourth : that the Bass must not move by skip from the chord of the Sixth-and- Fourth. The third error in example 349 consists both in the concealed fifth, which is made all the more prominent by the skip^of the Soprano in the same direction, and generallyau the distended movement of the parts. The concealed fifth in No. 4 is faulty because it was unnecessary, as the Tenor could move equally well from b to c. That in No. 5 is better, being allowable with the movement of the Alto and Bass in an opposite direction. Exercise No. 348 is better written out as follows : 352. I; p^ :3Z ISI IffiZ ~Sz i£te -ffi- .€z j^. s= :si isi -O- 1 352 b. u- - -^ , s= Ex —ts- ercis es. ■s>- fi F^ /■■J 2 - »'&■ en G c )S>- = c:z; jSU D a — D -& G — n — G 3 D a a 1 tS> 1 D Ctt e : G G> IS> — a Si . -..a G D-J 0,1 2>7 O 1G6 MANUAL OF EABMONY. USee -s-^ -^ , -^ , g -,— gz^ T- ^ ? , s , ~S1 ' G — D — e^ a The next exercise — Et a B 353. pE^ I22Z C G Vt G /#°7 -Bt _e zsz ISI i filled out thus : 364. I :| :te^ 1221 Iffil 13" -ffl- ISI -^^ ii!^^^ fe te^Ji- _^_jfe: gives us opportunity to speak of an error, called the Unharmonic" Cross-relation. The unharmonic cross-relation (relatio non harmonica) belongs to the unmelodious progressions and in general consists in this, that a tone is imme- dicUeJy followed ix axotheb part by the same tone chromaticaMy raised or lowered, as here the g in the Alto by the g sharp in the Bass. To avoid this error, the following rule is to be observed : Immediate chromatic alterations of a tone shoidd always take place in tlie same part exclusiirli/. in which the tone occurred unaltered just before. Much as this rule agrees with every principle of harmonic connection and progression, yet there is scarcely one to which more exceptions are found in practice. Hence in manuals of later methods the doctrine of the cross-relation has been strongly suspected, and instances cited where the imfaarmomc cross- relations occur in a perfectly natural way, without investigating the cause of their not being regarded as erroneous. A few of them mav be here introduced : 355. 2JSZ ^^ ¥ ^ MANUAL OF SABMONY. f. 167 In all these cases the cross-relation seems to be fox-med not by the sim/ply harmonic progression, but either in the character of appoggiaturas, as in a., b., g., or by the shortening (contraction) of harmonic connections which are natural,, thougli too minute for Tnetrical organization, as in c, d., e.,f., h. The first needs no demonstration, and it need only be added, that this kind of cross-relation would occur mostly in smaller divisions of the bar, and the above notation in half notes is rare and hence inappropriate, since by them is expressed the simple harmonic foundation, and not those tonic elements which serve for ornament. The original progression of parts in the above cross-relations resulting from contraction is as follows : 356. I S #H= ^^^ ^ :J_-^ =5^ -(2- -iS>- kr. §ff^ p^! ^=i=a: i g^ -©'■ -r w- zsz t=1= --^^ Compare these examples with those under No. 355 at c, d,, e., h. 168 MANUAL OF HARMONY. All these qualifications, by which cross-relations have become naturalized, are not to be found in the following and similar cases, and such progressions as these must be reckoned as erroneous : 357. Entire freedom therefore in the use of cross-relations caniiot be justified. In all the above passages taken from practice, but apart from their con- nection, there comes also the consideration of the Tempo, and the consistency of a whole resulting from rhythmical divisions, serving to render these forms not unpleasant, but rather, precise. Under cross-relations is classed also a progression, known as the Tritone, an explanation of which here follows. Concerning the Tritone. The tritone is contained in the diatonic major scale, and includes the dis- tance from the fourth to the seventh degree, in the C-major scale the aug- mented fourth f-h. This interval from / to 5 embraces three wliole degrees, whence also its name : 358.1 E 3SZ It is regarded as unmelodious and incapable of being sung, because each of its tones demands a special progression, properly belonging to two distinct voices : 3= 358. i one of which must be disregarded in the progression, when the step is given to one voice : 360,: ■m ■4- in which case the melodic series would have to be formed thus : 381. P *==t MANUAL OF HARMONY. 1G9 That this, however, is not the sole cause of the bad effect of this interval is shown by the very common inversion of the same, which would likewise require a two-part progression : ''^•%4^ X i and which is equally intelligible and easy of execution, as the tritone is diffi- cult and repulsive. Remark. — It may be further observed here, that the tritone is based upon the diminished triad and its progression, as is evident from the above example 3G2 (see p. 38). The reason why this interval was formerly especially insisted upon as erroneous, was this, that in the simple harmonic form of composition then in use it constituted the only augmented interval, which diatonically presented itself. At the present day, with the extended use of all the resources of art, it is simply reckoned among the augmented progressions, which in a pure harmonic movement of parts are to be avoided as unmelodious, or at least to be used with caution. The points to be considered in the use of the tritone lie in its position and appearance itself. It may occur based upon one chord (a) or upon two chords (b.) e. g. 363. u. b. ^ ISI IE -^szi .^_ - sf^ :3Sm is€= 72^ ik-'^ -- E a 67 ZSZ ^ r^ 6? :i- -a- E -O- -|^ P8^ ^° Bt e Bi ISlZ Z2Z1 -J2Z r- - D', af ■O7 2. Harmonic accompaniment to a given mdddle part. This practice, which properly belongs to contrapuntal studies, cannot be commenced soon enough. We shall introduce it at first, indicating the roots. MANUAL OF BABMONY. 171 Exercise. Aeto. G C F O a dnG ■tt*-7V-^ — n — ^- — ^ —e> — — 73 4MJlp.-'*- . 367. In working out this exercise, the sketching of the Bass again will be the fipiit and most important thing. At the same time, however, the Soprano may be added also as the most conspicuous part. e. g. 868.. C G ISZ zsz ail C F G a d-! G O ii^ zsz ZSEL ZZ£1 -zi e) 6 S The foregoing may answer for three-part harmony. By adding the Tenor it will appear thus : 368. 1 ^ 13= -zr zsz I^I ZZtL 4: -zr zsi ^^ 1 T \ ~ ''\ ^'^ ^ 121 Exercises with, a given Alto. zsi 369 b. -fa-.yL, <^ ■ r ^1 f^ ^TT- j ^ fj q. T *!^ ■rzte -0- 1 — '^^' — 1 W-m \ |W — F g Gt d gi G F 3 F B\} G ;r(? — r— 19 1 r fs J l.-4' w - w =R^^ r— «l 1 ry — tS" ,./«' - £b c .i^ 4 C7 J c <« fS _«^ /^ AJ -^ 1 [ i ■ /5 i J" a! — g Ct At d e^ Ai d ■JSZ ZZZl ZI21 m £t> O c#7° d 172 MANUAL OF HARMONY. m ;EfeEE: , T-'^ T-lS- ZlZl 53* 1^ g D —T g B\, c g The treatment of a Tenor part will be the same. Dn Tenob. O 370.$Efc^3^ Exercise. G a F a— Gi laz Sketch of the Bass and Soprano : 371. ^. 'JSZ ZZ2Z zsa pi^f— i^i^f^ In four parts : 372. P IS2I ZSZ Si- iiie 122= P^ 372 b,^^^ Exercises -with a given Tenor, a. $ '^eTJPiZ- C G-3 G a d 3 ^7 a c G C ■i "- - f « fj I ^ o Gi ^ zsz i J?7 o f7 O £7 This practice should be continued, until the sketching of the Bass, as well as the management of parts generally, is perfectly pure and safe. In closing this chapter it may be further observed, that for a good con- struction of these four-part movements, a good position of the parts is MANUAL OF BARMONY. 173 especially necessary. The limits of the parts themselves must not be transgressed, nor the distance between them too great ; neither must they be brought too near together, which, however, does not apply to two parts meeting, e. g., on one tone. Let the following rule be observed in this connection : Of the three upper parts the distance from one to the next must not cover more than an octave. The relation between Tenor and Bass, however, admits of exceptions. Remark. — Transferring these exercises to the Bass part would be useless, so far as they would bo precisely similar to the figured Basses used heretofore. They can be used only (ovfree harmonic treatment. CHAPTER XVIII. Extension of the Harmonic Accompaniment. A given part in whole notes with harmonic accompaniment in half notef alternating in the remaining parts. This can happen through two chords, through change of position in one choi'd, through suspensions. The exercises may be indicated in the same manner as heretofore. 373. ^ Exercise. Gi SI ISZ The Bass may be sketched as follows : 374. ISI 22: a^=j: =^ =^- it =t: :E^ j^ In the second and fourth measures there appear sevenths of collateral Seventh-chords without preparation. These are called passing Sevenths, 174 MANUAL OF HARMONY. They move from the root, and always fall on the arsis. They may occur in this manner in all the parts. The addition of the middle parts to the Basa sketched above gives the fol- lowing four-part harmony : 375. The same exercise with a richer variety of harmony may be written thus : 376. I ^ zz J^° 7 gj;^° 7 ag7b dP g— 7 G I^ Written, out. 377. ^ zsi ^^: J I r^ =22^ \w- -«- -(2- f=T g te:p g=E]fcfa £ C p — fl 1 — 4- P- — I — -(S. -et. :^ 7b 4 6 3b -/ -g~::: The next exercise will show the use of suspensions. 378.^ J* 5[j ^ <^ sr >" -Bb -£?■ I G F b" CFG O a C-,\) d a, aj^" =^ ia=:^: ■gi — - ;5=b^=:^ i G ai D Q C Gt G d-, G Ea E ^ ^l—^-7S Zf- This choral, harmonized as above indicated, could be written out thus : 381. I ■^ -'s- i^ J- :Sz :g2z =iP; err 3^^^ 3^ J- 176 MANUAL OF HARMONY. 1 m 3 :2^ .3=f iiE^ W- ^ ~SI1 :?= -i«- :^ F^= "S =32^:=;^ P^ :^: •g- 3 -Jt ist ip=»^-- :::5S=: ^t^= -bJ -(Z- ^ H«- ■(2- :^I in -|5^ ^ =r^' ^#- g^^iE :f=P^7 T ^E fe=' .^-,-, ^ 1=t: Z2S; After sufficient practice and sureness in the treatment of simple harmonvj one may pass on to the further development of the part-movement by means of passing notes and appoggiaturas. To this end we shall say more of melody and melodic progression in the next chapter. CHAPTER XIX. Formation of Melody. We are not to discuss here the invention of melody, but its formation, and, what is very important for our harmonic study, the method of recog- nizing and using by the treatment and formation of melodies that wliich is essentially harmonic in them. This will depend on the recognition and compreliension of the following principles : MANUAL OF BAItMOMl. 177 Every melody, however carried out arid developed, has a foundation fully as simple as those we have used as exercises in our last examples. Therefore every harmonic movement of parts, hoivever complicated, may be traced back to simple harmonic connection. To see the truth of this, one must learn to discriminate between the essential notes and what is extra and accessory. / For this we choose the analytic method, and seek to develop the following melody, which -we will set down in the simplest form with the fundamental tones indicated as heretofore : 382. F — Bi, F B\, q C F — d ■ F C, F I W- ffil 3?:: 321 ISI 3:: jSZ -JBZ Both melody and harmony are chosen with a view to simplicity, and the latter may be. introduced in four parts thus : 383. -^-- TZl -^il is: -isi -ig. -Ci- ^. . iip^^ zsz. lEZ i ZS3SZ ^-- SL. ZEg^tZSl 6 1 i ■ -zr- Before proceeding to the farther development of this passage, it will bo necessary to premise what ought to be mentioned concerning the rhythmical farmation of a melody. A melody may be either a musical phrase consisting of a greater or less number of .measures without any fixed limit, such as often occurs as the theme, motive of a composition, or by means of counter-phrases, a separate, distinct whole. In the latter case it is called a period, and contains usually eight measures, having as counter-phrases two sections of four measures each. These counter-phrases or sections are often called " antecedent and consequent." 178 ' MANUAL OF EABMONY. The details of this subject belong to the science of form. See the author's work : " The principles of musical' forms.'' It is clear from its complete termination that the above passage forms a period, and it is first of all necessary to find the division into sections. This division is very often found in the cadences which occur in the middle of the passage, either as imperfect whole, half, or plagal cadences. Such a half cadence (in general : a close on the dominant) we find in our exercise in the sixth and seventh measures, and we may take the point, where the sign f stands, as the dividing line of the two sections of the period. The first section, the antecedent, therefore would contain seven, the conse- quent six measures, and must each be rhythmically changed to four measures. This may be done thus : i ^ -} 384. w=^- -fs^- =^: -«- liz By adding the harmonic accompaniment above chosen, we have a complete musical period. Likewise it may be seen at a glance that all further transformations into different kinds of time, e. g. into ^, 2j 2 or 2! time, can be very easily arranged, e. g. : i E5 385.fet3£ :i=32: ?;=T t=t » -\-ziT P ^ &c. '^^M- If^E . &c. I r-t==^ :& •-=— •-=P= ^- ' ii- &0. We pass now to the tonic variations of the melody and add thereto pass- ing notes and appoggiaturas. e. g. : !ififi,ii--\i-ip—f^i— =33rE^ -Fr'f , ^=^—A ♦— r~1- _J_. ^^1-1-1- \ = -« - -f-^-: P1E^_,_ -9— — ^ — _f — ^ -?i + MANXIAL OF HARMONY. 179 A still further use of all the accessory tones would give the following form: 387. I Adagio. lEfe^teSl >l#-^- Ik: gg|^?^3^E| I Originally. lEt :a= :#=F^: E-i i :^ i H j-ri-ri— I— I — — i^ -^ r— a- ga- !c=tt^ "F-' U :^ The himple melodic progression underneath will be easily recognized as the foundation. That the upper melody, however, is carried out with refer- ence to the original harmony, will be at once evident, if we add the other parts witJi the few deviations required by the upper part : ■ . 88S.< Adagio. - T^~~"~- ,^_^ "^ ^^ , J:?S^ S:^ f 1 1 'ii f 1 1 V \ -J- -£. J- ,. — .1-, I -jL r~i giFi=§i =^ J — d— T " i I ;5 g! i ^^^ ^ ^ T ze.-- S«-Ei4^aE m 180 MANUAL OF HARMONY. 'l-Mjz^ jq=3- qr:1: :^=3: •^m m TT B*-"- I J. i=ii m -2:: 3E As to the consecutive octaves in the middle parts in the third measure of this example, it is to be observed that these may be considered faultless, when they do not occur singly, but in a longer series for the purpose of reinforcing and thus Ijringing out a harmonic and melodic progression. The movement in this case is to be viewed as in three parts. Slight as is the independent worth of this example, yet it is used here merely to show of what development the simplest melodic and harmonic phrase is capable. The advantage of studying and discerning these melodic and harmonic relations is too important for us to omit making another experiment in the following interesting phrase. The fundamental harmonic progression is quite as simple as those exhibited before. 389 This passage will form a peribd ; the middle close is easily found in the half cadence in the seventh measure. "We pass over the various kinds of measure and select the following 390.' ^m "^^ MANUAL OF HABMONY. 181 Tlie upper part, adhering to the harmonic progression, may be developed as follows : 391. fe^feE^=»-^: :Sit-^r: ■ftrizilt-. •=^^ Ef^i i^sigl^igS The following passage from Beethoven's E-flat major-Quartett will show how the other parts can partake of melodic development : Adagkr_^^^^^_ Z^^J.^ f f LJ-^-f: -^~ A comparison with No. 390 will show the melodic and harmonic changes. A still further variation of the original melody from the same piece fol- lows here : • ' 893 pii^^s^i^^ |6^ a^3>i gi^ gi^ES d53E JS2 MANUAL OF BARMQNY. The otber parts apjiear -with the following changes : _394, 3 These hints in regard to melodic development may suffice here and be left for individual practice or special instruction. Remark. — The mechanical character of this whole treatment must not lead astray ; for certain as it is, that in composition the above is not always the mode of procedur* (although BeethoTen in the subsequent variations of this original melody must have in part proceeded thus), so our only object here was, partly to place in the right light the relations of our previous exercises to the practical side, partly to gain a clear insight into complicated compositions themselves. As concerning the accompanying parts, they resulted naturally from the simple harmonizing and needed little change, sliuwing thcmselvet., if subor- dinate, yet not on that account unimportant. It now remains to speak of other modes oi - I2t but somewhat in this manner 397. ^ -TTi- :;i: 1=1:: :^ i In a change of harmony the last note of a figure and tlie first of the next must not form a false progression with any other pai't. e. g. : not: ^_ . letter: not: 398 The harmonic figuration enables us to arrange even orie-jjart movements with greater fulness. The examples may begin with the following : 399. In one part: I ^=E :^feg — »— p-i-p- t=5==zpzl3i=P=?rtEt— ^==^::t=trtit:tE^— p— :^p::t— i ^ tt±s bSs ti=a tta t=i=d^=-=^ ^ &c. JtlAITUAL OF HARMONY. 185 It is easily seen that tliese plu-ases are calculated for a single instrument, as a violin or clarinet. » 400. In two parts : mr.w. V^- fcp .fl.^_ In three parts: in the middle part: in the lowest part: ftE -Z\-g- -a- :=-^q^>s;qr*Si: if a=& —^ — i — ^ — I — ^^* in the highest part : ■>-t-^ in two parts: After 'liese experiments with the above example, the figuring in four-part movem at will be equally easy to accomplish. 186 MANUAL OF BABMONY. Instead of this we rather take as an example of varied iigiiring the follow- ing passage from the Quartett movement of BeettCoven cited above. 401. !— izipzri[ir^=p:iEpig=i pgp7tiijcr i pizz. itl*=:!2aii ^=^ -P^ ?•- -*- I ggfeai^?-^^? ^ i^i^?=i^?=j^^= -•- -^- -^- -•- -» — •- ^^^^^^ ii^^s ffl _j5 ««T_ 5?E3^gE 6^^^§^^^^=S^e!=^ iiig^^E^.^^^^^^^E& MANUAL OF BABMONY. 187 fe^ -^r- -r iS|=E ^=5=1: =^=F m ■pr-.— The whole of this rich development rests upon the base given in Nos. 390, 391 and 392, and in aU cases where there is a change of harmony, the progression of parts is carefully observed. — If one desires to gain a clear insight into compositions so elabotrated, and learn to comprehend their inner harmonic structure, it will be very well to trace back pieces of this kind to their simple basis ; labor of this sort will be repaid by enriching his knowledge on many pointy, and qualifying him for individual productions. CHAPTER XXI. Exercises in Three-part Movement. In our exercises thus far we have used with but few exceptions four-part harmony, and although the same admits of greater fulness and seems most suitable for harmonic connections, yet three-part movements also are of great use, being particularly adapted for greater skill and variety in the manage- ment of the parts. We be- SH^ ^^-- ?z^f^=^#z: ■«^T-^ ^-rlS- fl ^-^^ g£ ^. P- ii 8NB. :^=s== :?2=5: -7^^ r =?z- g=^7|:^=g -^ ^ rpa: fcfc -\= i 6 3 ii53 2fc -zi: In the fourth measure at NB. we find the chord of the Sixth-and-Fourtli of the diminished triad e-g-i\}. It stands in place of the chord of the Second h[)-c-e-ff, the root of which c is here omitted, for in four, parts the passage would stand thus : MANUAL OF HARMOITY. 189 404. < i -^ — ei^injss. 5 3 Compare remarks on p. 155 concerning this chord. In the fifth measure a fourth supplies the chord. Though a fotirth, to ba • sure, can neither in three-part, nor in two-part harmony, pass for a complete chord, as is the case with the third and sixth, yet in those instances where the chord of the Sixth-and-Fourth in four-part harmony can be used on the arsis as a passing chord, in three-part, for the sake of a better movement of parts, the Sixth, or the third, of the fundamental chord, can be omitted, so that the fourth shall stand alone, designating here the root and fifth of the original chord. Sometimes in two-part movement the fourth will represent the chord of the second, especially in the case of a passing seventh, e. g. : 405. :^E I I ist lai zsz With four parts the above passage in example 403 would be thus, when completed : 406, -w- 3^i=| ^ ib I w S By the skip in the Alto part, in the eighth measure of .example 403, the chord of the Sixth-Fourth-and-Third is made complete. In the tenth measure appears a chord of the Sixth-and-Fifth. Eeally the fifth here is only a suspension of the fourth, which, however, by the progres- sion of the Bass becomes a third. With four parts this too is made clearer : 190 MANUAL OF BABMONT. 407. I m ^^ 3: isr-^: -fi-s^ S^ =2t 2^r The last measure of example 403 shows in the Octave F that may appear in such cases even without the third and fifth. It is seen in the first and second measures of the next example movement of parts often requires the omission of the third. the triad that the 408. _^ o_ ^^_p^^^ -f--^— W- - a- -+ : ^-^-^ \ — ^h-r- -fzp^^S^ F5 — f ^-^r-ir^ — -fl? '^ — ^— + 6 5 4 # ^ .-C 1_ \- : 7 6 - * 3 eq . 1 F ^^^-1 fiJ iS^-^ - E^E =^ =^=F?2: I itJii =t=tt §^ fe -^-r^ 1- 6 6 — 57 te^=fl/ i t::tt 22= In the fifth measure at NB. what is really a suspension on the ninth appears through the position of the parts as a second, which must occur very rarely and only between Tenor and Bass. It should be observed liere that there can be no suspension on the second at all, because the second of itself 192 MANUAL OF HARMONY is based upon the inversion of tlie seventh, and conforms to the progression of the latter, e. g. : 413. ^ ^^- or: s- Iiivermm: -^- JExercise in a middle part. Tenob. d A JB\) ge° d 'rr 414. ^^ji^si c#= -zz=:.—s>- a^ 3JZ The Alto is taken here as most convenient for the highest part. fa... 415. ^-m. ■ze:x=^. :^ -TS^ ISI tetesB^li zsc s # ISI 3 6 fc # ^i3. Hi^pB^j =2=:;;=;^ is: e^ :fa:^ 1 i The same exercise with the following designation of chords : dg A—TBbGGF B\,e° d B\)F g 0"= d A d " "" zsz Written out: I^ :a= *=^ ?z= 417. J :I E^ lazi =221 |igEg=:3:[-^-Z=g^g^ zgfcit^; m -I u i ffl=p <>> -r pg 6,: £^E: 12=;: m^ I5E 3 =i=::?j 6 MANUAL OF HARMONY. 193 The last measure but one shows that even the sixth may be a suspeniiion. The former exercises, proposed for the four-part movement, can ' 3,lso be made use of here for further practice. CHAPTER XXII. Two-part Movement. The great barrenness of the two-part movement in a purely harmonic ••elation renders it seldom adapted for other than contrapuntal labors, in which alone it derives any pec\iliar importance, and even then is used in movements of several parts e. g. in fugues. If indped, for a simply har- monic use, a metrical and rhythmical variety in the formation of the parts will render a two-part movement tolerable, so the contrapuntal develop- ment of two ■ parts can alone free them from the monotony of nnmerous consecutive thirds and sixths, and give it essentially that completeness which every part-movement should have. There must always be in this movement an omission of one or more inter- vals. In triads it will oftenest be the fifth or the root. When Seventh- chords are used, the seventh of course must not be wanting. Octaves and fifths should seldom be introduced, as the effect is too bare : the fourth would only be admissible in a few cases, where the chord of the Sixth-and-fourth may properly stand, or when it occurs in ulace of the chord of the Second (see p. 182.) Example: G C -- F JZ. .s>- 418. 419. r — z^ — —^ T--— T-75^1 r~ — 1 fy ■y U * ' ■ 4JS WritUn out: „ ta f3 " \ f t? ^ 1 1 Wi o 1 ! 6 3 - «2 ■ 6 -rj ■ 6 — fii— 1 3 6 6 3 Cf- -1 3 -6>- 1 j2. V j-3-tp-*' l::=:i I 194 MANUAL OP HARMONY. The omission of intervals is plainly seen, on comparing the fundamental tones in exercise 418. There will seldom be a confusion of harmony, since each chord explains itself by its position, that is, by the harmony which pre- cedes and follows it. The same exercise with different harmony : F-n A zsz d ■€>- a fS Ca Z2ZZ lEZ 1 420.=^: zsi ^-- 421. Written out: -ea- -iS>- f >^ \ -V 1' 6 2 6 5-6 6 ^2 — 4, 1 f^ ^ •■■' { ^-^,-^ ?- "1 -F— ■ . >2. — 1 f s>—\s> ^- -J—^- \ —H ■ U 1 -1- I i| 1 b2z_| — i 2ZI w ^ ^- JO. ^ ^ Most of the exercises in the third section pass into the domain of counter- point. The difference lies in this, that here the succession of chords is prescribed and the part-movement remains to be carried out, whereas in contrapuntal studies a knowledge of harmony and a safe use of it is presup- posed, so that the series of harmonies can be left to individual choice. These studies may therefore be considered useful as preliminary to those, furnishing at the same time a view of the relation between harmony and counterpoint. The exercises in the following chapter are to be regarded in the same light, though the restriction to a fixed series of chords is done away with. MANUAL OF BAEMONY. 195 CHAPTER XXIII. Harmonic Treatment of a given Part in Melodic Form. By the melodic formation of a part is not to be understood here that richer ornamentation exhibited in chapter nineteen, but we merely mean to avoid by means of metrical variety the simple choral-like progression of our previous exercises, and thereby afford opportunity for learning to develope the parts better in the harmonic accompaniment. The following exercise will make this clearer : 422. 3ZI ■JSL -^^7?T Z?2jL r m *=^ ■^-7^3 1 ^^ rfj2^ 6 9 8 7 6 =^ :?z: 7 6 4 6 r ; ^ =35 Itt =1= This treatment needs no further explanation after the remarks under three-part movement. The harmonic treatment of this melody as a middle part will show its 0iany-sidedness, and may be recommended as a useful exercise. To be able to retain the Alto voice, we transpose the melody for the sake of a better position into F major. ]96 MANUAL OF HARMONY. 424^ r 5^e^ ar s>--- -JZ- &22: cantus Jirmus, ^~^_ .«. zsr S--iS>- -fSL -(SZ- -fii- :si= S^k -s^ i 5 8 3 9 8 4 TSZ ■JS>Z ^ a-^- m Efe =F -at :t The explanation of the unprepared chord of the Sixth-and-Fourth in the fourth measure is found in the remarks on passing chords in chapter fifteen. It arose incidentally from the progression by degrees in the Bass, and stands here in place of the chord of the second. The treatment of the same cantus Jirmus transferred to the Bass: ,425. ?=^: ^ ^■=^ ^«___Jtz. ?z= EE^ te ■.sz sfe :'*=^:J^: -t^T c. f. 6 l^^ '^' -'SZ^ =?c ^Z-v^S- =t=Ft=F ^ 6 - 3(j 2—45- ^Pt--t:- i This treatment displays one weak point in the third and fourth measures m the harmonizing of the sustained a in the Bass. So the bare fourth in the sixth measure is a very imperfect representative of a chord, unless it be explained as a passing note. If it be desired to develope the part-movement still further, passing-notes and appoggiaturas can be used alternately in the parts to be added, e. g. MANUAL OF HARMONY. 197 f— "F- z^tq^f r— ^^— ' j ■__Si.'- ~f r — ■ -i"- j> J. — ^*— r-f^F=r^^:^^F:F^-^i-^-^-^- -rh / 6 5 1 {' 1 1 ' ! " » J 1 L L 1. 3 5 6 3 7 -iri-f-f- -f-f-r-^ -^ ^ — : E : FF \^- ? J: i • p— [-- --!-•■ 1 '" \- .-..-■ u - ^> -Lb Of the rem'aining treatments, that with the cantus Jinnus in the middle part here follows : r ES .s: f=?=P=p: _^_f;»r^_,. :»-i— ^Sg 427. c.f. ■JST- w 9 6 6 =i=p: -0.—-rf^-^-o- 5tS- "?2: -^-•- itit («;i t:tit: ^^=F- -^ H« -• -F-r-^S^ >_^.. -»-* r ^SZ-' hS?- =t==fj:=t te §BE li^P- t=f=t=i=>i| 5 s-- -o- The following may serve here as examples of four-part treatment : 428. Given, ■part: ^ ff :a=zt :it=Ft:=t:= 198 MANUAL OF HARMONY. 429, Harmonized in four parts : c.f. — -sr nS" xM. -0-- -(2-^(2- a=t=t -^^&- rt 1 — "' gz::^^ =^= rgics »: te*=3i: N.B. 13: ^^ 135 Vi- -^^■ 6 4 3 ^§»^ 7 6 7^1 3 Sq 5 43 8 67 ■1*f — 1 h- zzL ist_ t=t NB. In the fifth measure at NB. the skip of the Tenor to the seventh should not be considered good for the reason that the Soprano simultaneously makes a long skip in the same direction to the root g ; this can only be justified by the position of the Alto. In the same measure we find the chord of the Sixth-and-Fourth of the augmented triad, whose original fifth is prepared, (p. 91 and 92.) It stands here in ^Khe character of a suspension from below, (see Suspensions, Chap. XII.. p. 116.) The same cantos j^rmws. transposed into D : =fe NB. ^^ -^r r cf. ^ Bl -1 — t 430. «t S= =i!^E iS =S2- -ZJ H 6 — 4 3 =221 ^ dsi 8 6 4 7 MANUAL OF HARMONY. 199 jO-' ZZH i 1^ 122.1 -«- -(»■ &^E := H2- =6 -(2- B: -^- isr N.B. 3= I22I -(5-i- ^^fe In the fourth measure are suspensions in three parts (see p. 117). In the fifth and sixth measures the position of the Alto and Tenor is not good, as they are more than an octave apart. Of the remaining treatments, that with the cantus firmus in the Bass may here follow : '%= ■at =^!z-«i- eS; glES =^ ;te « _azi .ffli ::e5^ c./. :^=^^ 6 — 4 3 6 i«?=^l?=ca: I ^giUl s? agagpjj ai 6 2 3 2 6 5 6 ^Sfq ^= 6 !l 6 ^1 ■ The introduction of the seventh-chord of the seventh degree in the fourth measure seems confused here, because the root lies immediately above the seventh (see p. 69.) In similar favorable positions it is well to use even the chord of the second or Vllf . Moreover the progression here is not according to the movement of the leading-tone, but in the same cadence-like form as with other seventh-chords : CJ±? f#- — (See pp. 68 and 69.) The treatment of this canlus firmus with more movement in the parts can be effected thus : 200 MANUAL OF HAILMONY. 432. -o- -&- ??:: r ~?g - — :: r^^ -0-(S- WTi==:^--=.-—iz\=j2. W- NB. :^: £ EEEEE :^ ii^^i&dziz^gj ^: 6 1 7 4 3 ST. I*=?I =ai=?i The progression of the seventh upwards in the last measure but one (at NB.) is caused by the movement of the Soprano (see p. 84.) , The treatment of the cantus Jirmus in the Tenor here follows : -P=»- llEiE 433. ^55 c.f. ISI y:S=3c A -#-^- -• See& :t=t:tit -•-^-. :p=F -la— — (Z- ZiSZ :3Z= ^i t=t ^m EiE V^ — . - - 1— r-ZJ=== =-?5 pr-i ■ 1^ " '"r " ::fc=^- — (S— -1 [■ ^ From ihe second Alto and Tenor in the second and third measures it may be seen that the parts, especially the middle ones, may often cross each othsr. For practii* in five-part movement chorals can be used to special advan- tage. The following may be annexed here : G — 442. P^ a D ODt G D^ eI^I? =^ G ■3Z: i » — G Dn G Eq a :^z= isr::r: 122: r- G G D r-O- I^ B G D a -^ :^= G Dt G I H IJ r -v-n Exercises in five parts and more require a simple and natural Bass-pro- gression, and the less artificial and difficult it is, the clearer and more intel- ligible will be the succession of harmonies, which is all the more important because very unintelligible progressions can easily arise where there is this fulness of chords and necessity for the free movement of the parts. The beginning of this exercise is here given : 443. At the repetition this series of harmonies may be used : 206 MANUAL OF BAEMONT. i 6 - •mi jbr rS= §1$^ :fe IS= ^=^-EgE^EEg^g±g= g:p^=^ t=^^ r- t:=t: f- ISO. ^E^=|E|^:Ete| a- §E^t^ =^ '^sz t=t :p= Jr^J. fe E^SE|;^E^E|E^E|E^|-^ §rE =22: :^ :^:: =ar 12^ 210 MANUAL OF HARMONY. 448. SOPEANO I. SOPEANO II. AliTO I. Alto II. Tbkoe. ^■ ^$^ Bass. ^ ^^ ^^^^^ ^^E= -^- :?ci^ / i^=z>: i=j: i^==& -W=i- 5=c: / tz=t :icz:e=:t: i 1-- WlE=E -p=^ -I 1 H ?2: / 1^ ^^S i^^ f^^& -h P •- / -P— •- ■^TiS: -42-' fe& t=:t zsz :^: =?2= -i?^ -^-_kf^*_,_ s= IS?:: 1^ »=d=3: SSi33: m^^^;^. 3: MANUAL OF HARMONY. 211 Se -I" — • i:£ ^^ r ST^^.^=4 i-=5^ r ■• — ft — s- ^-=F= ^= ^ ^:Ft: e i^z :f:=^ IP (S!-^ p^ e T2Z m In eight-part chorus-movements, where the customary four parts are usually doubled, these are not always employed as eight independent parts, which might result in overcrowding, but frequently two parts of similar register in unison (e. g. two sopranos, two altos, or two tenors and two basses in unison) so that the harmony often appears in four, five and six parts. We find also the eight parts divided into two distinct choruses, acting each by itself and in detached places. As showing the peculiar movement which many of these parts must adopt, the commencement of the above choral is here given in eight parts : 449- SOPEANO I. & II. 1^^ ^j =?: T^ IW- Alto I- •"'• P^|§ Tenok I. & II. E E g -^- Si 1= ISH !i^ B-I..II. II ^^E^^z^^lg ::?^ i i=!3g^[ ^ 212 MANUAL OF BARM0N7. ^^^t ^=3e iE I^Z =^s= 3SZ J- mm g^g~ 132= J- _i. i^ S: lu movements of many parts, divided into distinct choruses, the diificulty of this kind of writing is met by making, not alvrays a tonic, but often a metrical distinction between the parts, where two or more choruses co-operate ; but it must always be assumed tliat the succession of harmonies shall follow in the simplest manner and never by a sudden change. This is also under- stood to be the case, when we speak of chorus and movements in twelve and sixteen parts, and only single compositions of Bach are found, where eight and more parts, including, however, instrumental parts, are treated ohligato. These hints with regard to movements in several parts may suffice here, especially as further details, after a thorough knowledge of harmony, may be left to individual study and taste for movements of this kind. As to their application we would only remark further, that the use of the movement in many parts above exhibited, and its mode of treatment within the assigned compass, will occur for the most part in compositions for chorus, but not in instrumental music, e. g. in orchestral works, as may be conjectured from the participation of so many instruments of various kinds ; and that for these last in most cases the four-part movement is sufficient, concerning the farther treatment of which reference can only be had to actual systems of instru- mention, since the doubling relations, although often approximatino' the method above indicated, must yet be subjected to other principles. MANUAL OF HARMONY. 213 CHAPTER XXVI. Forms of Musical Endings. DiFFEKENT forms of ending have already been mentioned on pp. 32 and 33, likewise further remarks have followed in reference to the authentic close pp. 40 and 53, but throughout the whole treatise there has been no opportunity afforded of recurring to them, so that what remains to be said of these and other forms of ending shall here follow. We divide the forms of ending first into the authentic cadence and the plagal cadence. The authentic cadence has the formula V-I, the plagal cadence IV-I (or in minor : V-i, iv-i), as has been before observed. Both forms are used not only at the close of entire pieces, but also at the close of the chief divisions, of periods and their sections. The remainder of this subject belongs to the doctrine of form (see Book quoted on p. 142.) If the plagal cadence end a piece, it seldom stands alone, but follows the authentic cadence ; so in a piece in minor it often leads to major, e. g. : --4-4- aufh. Cadence. Plagal Cadence. 450. m^ =f=4^= ^MF m H -zi- It is then often introduced, as in the above example, by a modulation. Endings (cadences) are also divided into whole and half. By the former we understand the same as by an authentic cadence. But these we subdivide into perfect and imperfect. Perfect whole cadences are those in which the Bass contains the root of the dominant and tonic, and the Soprano likewise the root of the tonic. e.g.: 214 MANUAL OF RAEMONY. 451. i -zi- :3c ^- — I- is= 13?= not: ZSlL zsc m zsz When this is not the case, they are called imperfect, e. g. : iszr iSe: nsr r^^i 452. P^ If the Bass move from the dominant to another degree, they are called false cadences. 453. i ■^zdms. IZ2Z ^ 3S= &c See examples p. 82-85. Half cadences have the formula I-V. e. g. : 454. m V They consist also in this, that the dominant triad ends the phrase. Beside the tonic triad, chords of other degrees also may precede the dominant triad in the formation of a half-cadence, e. g. : 456. i ler ■75 II ^^ ^^^Ej^^a; -(9- VI -^■ V 117 V IV V Under half cadences we include also those endings in the dominant key, MANUAL OF HARMONY. 215 which are formed by a modulation into the same, not a decisive one, how- ever, through the fundamental position of the dommant-seventh harmony, but either through its inversions or the seventh chord of the seventh degree, e.g.: 458. I^ P ^ XjSZ G: vii^. ^ -O.- :fe ^ ^: kSS ^ flffco. y: vii°7 C: V a: 11 = 7 This is the case, howexer, only in relation to the key which has prevailed immediately before. For the further understanding of these kinds of cadence, those which are found in the examples of this book may be compared. In No. 388 in the third and fourth measures there is a half cadence formed by 11- V, which constitutes the close of the first section of the eiitire period : in the seventh and eighth measures, however, a perfect whole or authentic cadence. In example 392 a /laZ/ cadence is formed in the third and fourth measures through I-V, and a perfect whole or authentic cadence in the key of the , dominant at the end. (Here therefore no half cadence, because the domi- nant-seventh harmony renders the modulation decisive.) In the choral written out under No. 446 the first strophe ends with an imperfect whole cadence, the second with a perfect lohole, the third with a half in E minor (iv-V), the fourth with a perfect whole in G major, the fifth also with a perfect whole in A minor, the sixth with a half in E minor iv-V), and the seventh with ^perfect whole cadence in G major. In chorals the application of the various cadences is easily found ; for larger pieces they furnish means for separating and connecting the smaller and larger divisions, and are therefore to be used with great care, since upon them the construction of a piece as regards form in a great measure depends. . B. KIDDEE & g0N'i3 MUSIC TTPOGEAPUT.