NEWLY REVISED EDITION OF RICHTER'S MANUAL OF HARMONY A PRACTICAL GUIDE TO ITS STUDY. PREPARED ESPECIALLY FOR THE CONSERVATORY OF MUSIC AT LEIPSIC Ernst Friedrich Richter. REVISED AND EDITED FROM THE LATEST EDITION BV OSCAR COON, WITH EXPLANATORY NOTES AND ADDITIONAL EXERCISES. New York : CARL FISCHER, Publisher, 6, 8, AND lo Fourth Avenue, v^^> Copyright, 1896, by Carl Fischer. f, N. OILiON OOUrANV, PRINTEIIS AND BOOKtlNDCM^ aOITON, U. t. A. EDITOR'S PREFACE. That Richter's Manual of Harmony is one of the best text-books ever written on the subject, no one will now deny. In 1843, Richter became professor of harmony and counterpoint in the Conservatory of Leipsic, and this work is the result of his experience as a teacher in that institution. The twelfth edition was published as early as 1876, and the work has been translated into Dutch, Swedish, Italian, Russian, Polish and English. The enormous success of the work be- comes apparent when we reflect that it has passed through its twen- tieth German edition. In preparing this edition of the manual, the editor has endeavored to make the language, which in other editions is often somewhat ob- scure, more explicit and to the point. Pupils frequently complain that they cannot catch the meaning of many of the explanations. The reason is, that they are not sufficiently advanced in musical know- ledge to enable them to comprehend the meaning of the prolix lan- guage used. .Students, and especially those who have not the advan- tage of a teacher^ require clear and concise directions. Having used this manual many years as a text-book in teaching harmony, the ed- itor has learned by experience where the difficulties lie, and has done what he could to remedy them. Many additional exercises have been appended to the work and also some notes of explanation. The Editor. m21()1.8*? FROM THE PREFACE TO THE FIRST EDITION. The reason for publishing this manual of harmony is given in the title. During the course of studies in the theory of music, it was de- sirable to furnish the pupils with some aid in explaining and illustrat- ing the principles brought before them. The qualities of such a work the author believes to be these : // must contain the essential fundamental principles of musical theory in the most concise and complete form possible; that these principles jnust be accompanied by practical directions for their ap- plication in order to qualify for future attempts in composition. The book contains no scientific theoretical treatise on harmony, so to speak, but ( as with any system of harmony it rests upon a firm basis ) is devoted only to the practical object, which, with the scanty means now accessible, would be difficult to obtain in an abstractly scientific manner. There has, indeed, always been a disposition to inquire after mathe- matical precision in musical rules, and especially among the young, opposed to authority, who wish to have everything so clear that doubt would be impossible, yet shrink from learning the beauties of this beautiful art by means of the anatomical knife ; and, it is not to be de- nied that in this regard there is a want in musical literature which has not yet been fully supplied. All attempts of this kind have so far failed to produce a really tenable scientifically musical system, according to which all phenomena in the world of music can be shown as the nec- essary result of one fundamental principle. What philosophers, mathematicians and physicists have achieved in this regard is worthy of attention, but is on the one hand, too much divided to form a com- plete whole, and on the other, too abstract, serving music less than other purposes; and notwithstanding the knowledge of musical tilings shown, has but little reference to that which is really musical, which is of the most importance to th- musician after all. What is laid down in musical text-books as a scientific basis has thus far not been jus- tified, partly, because as the result of learned individual investigation, it was impossil)le to form a complete system with indisputable con- clusions, and partly, because as a fanciful structure, it was entirely (iv) without scientific support. (^'The Nature of Harmony and Metre," by M. Ilauptmann, might supply a palpable want.) Still, properly considered, this deficiency is felt only by the riper and more cultivated musician who likes to busy himself with theory ; not, however, so detrimental to the advancing student that his pro- gress must suffer in consequence of it ; and the above mentioned skepticism might be regarded in a certain way like the childish de- sire to learn the cause of everything by questions which can seldom be answered clearly enough for his stage of learning. At first, the student of music has to devote his whole attention to his technical studies, as it will cost him time and trouble enough to reach the standpoint from which he may more easily advance to the position of an artist. Here the question is not ivhy^ but rather hoiv^ to learn from experience and the best models the necessity of certain principles, not to calculate it. Afterwards, should education, inclina- tion and calling require, it will be time enough to reason out thexf^jj/, and the knowledge derived from experience will be an aid not to be despised in discovering the natural laws of music. With this prac- tical aim in view, the author has undertaken to give, in a clear and simple manner, the representation of harmony, and the results of ob- servation and experience ; and as the book was intented for study ^ to let the principles which it contained work through themselves, with- out wishing to attract a large circle of readers through a learned dress or a winning form. It contains the complete doctrine of harmony, with hints for a rational method of working exercises for fixing the same, and for the skilful use of all harmonic fundamental principles. These exercises extend to the beginning of contrapuntal studies. The doctrine of counterpoint itself will follow in a later volume on the same plan. In conclusion, still a word to the student of art, an earnest one, but well meant. Our object is to reach a distant goal ; it is to produce works of art. For this, vigorous, untiring industry is necessary to comprehend the fundamental principles of music and to form that which is won and understood into a living structure. They will be bitterly disappointed who think to pluck the blossoms without learn- ing thoroughly to know and prove the technical requirements ; who cling to the notion that the charm of beauty which overspreads a work of art would be lost through the analysis of the material, or that the primary forms of the latter could never be developed into that requi- site beauty. Talent alone, without thorough knowledge, has never yet reached that point where artistic efforts are really successful. Practice without knowledge is not artistic skill, but only the working of the instinct, which will make the want of proper education al- ways apparent. The spiritual thought cannot dispense with the form, and this must be recognized and learned. Even if this comes with the thought itself, still, it is of more importance in music than anything else, to analyze the thought logically, to remodel it into new forms, and transform it in the most manifold way. The knowledge of these things and the skill in their use must be acquired by the talented also, and this can only be done by taking pains to recognize the musical laws, and by seeking to imitate and further develop what others have long since discovered. Earnest persevering work, and above all, a rational method of developing to maturity, and for the creation of, living works of art, will, in connection with musical ability, surely lead to the goal. E. F. RiCHTER. TABLE OF CONTENTS. PAGE. Introduction' — Ititervals . . . • • • • ^3 PART I. THE FUNDAMENTAL HARMONIES AND THE CHORDS DERIVED FROM THEM. CHAPTER. PAGE. I. The Triads of the Major Scale . . . .21 II. The Triads of the Minor Scale . . . .42 III. The Inversion of the Triads . . . • 5^ IV. Harmonies of the Seventh . . . . '57 V. The Inversions of the Chord of the Seventh . 63 VI. Secondary Harmonies of the Seventh . . 69 VII. The Inversion of the Secondary Chords of the Seventh ........ S7 VIII. The Chords of the Seventh in connection with Chords of Other Degrees . . . .90 IX. On Chords of the Ninth, Eleventh and Thir- teenth ........ 98 X. Chromatic Alteration of the Fundamental Harmonies; Altered Chords .... loi XI. On Modulation . . . • . • • ^^5 (vii) CONTENTS. PART II. ACCIDENTAL CHORD FORMATIONS. TONES FOREIGN TO THE HARMONY. XII. Suspensions ..... XIII. The Organ-Point ; Sustained Tones XIV. Passing Notes ; Changing Notes XV. Passing Chords .... XVI. On the Means for Modulation . PAGE. 119 144 PART III. PRACTICAL APPLICATION OF HARMONIC EXERCISES FOR THEIR USE IN THE PURE HARMONIC STRUCTURE. CHAPTER. PAGE. XVII. The Simple Harmonic Accompaniment to a Given Voice . . . . . . .166 XVIII. Extension of the Harmonic Accompaniment . 1S9 XIX. On the Formation of Melody .... 192 XX. On Development of the Accompanying Voices 198 XXI. The Exercises in Three-Voiced Movement . 202 XXII. On the Two-Voiced Movement . . . 208 XXIII. Harmonic Treatment of a Given Voice in Melodic Form ....... 209 XXIV. The Five-Voiced Movement .... 216 XXV. The Six, Seven and Eight- Voiced Movement . 221 XXVI. On the Musical Forms of Close .... 228 Index of Subjects ........ 233 INTRODUCTION. Of the elementary knowledge of music, an acquaintance with which must be assumed before beginning the study of harmony, that portion which stands in the nearest relation to it, The Theory of Intervals^ will be briefly discussed. Intervals. Interval is the relation in which one tone stands to another in re- spect to distance. The distance between any two tones is reckoned by the number of degrees of the diatonic scale which it contains, and the interval formed by those tones is named accordingly. Remark. — By diatonic degrees is understood the progression of tones formed by any major or minor scale. Thus, if G be the lower note of an interval and considered as the first degree of the scale, A will be the second degree, and the interval G — A will be that of a second. E will be the sixth degree, and the interval G — E will therefore be a sixth. etc. Counting always from the lower note, or first degree, the major scale gives the following result : 6 7 8 -(9- -G>- -^- Unison or Prime. Second. Third. Fourth. Fifth. Si.Kth. Seventh. Octave. The intervals are generallv only counted as far as the octave, the (13) I^ MANUAL OF HARMONY. same order being repeated for those intervals which lie beyond that compass; thus, the ninth degree is considered as the second, the tenth as the third, and so on. There are, however, reasons which will be perceived hereafter for giving names also to those intervals which are greater than the octave. All such will therefore have two names, as follows : Octave. Ninth. Tenth. Eleventh. Twelfth. Thirteenth.Fourteenth.Fifteenth. Seventh. Octave. When distances between t\\^o tones are greater, they are simply brought down to the lower octave. More Exact Designation of Intervals. It will be seen that the above series of intervals is composed entirely of the notes of the diatonic major scale of C, and has always Xkx&Jirst degree of that scale for the lower note of each intei-val. It is, how- ever, easy to understand that any other degree of the scale can serve as the lower note of an interval, in which case the numbers of the two tones forming the interval will be changed, inasmuch as the lower note of an interval is always considered as \\\& first degree., and other slight differences will occur. In order to obtain a clear insight into these differences, the follow- ing principles must be carefully noted : The above series of intervals, in which the lower note is the first degree of a major scale, while all the other degrees of the scale are employed as upper notes, serves as the foundation for the determina- tion of all intervals. These intervals are called major, some perfect. Any chromatic alteration of either of the two notes which form an interval, alters neither the number of the degree, nor the name of the interval, but makes necessary a more exact definition. If, for example, a sharp or flat be added to either of the notes form- ing the fifth, C— G, it remains a^T/Z/^ still, hut a difi'e rent fifth from what it originally was. i ^^^^ MANUAL OF HARMONY. 15 In order to distinguish between the various chromatic alterations of intervals, the following terms are used : I . Primes (unisons) ^fourths, fifths and octaves, which are formed of the notes of the diatonic major scale, and have the first degree of the scale for the lower tone, are called perfect. All the other inter- vals of the same scale are called major. Perfect. Major. Major. Perfect. Perfect. Major. Major. Perfect. Major. ^ ^_ , _ -'9- -<^- "1^" '^' PHme. Second. Third. Fourth. Fifth. Sixth. Seventh. Octave. Ninth. 2. If the upper tone of a major interval be chromatically lowered half-step, a minor interval is formed. i Minor. Minor. Minor. Minor. Minor. -\>^. ^-f- -i9- -&- -^- Second. Third. Sixth. Seventh. Ninth. 3. If the upper tone of the prime, secmid, fourth, ffth, and sixth be chromatically raised a half-step, augmented intervals are formed. Augmented. Augmented. *Augmented. Augmented. Augmented. 4, By raising the lower tone of the minor third, perfect fourth^ perfect ffth, viinor seventh, and perfect octave, a chromatic half step, diminished intervals are formed. Diminished. Diminished. Diminished. Diminished. Diminished. i =fer - p. p . ^. 1^ Third. Fourth. Fifth. Seventh. Octave. Remark.— Diminished primes, seconds, sixths and ninths are harmonically incon- ceivable, but may exist in melodic relations — in reference to progressing intervals, but not to those which sound together. ♦Augmented thirds, sevenths and ninths do not occur in harmonic relations, .\ugmented octaves are to be regarded as augmented primes. I6 MANUAL OF HARMONY. Remark on the fortnation of Jtitervals. The reason why, in the formation of the diminished intervals, the lower tone was. raised, notwithstanding that a similar interval would result if the upper tone were lowered, lies in the peculiar relations of all intervals in respect to their inversion,, which will be spoken of hereafter. General View and Classification of Intervals most in use. i 1F -K Perfect. Augmented. Major. ->9- ^^ -&- Minor. Augmented. i n m r^ :«*: Major. -P^ Diminished. Perfect. ■r Augmented. Diminished. i ~m ■^ -¥- ±t Augmented. Diminished. Major. Augmented. i a :?r 1^ 1^ Majc Minor. Diminished. Diminished. Major. Division of Intervals into Consonances and Dissonances. By the expression consonant and dissonant intervals, we do not understand such as do or do not sound well, as the terms might seem to imply, but by the former is meant those which produce a final and complete effect on the ear by themselves, and by the latter those which require to be followed by another harmony, without which their effect would be unsatisfactory and incomplete. Consonances are all those intervals called perfect^ and also the major and nihior thirds and sixths. The first are called complete, the last incomplete consonances. MANUAL OF HARMONY. '7 The dissonances comprise \.\\q major and minor seconds., major and minor sevenths^ and all the angmented and diminished intervals. The following table gives a general view : I. CONSONANCES. a. Complete. The periect prime, perfect yc?/;'//^ periectjifi/i, perfect octave. N. B. The peculiar relations of the fourth will be explained later, when treating of harmony. b. Incomplete. The major and minor third., the major and minor sixth. i w II. DISSONANCES. The augmented prime, the major, minor and augmented second, the diminished third, the augmented and diminishedyoz/r///, the aug- mented and diminishedyf/'//^, the augmented sixth, the major, minor and diminished seventh, the diminished octave, and the major and minor ninth. Augmented 2. Diminished 3. Augmented. Diminished 4. Augmented. Diminished 5. Augmented 6. Major. Minor. Diminished 7. Diminished 8. Major. Minor 9. MANUAL OF HARMONY. Inversion of Intervals. As has already been shown, the interval is usually counted upward from the lower tone. Should there be reasons, however, for revers- ing this principle and counting downward from the upper tone, they are called intervals below. '^^^"S' [^ ^k =f-"= D is the fifth above G. G would also be the fifth below D. It will be seen that the interval has undergone no change by this proceeding. It is, however, otherwise, when the upper tone of an interval is placed an octave lower, and consequently below the original lower tone. If, for example, the upper tone D, of the fifth G — D, be trans- posed an octave lower, the interval will change from a fifth to a fourth ; thus, W^=-p This transposition of a tone is termed an inversion of the interval. By means of inversion, the intervals of the diatonic major scale will be altered as follows : * Intervals Above 1 2 8 7 Intervals Below. The following: series of numbers result : « 7 b 5 4 3 2 I that is, through inversion the prime becomes an octave., the second a seventh.) etc. Taking the inverted major scale as a basis, we find — 1. All perfect intervals remain perfect when inverted an octave. 2. All major intervals become minor, all minor, major, the aug- mented, diminished, and the diminished, augmented. A view of all the inversions is shown in the following table: MANUAL OF HARMONY. 19 Original Intervals. Inversion, Primes. ^^'s^ ^^ Seconds. Perfect. Augmented. Octaves. Major. Minor. Sevenths. Augmtnted. -¥-_ -¥ I Perfect. Diminished. Major. i Thirds. 4= --^ :epc Fourths. :»=: Major. Minor. Diminished. Sixths. Perfect, Augmented. Diminished. Fifths. Major. _(2_ Augmented. :#t :?N= PI Diminished. Augmented. Fifths. ::s: -t^ .Ji> t i Perfect. Augmented. Diminished. Fourths. Major. Minor. Augmented. Thirds. m '4^- m SL- ^ -■2— tt _£2- Diminished. Augmented. Major. i Sevenths. :|^ Octaves. -^- Major. Minor. Diminished. i 42 — ^M— ^ Primes. Minor.' Major.' Augmented. Perfect. Augmented. An accurate knowledge of the inversions of intervals is not only important for the study of double counterpoint, but also because it ren- ders the comprehension of the simple harmonic structure much easier, for which reasons their study is urgently to be recommended. A few remarks may follow here : 20 MANUAL OF HARMONY. The reason why. in the first table of intervals (p. i6) all diminished intervals were formed by raising the lower tone a chromatic half-step, and not by lowering the upper, is easily to be seen from the above table of inversions. Since diminished intervals result from the aug- mented by the inversion in the octave, this formation comes of itself. For example, the augmented fourth ' ^ "^ t must, through inver- — . Also, the sion produce the following diminished fifth perfect fourth belongs originally to the consonances, since it is changed to the perfect fifth by inversion, just as ^^ perfect fifth can produce only the perfect fourth. A dissonance can never result from the inversion in the octave of a consonance. Mention is made here of this because, in special cases to be noticed later, the fourth has to be treated like some of the dissonances, which in former times led some theorists to treat it only as a dissonance. Likewise it will be clear that the augmented octave, and also the ninth, cannot be inverted (in the octave), as they can never become intervals below. Other kinds of inversions, as in the tenth and twelfth, which pro- duce entirely different results, may be passed over here, as they have no bearing on our immediate studies. Since a complete and thorough knowledge of all the intervals is in- dispensable for the study of harmony, written exercises, as well as oral solution of given intervals, will greatly facilitate their compre hension, and should be practiced diligently. HARMONY. Combinations of tones, sounding at the same time, and composed of different intervals according to certain fundamental principles, are called in general, har7)2onies^ chords. The doctrine of harmony acquaints us with the different kinds of chords and their natural treatment. This consists in the correct and nat?iral co?mecttofi of the chords with one another; that is, in the transition, resolution, or blending of one chord in and with the following. PART I, THE FUNDAMENTAL HARMONIES AND THE CHORDS DERIVED FROM THEM. Among the various chords which may serve as the harmonic basis of a composition, it is easy to distinguish between those which are independent, without a definite connection with others, and those which require a connection with preceding and succeeding chords to render them intelligible — therefore tiot independent. To the first class belong most of the triads, to the second the chords of the seventh. These two varieties of chords form the fu7idamental hai'tnojties from which all others are derived. CHAPTER I. THE TRIADS OF THE MAJOR SCALE. A triad Is formed by a combination of three different tones, hence the name triad. The lowest of these tones is called the fundamen- tal tone, to which are added its third ^ndffth, for example : ;b 22 MANUAL OF HARMONY. These triads, formed on C, G, and a, show a difference in their intervals. While the triads of C and G are formed of major thirds and perfect Jiftks, that of a has a minor third &nd perfect Jifth.* A triad with a major third and perfect fifth is termed a major triad; a triad with a ??iinor third and petfect fifth, a minor triad. Remark. — Triads of other kinds cannot be explained until later. As the diatonic scale makes up the essence of a key, and forms the groundwork of the melodic successions, so also the triads, which are built upon the different degrees of the scale, will form the essential part of the harmonic substance. Natural Connection of the Triads of a Key. The triad which is based upon the first degree of a key is the most important, since it determines the key. There are, however, others which are nearly related and next in importance to it, which serve to explain its position. In the natural position of the triad, third above third, the lowest tone is the fundamental, \\\q fifth the highest tone. m- The addition of any new interval would either alter the chord or double some of its tones already present. The triad which is nearest related to this (the triad on the first de- gree) must, as an independent chord, lie outside of it, yet rest upon one of its tones. This tone (connecting link) can only be found in the extreme boundaries of the chord, namely C and G. Therefore, G, which is the fifth, will form the fundamental of the nearest re- lated triad; while C will serve a?, fifth of the other, the fundamental of which will be F. The relationship of these three chords is clearly shown in the fol- lowing example : 3. ^ F C G It will be observed that these three nearly related triads comprise all the tones of the scale. They form the foundation of the key and ♦Capital letters denote major, small letters minor, chords. MANUAL OF HARMONY. 23 are, and must be, more frequently employed in practical composition than any others, if the key is to be clearly and distinctly presented. On account of their importance, they have received special names. The chord standing on the first degree of the scale is called the tonic triad; that on the fifth degree, the dominant triad; that on the fourth degree, the sub-dominant triad. If w^e place these three chords in their order in the scale, without showing their inner connection, they will stand thus: * I IV V and they are also seen to be all major triads. Application of the Foregoing Harmonies. In the application of these three, as well as other chords, we will employ the four-voiced phrase. Remark. — Theoretical chord connection can, indeed, be illustrated in many ways by the three-voiced phrase. It would, however, keep us too long from our prac- tical object, and may be left for special treatment. The four-voiced movement will always maintain its importance as the basis of all kinds of composition. We regard each harmony (chord), not as a mere mass, as com- positions for the pianoforte often exhibit them, but as a combination of tones to be divided mto four different voices. The upper part is called the soprano, the lowest bass. These two are called the extreme or outer voices. The voice next under the soprano is called the alto, the one next above the bass, tenor. The alto and tenor are termed 7niddle voices. These voices arranged in the manner of a score will be as follows, and the triad appears thus : 5. Alto. i S i± 24 MANUAL OF HARMONY. For the three upper voices, or parts, different clefs are used, which are more suitable to their compass than the violin ( or G clef) . These wall be treated of hereafter. For the present we will not employ a separate stave for each voice, but for greater ease in reading the examples, we will make use of two, such as are used for piano music. The distribution of voices in No. 5, may be shown thus: Soprano. Alto. Tenor. 9t 1^^ t ;i=^i^e=i^i=^=^eb In writing in four parts, attention must be paid to two things — first, to the progression of each part for itself alofie, and then to the relationship of each part to the three others, so that both shall be pure and ivell-constructed . The fulfilment of these two conditions results in what is termed pure voice leading. This purity of harmony and progression is attained by seeking out and practicing that which is natural and laivful in the connection of harmonies. / Thus arises the so-called pure part-writing, or strict style, which imposes rules and laws which belong to the nature of music itself. The observance of these laws will secure the surest foundation for a free use of the materials for composition. Exercises in pure part- writing sharpens the judgment, the sense of what is true and correct is formed, and the taste cultivated and refined. Remark. — In so far as every composition should be the result of a proper use of all available means and the purity ( natural expression ) obtained thereby, the term pure harmonic structure, or pure part-writing, would, in a general sense require no further explanation, as being a matter of course. In a narrower sense, however, by pure harmonic structure, something more is understood which might be better and more exactly indicated by the expression of similar meaning, strict covipositiou, strict style, to distinguish it from free style, whereas, properly speaking, nothing as op- posed to pure structure, as for instance, impure structure, is to be assumed ; since, however often it may occur, is always to be designated as false, while the free structure could be based upon what is legitimate in the pure style. As was said before, by pure harmonic structure, in the narrower sense, is under- stood such a one as in the natural development of tone relations, allows the fewest MANUAL OF HARMONY. 25 deviations from what is legitimate, and only such as do not trench upon that which is essential or fundamental. If the idea of pure harmonic structure is thus determined in a general way, still its limits are not yet drawn ; and it is just this point which creates all the more difficul- ties for the beginner, since the limits are so variously fixed by theorists themselves. This difficulty has caused many of them, especially some of the more modern ones, to say nothing of pure construction, or strict style, but to begin at once with compo- sition, and teach the laws of harmony incidentally. Whether this indulgence with youthful impatience which does not like to busy itself with the abstract — this ten- dency towards premature living creation before the organic has developed into a creative capability, can produce anything really mature, will not be further investigated here. Those who follow the views of this book and conform their studies to them, as well as those who have to go through a strict school, may be assured that their free- dom for future creation will by no means be lost by means of that which is forbidden them, but will develop itself more fully and with more vital power upon a basis con- formable to nature. Real mastery has ever learned to make itself felt most genially with- in certain limits, whereas the most fantastic ideas often furnish proof of a weak and morbid mind. On the other hand the student will not be justified, where rules are concerned, in making use of exceptions to those rules which, perhaps, may be found in the works of the best masters, or in general, in wishing to produce composition, when the proper thing is to work exercises theoretically well. The employment of the three chords already found, when applied in four-part harmony, will afford opportunity for remarks and obser- vations, and necessitate certain rules and fundamental principles. As the triad is composed of only three tones, one of its intervals must be doubled when four parts (voices) are to be used. Any interval of the triad may be doubled^ but the fundamental is the one best adapted for this purpose, more seldom the fifth and third, while there are cases in which the third is not to be doubled at all. To accomplish the connection of two triads, one with another, the following rule must be observed : When any one tone occurs in two chords which are to be connected, it is to be retained in the same voice, e. g. ^ I 26 MANUAL OF HARMONY. In the example a, C is a tone found in both chords. The soprano, which had the C in the first chord, retains it also as the fifth of the next chord. Likewise in example (5, the alto makes the connection by taking G in both chords. The remaining voices proceed to those tones of the following chord w^hich lie ?iearest to thetn^ as in example a, the alto from G to A, and the tenor from E to F, etc. When two consecutive chords are composed of entirely different notes, the voices are led in such a manner as to avoid what are termed parallel fifths and octaves. In order to explain this objectionable progression more fully, we must first consider the relation of one part to another as regards the movement of the voices. The Movement of Voices in respect to each other. One voice can progress with another in Parallel [direct] motion {inohis rectzis), Contrary motion, {inotus contrarius) and Oblique motion, {motus obliquus) . Parallel motion occurs if two voices rise or fall at the same time, $ z^t. ^^^glH Thev move in contrary motion if the one rises and the other falls, e. (T. % I [- -^- ' I 1 I . Oblique motion occurs when one voice remains on the same tone while the other ascends or descends, e. g. 1 o. trfcz:^ ?^ g I MANUAL OF HARMONY. 27 A mixture of tliese three kinds of motion occur in ciiord connections. Tlius, in No. 7, at <5, the soprano and tenor move in parallel motion, while contrary motion is found between soprano, tenor and bass, and oblique motion between the alto and all the other voices. The above-mentioned faulty progression in parallel octaves and Jift/is, can only occur in parallel motion, if for example, two voices move by degrees or skips from a perfect fifth or octave, to another perfect fifth or octave, thus : Parallel octaves Parallel fifths Parallel octaves Parallel fifths by degrees. by degrees. by skips. by skips. ^^^^- These movements are regarded i\.?, faulty for all voices. The following progressions of harmony contain both faults : ,..! n^^^m-_ W^eMi '-^ The faulty parallels are indicated by the oblique lines. In example a, there are jDarallel octaves, by skips, between soprano and bass, and parallel fifths between alto and bass. In example 6^ parallel octaves, by degrees, are found between alto and bass, and fifths between tenor and bass, and in example c, octaves, by degrees, between tenor and bass, and fifths between soprano and tenor, and soprano and bass. To avoid these and similiar faulty movements of the voices, it is necessary that the voices, between which the fault lies, should be led in contrary or oblique motion with each other ; that is, the voice which forms an octave or fifth with another, must move in contrary motion with it, or in case the next chord contains the same to?ze, fnust remain stationary., thus producing oblique motion. The remaining voices then move to the nearest intervals of the new harmony. Thus, in example I3, a., one voice must remain on C, while the others pass upward, resulting in oblique motion between the alto and all the otlier parts. At b and c, contrary motion to the bass must 28 MANUAL OF HARMONY. be used in all the parts — at b, toward the bass, at r, fro??i it, for example : Remark. — The reason for x)\& prohibition of octaves (also the unison) can be eas- ily found in the necessary independence of the parts. The reason for the prohibition of Ji/th progressions is more difficult to discover, however much we may feel the necessity of it ; and from the earliest times, much pains have been taken to express it clearly and definitely. Let the following view on this point be examined. If each chord-formation presents for itself a distinct whoie, which, however else it may be formed, yet, in respect to its fundamental and fifth mainly, unites itself as it were into z. circle (the seventh, as an addition, not being considered here), and if connections of harmony can only be produced by one chord, so to speak, going over and passing, or resolvmg into another, then it is plain that two chords having their extremes fifth following fifth, cannot resolve themselves into each other, but, when placed side by side, will appear without any relation to each other. This can be seen by comparing the following: 14-, a. ^ The sevenths do not form essentially new chords, neither do they lie beyond the circle of the primary chord: they only serve to indicate more distinctly the relation- ship of two chords, and make the connections more intimate and firm. Now, wherever the pe7'fect fifth appears, it will carry in itself the character of bound- ary; and whether the remaining 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 disagreeable effect of tivo perfect fifths in succession will always be found to consist in the lack of connection. While speaking here of the fifths of triads only, it may still be observed, that in the case oi perfect fifths which arise from added sevenths, the requirement of their prepa- ration, partly of itself, prevents parallel fifths ; but in the case of the progression of such a seventh which forms a perfect fifth with another voice, to another perfect fifth, the unpleasantness and lack of connection will be preceptible in the second'^i'Cn. only which enters without connection, e. g. i "m MANUAL OF HARMONY. 29 Concerning the diminished fifth, however, which in the dominant seventh chord can enter free (unprepared) in certain cases, its entrance unprepared, even in the case of parallels, perfectly justifies the views expressed above, for whenever \\. follows the perfect fifth, its connecting character is felt, but when \i precedes it, the latter, taking no account of the laws of progression, steps at once outside of the connecting circle of both harmonies. Compare the following: a. , b. c. 4=^^ ji^ t^=F -^ ^ fe _g. If passages like the following are frequently found in compositions of the stricter fltyle : 1^ iPB it may be assumed that the doubling of the diminished fifth (the F) requires a double progression of the same, and that the succession of fifths are justified because they lie in the middle voices, but that the following progressions could not be called pure, J i=^ J 9t ^=^~ partly because they are too prominent in the upper voice; partly because the above condition of a necessary double progression is wanting, although passages like No. 16, c, are plentiful enough. Here it also becomes clear why such parallel fifths as arise through passing notes, in many cases do not sound as disagreeably as those mentioned above, and for this reason many theorists regard them as faultless. This, however, cannot be admitted altogether, since many of them are based upon other false progressions (for exam- ple, upon covered fifths), and it is not to be denied, that with a very open position and a sufficiently long duration, their unpleasant effect is noticable. 30 MANUAL OF HARMONY. It is not the place here to treat further of these relations, and there would be much to say on many points, as for example, the progression of the fifth in the augmented chord of the sixth and fifth, but which would lead us too far. Individual cases will lead us back to this point in connection with our practical exercises. If the meaning of the foregoing remarks be too obscure for the beginner, with more advanced knowl- edge and practice in the entire harmonic system, it will soon be comprehended. The faulty progression, thus far mentioned, is called Open fifth and octave progression. They are called covered if, in parallel motion of two voices, the second interval forms a fifth or octave, e. g. 19. Open parallel fifths and octaves for harmonic connections are never admissable ; the worth of covered fifths and octaves will be discussed later (Chap. XVII.) ; for the present this must be left for oral instruc- tion, as, in general, with a correct understanding of the exercises, there will be, at present, little opportunity for errors in making objectionable fifths and octaves. Remark. — The beginner will do well, when working out his first exercises, to pay no attention to covered fifths and octaves, because, in his anxiety to avoid them, th* first principles of chord connection are violated, and worse faults may easily arise. Exercises. The n6xt exercise will be to employ the three primary triads in con- nection with each other, musically and with observance of the rules thus far established. For this purpose we select the following bass progression : iili* C: I I IV t & s^:: lis^il^ I *When a figure appears over the^rj/ bass note the soprano should take the interval indicated; thus, 3 indicates the third of the chord, s, the fifth, etc. MANUAL OF HARMONY. 31 Remark. — These, and all following exercises, indicate the way and method in which our exercises will proceed. They should be continued as long as the subject in hand requires it. The disposal of the three upper voices of the first chord, wliich are to be added, will give occasion for important remarks. We have already seen in example 5, that the situation of the voices in a chord may vary greatly. This situation of the voices is called the position of the chord. Close and Open Position. A chord is said to be in close position, when the upper voices lie so near each other that neither the soprano nor tenor, if transposed an octave, would fall between the other two voices, the bass being more or less distant, e. g. )i d. ;r^ig^l=i ^=g: il^^E^H 91: The first position of the chord, «, is so changed in /^, that the former E of the tenor is placed an octave higher in the soprano ; in c, the case is the same with both tones G and E ; in fl^, the C of the soprano is placed an octave lower and becomes the tenor. In all these trans- positions the distribution is altered, but the close positiott is still retained. It is otherwise when the chord appears in open position (also called dispersed, sometimes extended position), which is the case if either the soprano can be placed between the alto and tenor, or the tenor be- tween the alto and soprano, so that the result will be close, e. g. t i^r^g^si sgSBrii / 9t -o'- 32 MANUAL OF HARMONY. At a, the chord appears in open position ; by transposing the G an octave higher (between alto and soprano), in close position, as at (5; the same at c and d. At/, the G of the soprano of the chord at e is placed an octave lower and between alto and tenor. The following situation of the voices, a, (No. 23) would not, how- ever, be an open position in this sense, for by transposing the tenor, the situation of the upper voices would not be changed, b^ and only the transposition of the soprano would give the chord in the real opea position, as at c. 23. I ll^l^] The open position, although it makes the chord appear fuller, is not always to be used, not being clear enough to the view ; therefore, for the present, the exercises will be written in close position. Remark. — It will always be better, at first, to write the examples in close position, and only use the open position later, from the exercises in the second and third part, where it will be found necessary. By using the open position in the beginning, the pupil stumbles upon difficulties which is not to our immediate purpose to surmount, and which may, therefore, be better to avoid. The different positions do not usually appear singly, but occur to- gether, as the leading of the voices requires. The position of the jfr^/ chord having been decided, the chords fol- lowing are no longer so free that their positions may be chosen at will, but must be governed by the rules already given for the connection of chords. (Pages 25 and 26.) The connection of chords and leading of voices in the first exercise. No. 20, may be as follows : ^^gi^i^^^H 9t I C: I IV MANUAL OF HARMONY. 33 The natural relationship of these chords to one another can be clearly seen bv observing the connections. But especially from the last two chords does the close connection show how one completes the other. From the feeling of rest and satisfaction induced by the concluding progression in the above example, it has been named the authentic close or cadence. Another form of close, or cadence, is formed through the sub- dominant triad, as in No. 20, fourth example, and is called the plagal close or cadence. N, B. The last chord of a cadence (close) always falls on the accented part o! the measure. — PZd. Of these and other kinds of close, we cannot speak at length until later. In order to become accustomed to the succession of chords which occurs when the bass progresses by degrees (as in Ex. 34, F — G), it w^ould be advisable to write out the progressions IV — V and V — IV, in various positions and keys. The Triads of the Remaining Degrees of the Major Scale. All the triads situated on the remaining degrees of the major scale, although they certainly belong to that scale, do not indicate it so plainly as, for instance, the chord connection V — I. These triads are called, to distinguish them from the primary triads, secondary triads. 34 MANUAL OF HARMONY. SECONDARY TRIADS. They are situated upon the second, third, sixth and seventh degrees of the scale. 27 •a^ii ^=i -G—^ « ^ The triads of the second, third and sixth degrees are minor triads, as their thirds are minor and their fifths perfect. The triad of the seventh degree differs from all the others, since, beside the minor third, it has a diminished fifth ; hence, it is called the diminished triad. In order to distinguish between major and minor triads in the sys- tem of Roman numerals under the bass notes, we will employ a large numeral for the major, a small one for the minor, and for the dimin- ished triad we add a °, as above, vii°, a method introduced by the theorist, G. Weber. All the triads of the major scale will now stand thus : 28. Remark. — The beginner must beware of mistaking any of these chords for tonic triads, an error which malics an insight of harmonic relations much more difficult. As long as the key remains in C major, as in the above example, the various chords of F, G, D, andC, are merely chords of the different degrees of C major, and cannot belong to the key of F, or G, unless such keys are reached by and through tnoJulatioti. Hereby arises an ambiguity of the chords which should be carefully noticed. Each triad can belong to different keys. Thus, in the following example, the major triad of C can be : 29. i C: I 7^ I If, therefore, with respect to this chord, C major is spoken of (meaning the key, according to ordinary usage ) this would be true only in the first case where the C major triad stands on \.)\&Jirst degree, but in all other cases is incorrect. MANUAL OF HARMONY. 35 Application. No new rules are required, at 25resent, for the connection ot tiie secondary chords with each other, or with the three primary triads. Several new features will appear, however, in this connection. The bass can move either by skips or by degrees. In the former case there will always Idc a connecting tone, a tone common to two consecutive chords, and this tone should be allowed to remain in the same voice^ as shown in Ex. 24. In the latter case there will be no connecting tone, and the voices must be led in contrary tnotion with the bass, in order to establish the inner connection of the chords. a. The Bass moves by Skips. b. N.B. better. SO. ^Eia; n^ir^a^iTr^ii^^ iSil^igilg^igia II IV II V II VI In the above example, the bass proceeds by skips of various degrees, tile upper parts being connected by tones common to both chords, and iv/iick remain in the same voice. There are exceptions in many cases, however, to this rule. In Ex. 30, at N. B., is a progression of the voices formed accord- ing to this rule, where are found covered octaves between the tenor and bass, which it would be better to avoid by means of the progres- sion which follows. Though the local connection would thus be lacking, still, the /V?« f=2_ : z^ III IV giiEiB iPii&'^ :2-=^ 13. 5 as ;=F=* E3E^: :| ^: i I II The fourth of the above exercises gives occasion for some remarks. It will be observed that the movement of the bass in the first measure is repeated in the three vv^hich follow. Any such regular harmonic or See Ex. 30. t See Ex. 42. *• See Ex. 34. $ See Ex. 34. MANUAL OF HARMONY. 39 melodic progression is called a sequence, and demands a correspond- ing regularity in the other voices. This regularity could not be ob- tained by working exactly according to the rules already given, thus : i ^ m r- r ^ -6^ etc. t ^i It will therefore be necessary to lead the soprano by a skip at the end of the first measure, in order to bring the Jirst chord in each Tncasta-e into the same position, and thus preserve the uniformity of the sequence. The following will make it plain. 39. ^ J V N. l^ a-Fg= g 1 §±ffiE3^ IV II VI III viio In the first example, the covered octaves are tolerated on account of the sequence, but they cannot be allowed in the outer voices. The first exercise in No. 37 can also be worked as a sequence. In the third measure of Ex. 4, we find a chord which we have not yet used, called the diminished triad. This chord rests upon the seventh degree of the major scale, and is not as independent as those on the other degrees, since its diminished fifth, which is a dissonance, plainly indicates a progression. The natural progression of dimin- ished intervals is, in general, that both tones approach each other by a degree (a), or that one moves while the other remains stationary (<5, c), a sort of progression which only becomes plain by actual chord-connection. e. Inversion. ^^i^^^^i^l^ In the third which follows the diminished fifth (triad), the triad on 40 MANUAL OF HARMONY. the first degree (c) will appear in an incomplete form— without its fifth, as at d. Since, according to the relations of intervals in regard to inversion (which has been explained under "intervals"), an augmented fourth results from the diminished fifth, its progression will also take place in an inverted manner. (See 40, e.) N. B. It should be noticed that the fundamental rises and the fifth /rZ/j- in the in- version, just the same as in the fundamental position of the chord. The tendency of the half-steps to proceed to the nearest tones is thus shown. — Ed. The fundamental tone, upon which the diminished triad is formed, is called the leading tone. It senses as third in the dominant triad, and Sisjifth in the triad on the third degree. 41. ^ =^ijS=^ Jtz:H As the leading- tone., of itself, is heard very distinctly, it is 7iot doubled in simple four-part harmony. Also, its progression should be upward a half-step to the tonic, providing that tone is contained in the next chord. This tendency to an upward progression lies in the melodic char- acter of the leading tone, as it stands but a half-step below the tonic of the scale. This is particularly observable in the dominant triad, when the leading tone appears in the highest voice, as Ex. 42, a, is more satisfying than b or c. When appearing in a middle voice the upward tendency is not so de- cided, as at d. Skips from the leading tone downward, when taken by the upper voice (c) are intolerable, but when in a middle voice can be taken if the bass moves in contrary motion, as at c. MANUAL OF HARMONY. 41 In Ex. 39, in the third measure, at N. B., the leading tone is found doubled and progressing contrary to the above rule. Both were the result of the sequence contained in the example, which would not admit of change in the position or progression of the chords. On the More Complete Formation of the Close. The close by means of the dominant chord (authentic close), appears in a still more definite form in the last examples. For, while the natural i-elationship of the dominant triad to that of the tonic makes these two chords the most suitable for the formation of the close, in the first and second exercises of Ex. 37 may be observed a prepara- tion of a close by means of the triad on the second degree., which bears the same relation to the chord of the dominant as this latter does to the tonic triad, e. g. t g^i; Instead of the triad on the second degree, the subdominant can also be used to prepare the authentic close, e. g. iES IV ;h The forms of closing resulting from this connection of chords, will assume a more definite form by the use of chords to be explained hereafter. .2 MANUAL OF HARMONY. CHAPTER II. THE TRIADS OF THE MINOR SCALE. a. Primary Triads. The primary triads of the major scale were found on the Jirst., foiirth., Sim\Jifth degrees. Those of the minor scale are found on the same degrees. The pecuUar j^«a/ feeUng induced by the authentic close, is caused by the fact that the last chord but one contains the seventh degree of the scale, or leading tone, and that this tone is only a half-step distant from the tonic, or key-note. For if the seventh degree were distant from the tonic a -whole step, which according to the signature of the minor scale is the case, it would not possess the characteristics of the leading tone. Therefore, to make the authentic close in the minor key, it is necessary lo raise the seventh degree chromatically a half- step, by which means it acquires the character of the leading tone, e. g. 45. i i -7S—S>- sr-^- N.B. In consequence of this alteration the dominant triad is precisely the same in major or minor, or in other words, the dominant is al-ways a major triad. A major. ma * a: V A:Y This will be clearly shown by comparing the close in both keys ; • In the indications below the staff, observe, that a large letter indicates a major key, a small letter a minor key, a large Roman numeral a major triad, a small numeral a minor triad, etc.— Eu. MANUAL OF HARMONY. 43 ^ C major. C minor. fipiiiiipni"] 11 As a proof, however, that a similar alteration of the sixth degree is not allowable in harmony, though continually adopted in melody, it is only necessary to examine the plagal close, shown at a in the fol- lowing example, which, it will readily be seen, could not possibly be conceived of, as at b. H Si: -^-■- -^ 1 The three primary triads of the minor scale and their relationship, may be shown thus : . ^i==S=fe| IV I V The minor scale, as a basis for the harmonic structure, will there- fore stand thus : ^^•" P^—^ ^^ t Remark. — All other forms of the minor scale, as : i ^ <^ j^fc ;i 44 or descending: MANUAL OF HARMONY. 52. * -^ ^ rest upon melodic conditions which prohibit the step of an augmented sc-ond between the sixth and seventh degrees, as seen in No. 50. In the abstract, these forms have no influence on the harmonic structure ; still the harmonic foundation reacts on the minor scale itself, as the following examples show : H: m- Wz The last case, in which the descending scale makes the step of an augmented second, B — Ab, and which we shall carefully avoid in future chord-connections, is to be explained in this way — that the B was necessary as a component part of the chord (the third in the dominant), but the Aft, however, was needed so as not to destroy the minor charac- ter of the passage which would have been the case very perceptibly by Aj, while in the ascending scale (in the first example) this minor character is already well preserved by the minor third, d?. b. The Triads of the Other Degrees of the Minor Scale. SECONDARY TRIADS. According to the establishment of the minor scale, the secondary triads will appear as follows : iF=li= iio N. B. IV PI V VI VI lO 'Y\\Q second degree gives a dhniiiisJicd triad, similar to that already found on the seventh degree of the major scale ; a diminished triad is MANUAL OF HARMONY. 45 also found upon the seventh degree. The sixth degree forms here a major triad. The third degree produces a new form of the triad. It has a fnajor third and an augmented fifth and is known as the augmented triad. The peculiar nature of this chord renders its connection with other chords in the same key very difficult ; therefore, it can seldom be used as \hQ fundamental harmony of the third degree of the minor scale. The following examples show this : /. 55. 1 EEiEbiESEl^pfe=l3iEfil^^l ;i^^ii^ii^ii^:] IlO Of these examples, those under cand e will be the most useful. The introduction of this chord is still more difficult : 56. ^3*^li=S?^l?^#i3daJi^d &- -G>- -a- :s=^ iio VI Its introduction is the most agreeable when the augmented fifth has been heard in the previous chord, that is, has been prepared, as under d. Remark. — There seems to be something peculiarly foreign in the triad on the third degree, whether in the major or minor scale, so that, even when it appears simply as a minor triad in the major scale, it is very difficult to connect it naturally with other chords, and is therefore seldom used. Most of the practicable chord-connections shown above will occur in other situations which will not allow the augmented triad to be recognized as the triad belonging on the third degree of the minor scale. The augmented triad whicli is so much used in modern music, belongs to the chromatically altered chords, and will be explained in Chap. X, on Altered Chords. 46 MANUAL OF HARMONY, Application. The principles concerning the connection of harmonies and the leading of voices which have been so far developed, will be particu- larly applicable to the connection of the primary chords in minor. What was said regarding the progression of the leading tone, comes very prominently into view in consequence of the step of an aug- mented second occurring between the sixth and seventh degrees of the minor scale, which step has to be avoided either ascending or de- scending as un?nelodious, if both tones, which include the interval of an augmented second, belong to different harmonies^ e. g. 57. i± I VI Therefore, in connecting the triads of the fifth and sixth degrees, which is a very common progression, it will be necessary to carry the leading tone upward, in consequence of which the triad on the sixth degree will appear with its third doubled^ e. g. i & H: :te i^gi^a 9i=^ m VI VI VI VI V VI Thus, it would be impossible to present correctly the example given under 57, ^, without making use of an intermediate tone, as for ex- ample : i -fe- 1 i MANUAL OF HARMONY. 47 Remark. — Practice deviates from this rule in certain special cases. But it will he ■well to become accustomed to the above leading of the voices, because we must not overlook the fact that every deviation from the rules in practice should be only a well founded exception, whereas the observance of them can be cited in numberless Exercises in Connecting the Triads of the Minor Scale. aE$: ilii :H I I ^ and the upper parts may then proceed thus : 54 MANUAL OF HARMONY. 72. From the above examples it is evident that the inversion of the diminished fifth, that is, the augmented fourth, does not require so strict a resohition mfour parts as was given in Ex. 40, for the same interval in two parts. Thus, in the first example, and others, we see B of the soprano and F of the alto progress to C in the soprano and G in the alto. As this chord has a similar sound to the chord of the dominant seventh, beginners often feel the necessity of leading the original diminished fifth downward, even when it has been changed by inver- sion into the augmented fourth. As the examples show, this is only necessary when the diminished fifth appears above the fundamental. A progression like the following would be faulty on account of the parallel fifths. It may here be observed that parallel fifths, the second of ivkich is diminished., are allowable, but a perfect should 7iot follotv a dimin- ished ffth. Not good. 75. MANUAL 01'' JIAKMONY. 55 The progression of the voices In the inversion of the diminished triad, takes a different form when the bass does not proceed to the tonic triad. Here follow a few chord-connections : Not pure. VIlO III VI lO IV VIlO VI The diminished triad on the second degree in minor is capable of yet other resolutions, as its fundamental can be doubled. The succession of two or more chords of the sixth on a bass which moves by degrees, as in Ex. 70, No. 3, and others, requires that one or more of the upper parts shall move in contrary motion to the bass ; and generally that the bass shall be doubled in one if not both chords. 77. ^6 MANUAL OF HARMONY. The sequence of chords of the sixth in the fifth and sixth exercises of No. 70 is best accompanied when the regular movement of the bass is carried out in all the other parts also, thus : § \ -6> ■-" etc. i^f^^=S^i§H Covered octaves, such as occur between tenor and bass in the second and third measures, are not to be avoided in such cases. In fact, excep- tional progressions like the above must sometimes be permitted, when to have adhered strictly to rule would be to mar the proportion of the phrase. Remark. — That the principle just laid down can be easily misunderstood by the be- ginner is evident. But the statement of the principle was unavoidable. To avoid all possible error, it may be added, that a final decision on these points is only possible to a judgment fully ripened by experience and practice. The Signs used in Thorough-Bass Notation. The figures and signs in thorough-bass are called in general, signa- tures. Some of them have been already explained, as the chro- matic sign so much used in minor. The figuring of the chords of the sixth and of the sixth and fourth was given on page 51. A stroke through the figure is used when a chromatic elevation of the interval is required, for example, in exercises 8, 9, 10, of Np. 70, a stroke through the 6 : $ ; instead of which, however, aj^ or H is often placed by the side of the figure, for example, 6||;or6t[, h\. Other figures will be explained later in connection with the chords where they are used. Formation of the Close through the Chord of the Sixth and Fourth. In the exercises of No. 70 we find the close, already mentioned, rendered clearer and more decided by the chord of the sixth and fourth ; and it may be accepted as a rule that the second inversion of the tonic triad (chord of |), w//ipIete ; in most cases the omitted interval will be t\\ejift/i of the fundamental chord. Exercises. .Eiii: ^B -6* -(2- =f=t 3. 3 S^E F — \~V^ ^ = ^^ ^m ^=^=x 6 4 7 ?=3= I 5. :g±$: 2=E 6 7 4 t I -^ 5- p-=^-±t=^^ :iSE ^^m t^ 6' 6 , 4< t=l: t=n %-■• ^ g!,1i 8 E^g =^ r=^=ff^:.g| EEJEpEi 6 6 6 4 37 MANUAL OF HARMONY. -«>- P. SSsiS^^^^I 6 7 Ha 10. 7 6 Q §^ g-rf--=^^=i g i£5 = ^ ^gi^^-^£BI l#jte 6 7 6 X m Note. In the sixth measure of Ex. 4, of the above exercises, the same division of the measure into two halves takes place which has been noticed before in No. 70. Here the first half of the measure requires the tonic (§) followed by the chord of the seventh in the last half of the measure. In the fifth measure of Ex. 7, the second chord \s that of the tonic (|), then follows the dominant triad, \\.?> fifth passing after- wards (by skip) to the seventh. It should be remembered that accidentals placed over bass notes always refer to the third oi that note ; when placed by the side of figures, they mdicate that that interval above the ^^.fjmust be raised or lowered, as the case may be. — Ed. CHAPTER V. THE INVERSIONS OF THE CHORD OF THE SEVENTH. The inversions of the chord of the seventh are formed in the same manner as those of the triad. The first inversion is formed by taking the third of the chord for the bass; the second, by giving the fifth to the bass; and the thirds when the bass receives the original seventh. 54 MANUAL OF HARMONY. In close position the inversions appear thus : 83. S£ _^ffi_ 'G7 G7 G7 G7 A comparison of these inversions of the chord of the seventh, with those of the simple triad, will show their relative positions: 6 6 4 -jg— t(t) 2(22) ^^ G7 G7 G7 G7 These derived chords receive their names from the intervals which are found over the bass : T\\^ first inversion is called the chord of the sixth and fifth. The second: the chord of the sixth, fourth, and third, or briefly, the chord of the fourth and third. The third: the chord of the sixth, fourth and second, or briefly, the chord of the second. The thorough-bass figuring may be seen above, in Ex. 94. As is the case with the inversions of the triad, these chords de- pend only on the position of the bass, and the upper voices may be arranged in various ways, e. g. MANUAL OF HARMONY. Application. 65 The regular progression (resolution) of these derived chords is founded on that of the original chord. As the dissonance, the seventh, caused the progression of it in one direction, the tendency to the same progression will exist in the de- rived chords where the fundamental and seventh appear again, or the two tones become seconds bv inversion. Progression of the Chord of the Sixth and Fifth. In the chord of the sixth and fifth, the original seventh still forms a dissonance with the bass, but in this case it is a diminished fifth, the resolution of which has already been explained . ■m ;l:l The resolution of the complete chord of the sixth and fifth will nat- urally be as follows : m ^^^^^-_ ^1 G7 That is, all the voices (except the fundamental G) will have the same progression as they had in the original chord. The fundamental remains stationary, as it is not suited to the character of an upper or middle part to proceed by such large intervals as the fundamental did when it appeared as bass of the original chord. That the G, however, forms the foundation of this connection of harmony, is shown by the marking G7 — C, in Ex, 98. Remark.— Different progressions of the fundamental, due to a freer leading of the voices, are not hereby excluded, but there must be an inner connection between the chords. ^ MANUAL OF HARMONY. Progression of the Chord of the Sixth, Fourth, and Third. This chord contains between its component parts not only the inter- val of a seventh, or its inversion, the second, but also that of the diminished fifth, or its inversion, the augmented fourth. -^ [-1 1 The resolution of this chord follov^^s thus ^i=^'- ^^ G7 C G7 C The bass, being the original fifth, is free to move both ways. Progression of the Chord of the Second. This chord has the peculiarity, that the dissonances of the original chord, the seventh and the diminished Jifth, can only appear in their inverted form, as second beloiv^ and augmented fourth below. The resolution of this chord is to a chord of the sixth on the tonic : lOl It will be seen that all these resolutions are based upon the natural progression of the dominant seventh chord (cadence), since we find throughout the same marking of the fundamentals, G7 C, or V7 I. Therefore, these resolutions will of themselves form cadences, but not so complete as those mentioned before. As those were called perfect cadences, we describe these as imperfect candences. MANUAL OF HARMONY. 67 Note. — In the inversions of the chord of the seventh all of the four intervals are usually present, the three upper voices taking those not required by the bass, which latter is seldom doubled in four-part harmony. — Ed. View of the Natural Progression of all Inversions of the Chord of the Dominant Seventh in Various Positions. a. THE CHORD OF THE SIXTH AND FIFTH. 102.< \ ^^^1: P^E^E j^^H->g j =^ -5^ j^^- Gt c :H THE CHORD OF THE SIXTH, FOURTH AND THIRD. Or. g.-^*i=tesi^l=J^fcl 4 4 4 3 3 6 3 ->^ "'^ a. 5i 2^: a — 1 Gv % <=»=-«- «— =.2: li^^l^^ i c. THE CHORD OF THE SECOND. g^^^^^^i^ G>^^^ ^^li^ ,6 2 6 ^^7^1 G7 C 68 MANUAL OF HARMONY. Exercises for using these Chords. 6 6 6 ( 32 6 6 4 7 6 47 3±^ I ^m 6 5. 3 5 ^ -#^ i=^: ' 87 6 % t=T g e J- -0 ^ =F==t= 2 6$ 6 7 4« asiE -Ig— t— fg — s)- 4 3 6 §i^ =^=F!=2- £Ef^l g^^% ^ 6 7 6 4 J ^ss$^^ ^ 4 6 t „ 3 2 6 3 6 7 6 4$ i WP 6 5 6 2 6 ,457 -S* -t-!g & j — --— ^ P^i MANUAL OF HARMONY. 83 '^^ ^*b«i Application of the Secondary Chords of the Seventh in Minor. The use of the secondary chords of the seventh in minor is not so general as those of the major scale. Many of them are either uncer- tain and ambiguous, or their resolutions produce harsh and unmelo- dious progressions of the voices. With these last may be classed the chord of the seventh on the first degree of the minor scale, w'hich if resolved like those given above, would produce a chord connection w^hich is not conceivable. ..3.| Remark. — Even supposing progressions with the above combination of intervals can be formed like this : ji^te ;i ^fc n 6 still, it would hardly prove that it is really a progression of the chord of the seventh on the first degree in minor. The natural resolution of the chord of the seventh on the secoftd decree is to the dominant, and is much used. 125. i 9fc K \Z^^' | = ^gE| =H ^ 1 a: 11O7 V 84 MANUAL OF HARMONY, A resolution of the chord of the seventh on the third degree is pos- sible ; it is, however, ambiguous, and belongs rather to C major than to a mimr. (See Altered Chords.) -f e>^ 27— — & — -^- -n <^\ --^^^ "13^= G>— -&- =f| ^ 5? — 1 '^- ==-^ e^ ^ ^^ — z: -1 a: IIIV. VI — It should be observed that thejifth in this chord, as an augmented interval^ will always ascend one degree. The seventh chords on the fourth and sixth degrees are seldom used, as their resolution occasions harsh and unmelodious progressions. .^- .£2. Good. 127. -^^ a: IV7 vii*- T--^^ :|^t==^: "¥ 1 i^^^l^^^^lii^l The unnatural character of most of the above progressions is very apparent and prevents their general use. The seventh degree carries a very important chord, generally known by the name of the chord of the diminished seventh. A resolution of this chord in the same manner as the others (to a fundamental a fourth above) is impossible, as it would lead to the triad on the third degree, which was shown above to be doubtful and ambiguous. MANUAL OF HARMONY. 85 Instead of this, its resolution, as in the case of the chord of the seventh on the seventh degree in major, is based on the natural up- ward tendency of its fundamental, which is the leading tone of the scale : li ^^EEfs V1107 c: VI1O7 Thus, while the fundamental of this chord rises, and the seventh falls one degree, the third and fifth are led as in other chords of the seventh, but the leading of the third must be carefully looked to, as in many positions (130, a) it may lead to faulty progressions: a. h. _ C. t whereas, in the position at b and c the third has more freedom. Remark.— The natural progression of this chord to the tonic, as well as of that on the seventh degree in major, led the older theorists to regard the dominant as the funda- mental basis of the chord. They conceived it to be a chord of the dominant seventh with an added ninth — major or minor — and with the fundamental omitted, thus form- ing both chords of the seventh degree. In referring to what is said later (Chap. IX), of the chord of the ninth, we need only state here as a reason for the view offered that this assumption of the chord of the ninth is needless and far-fetched, and that simplicity, for practical purposes, is preferable to any complicated theoretical explanation. In the application of the chord of the diminished seventh, observe the following : The diminished seventh, the least harsh of all the secondary sev- enths, needs ?to preparation. Exercises. gg 7 5J 62 6 6 7 4 i ^£=1= 86 MANUAL OF HARMONY. ^m 7 6^ * 4 2 7 7 8 &- a :«^-« i=f Sisf^ * • .,L^-J_^ 6 7 6 4 $ e^ii -\=± 6 4 7 7 6 $ 7 7 { §*3 g?=^ I 44=4: t=^ -■^H-ti^ — '^- Ute^i 53f 7 il 4H gj =^ «'-F^ 5= (^ -4 — =3 7. 8 7 6 J 5 g%=p= ^^=S? -F^ — d- ?i==t us 6 7 X ISE^iS 7 7 X :i;i ^==s: ^^=f= These and all former exercises in this chapter, the object of which was only to assist us in learning the mechanical use of the chords and to test the rules and remarks, have something hard and inflexible in their structure, since the great number of seventh chords here were only possible in their fundajnetital positions.^ and because the intro- duction of many of them, from our present standpoint, which did not allow us to select other means, was difficult and could only seem forced. The following may help to explain them : The fundamental of these chords of the seventh move everywhere by skips of a fourth or ffth^ as the bass parts show. Only, in the third exercise of Nos. 122 and 131, there seems to be an exception. In the fourth measure of the third exercise of No. 122 the bass tone remains stationary (on a), but the regular fundamental progression is maintained in the two chords according to rule : ^7, D7: The bass tone could be sustained here, as we have already learned how to use MANUAL OF HARMONY. 87 the inversions of the chord of the dominant seventh. The case is the same in the third exercise of No. 131, where the fundamental pro- gression is A^ — d^ on the sustained A of the bass. In the second example of No. 131, the chord of the seventh on the third degree in minor is introduced. It is strictly prepared, and on that account w^ill not appear harsh or unnatural. CHAPTER VII. INVERSIONS OF THE SECONDARY CHORDS OF THE SEVENTH. The inversions of the secondary chords of the seventh in major or minor give the same derived chords, as those of the dominant sev- enth, namely : the chord of the sixth and fifth, of the sixth, fourth and third, and of the second. The differences in the thirds, fifths and sevenths in the fundamental chords will require no alteration in the treatment of the inversions. Notwithstanding that the major seventh is changed by inversion into a minor second, and the dimin- ished intervals into augmented, yet their progression takes place in the same manner already described. No new rules are required for the resolution of these chords, only in the resolution of the inversions of the chord of the seventh on the seventh degree, care is necessary, as was said before, to avoid the parallel fifths which creep in so easily. This may be added here : Progression of the Chord of the Seventh Degree in Major. 183. 88 MANUAL OF HARMONY. All the above inversions are good. That of the cliord of the sec- ond., however, is less used, as its resolution is to the chord of the sixth and fourth, which can seldom be used but as a passing chord. We should not be misled by the compact form of these chords in No. 133 as to their usefulness. The only important point, as mentioned before, is whether the seventh appears above or beloiv the fundamental. Positions of the chords of the sixth and fifth and of the fourth and third, like the following : are more satisfactory, because the seventh is heard above the funda- mental. The chord of the diminished seventh requires a resolution similar to the above, e. g. 6 V1107 1 The third inversion, the chord of the second, will here also be the least satisfactory, on account of its resolution into the chord of the sixth and fourth, a chord which requires most careful treatment. The parallel fifths which appear in the resolution of the chord of the sixth and fifth, and of the fourth and third, like those below, are consid- ered faulty, as was said before, e. g. fe'.L-^i— =fe:^£ i^ With this very pliable chord, the position of the fundamental in regard to the seventh, makes no such material difference as is the case with the chord of the seventh on the seventh degree in major. MANUAL OF HARMONY. 89 Whether the seventh \\q.% above or below the fundamental, the siniihir- ity of sound between the augmented second and tlie minor third always softens the chord, and causes the former to be felt as such only in respect of the key. Exercises. 37.^§^|^|| ^=i 4 .3 7. §J^JEEgE ^ pEEgE§E3: ^t=f=P=F=F^p=^^^ :t^ -f=^= 2 6 6 6 ^^=t i M 6 5 2 4 7 3 6 6 6 6 ^fE^=^^ ^^ ^ g> p2 iS* P' SI Bife 3 2 6 t- 6 6 2 6 6 5 (^ 7 7 — ^H --C — \\i— r^- -L- tf- -<&- L-t= t^Z -M t^ §3E ^F==t -« — ^ 4 6 6 7 7 3 6 5 Jt ;tt± z^ s> g f==t a aii^^feS^ 6 5 J F E3 -^ — ^2- 1=1= I 90 MANUAL OF HARMONY. g a!>"TrTT^giEg£=5 7 6 6 7 « 4 4 « I 10. ^» 4 7 3 J ^^ 6 6 4 E#=E^ I CHAPTER VIII. THE CONNECTION OF THE CHORDS OF THE SEVENTH WITH CHORDS OF OTHER DEGREES NOT YET USED. The rule that the seventh must d/e^ce?zfl^ one degree, is, indeed, justi- fied in the chord-connections previously shown, but it has as little positive authority as anything else which is subject to the necessary changes which occur in the great variety of chord-connections. The progression of the seventh.^ or its inversion, the second., de- pends entirely on that of \\\q fundamental. If this is in such a way that a satisfactory and intelligible effect is only possible through a descent of the seventh, then the above rule will hold good. The progression of the fundamental may, however, be such that the seventh shall remain statio?iary or even ascend^ e. g. 13S. h=A -7^- The above example shows the possibility of connecting the chords of the seventh with other chords than those hitherto employed. A few known kinds of chord-connections will follow with remarks, that we may be able in forming new ones, to proceed in accordance with criticial principles. We begin with the chord of the dominant seventh. The resolution of the choixls of the seventh according to previous rules was called cadence, and that of the chord of the dominant seventh the closing cadence. MANUAL OF HARMONY. _ 9 1 When the chord of the dominant seventh is followed by a chord ether tha?t the tonic triads the fiatural tendency to a close is either delayed or destroyed altogether. Thus, the feeling, or anticipation of the natural resolution experiences a disappointment; hence these unexpected resolutions are called deceptive cadences (false cadence). Some methods of making these cadences follow : I. The cofinectio7i of the chord of the dojninant seventh with triads other than the tonic, the seventh descending by a degree. a. Connection with the sixth degree. In major 139 C: V7 VI '^ " a: V7 VI This progression (deceptive cadence) is very often used. The effect of the inversions of the chord of the seventh is less de- cided than in the fundamental position; they are therefore seldom used. In major, 6 6 J> -'^ C: V7 VI b. Connection with the third degree. Better position. 7 6 s^=l^^=l^^] a: V7 VI C: V7 Remark.— The inversions of the chord are omitted here. They can easily be made. This progression becomes still more effective if a modulation- towards a minor be introduced : 142. 92 MANUAL OF HARMONY. A connection with the triad on the third degree in minor can also be made. The latter chord, however, being also a dissonance, on account of its augmented fifth, will also require a resolution. -fe- 11^^ 3&: I a: V7 111' VI 2. Conitection with triads^ while the sevetith remaiiis stationary, a. With the second degree. Not. Not good in minor. 14-4. W- ^ ^=i^Ea^:l C: V7 b. With the fourth degree. In major a: V7 11° 6 ■'5' &- -I g > ^ s? — I ^ c^ _^_ -rr -<^' -7:3- -<5>- C: V7 IV a: V7 IV Connection of the chord of dominant seventh with other chords of the seventh besides those already used, is possible. A few here follow : Sixth degree. Third degree. Or. Minor. Third degree. 1 46. f fes=i=M=M=^=M- &^! t Z/- -27- C\ V7 V17 -Z7- V7 -ST III7 V7 cv. V7 |g g -gj 61- 3*0: 6 6 6 5 6 6 6 7 6 5 ^ ^- -G>—^ m^^^^ 5. Open 4 position. 3 6 6 7 a i^^l^p^ 6 5 - 6 7 4 « gS=i 6 7 4^6 % ^^ 6 6 4 6 7 6 ,6 43 66,4$ ila^ z?- n S^i 6 6 6 6 6 47 H Remark. — The open position in the 5th exercise above, has reference to a move- ment of the voices shown at Ex. 152. 96 MANUAL OF HARMONY. Connection of the Secondary Chords of the Seventh with other Chords of Various Degrees or Keys. It would be impossible as well as unneccessary to give examples of all the comiections o£ the secondary chords of the seventh with other chords. A few more connections of chords with secondary chords of the seventh may, however, follow here. a. With regular progressio7t of the seventh. b. With free progression of the seventh. S 1 58. i: --^-. viZL^rzz:^^ C:n1 G:Vr S5~ * '-Wr Remark.— The reason why the last example is not good, lies in the so-called cross relation, an explanation of which follows later. 59. The last progression above is much used. The cadencing progres- sion (II — V) is delayed by inserting the chord of the sixth and fourth of the tonic between them. The chord of the sixth also often appears between the seventh chord and its resolution, as in example c. The chord of the di7ninished seventh is often resolved in the same manner : MANUAL OF HARMONY. 97 g, viio^ C: I V - c. The natural progression is here also only delayed by the use of the chord of the sixth and fourth. The mechanical combination of such progressions of chords may be left to personal practice and examination. The advantages to be de- rived from it vs'ill be found in the insight which is gained of the rela- tionship of chords, and therefore should not be too lightly esteemed. This practice will stand in about the same relation to composition itself, as technical studies and exercises do to the practical representa- tion of musical works. Both produce readiness and skill, develop the powers, and make possible meritorious productions. It may still be I'emarked in addition, that the I'elation of the seventh to the fundamental and its progression will always be regarded as the test of the above combinations. If this is pure and the other voices contain none of the faults before mentioned, the chord connection may be used for particular cases. Exercises. 161 ■•Ei±$: gaSE^s t=|: t^t 4 7 6 7 3 5 6 2 7 6 6 5 6 4 6 "^^^i^j^^^^E^^^Em^^t^^ x 5 4 7 7 7 §a$^ 6 6 7 4 7 -a ^^_ v=t t=^-=^^ 98 MANUAL OF HARMONY. §±f; 6 6 6 67 1 6$ 6 $ 6 6 4 6 7 4 $ x==x s Sii^ ^ :^tt* 1* EP f 2 ^ 87 6 » -^-M^ 1 M I L[ EEi! feTEE :§Sffi^ 6 7 43f =#^ 1: 1 Remark. — Many of the cases cited above were not included in these exercises, as they are based upon modulation, which is not fully explained until later. (The sixth, exercise, second measure, has an application of modulation.) Many of the above exer- cises would have been smoother and more melodious by the application of modulation^ CHAPTER IX. CHORDS OF THE NINTH, ELEVENTH AND THIRTEENTH. Lengthy discussions respecting these chord-formations are found in most text-books. The views which may be entertained respecting these chords are various, but they all tend to one practical result. It may be taken for granted that these are either real chords, such as the chord of the seventh, in which case they must be considered and treated as such, or else they belong to the list of suspensions, or occur accidentally when one or more parts remain stationary. In the first case their explanation, and especially that of their inver- sions, would be extremely prolix, and moreover the chords them- selves would often be difficult to recognize, inasmuch as in four-part MANUAL OF HARMONY. 99 harmony one or more of their intervals must always be omitted. If, however, they are considered as suspensions or accidental chords, their explanation becomes very simple. Remark. — The chords of the ninth, eleventh, etc., are but a relic of the old systems of thorough-bass, so-called, in which every combination, no matter how transitory or accidental, was usually treated and taught as a fundamental harmony, the consequence ot which was to render the study of the theory of music much more complicated and difficult. While being unable here to go further into the theoretic reasons for classifying these formations as accidental ones, the possibility of sim- plifying the harmonic system without real practical disadvantage has determined us to take the latter view. (More upon this subject in Part II.) In order to obtain a clear insight into their nature, we will show the formation of these unessential chords, and add some remarks. By adding to the chord of the dominant seventh another third dis- tant a ninth above the fundamental, a chord is formed which is known as the chord of the dominant ninth. In the major scale the ninth will be jiiajoi-^ and in the minor scale minor : In minor. — ^ I — J" &< 162. M In strict harmonic progression it is necessary that either the ninth or the fundamental should be prepared, as in the case of the domi- nant seventh. The following example, therefore, in which both fun- damental and ninth enter free^ is objectionable on account of the stiffness and lack of connection. 163.< \ -&- -G- MANUAL OF HARMONY. The preparation may take place as follows : 164. In what respect the first examples are to be regarded as suspensions, and the last as accidental combinations, will be seen in Part II. Remark. — From the chord of the ninth in major they derive the chord of the sev- enth on the seventh degree, which has been already fully treated, also the chord of the diminished seventh from the chord of the ninth in minor, in order to be able to form their cadencing progression in a manner similar to the other chords of the sev- enth, asserting that these chords are themselves chords of the dominant seventh with the ninth added and the fundamental omitted, e. g. In the first instance arises the difficulty, that we must accept two chords of the sev- enth degree in major — one, whose natural cadence is the following: i and the other as derived from the chord of the dominant seventh. It seems that the clearest way is to refer to the leading tone upon which these chords are built. Many theoretical works treat also of the formation of other chords of the ninth, called secondary chords of the ninth ; this is, however, quite unnecessary, for inasmuch as they can never appear without preparation, their treatment, resolution, etc., will be in every respect similar to that of suspensions. That which applies to chords of the ninth, will apply in a greater degree to chords of the eleventh and thirteenth, which are still less worthy to be regarded as real chords. MANUAL OF HARMONY. These formidable looking chords are as follows: 167. 1 3 1 1 It is evident that they can never be employed in pure four-part writing, since the necessary omission of some of their intervals would completely alter their nature, and transform them into simple suspen- sions, thus : 168. i ±=F= ^ ^m :i^i^ And even in compositions with more than four voices, where they might appear in their complete form, their character and treatment will still be that of suspensions, while in the more free style, where they may also occur without preparation, they can be regarded as ■changing or auxiliary notes. CHAPTER. X. CHROMATIC ALTERATION OF FUNDAMENTAL HARMONIES ; ALTERED CHORDS. The chromatic alteration of one or more intervals of a fundamental chord produces one of two different effects : it either causes a modu- lation into some new key, or, it gives an entirely new form and con- struction to the chord itself. If, for example, the major triad be chromatically altered in the following manner, there will arise : a. Modulations. a.. ^§Ej=^=^^g;Ep^°|^^^^ I03 TylANUAL OF HARMONY. Through C^, the diminished triad of the seventh degree in D major or d minor, or of the second degree in b minor; Through El?, the c minor triad ; Through Ej? and Gb, the diminished triad of the seventh degree of DI2 major or minor, or of the second degree of b\> minor. The last X^no alterations are only transpositiotis of the same chord into other keys, namely, C^ major and C^ major. b. New forms. ,70. pt^ E^ p^^^1^f^ | ^«^H Of these, the formations at a, b, d, f, can occur accidentally by the means of passing tones, but they have no harmonic value. It is different with those at c and e, which have the character of real chords. The first form of the triad {c) is known as the augmented triad. This chord was first found on the third degree of the minor scale. As before mentioned, it seldom appears in this connection, but more fre- quently as triad on thtjirst, fourth Sindjifth degrees in major, with its fifth raised chromatically. It is easy of explanation, as the pass- ing tone (G||) to the following note (A) and its progression is in- cated by this tone (Gj:|) as an augmented interval : SEEg- r-§- The inversions of this chord are also practicable li^lilili^lH IV Although these chords are generally used either as passing chords, or with the fifth prepared, yet in rapid changes of harmony they may also enter free, that is, without preparation : MANUAL OF HARMONY. [03 173. i-,LiJ ^S^^ 9fc I To the augmented triads on the first, fourth and fifth degrees may be added the sevenths belonging to those degrees. The chord of the dominant seventh is the one most used. a. The augrmented triad in connection with the dominant seventh. 1 74. 4 4 3 6 3 6 S X 2 6 2 6 ^=^^^^^^m ^'^^ ,^Z | 7_^^2_ | _^_^ |ig^ ^i^ C: V7 I - 6. In connection with the seventh of the first degree ft .-^ ^S> 5;: _^_ ^ -^- ^_ \ ^^^3^E^^p^J3^ E^=S--J^^-=^ f^^ C: Irr. IV c. The addition of the seventh to the augmented triad of the fourth degree is very seldom used. 4 4 3 6 2 6 — ''-^ e J — H 176.< _-gl -to: -f5> a.- I C: IV7, viio I04 MANUAL OF HARMONY. In all the above examples the ordinary cadencing progression of the fundamental has been adopted. The following examples will serve to show that the chords of the seventh with the augmented fifth can also be used with other chords of various degrees and in different keys, and with different bass progressions. ==l^fetl C: V7 e: V7 C: III l7. d: V C: ill I7. G: V7 These harmonic combinations which occasionally sound so unusual and harsh acquire importance only through their connection with other chords, and especially if in a certain degree they are brought about through an inner necessity of the voice-leading. If it is the duty of a text-book to show the possibility of such har- monic combinations, it is also its duty to caution the Student against employing them until he is thoroughly conversant with the simpler and more important forms of harmonic progression. Exercises. MANUAL OF HARMONY. 105 6 6S 6 4 3 2 6 aa 6 4 7 II 4. 6 3», li 6 N.I 3 6$ 6 6 6 II [')•#/* ^ 1 1 1 /J 11 y T \\j "1 ^ (d ^ 11 ' Lfii 1 L_s'_IJ gi frp= r iS 6 $ 4 — 2 — 25- I 6P 7 6 5 5 6 45 Q a_%ia3 H eq 4 4 2 6 3 35tef?^E a2¥ 6 6 4 5 :1=P ■^zf^zi^ :^ aaSE^^ ^==1= ^ 6 4 6$ ii 6- 5- t §-%* 1=i=t IB e ^ In the fourth exercise at N. B., the fifth of the minor triad on the second degree is augmented. The effect of this unusual combination is not unpleasant in its present position. From this it will be seen that the natural progression of parts will often lead to new combina- io6 MANUAL OF 1/ A R MO NY. tions, which, however, are not of sufficient importance to require sep- arate consideration. Note.— In the fifth measure of No. i in the above exercises, a sign occurs which has not been used before ; this is the horizontal line, , which being placed after a figure indicates that the interval is to be sustained. To illustrate the proper manner of working out these exercises, the first example above is here given: :]==t S5 xig: 6$ H 3 m -^ Ed. ^ C: I • IV II viiO I V?- I 117 V From the formation at e of example 1 70 : (which is also known as the double-diminished triad) arises a chord which is often used, namely : the chord of the augmented sixth. The first inversion of this chord gives : feiii^ P^: W Its resolution (as at b) is determined by the rule that augmented intervals must ascend. This chord is naturally resolved into the chord of the dominant, as in 179, where the chord of the augmented sixth, which is derived from the minor triad on the fotirth degree of the scale of g minor., is resolved into the triad of the fifth degree. NoTK. — The natural tendency of the subdominattt triad is to pass into that of the dominant. When its fundamental is raised.a chromatic half-step, and the chord in- verted, the pressure towards the dominant is very much increased by the direction which the altered interval fnust take. — Ed. The chord of the augmented sixth is peculiar, from the fact that its third (original fifth) only can be doubled in four-voiced writing. MANUAL OF HARMONY. 107 180. < i^^i^iiB :&g: :b The other positions of the original chord (tlie so-called donhle-dim- inished triad) are also available. The second inversion (|) can be used in four parts when the voices lie in a very open position. The fundamental position can be used in three parts, but seldom occurs. 181. 1- d22: =f:^^ h. Not 1^ m^B^^m Remark. — The chromatic alteration of an interval of the minor triad is already shown in the formations at 169 and 17c, and needs no further investigation. Also, the chromatic alteration of an interval of the diminished triad will result in either a major or minor triad, or formations already contained in the examples referred to above. Thus, the form of the triad in No. 170, d, will be like the following which belongs to C major: Better in open position. i K I C\ vuo In many text-books this chord is termed the harsh diminished triad. Such chords appear only incidentally, in passing, and their progression is determined by their intervals — the augmented ascending a degree, the diminished descending a degree. T/ie chrotnatic alteration of an interval of the chord of the seventh, has already been noticed (page 103), where the chord of the seventh was found combined with the augmented triad. Of the other second- ary chords of the seventh, that on Xhesecofzd degree oj" the minor scale is of especial importance among the altered chords which in the fol- lowing form produces chords very much used. Io8 MANUAL OF HARMONY. By chromatically raising the third: 183. * I1O7 If the following inversions are given 184. "# *■ Of these, the second inversion is most used ; the others appear very rarely. This chord in its second inversion is known as the chord of the augmented sixth, fourth and third. Its resolution is founded on that of the fundamental chord ; thus, as the chord of the seventh on the second degree resolves naturally into the dominant, this will also be the case with the altered chord and its inversions : 3^ -fe- ^ -~sr- I a: IIO7 If the fundamental be omitted in this chord, we have the augmented sixth chord, shown above, thus explaining the natural tendency of the chord to the dominant : ^^E With omission of the fundamental. a: I1O7 * a: I1O7 V or compared with No. 179, in G minor : •"undament Fundamental chord. Chro. raising of the third. Aug. chord of the sixth, Aug. chord of the sixth. burth and third. :^i= ^1107 it «^ g-. 1107 fe =«§= 1107 MANUAL OF HARMONY. [09 Remark. — It may be further remarked that the chord of the augmented sixth, fourth and third can also be formed by adding a seventh to the harsh diminished triad, mentioned on page 107. The resolution would be different, however, as Ma/ chord was found to rest on the seventh degree, while this rests on the second. Instead of the fundamental, the ninth of the original chord can be added, whence is formed the chord of the augmented sixth and fifth. It is formed as follows : Fundamental chord. Without fundamental, Inversions. With ninth. with elevation a $ h of the third. ' 5 •^iE^=i=E^^i^ S&7 w m^m Of these chords, the ^rst inversion (a) is the most practicable. The other inversions are seldom used. Its natural resolution is again the same as that of the already men- tioned nearly related chords, namely, to the dominant, but the direct resolution always causes parallel fifths. -■^^^^^m These fifths, which are not among the most objectional ones, may be avoided in three ways ; firstly, by an anticipated resohction of the fifth (the original, above-inentioned ninth as a supension), as in Ex. 190 at «; secondly, by a free progression of the fifth to the third of the same chord, as at b ; and thirdly, by delaying the resolution of both third and fifth, whereby the chord of the sixth and fourth is in- troduced between the augmented chord of the sixth and fifth and its resolution, as at c. The latter method is the one most frequently used. •i^H^lfc^Si^fe Not. I Better. I -G>- Ete =g=±=i=l=g _l^^-F5^4r-^rfE H ■fe Note.— The above three chords may be used in major as well as minor, as the dominant harmony, into which they all resolve, is the same in both. — Ed. ,IO MANUAL OF HARMONY. Remark. — The addition of a ninth is not sufificient to warrant us in classing this harmony as a chord of the ninth. . The progression at a shows very clearly that the ninth has here, as elsewhere, the character of a suspension, and the same may be said of the progressions at b and ^:^s= /f> ^o 51^ .xa I.I B\): V7 a: iVy I V? I At the close of this chapter, we review oiice more the broad field which it has opened for harmonic formations. We have found much that was generally known and useful, and much appeared which was worthless or unfit for use. Nothing appeared, however, in its origi- nal state ; everything had undergone some change, an addition, or to an extent an embellishment. This forsaking of the original form gives occasion to refer again to what was said on page 104. While it was a long time before these harmonic transformations were discovered, it was yet longer before they were brought to prac- tical use. Much that has heretofore seemed unfit for use may yet, with time, be perfected ; but it is unadvisible to direct the whole effort to the discovery of new harmonic formations and their unwholesome use, merely from a desire for originality, lest we lose sight of the more \n\Tporta.\\\. J'tindame?2tal principles -which, contain the healthy germ of art. All these transformations should serve more for embellishment in carrying out the fundamental idea, and unless sparing use be made of them, our work will appear overloaded and ourselves be regarded as devoid of taste. MANUAL OF HARMONY. »i3 At the close of the presentation of all the essential harmonies and their immediate use, we append a table giving their varieties and derivations. View of all the Chords belonging to a Major or Minor Key. I. FUNDAMENTAL HARMONIES. a. The triad. I b. The chord of the seventh. 1=11 A. The Varieties of the Triad: Major, Minor, Diminished, Augmented. Major Triads. Of the major scale. Of the minor scale. C:T IV V «:V VI Minor Triads. Of the major scale. Of the minor scale. m^ i^sa a: I IV C: II III VI Diminished Triads. Of the major scale. Of the minor scale. C: viio a: 11° viiO Augmented Triad of the Minor Scale. J:. a: III' N. B. For other augmented triads see under II.: Altered Chords. Inversions of the Triads. a. The chord of the sixth. b. The chord of the s^xth and fourth. 114 MANUAL OF HARMONY. B. The Varieties of the Chord of the Seventh. a. The chord of the dominant or primary seventh. b. Secondary chords of the seventh. a. Chord of the dotninant seventh ( major triad with minor seventh.) Formed alike in major and minor. 1 ^11 C: \\ i 0^^{m b. Secondary chords of the seventh. 1. Major triad with major seventh. ^ In major. In minor. 2. Minor triad with minor seventh. In major. C: 11^ 11I7 vi^ Diminished triad with minor seventh. In major. ^eJ ^m C: VIJO. Diminished triad with diminished seventh ( chord of the diminished seventh.) In minor. a: viio 5. Augmented triad with major seventh. In minor. #^=0 MANUAL OF HARMONY. IS Inversions of the chords of the seventh. a. The chord of the sixth and fifth b. The chord of the tth, fourth and third. II. ALTERED (CHROMATICALLY CHANGED) CHORDS. The augmented triad, formed from the major triad. In major. b. The chord of the augmented sixth, formed I. From the minor triad with raised fundamental ( so-called double diminished triad ) : i t=^%-=^^. 2. From the chord of the seventh of the second degree in minor. (See the following chords.) c. The chord of the augmented sixth, fourth and third. d. The chord of the augmented sixth and fifth, — both formed from the chord of the seventh of the second degree in minor : Without fundamental, With the ninth from Raising of Second chord of the fundamental the third: inversion. aug. sixth: and without the latter. :ig i=i^gg CHAPTER XI. ON MODULATION. The term modulation formerly signified the manner in which harmonies were arranged to a given part or melody. By it is now un- jl6 MANUAL OF HARMONY. derstood the digression, or passing, from one key into another. The meaning of the term having been decided, it will next be necessary to learn to properly recognize and define each occurring modulation or digression into a foreign key. In a later chapter, the means by which modulations are effected will be more fully set forth. A modulation takes place whenever a chord appears which is for- eign to the previous key. The original key is then entirely abandoned and all succeeding chords must be considered as belonging to the new key until another foreign chord is introduced, when a new modulation will naturally arise. 192. Thus, in the above example, a chord appears in the third measure which cannot belong to the key of C, but which is easily recognized as the chord of the diminished seventh, on the seventh degree of d minor. In the fourth measure we find the triad of C, which now cannot be in the key of d minor, but it is doubtful whether it belongs to C major or to G major, as the chord may belong to either of those keys. [It is most likely that in this case it belongs to G major, as this modulation is decided by the next chord.] The concluding mod- ulation to a minor in the fifth measure is evident enough. The chord of the dominant seventh^ and also the chord of the diminished seventh are the most decisive means for modulating. All other chords are ambiguous, as they may belong to several keys. Thus, the triad of G major does not belong to the key of G alone, but is also the dominant of C major and c minor, the subdominant of D major, and triad on the sixth degree of b minor. Owing to this ambiguity, it will often be necessary to consider the situation in which a chord appears — that is, what precedes and follows it — before decid- ing its place in a key. A decided modulation can only be effected through the chord of the dominant seventh or its inversions. A musical ear will, of itself, easily grasp a modulation. It will always MANUAL OF HARMONY. 117 take the foreign harmony as being the one which is nearest related to the present key. Thus, for example, in 193.bfc=S:=u the major triad of D taken by itself, would belong to the key of D major, but in connection with C major, the ear at once recognizes it as the dominant of G major, and the following chords will only decide the permanent key. The following exercises are for practice in ascer- taining the course of modulation. The markings under the bass should be strictly followed in all cases as shown in the first exercise. Exercises. 194. §tffi :fc# C: I C;V, I C: IV V, :F=f S ;==t w 1e£ a §5 6-7 4-1 ^^m 6$ ii8 MANUAL OF HARMONY. 7. 3 3 4b 4 6b 6 2 3 4 6 6 6 6 4 6 6 ^»$g #^F^^g#g ^=&^&^ ppS 4 7 3 2 6 gjr ^^= i:tgs|g-^ fE^'j=5=3 fEjE;i^:=^ 8 7b 7 $ 6 6 6 4 ^ 4b 317 2 6 2 r-r~£ i=^ ffi -<9 I gy g )- 6 3 2 7 47 10. 8 6 4 3 3 6 ^^^s^^^^^m m ^-^ if^ 1$ 6 Z% pi^i^^ ^ 6 6 3 4 ^ 4 7 2 6 7 3 ^^^^ ^-^js? ^- F= H— I — r en g y-pr^j — -.^^T — f^T= ^ 4=t: MANUAL OF HARMONY. 19 PART II. ACCIDENTAL CHORD-FORMATIONS.— TONES FOREIGN TO THE HARMONY. CHAPTER XII. SUSPENSIONS. The simultaneous progression of all the parts of a chord, especially when, as in the foregoing examples, there is no variety of rhythm, occasions a certain monotony and sameness. Sometimes, however, instead of all the parts proceeding at the same time from one chord to the next following, one or more will remain stationary, while the remainder proceed to their respective positions in the succeeding chord. The most important of this class of progressions is termed the sus- pension. A suspension occurs when a certain expected or even neces- sary progression is delayed in such a manner that a voice which should descend one degree in order to take up its position in the suc- ceeding chord remains stationary, while the other parts proceed inde- pendently of it. The delayed or suspended voice proceeds to occupy its proper position later in the measure. Thus, in the following ex- ample — i 9t H the soprano may remain on C, while the other voices take the chord of G in the second measure ; the suspended part being then re- solved into the note B in the second half of the measure: 1 15^ I 120 MANUAL OF HARMONY. In the same manner a supension can be formed from Ex. No. 195 by delaying the tenor : 1 ifc ist The principal feature of the supension, is that it generally forms a dissonance with the chord in which it appears, and acts as a means for the closer connection of harmonies through the expected resolution of the dissonance. That the dissonant character of the suspension does not always exist is shown in Ex. 197, where the suspension is not dissonant with any interval of the chord, but only a chord of the sixth over the bass note G. In this case the unusual appearance of the minor triad on the third degree, between the triads of the first and fifth degrees, as well as its peculiar position, together with the delayed progression of the tenor, all combine to give the phrase the character of the suspension. The necessary rules for forming suspensions are given in the above examples : A suspension may be formed by delaying the progression of any voice which would naturally descend one degree, provided the tone which forms the suspension be prepared. The suspension in its com- plete form may therefore be considered under three heads, namely, the preparation^ the suspension itself and its position, and its res- olution^ or progression. a. The preparation. The preparation of a suspension is precisely like that of any other dissonance, and may be effected by means of any one of the intervals of a triad, and also, though more rarely, by means of a seventh, gen- erally the dominant seventh. Preparation through the octave of the fundamental: -^— tgp- 1^2 Through the third: aiSii C:I I a: VII07 C\ I MANUAL OF JIAkMONY. $ Through the fifth m ^ I ^ C: I G: V VI C: I IV I e: viio. Through the dominant seventh. I ^- C: Vt V7 a: V The preparation must take place on the unaccented part of the measure (arsis) ; the suspension enters on the accented part (thesis). The note of preparation must be a^ least as long as the suspension itself, in conformity with the rule previously given for the preparation of dissonances. b. The suspension. The entrance of the suspension on the thesis has been mentioned, but its position in other respects must be more minutely explained. The suspension may appear in any voice and before any interval of the triad, ^ — before the seventh very seldom. I 199. / Suspensions before the octave of the fundamental. C: V7 I |=g^5fe m V7 I V7 m MANUAL OF HARMONY. Before the third. J=E=«=d= 5 _ 4 3 ,^i ii ^ Before the fifth seldom, only in certain positions. a. _ b. c. C:\ V7 C: I The remarks on Ex. 197, will apply to all suspensions before the fifth. Thus, in the above example the progressions at a and c will have the entire character and effect of suspensions, while that at a^ will not. If a seventh be added to the chord into which the suspension is resolved, as at b in the above example, the dissonance of the suspen- sion is at once perceived; also at e. The reason why the seventh can seldom be suspended, is that the suspension would in most cases form a perfect octave, and as such would not have that dissonant character which is essential to a suspension. If, however, the octave be dimin- ished instead of perfect, a suspension of the seventh is "possible, as at b in the following example : ^-^ w The progression at a in the above example is called a passing seventh. MANUAL OF HARMONY. »3 c. The resolution. The resolution of the suspension, as before remarked, takes place by the same voice descending one degree. Remark. — different ways of making resolutions will be treated later. It should here be observed, that the tone of resolution (the tone which has been delayed) must not appear in any other voice except the bass. P b. Better. J=i .-=U L \ ^ e ^- WE^ -<2U^,2_ ±^ -%- ^^Ei^T^- In example a, the tenor moves from A to C, the C being also the resolution note of the soprano ; in example c, the tenor takes the note G which is already suspended in the alto. Both of these cases are faulty, especially because the third and Jiftk of the chord are doubled. The effect of doubling the ftinda?7iental^ as in example d^ at N. B., is better, particularly when the natural flow of the voices require it, as in the following passage : Fundamental. Third. Remark. — It may be here observed, that when the fundamental is doubled it should always be at a distance of at least an octave from the suspended note, and that doub- ling in the unison is to be avoided, e. g. ^ \ m ^ Between bass and tenor, however, such a progression as the above may be possible. 124 MANUAL OF HARMONY. Other intervals besides the fundamental may, however, be doubled in the bass. That voice being the one which determines the chord, has the power of resisting the dissonance of the suspension, and such doublings are therefore admissible if the intei^val so doubled be intro- duced by a good leading of the voices, e. g. 2.0)3. Faulty. The fault contained in the last example becomes j^lain if the sus- pension be omitted, when open octaves will be found between soprano and bass : te e It is the same with fifth progressions which are covered by the suspension : J— I- Wmm These remarks may be condensed into the following rule : The suspetision does not remove parallel octaves and Jifths. Hence, the following is faulty. MANUAL OF HARMONY. 125 Nevertheless, paralled Jift}is^ covered by suspensions, are not to be unconditionally forbidden. Their employment is rare, however, and must depend on the leading of the other parts being such that the un- pleasant effect of open fifths is not perceived. It is impossible to give positive directions regarding them, and to reject them totally would be going too fai. The suspension in the bass^ which usually occurs before the third of the chord, or, which is the same thing, before the chord of the sixth, or the sixth and fifth, does not allow the suspended ttote to ap- pear in any other part. The suspensions before the fundamental, and the fifth, are seldom used in the bass. See Ex. 199, at the end. 208. The method of figuring the suspension has already been partly shown in the foregoing examples. When the suspension lies in one of the three upper parts, the interval found between the suspension and the bass is indicated, together with its resolution. For example :|-, 9 8, 7 6. Where necessary, other figures are added to indicate the chord into which the suspension is resolved, c. ^., the chord of the sixth H, the chord of the sixth and fourth 6- or 4^. If the suspension lies in the bass, or lower voice, the accidental intervals of the upper voices are indicated by figures, e. g., |-, or if it be a chord of the seventh 4-, the dashes signifying that the voices remain stationarv during the resolution of the suspension. 126 MANUAL OF HARMONY. The suspension in the bass is also indicated by an oblique line ovei* the suspended note, and the proper figuring over the note of resolu- tion ; for example : i ^ I ^ T=^ -gr-Y^- In the following exercises the former manner is adopted, as the most usual. . Note. — As the suspension is not considered a real harmony, it will be necessary when adding the Roman numerals under the bass, to make them apply to the fun- damental of the resolution, which is the real chord. An examination of No. 211 will show how these exercises are to be worked out. It should also be observed, when the figure 7 is followed by a 6 over the same bass note, that it does not imply a chord of the seventh, but a chord of the sixth with the sixth suspended by the seventh. See No. 211, third measure. — Ed. Exercises. o. I 5 - 4 3 7 6 5 _ 5 7 4 3 g5 ^='^^^giiigiga ] lgg-^^gf^ IV V7 117 V7 I 6 7 41t :b ^i 4=tFi=3:^ 3. 3 s3e 5 - 2 6 3G 98 2 62 si^E^^ S3 ^ 6 't4 ° 75*— "g- ^a MANUAL OF HARMONY. 127 7 6tJ 4 7 7 98 3 - 6 6b J a^ 6 5-6 6 4 3 6 ilH -^ ^^m 7 $ 4 6 6 3-4 2 7 -t9-h^ :[=£[= :if^ 4:^^ 6 5- 6 4 4 3$ Ft Ei$S: 68 5- 5 - ^ 3 8 6 432 620^ 3b6 2 ^ r-^r ^-~-:=jn .: d. 4=^: s*— V ay|^=j^;^gEg 987 5 6 6 4 6 5 3 7 7 6 4- 76 - 3 2 6 6- 6 4 3 4 765 -?d ^ 7 — : H -^^-^ 1 Lrt ^ ="-^ 3^.J In working out the above exercises it will be advisable to write each voice on a separate line or staff, both in order to obtain a cleai'er view of the progression of each part, and also as a useful preparatory exercise in reading from score. Inasmuch as the four different parts are always considered as vocal parts, it will also be better to write each part in the clef which properly belongs to it, instead of the violin clef as heretofore. Familiarity with these clefs is necessary in the study of counterpoint, and they are easily learned by practice and comparison with those already known. Remark. — A knowledge of the alto and tenor clefs is indispensable for the read- ing and understanding of scores, as many voices and instruments have their parts written entirely or partially in then), 128 MANUAL OF HARMONY. The clef proper to be used by the soprano, alto and tenor, is called the C clef. For the lowest voice, the bass, the F, or bass clef is still used. The position of the C clef always indicates the once marked (mid- dle) C, and for the soprano this C is placed on the Jirst^ for the alta on the thirds and for the tenor on i\\e foztrth li'nc^ e. g. Soprano clefs. h^' 3SEES =a Tenor clefs. The ordinary compass of the voices in these clefs, as well as the relative position of the same notes, is clearly shown in the following example : ^ i fm ^- :i=^ -t-^- V^ v^ I I Soprano clef. ^^ T=p= ^^^ Alto clef. i^ , Li * Tenor clef. ^— • fc^.^^^^ m 9i=J: ^ \m^ii t^^^ Probably the best method of fixing these clefs in the memory, is to carefully observe the position of the C triad, written for the different voices; then the neighboring tones are easily found. Thus the posi- tion of the C triad, with the fundamental doubled, will be : In the soprano : t3=«---- MANUAL OF HARMONY. 29 In the alto -«- c In the tenor, best in the position of the chord of the sixth and foin'th : -#-0 The first exercise of No. 210 worked out in these clefs follows here 21 1. TtT-^^— -f^ ^- — — L 1 ^ 1 rj — ^- ^1 F=5=i; Itaiji f= — — -i9 (^ f5>— -G>~ £i£d=d — =1 5 - 4 3 Rf Ttr ~ 1 B\, CI F g: \ - IV - 7 Ii07>5b:lll V7 I IV I F:\1 I ^--. :p=t: 7 7 ^b;VT fflS^ :l=-^ =^4 -(S-^"- s 7 6 5 - 4 - 5-6 32643 4 76 5 5 I 7 9i^ i=± :}i!2 — ^. s'-'g- I Dt g c V7 I IV /^7 ^b^ ^b:V7 I II ^"■- I iS'b "°7 >9 7 VI li«^7 V 7 The following will explain this treatment: The close position in which the above example begins is exchanged in the fifth measure for open position, which continues until the elev- enth measure, when close position appears again. This variety of position was due to a freer leading of the soprano and tenor. In the fifth measure, the soprano skips from its natural position to the seventh., El2 (at N. B.), a skip which is good when the J'ti?idat}tental is already present in the previous chord, as here the F in the bass. Again, in the seventh measure, the soprano leaves its MAlsrUAL OF HARMONY. '31 position and skips to the fifth of the chord, the other farts remaining stationary, whereby the suspension appears in a better position. Fi- nally, the close position is resumed at the end of the tenth measure by means of a free movement of the tenor. Suspensions from Below; Resolving Upward. Suspensions from below are only regarded as such in a few individual cases. Most progressions of this kind are caused by a shortening or contraction of an ordinary suspension followed by an upward move- ment, e. g. ■ST -G> The suspension from below may be formed by delaying the pro- gression of the leading tone : and also with many intervals which ascend a half-step, especially in the case of those chromatically altered chords which contain aug- mented intervals, e.g. 215. Observe, that as in the case of suspensions from above, the note of resolution must not be found in any other voice except the bass. The last of the above examples gives us the combination which has already been found as a chord of the seventh on the first degree of the minor scale, and which was pronounced unfit for use as a fundamen- J 2 2 MANUAL OF HA RMONY. tal harmony. It is evident, however, that when employed as above, it is only to be explained as a suspension (or retardation) of the lead- ing tone. Of other suspensions, especially those progressing a ivhole-step upward : 216. J__l'___^-.f«-J_i''-^4^>^4-J J- ii^Elife-liii^jsi] some show in themselves their unnatural progression ; while others, however often they may find place in practice, in theory must be condemned as unfit for use in pure part-writing. Should these irreg- ular suspensions be carried out in the manner shown in No. 213, the faulty progressions upon which they are based would show them- selves : . d. , 1-^- - \^_ a. b. ^ c. 1,1 ^ 1*1 l^- Suspensions in Two or More Voices. Suspensions may appear in two or more voices at the same time : Suspensions in two voices. Ii> three voices. . I 1^ I I \^%% The chord of the sixth and fourth often appears as a douole sus- pension, e. g. - t i- -^ ' 1 I r I I i_^eEE Its: t^ •-#- ^ I To break off in the following manner would not be good I I etc. §iE: ^^ £P 142 MANUAL OF HARMONY. Stationary Voices : Sustained Tones. Sustained or stationary voices in the upper parts are less frequent than the organ-point, and require more careful treatment. Sustained tones of this sort only suit the character of these voices when the chords not belonging to them appear but seldom, as these voices have not the power to counterbalance the effect of the foreign chords, which is a pecuHarity of the bass as the voice which determines the harmony. Thus, the organ-point in Ex. 234, a, if placed above the other voices, will not sound well in the last measures : 240. but the following with the dominant as the sustained tone, is better, because the last chords belong to it : The " Gloria" of Cherubini's Mass in C-major, contains an exam- ple of the effective treatment of the sustained tones, where an Ab in the violins is held for some time while the chorus and the other instru- ments carry out their respective parts below; also the D of the violins in the introduction of Mendelssohn's overture "Calm Sea and Happy Voyage." In either example few chords are found which do not con- tain the sustained tone as one of the intervals. The Trio of the Scherzo of Beethoven's Symphony in A, contains an A which appears as stationary tone in the upper and middle voices, and also as organ- point below, and which serves as harmonic basis throughout the movement. Stationary tones in the middle voices require as careful management as those in the upper voice. In instrumental works they may be MANUAL OF HARMONY. 143 doubled according to circumstances ; they rarely occur in four-part writing, and not at too great a length, e. g. m i J. t^-r I r I I 9i=E rt^yr Remark. — In addition to what has been said of the chords of the ninth, the follow- ing may still find place : In the above Ex. b, if the stationary tone be included, a complete chord of the ninth is found, inverted, and with a regular resolution. The objection to chords of the ninth, as already stated, is, that they cannot be inverted so that the fundamental and ninth can be brought into close proximity, as is the case with sevenths. That they may occur together at a greater distance, as above, is no reason for regarding them as independent chords, as they only occur in connection with a stationary tone, the character of which is to carry harmonies foreign to it, as for instance, in the case of the following ninth, which surely forms no chord of the ninth. 243. =^=5= ^^^^^- ^\ ^^ mm m^ f=t ^^ I When the harmonic progression above the organ-point is to be indi- cated by figures, the intervals above the stationary tone must be given, thus changing sometimes the usual figuring of the chords. The organ-point in No. 234, 6, might be marked thus : 6 — 76 4 — 5 3fc 7 6 4 4 244. gt 7 6 7 7 6 4 4 8 6 4 7 4 2 7 i On account of the difficulty of reading, as well as its lack of com- pleteness, this method of marking is only used in special cases. In scores where figuring is used, the words " taste solo" is often found, which indicates that the organ-point only is to be played. r44 MANUAL OF HARMONY. CHAPTER XIV. PASSING NOTES : CHANGING NOTES. Among tones foreign to the harmony are especially to be included passing and changing notes. Passing notes result from inserting tones between the greater or smaller intervals of the harmony. b. % J^^i^ m m The notes marked ^ are the passing notes^ those marked o are har- monic by-tones., that is, in so far as we take the first note as belonging to the triad of C , or a, e. g. 246. ( r r m pt3 The passing notes under a, Ex. 245, are called diatonic^ those under ^, chromatic. Passing notes lead from one harmonic note to another, and cannot, therefore, appear on the entrance of a chord but after it, upon smaller parts of the measure, and progress onl}^ by degrees. Changing notes are those tones foreign to the harmony which appear, like the suspension or appoggiatura., at the entrance of the harmony (in this sense on the accented part of the measure), and join themselves to the harmonic note (No. 247, (?), or, like passing notes on the unaccented part of the measure, serve as a melodic embel- lishment of two notes of like pitch. (247, b.) MANUAL OF HARMONY. HS ©J-p^^ Changing notes., therefore., may enter by skips, but must be closely joined to the har?nonic note., as shown in Ex. 247. That changing notes can be formed by the note lying below as well as the one above., may be seen from the above example. The chang- ing note below the harmonic note, especially if it occurs on the accent, inclines naturally, like the appoggiatura, to form a ?ninor second to the principal note, giving rise thereby to chromatic tones, as may be seen from No. 247 ; consequently, passages like the following would be objectionable : i±i * * J- ^ This is especially the case with changing notes which are introduced by skips. When they follow each other by degrees, as in a scale passage, they assume more the character of passing notes, and the following passage of changing notes at <7, need not of necessity be written, as at b: 24-9. TX^-. ^-. ^-. ^-. Those changing notes below which do not fall upon the accent, do not always require the minor second. Thus, Ex. 250, «, need not be written like /;, but c, is not as good as at d. 250. r r It is impossible to give definite rules on this point, nor are they nec- essary, as every musical ear can ascertain that which is right. Remark. — The third of the triad admits of the changing note taking a whole-step better than the fifth or octave. As the changing note before (under) the octave may also appear as the seventh, the harmonic progression only can decide respecting it. 1^6 MANUAL OF HARMONY. Changing notes above the harmonic note, whether they enter by skips, or as in No. 250, may form either major or minor seconds to the chord note because they occur diatonically, and are therefore gov- erned by the key and moduUition. Changing notes, one after the other, above and below the chord note, are often used, e. g. .r^ This is the origin of the following much used embellishment : C5 I i ^ggg T— P Passing and changing notes may occur in any of the voices. If, by preference, this takes place in but 07ie voice, this one will assume a more prominent character, while the others will serve as an accom- paniment ; or, if desired, all the voices can be made to participate alter- nately and thereby gain in importance. As a general rule, whenever the position and progression of a voice will admit of it, the applica- tion of these help-tones will give it greater melodic importance, but here again there must be a limit, as too much development in all the voices at once will produce confusion and lack of clearness. The following simple movement. 254, # i^=^ -i-l -^- MANUAL OF HARMONY. H7 ^ e :^^ 1 A lA. I =F=F by tlie use of these help-tones, might be written thus : 255. ^^^^^mm- as3K ^•^^Epgj t=t: =^E ^ J=d=d^d=3: t=i ;^] \ I iJt-j- -««.- ^ The passing and changing notes are here marked by crosses. How easily such a passage may be made to suffer from the addition of so many tones foreign to the harmony, may be seen if the above example be played in a somewhat rapid tempo. This style of writing is better adapted to slow movements. The same rule that applies to suspensions holds good here — the har- mony note following a changing note must not appear in any other voice., e. g. * g: t This can only take place when the parts are distant from each other at least an octave, c. g. ^E^d^Ehp^ *= MANUAL OF HARMONY. In accordance with the principles of doubling, the fundamental or fifth is better for the purpose than the third of the chord. In quick movements and with more lengthy application of figures formed by changing notes, other questions will arise, as will be seen from the following passage, which, however, cannot be taken as a four- voiced vocal phrase : f As to the regular passing notes, the same rule is to be observed regarding their proximity to harmonic tones, and figures like No. 259, a, (5, are not so pure as c, (/, e. Here, also, more rapid figures make this proximity more tolerable. 260., i ^TW ^^ ^-^- •^ =F=i= I Faulty Progressions through Connection with Passing and Changing Notes. As passing notes are used to fill up the intervals where skips are made in the harmonic progression, care must be taken when the har- mony changes, that no false progressions arise through covered fifths being changed to open fifths by the leading of the passing notes : J- P 4 ^m 261. -^^*i r— f MANUAL OF HARMONY. [49 Open octaves, formed by passing tones, may not occur, because the first of them will be harmonic as well as the second. 262. ^I^i ^ In the following cases, however, the passing notes will not cover the open octaves, and are therefore faulty : 263. ^^ -•- I r I -•- The entrance or progression of the changing note in parallel motion will also be faultv if it occurs in the following manner : better. The last example is better, because the octave progression is covered. Passing and Changing Notes in more than one Voice at Once. Parallel movements of thirds and sixths are most effective for pass- ing notes in several voices at the same time, e. g. 265. '50 MANUAL OF HARMONY. The free movement of the voices with the use of passing notes may also give rise to parallel seconds, fourths, fifths, and sevenths, of all kinds, and require great care in their treatment, and on account of their harshness are only to be admitted singly and in very favorable positions. Progressions of fourths are allowed when another voice is added a third below : 266. 33^ Single fifth-progressions, caused by passing notes, are sometimes found in good compositions, but that is no reason why they should be regarded as faultless. In the same way the harshness of seventh-suc- cessions can only be modified by a favorable position, a good pro- gression of the voices, and through tempo, movement, etc. In contrary motion., the various intervals of the passing notes often give the passage a peculiar coloring, and add materially to the inde- pendence of the voices, but they should not appear too plentifully or in too many voices at once. :ffi3 1^^ 267. Here also it will be seen, that those passing notes which, in con- nection with others lying beyond the simple harmonic structure, form a new (passing) harmonic leading, are smoother and more natural than those whose formation cannot be explained harmonically. The value of such movements can only be arrived at by taking into con- sideration their character and tempo. In regular harmonic progressions, several voices may receive pass- ing tones simultaneously, e. g. ^^^^mm\ 268. MANUAL OF HARMONY. 151 In all such passages, the main point is whether, at the change of the harmony., the voices shall be in a position to admit of their form- ing a regular progression. Changing notes can occur in different voices. a. In txvo voices : In parallel motion. •« I 3^^ td^^^l^^^^^ In contrary motion. f ^i :^l-i •LJi I I bJ J M Tf^ =R^ i^' <5. In ////'i'c voices 271. In/c c. in /oz^r voices. ip^ Remark. — Most of the above examples may be taken as harmonic progressions over an organ-point. It is plain from these examples, that in the parallel movement of two voices in changing notes, the progressions in thirds and sixths are the most natural, while parallel seconds, fourths, fifths and sevenths always produce a very harsh effect. Thus, no one would be apt to call changing notes like the following, good : Good. — — 273. i ^l^s^^ i± & f^ m r-r^ rife i JC2 MANUAL OF HARMONY. Chano-ing notes may also be of greater duration than the harmonic note which follows them, e. g. I 274. -^^^ --^.,^^^&,^^ :8<±^ The importance in composition of the subjects explained in Chap- ters XII, XIII, and XIV, is sufficiently great to warrant a careful in- vestigation of them, as a thorough knowledge of them will assist ma- terially in understanding the inner harmonic structure. It still remains to speak of their relation to the pure harmonic structure, the object of our next studies. Since the term "pure harmonic structure" has only been spoken of generally, it will be necessary to examine the question more closely and to present it somewhat in this manner : What application does our exercises in pure part-ivriting allonv us to make of these materials for composition ? It is undeniable that these materials are particularly adapted for the development and embellishment of the voices. If, however, our immediate task be to recognize and work out simple harmonic formations^ then everything which is adapted to de- veloping the voices may be used ; but whatever serves for embellish- ment only, must be rejected ; in short, the essential must be distin- guished from the unessential. First, as unessential, must always be classed : All unnatural and unusual hartnotiies in general^ zvhere they are not founded upon an imter necessity. Thev may easily cause overloading and confusion in a passage, and give evidence of a disordered or weak mental condition rather than strong, original work ; next. Irregular introduction ofsuspe?zsions; the use of sustained voices,, and anticipated and delayed, or after-struck tones ; and especially The changing notes which enter free, and the figures formed frofn them, in short, whatever is not appropriate to a good, plain four-voiced song. Vocal composition being generally regarded as the basis upon which all music is founded, much will have to be excluded which properly belongs to instrumental works. If the use of chorals or MANUAL OF HARMONY. 1^2 movements in that style is suggested for practice in learning a good and pure leading of the voices, yet, even this will not exclude the use of those materials when they serve not only for ornament, but for developing the leading of the voices. Especially to be reckoned among these, is the use of suspensions and the regular passing and changing notes. From the foregoing, it may now be understood that much which was forbidden as immaterial and not to the purpose in connection with the first study of the pure harmonic structure, may still be readily used in practice, whenever favorable opportunities present themselves. A complete understanding of the subjects so far discussed will be greatly facilitated by studying good compositions. We shall return to this subject in Chapter XIX, when opportunity will be afforded for attempts of our own. CHAPTER XV. PASSING CHORDS. Passing chords are those which appear in the weaker parts of the measure, like passing notes in several parts, and which sometimes deviate from the general rules of chord-connection. One variety has appeared already in those passing and changing notes in three voices, which assume the form of a chord, e. g. in Nos. 271 and 272. So that in one sense, the chords formed over an organ-point may be called passing chords. There are, however, still other phenomena of the sort which must be explained. As passing and changing notes generally depend upon rhythmical conditions, it becomes necessary for the explanation of passing chords, to glance at the different divisions of the measure. It is known that in simple even kinds of time., the accent naturally falls upon the first part of the measure, while the second part receives less weight. Now, if the harmonic progression be based upon the two divisions of the measure, the harmonies which fall upon the accented part will 154 MANUAL OF HARMONY. always be regarded as the more weighty and important, and as the point to which the chords of the second part will lead : o I o I 275. m^^i T ^ r mm. ^ In this sense, the chords on the second half of the measure may be called passing chords, although the regularity of the movement some- what obscures their chai-acter. That this has been so understood in theory, if not plainly expressed, is shown by the fact that much more care has always been given to chords which appeared on the accent, and much allowed to those on the unaccented part which was not permitted to those on the accent. The character of passing chords, however, appears more clearly with such harmonies as appear on the smaller division of the meas- ure, as in the following examples: m u u 2 7b 6 4 7 i±E =tf 7b 8 --4 7 277. * 9i: gp The peculiar appearance of the chord of the sixth and fourth in Ex. 276, a and c, and also of the chord of the seventh at c, is only to be ex- plained as a movement of all the voices by degrees, in the manner of passing notes, to the nearest chord — that on the accent of the next measure. MANUAL OF HARMONY. ^55 These voices may be still more easily identified in their character as passing if one voice remains stationary, for example, the bass of No. 277, a, or the upper voices, at b. The leading of the voices in No. 276, a, arose from applying both modes. If this condition (the progression of the voices by degrees) be ful- filled, all the chords can enter free, and find their explanation in the chord which next succeeds them. N.B. _ J33 ii Remark. — The free (upward) leading of the seventh, before mentioned, is here jus- tified in this explanation of the passing chords. In the simple tmeven measure, the accent will also fall upon the first part of the measure, while there will be two divisions of less weight. Passing chords will appear thus : 279. Smaller divisions of the measure can also contain passing chords, but after the above no further explanation is necessary. Here, also, the study of good compositions will be advantageous. The following remarks may still apply for personal attempts : All chords denominated as passing, will either progress in accord- ance with the known rules for harmonic progression, or deviate from them. In the first case, which is the more frequent, nothing further need be said ; in the latter, it will depend upon a flowing, melodious movement of the voices, individually, as well as in relation with each other, whether formations of this kind are to be considered correct. 156 MANUAL OF HARMONY. It can only be observed generally, that here also the movement of the voices by degrees ivill determine the character of the passing chords^ and that all such passages must be judged with reference to the rhythm, tempo and character of the piece. CHAPTER XVI. THE MEANS FOR MODULATION. The term modulation has already been explained in Chapter XT. The object there was to designate each modulation correctly. We have now to treat of the best means of effecting modulations. The art of modulation consists in finding those chords which are related to two or more keys, in order by their aid to pass from one key to another. Modulations can be effected in many ways, and serve various purposes. Firstly, they may appear abruptly, and the new key may pass away quickly; or Secondly, they may be more gradually prepared, in which case the new key will serve for some time as the foundation for the har- monies employed. In the first case the modulation will be introduced by the simplest and quickest means, and although it maybe distinct and unmistakable, the new key will soon be abandoned and a fresh modulation intro- duced. In the second case the modulation will generally be gradu- ally prepared bv various means, and the new key will remain long enough to become familiar to the ear, and may even lead to a cadence or perfect close. Thus, in the following example, the modulations are transitory, and the key changes rapidly without wandering far from the original key of C major : 4 — ^__4 — 1_4__^_^'^_4 280. 153. (i±s n 2 i ^r^^ i^ii C: F:Yi G: V7 ^^^ iE^t V7 MANUAL OF HARMONY. 157 This kind of modulation is only suitable for the more nearly related keys. In the next example the more distant key of El2 is gradually ap- proached, and when it is reached the original key is entirely aban- doned. It will be seen how the transitory modulations are employed as means of introducing the final modulation into Et?, which is the ob- ject of the phrase : 281 e :S: ±1 :^:^ ^S ^=^=i^ :&# ll] iiE .b»- ss ^ -^ ^^* ±21 C: I b\>: VII07 B\)-l /: V7 E\): V7 Unless these short passages are employed as interludes between two compositions in different keys, or as exercises, they must be made use of in a prescribed manner, since upon this formation of modulation rests also that of the periods and their divisions. This, however, is an important part of the doctrine of form, and is foreign to our present purpose. We take at present the formation of such modulations as exercises, in order to develop skill in the use of harmonies and their proper connection. In considering the means by which modulations are effected, it will not be necessary to distinguish between the above two methods, since the same will serve for both kinds. The first and most simple means of modulation will be the tOnic triad of the new key itself. If this triad is identical with one of the chords of the original key, it will only require the dominant harmony of the new ke}' to make the modulation complete. Thus, in the fol- lowing example at a, no modulation will be perceived, while at ^, the key of G major is only recognized when the third chord is heard : 282. ^i|i*Ei; "TTgFZ In the case of remote keys, the tonic 7)iinor triad is certainly more decided, but even this chord requires the dominant harmony of the new 1^8 MANUAL OF HARMONY, key to render the modulation unmistakable (at a) . The major triad of the new key, when not followed by its own dominant harmony, has in itself somewhat the effect of a dominant chord (3). i 1 :j(^ I C: I a: V C:\ As the tonic triad used as above for modulation shows itself to be weak and unsatisfactory, it is seldom used in its fundamental position, but its second inversion, the chord of the sixth and fourth^ has the property of rendering the modulation particularly decided. In this case also, the tonic triad is followed by the dominant, which completes the modulation, and at the same time forms the closing cadence. 284.' i^e^ C:lG:l =F=4^ : | ^ I V7 If this chord be employed on the unaccented part of the measure, the modulation will not be so decided : i ' 676 -«- 4 « 4 « S: i^e 7|j I MANUAL OF HARMONY. 159 A still more effectual means of modulation is the domina7it triad., and especially the chord of the dominant seventh^ which renders the new key clear and unmistakable. According to the principle that the connection of chords, one with another, is best effected by means of tones belonging to two succes- sive chords, and remaining in the same voice, modulations may be formed through the chord of the dominant seventh from the chord of the tonic of the original key to any other key, excepting those of the minor and major thirds and the augmented fourth. Thus, from the key of C major into all keys (whether major or minor is immaterial at present) except Eb, E, and F^, modulations may be formed as follows, the connection being in each case observed by means of tones which remain stationary, and indicated by ties. 286. i^-j^^ii=5-J^3^i=ll^^' Db: Or: , C to At>: C to Bb: (2 t?i2_t-^_ '^=^'^^=^\l'^-' -y--- ;-";— i?j ^=*i^r^i^|r*^'-*-^^^^-#l-ir^4^ii It is obvious that these modulations may be made in various posi- tions of the same harmonies, e. g. --fegi^=iEPa^3 In order to modulate into the remaining three keys (Eb, E, Y^ an- other chord will be required, usually a triad, which will supply the needed connection, e. ". From C to Eb: C to E: C to Fj. — *«'- - -#^r- i6o MANUAL OF HARMONY. Similar modulations may be formed from the minor, as follows. From a to b\ a to d: a to e: Into the remaining keys C, Dj?, Eb, Fji and At? through a connecting chord : From a to C: a to Db; 290.^^^ gig 1 -27- to Ab: It is of course understood that the above examples merely show the simplest principle of modulation, and that it is not necessary that modulations should always be carried out in this way. Nor is the above mentioned connection of chords alwavs requisite, as will be seen by the following example : From C to Eb; C to ^: a to C: Lfi=«: 3: ^-=|tfe 5S^ % -g^ g The student is here recommended to write out modulations from, and to, all keys, major and minor, through the chord of the new tonic, or the dominant seventh, and in doing so to employ all the various positions of the chords, and to play them on the pianoforte when written, in order to become well accjuainted with their effect. MANUAL OF HARMONY. l6l Another equally important chord with the chord of the dominant seventh, is the chord of the diminished seventh, which is often more peculiarly suited for jHuposes of modulation than the former, especially in those cases in which the seventh and fundamental of the dominant harmonv would be obliged to enter without preparation. The fol- lowing examples will show the application of this chord to modula- tion : From C to Bb: C to B : C to d\ a to e\ Beside this simple and natural use of the chord, especial advantage in modulation may be taken of its enharvionic nature. The following chord, being wa-itten with different notation, will belong to foiir different keys, although the sound will in each case be the same. %J^^^^i In the first of the above cases, the chord belongs toy minor, in the second to d minor, in the third to b minor, and in the fourth of a\i minor. Thus, by means of one chord, four modulations are possible : FromC to /: C to ^- The above examples will be sufficient to indicate the manner in which other modulations may be formed according to the same principles. Extension of the Modulation and its Completion by means of the Cadence. The process shown above, for passing from one key into another, was founded upon the simplest and most natural means. If we wish to form a longer and more gradual modulation than any that have hitherto been met with, the same means will be employed, but not in so direct a manner. That is to say, instead ot proceeding to the new key by the shortest and most direct means, transitory modulations will be used, and the new key be introduced by degrees, and when reached, will be, as it were, fixed and rendered distinct by means of the cadence. For this practice we can form for ourselves exercises of the following kind : Modulate from C major through d minor, a minor and G major to e minor. This could be done something like this : I I ^-^ 1 I 1 , . - 4_ -19 '$'- "I — r -1—4-^-4 is :^ ^F^*tf m^^^^^^m^^^^ C: I d:\nO„ a: viiO„ ^.- V, When adding the cadence, the following should be noted : If the final modulation he effected through the chord of the sixth and fourth of the tonic triad of the new key (see Ex. 284), then it will only require to be followed by the dominant chord to complete the cadence, 302 i J 264 MANUAL OF HARMONY. In other cases the extended or prepared cadence must be added to the modulation in order to confirm the key. The simplest forms of the extended cadence are I — V — I, the first of the three chords being usually in the form of a chord of the sixth and fourth, and 11 — ^V — I, the chord on the second degree generally appearing as a chord of the sixth or sixth and fifth, e. g. , In other positions. 1 iiE: s :i: 33g \ -^ i In other positions. iSJ^ m §i: ^^- t The position of the chords forming the cadence will depend upon that of the last chord of the modulation to which they are added. This is shown in connection with some former examples. The mod- ulation from C to Et? (No. 388), closes with the fifth in the soprano- To this is added the cadence in the position which will connect nat- urally with this last chord, e. g. From C to Eb. Cadence. 304-. 1^ %-- Ji: -P^; 5^ '^ % fe i^ ±^ 6 4b 7b ^■^- $^ % ±2: fi i MANUAL OF HARMONY. 165 The following modulation from C to a in No. 2S6, would require a cadence in this position. SOS. The modulation from C to B with the cadence under No. 303 b : From C to B. Cadence. 306.< Or from C to Dl2. -IS &,2. We conclude with an example on a more extended plan : From G through e minor, C major, and i^ minor to AP major. Cadence. ^^S: -gj 1^: --^^w<^- i==t. hi^zdn^. S^#^ ^- ^ The above will give an idea of how we can form for our.selves a great variety of exercises. i66 MANUAL OF HARMONY. PART III. THE PRACTICAL APPLICATION OF HARMONIES — EXERCISES FOR THEIR USE IN THE PURE HARMONIC STRUCTURE. The following hints regarding the most practicable application of harmonies, will serve still further to explain, elaborate, and make more complete the principles thus far developed. Individual cases will give occasion for further remarks. CHAPTER XVII. THE SIMPLE HARMONIC ACCOMPANIMENT TO A GIVEN VOICE. In treating of the harmonic accompaniment to a given voice, we have to consider the simple melodic progression of each part, and all other elements of a melody, such as metrical and rhythmical varia- tions, will remain for the present out of the question. I. Harmonic accompaniment of a soprano. The following simple exercise is selected : 309. "^ ^E^- i The letters used before to indicate the fundamental tones which are to serve as the harmonic basis, will be added above : C Q Q, d G — ?> I ^ 1 & " 1 ^~ =H ^•n^ 6 6 & s> LI i-l rs =u The above will serve, for the present, as an explanation of the ex- ercises themselves. In order more clearly to explain the principles of a good progres- sion both of the bass and middle voices, we shall make use of exam- ples incorrectly worked out. G7 314. P G7 i 1 68 MANUAL OF HARMONY. Remark. — For the sake of saving space, we shall use the violin clef in the follow- ing examples, and write the voices together on two staves. The pupil is advised, however, for personal work to practice the method used in No. 313. This exercise may be worked out thus : C F G7 C d W (a G7 t The above example contains no violation of any of the rules of pro- gression or chord-connection hitherto shown, nevertheless, it is meager on account of the stiffness, weakness, and insecurity of the bass. In a good progression of the bass (except in case of an organ-point), no tone must remain stationary unless it is required to do so in order to serve as the preparation of some dissonance, or unless it is equal- ized and counterbalanced by a very decided movement in all the other voices. The above example also contains, in two places, a faulty use of the chord of the sixth a7td fourth., ysA\\cX\ W\\\ afford an opportunity to speak of the employment of this peculiar and difficult chord. Of the Use of the Chord of the Sixth and Fourth. The chord of the sixth and fourth (second inversion of the triad) is far less frequently met with than either the fundamental position or the first inversion of the chord. The reason of this is that its proper use depends upon certain conditions. We have already seen how it is used in the formation of the cadence, and also in connection with modulation, where its effect is somewhat similar. In both these cases it may enter without preparation, but always on the accented part of the measure (thesis). Apart from these uses of the chord, it produces the best effect when placed on a bass which either remains stationary or moves by degrees. In this case it should be an inversion of either the tonic, dominant, or subdominant, and \is fourth should be prepared. MANUAL OF HARMONY 169 The following examples show the application : 6 6 \ 6 6 66666 66 In the above examples, the chord appears most naturally when rest- ing upon the three primary triads, as at «, while upon other degrees (^) it easily gives rise to an impression of modulation. If used on the unaccented part of the measure (arsis) it may appear under the same conditions as in the above examples, and, in addition, may be used with the bass prepared instead of the fourth, e. g: 317. f m^ I If the chord of the sixth and fourth appears on the arsis, it must be considered as a passing" chord, if on the thesis it will have the char- acter of a suspension ; its effect will, however, be very weak if intro- duced on the thesis with the bass prepared. This was the fault in Ex. 315. 318.' ^zig: 9- --^ ii^ i^i It also often appears as a real suspension, in which case the prep- aration of the fourth is fully explained and justified; in the second 170 MANUAL OF HARMONY. case (at a) still more decidedly on account of its appearing with the chord on the third degree, which occurs so rarely : 319. i =1^ r 1 — H -2?- 1 31 c: 1 ^ 6 ^ 4 3 2 6 5 ^ -I-— 6 4 6 6 = 1 When all the parts proceed by degrees, and the notes are of short duration, the chord of the sixth and fourth may enter without preparation : \- W^ 1 T n ii3 a=F % i This will require no further explanation after what was said in Chap- ter XV., regarding passing chords, and after the examples 276 and 279. Remark. — The fact that a preparation of the perfect fourth in the cliord of the sixtb and fourth is often necessary has led many theorists to consider the interval a disso- nance. In the introduction to this work it was classed among the consonances, and the grounds for this view were stated. The necessity for preparation is only felt when the fourth occurs between an upper part and the bass, and even then only in the chord of the sixth and fourth, for the chord of the sixth, fourth and third may often appear without preparation. Occurring between two upper parts the fourth is as free in its treatment as any other consonance, while this is never the case with a dissonance, which always preserves its character whatever its position. The chord of the sixth and fourth derived from the diminished triad is seldom used in four-part harmony on accoimt of its incom- pleteness. 821. f-=f 9r MANUAL OF HARMONY. 171 In the three-part phrase, however, it may he used, and frequently supplies the place of the chord of the second. (See later, the three voiced movement.) A correct and pure harmonic progression not only requires that the bass shall form a clear and intelligible harmonic foundation to the phrase, but also that each voice shall proceed according to certain melodic rules. Certain progressions have always been considered unmelodious — among them two consecutive skips of a fourth or a fifth in the same direction, e. ir. ii! The above are improved thus : 323. .9t I Even skips of a sixth are better avoided, and the progression altered to that of a third In the contrary direction, if the compass of the voices admit of them : Better. _ Better. .^t I Progressions of atigmented intervals are to be avoided as tin?)ielo' dious ; diminished, however, are allowable. Not. ^ Better. Not. Better. 1^ 9i: * m -r The skip of a major seventh is always to be avoided, that of the minor seventh onlv in case of an inversion of the same chord, but not when the harmonv changes. Not. _j2Z he 326. 1^2 MANUAL OF HARMONY. The last, in something like the following progression of harmony; Not very good. Not. Not. j =gEgg |i§= teS33 i;H j^ l^^l: ^^ These few remarks will be found to contain the principles of a good melodic progression, and will suffice for the present simple ex- ercises. It must be observed that the above rules of melody do not refer to the movement of the bass alone, but apply in general to that of all the voices. Exercise No. 314, with an improved progression of the bass, may be written as follows : 328 a. i m^ iiEi Exercises. 1. ^ -I5>- ^2 2. 1 r^ 328 b. 1, V^ ■ III \i/ '-' 1^ II U ' ii3 11 J C G C F C G C C — F ^- fe - g \ e > \^ -ig I Ei=E :[=^ i^izt IH^^feli^iH 9^ i^^ ^B^i:^i^ Such progressions are not faulty, however, when they only form inversions of the same chord., because in that case they do not pro- gress to other chords which Sive fundamentally different. 34-1. (i j= ^^S. ;i 9t m^^i \ Covered Fifths and Octaves in the Middle Voices. Although the progression of the middle voices ought to be as pure as that of the outer voices, yet on account of their position, being as it were covered by the outer voices, they may be allowed a greater MANUAL OF JIARiMONY. 77 freedom of movement, especially with regard to covered fifths. Hid- den octaves between the middle parts are seldom good, on account of the voices becoming too widely separated ; and with respect to covered fifths, their good or bad effect will depend on the good con- nection of the chords in other respects, and also upon their agreement with the rules relating to covered fifths between the outer voices. A few cases are here given : l^g^^ ( ^ Not. Not. ^ Covered Fifths and Octaves between the Outer and Middle Voices. Here also the conditions under which such progressions maj' be used cannot be determined by merely mechanical rules, but must depend on a good natural connection of the harmony. The following are a few examples : ±=gSS^^S3 r /n r ^^ H^ 1^ Not good. ■■"■~ ^ g? "^^ ■^-r ^ : i ^g^ p=r=g ^i i 178 MANUAL OF HARMONY. One peculiar kind of covered octave has still to be mentioned, namely, that which passes over the seventh. This progression is faulty in all the voices. ( See Ex. 149 and what follows.) All that has been said of covered octaves applies also to covered unisons. These are forbidden between soprano, alto, and tenor, but may occur between tenor and bass, where they are to be treated as covered octaves — according to the position of the chord and of the voices themselves. The cases in which covered fifths and octaves may appear are so numerous, that it would be impossible, even if it were not useless, to cite them all. The above remarks may be sufiicient, if we add the following maxim, which, however, is not for those beginners who are still engaged with the technical, or purely mechanical harmonic structure, without regard to the higher requirements of art : Avoid, indeed, covered fifths and octaves whenever possible ; but regard them as permissible, where, on the one hand, an otherwise natural, good connection of harmony is obtained, or on the other, reasons of a higher order prevail, such as melodious movement of the voices, employment of given motives, etc. After this digression, we return to No. 330, in order to correct the faults it contains. The covered fifth found there, which belongs to that class where both voices skip, can scarcely be remedied, since if we lead the bass in contary motion, the same fault will appear in another place, though it will be less perceptible on account of its occurring between a middle and an outer voice instead of between the outer v oices, e. g. MANUAL OF HARMONY, 179 In such a case, therefore, we have no choice but to alter the har- mony itself, and select a different marking of the fundamental tones, thus : C F <50 C — — 1 F c ■^ 5^ . C II F II — -^j — — t^i— -5^ li-^ ^ F 4. ^. Bb g ^ Bb C7 F ^7 C7 F —^ — iS* — _^c J ~^' ■ - --(5' — 1 — «>— =S=J 4^ ' — ' — FC^C^^F^^C^F [8o MANUAL OF HARMONY. The following exercise we will work out thus 1. 349. The faults of the above have been numbered for reference. The movement of the three upper parts by skips in paralled motion at No. I, is not good, since it deviates from all the rules of harmonic connection, and moreover is not necessary. The progression of one or two voices by skips is only allowable when some other voice preserves the harmonic connection by remain- ino- stationary or by moving in the contrary direction. No. 2 has the same fault, and is made still harsher by the free entrance of both fundamental and seventh, coming thereby in an awk- ward position where one crowds the other. It has already been said, that either the dominant seventh or the fundamental ought to be prepared. Thus, all of the following examples are defective : , ^ I'jiSl^i^i^^ 350. If the free entrance of the fundamental and seventh takes place in contrary motion, the effect, as already stated, is less unpleasant, e. g. MANUAL OF HARMONY. i8i Example No. 349 also contains another fault at No. 2, namely, a skip in the bass^Vow the chord of the sixth and fourth, which is contrary to rule. The third fault in Ex. 349 lies in the covered fifth which appears between tenor and alto, and which is made more apparent by the skip in the soprano. The covered fifth at No. 4 is objectionable, because unnecessary; that at No. 5 is better on account of both alto and bass moving in contrary motion with tenor and soprano. The following will be a more correct working of Exercise 348 : 352 a. 352 b.^ G C Exercises. G - D D7 G f i* D7 I ^ s* D7 G -laizt-^i i ^ m .a, -^- i ,82 MANUAL OF HARMONY. The next exercise, m 353. E7 a /J07 B7 e with the following treatment : contains an incorrect progression known by the nam^e of unharmonic cross-relation, or false relation. The tmharmonic cross-relation^ which belongs to the unmelodious progressions, occurs when any tone is immediately followed by the same tone chromatically altered in another voice, as in the second and third measures of the above example, where the G in the alto is immediately followed by the Q\ in the bass. In order to avoid this fault, the following rule must be observed : , When any tone is to be immediately followed by the same tone chromatically raised or lowered, such chromatic alteration must take place in one and the same voice. Although this rule is perfectly consistent with all the theoretical principles of harmony, there is perhaps none which admits of so many exceptions. In consequence, in manuals of later methods, the doctrine of the cross-relation has been regarded with suspicion, and instances cited in which the unharmonic cross-relations occur in a per- fectly natural way, without ascertaining the reason why they do not sound faulty. Here are a few that do not have a bad effect : 355. T m MANUAL OF HARMONY. ^83 In all these cases, the cross-relation is not formed by essential notes of a simple harmonic progression, but is the result of a contraction., or abridgment, of certain natural progressions which, had they been employed in their complete form, would not have agreed with the metrical character of the phrase. Thus, in the character of changing notes, as at a, ^, g; or through contraction, as at <:, (/, £',/', h. The original progressions, by the contraction of which the above cross-relations were formed, are as follows : Compare these examples with those under No. 355, at c, ■ F ^ 1 ^ \=\ E^3 "^ =^=H »^ "^ — G L-^ — 1 c F G a a, G 1= — (S- —a. — rs 1— S' L^- \ y=i ^— fl The foregoing is complete as a three-voiced movement ; with the addition of the tenor it will appear thus : 369 a. w -jS 1 i2- :s-Jizt=2^ i I I m Exercises with given Alto. 1. 369b.-|l^^-<|^^:^ ^ ~<9— I ^ r-^ ^ C7 ^ ^^ C F F Bij C -mr^ — ~—^=^-^ — ^ — ^l-t^TTT^ — ^^ — ^ — ^--- hlj^t? |-|^^i2iU ^ _| B|? C F ^ C F 4. Il^jii F C F C a- -<&— I — <5^ ^ C F 5. _ C At rt' <^ A7 G— 7 376. •M= Worked out 377. '.31 111 f=r ^^ :^=^ \ ? \ \ ^ iA f=T :0 6 75 7 4, 6 - 8 7 3b The next exercise will exhibit the application of suspensions. F Bb C ^ p- F Bb C7 F 378 ^gi$EE ;[| Worked out : We pass over the exercises in the middle voices. The object in using the simply melodic progression in whole notes for exercises {cantus Jirmus) was to show the simple harmonic con- tents of a measure, or, if in Alla-breve time, its principal divisions — half notes. If the exercise is to be in half-notes, chorals may be used for the purpose. For individual practice, the fundamentals of well harmo- nized chorals may be taken of, as shown below, and the working out attempted as follows : MANUAL OF HARMONY. Kt d a di IPl E E 191 E -7 380. S: rpj: -f9- Sie •5- 1 ^S"— rr\ Ir ^. — Bb F Bo ^ C F d F C7 F Both melody and harmony are simple, and the latter may be written out for four voices, thus : "mt- n «>■ «- ■" G> ^ _^s? V ^ — 1 ry b a. -i5>- U2- jS- 9^^?}F= — f — i G> 1 & G> 1 ^ ~l MANUAL OF HARMONY. 193 Before proceeding to further develop this movement, it will be necessary to premise what is to be mentioned concerning the rhyth- mical formation of a melody. A melody may be either a musical movement containing more or less measures, without any fixed limit, as often occurs with themes or motives of a composition, or it can be a distinct whole, separated and bounded by antitheses. In the latter case it is called a period, and contains usually eight measures, which, divided into two sections of four measures each, form antitheses. These sections are often called "thesis and antithe- ses" — sometimes " antecedent and consequent." That the above movement forms a period is evident from the close at the end. It will next be in order to ascertain the divisions into sections. These points of division are very often marked by the cadences which occur in the middle of the passage, either as imperfect whole, half, or plagal cadences. Such a half -cadence., usually a close on the dominant, occurs in our exercise at the sixth and seventh meas- ures, and the point of division between the two sections of the period will be at the place where the sign f stands. The first section, the thesis, will therefore contain seven^ the anti- thesis six measures, and each must be rhythmically changed to four measures. This may be effected in the following manner : •=P§^ ;@ By adding the harmonic accompaniment selected above, a complete musical period is obtained. 194 MANUAL OF HARMONY. Transformations into different kinds of time, as for example, into |, I, I, or i time, are very easily managed, e. g. •is 3t::* g^f?^f g^g^ is '=^f=^=B S^Ji^^^p^ '-i^^^l^^Ei We come next to the tonic variations of the melody, and add to it passing and changing notes, e. g. 386. E^ gt|t^=5y|p^^g^p| ir = J_^t^ tq 3^=^=^l -• hs* A still freer use of all auxiliary tones could give the following form : ^ ^ Adagio. MANUAL OF HARMONY. ,gc The simple melodic progression underneath is easily recognized as the original foundation. It will be evident, if we add the other voices, with the few deviations made necessary by the upper voice, tnat the above melody is carried out with reference to the original harmony : Adagio. ....^--^ , — ^ 'TI ^ rn^^ S ^m%^m iii 5±* tf — rP i i ?=^ I sSSeSi^^ As to the parallel octaves in the middle voices in the third measure of this example, they may be regarded as faultless when they do not occur singly, but in longer passages as a doubling of another voice for the purpose of giving it greater prominence. In this case the movement would be regarded as three-voiced. Notwithstanding the small independent worth of this example, it has served to show how- the simplest melodic and harmonic movement can be developed. The advantage to be derived from studying and recognizing these melodic and harmonic relations is too great for us to refrain from giving another example in the following interesting movement. The fundamental harmonic progression is just as simple as in the previous example. 389. if=&feH i-^fe* I This passage forms a period. The middle close is found in the half -cadence in the seventh measure. T96 MANUAL OF HARMONY. We omit the different kinds of measure, and select the following section : 390, . J. i =* S§i^^^.-^^ mga The upper voice may be developed in the following manner, at the same time adhering to the harmonic progression. The following passage from Beethoven's El? major quartet will show how the other voices can take part in melodic development: 392. ViOLINO I. ViOLINO II. Viola. Violoncello. ^3^ ^nrv^x^ w. 3^3=^ :r-5=?: J -J- i^ flai • §te! EE?E^ lf^=*=*^3 MANUAL OF HARMONY. 197 A comparison with No. 390 will show the melodic and harmonic variations. Here follows still another variation of the original melody from the same composition : 393, fc^= ^^S^p^pi^^^^^ The other voices aj^pear with the following variations. 394. sa P^^^ii ^^Pg r^: •^- iiS! ^ i^^ l2ziiS ^ ^ P gJ These hints regarding the development of melody will be sufhcient here, while further practice may be left to the personal efforts of the student. Remark. — The mechanical character of this whole treatment should not mislead us; for certainly in composition one does not always proceed in the way shown above. Our only object here was, partly, to place in the right light the relation of our pre- vious exercises to the practical side, and partly, to gain a clear insight into complicated compositions themselves. Concerning the accompanying voices, they arose naturally from the simpler harmonizing and required little change, showing them- selves, even if subordinate, yet not unimportant on that account. Other kinds of accompaniment will be spoken of in the next chapter. 198 MANUAL OF HARMONY. CHAPTER XX. ON DEVELOPMENT OF THE ACCOMPANYING VOICES. The manner in which the voices take part in harmonic, metrical and melodic development has been shown in the previous chapter. There are, however, still other styles of accomjDaniment, known as the figured accompaniment. It is not adapted to the character of the vocal parts, and its use is therefore very limited. In the following inves- tigation, instrumental music only will be discussed. By figured accompaniment is understood that kind which arises through metrically uniform transformations of the simple chord tones, e. g. Simple harmony. Figured accompaniment. ; =^ ^ 'V^ -9—\ •—\ •- rroLf-D-^-^^^-ti i ^ i=5=F^ ^=S=^=f?=^?=f fSf^E^ -^x ^^^ ^^' ^S^ '^ ! I I ^-^— L_^i ^^ The accompaniment at a is tiarmonically figured. These figures are also called broken chords. That at b is metrically figured, and that at c is melodically figured. These last are formed from chang- ing and passing notes. Any accompanying voice can be used for such figuration, either alone or with the other voices. We select the beginning of No. 382 for an attempt in some kinds of accompaniment. The following remarks may be presented : When the figures are uniformly repeated, for example, in broken MANUAL OF HARMONY. r99 chords, all the rules for the leading of the voices must be observed at the change of chords^ as v^^ell as in doubling. We must not write : 396. but somewhat in this manner : ^Sl^l f p-^ Or. ^P^^L ^W=^^ ^-^- i When the harmony changes, the last note of one figure and the first of the next must not form a false progression with an}- other voice, e. g. Not. Not better. EEEIEE3 Harmonic figuration enables us to form one-voiced movef?ients more perfectly. The examples may begin thus: A., ;!§ si One voiced. N ^t=± ^ ^^ig^ i^^ifei^as^iiiiiii It is evident that these movements are suitable for an instrument like a violin or clarionet. MANUAL OF HARMONY. Three voiced. In the middle voice In the lower voice. In the upper voice. 3 w^^ i±, gj^a^ggg^ - , f^ In two voices. MANUAL OF HARMONY. Figuration in the four-voiced phrase, will be an easy task after these attempts with the above example. We prefer, instead, to quote an example of varied figuring from the quartet bv Beethoven, mentioned above. 401. ^|^^?^^"^^=F^^=^^=^=JVt-,: '-hE3^=\ I ^ pizz ftE?i^ ^^Np^^^P^ iife l^ g; q ^1^- 4,^ j! ^^^-g— g; s^ iJs^gS^ =E^ ^g =i ^4 5— ^-q ^^ -F^ MANUAL OF HARMONY. g^; ^j^^^t:;g^agg fe^g^^^^ E^ Wr- 1 ^ S^ SS^E 1^ F- TJ? i The whole of this rich development rests on the harmonic hasis given in Nos. 390, 391 and 392 ; and in every case where the harmony changes the leading of the voices is carefully ol^served. If a clear insight into such elaborate compositions, and a comphre- hension of their inner harmonic structure is desired, it will be very useful to reduce works of this kind back to their simple harmonic basis. CHAPTER XXI. THE EXERCISES IN THREE-VOICED MOVEMENT. With few exceptions, our exercises thus far have been written in the four-voiced form, and although it affords greater completeness, and seems best adapted for harmonic connections, the three-voiced move- ments are also of great value, being particularly adapted for greater skill and freedom in the leading of the voices. We begin as before, with exercises witli figured l:)asses. ■i!* -^ l==t 6 6 6 4 ^P^ ^i e=5^ 1^ ^ MANUAL OF HARMONY. 203 The three-part phrase is sufficient for the triad, but through the leading of the voices one of its intervals may sometimes be wanting. In the case of the seventh chords, one interval, of course, will always be lacking, but this must never be the seventh itself. As a rule, the fifth can be omitted, as was the case with four parts, and also in many cases the fundamental also, but the third, the interval which determines the nature of tlie chord, can seldom be omitted without causing an especial vagueness. The exercise will be as follows, to which we append a few remarks : 4-03. N.B.5 N.B.6 (^ r- l- <5> v~r^ — '^^T!^ — r — 1 I'/U f3 ?> 1 r <3 ■ \ \ \ 1|3 1 11^-^.7^-^ " ^ ' ' -* — -v^f—r- -(2 <9— -tt^ — \ — -H \ 1 ^ — 7876,64 $4 6 62 rv- 1 ,r? 1^ 1 1 ^ \}\' \ \ « v^ ^ 8 N.B. 9 10 11 _ 12 F~T7 — ^ II Vr-x. 1 1 -^ ^^— H H^,^— -|2 • \ ^-(2. — -1 -f- 1 FF= -f^- ■^ --P- -^ — n li^— 1 1 4 6 3 ^^: — 1 1 ' 1 6 —^ ^-^ _J 1 6 -A 6 6 — 1= : U H -^-^ — 5 — 1 S 'T^ -J— . ^=^\ In the fourth measure, at N. B., the chord of the sixth and fourth of the diminished triad, E — G — Bb, appears. It takes the place of the chord of the second, Bt? — C — E — G, the fundamental of which is here omitted. For four voices the chord would appear thus : i p ■^w- i See pages 170, and 171, concerning this chord. 204 MANUAL OF HARMONY. In the fifth measure, a fourth represents the chord. While a fourth can neither in three-part nor in two-part writing supply the place of a full chord, as is the case with the third or sixth, yet, in those cases where the chord of the sixth and fourth can be used in four-part harmony as a passing chord on the arsis, in three parts, in order to secure a better leading of the voices, the sixth (third of fun- damental chord) can be omitted, leaving the fourth alone to represent the fundamental and fifth of the original chord. In two-part movements, the fourth will sometimes stand instead of the chord of the second, especially in the case of a passing seventh, e.g. \ I w 4 4 With four parts, the above place in Ex. 403 would stand thus : i^ P I In Ex. 403, eighth measure, the chord of the sixth and fourth is formed complete through the skip in the alto. In the tenth measure appears a chord of the sixth and fifth, which is really a suspension of the fourth, which by the movement of the bass resolvas into a third. This appears plainer in four parts : 407. The last measure of No. 403 shows, through the octave F, that the triad can appear in such cases even without the third and fifth. That the leading of the voices will often cause the omission of the third is shown in the first and second measure of the next example. MANUAL OF HARMONY. X 205 -\f^^- ■~1 — (2_ 1"^ r^ _h2 s^ ^— hi 1= 1 1 rzp ^: p„ii4j; 6 6 — 1 J \ — 6 4 t 7 5 4 ' 1 3 6B 2S:i=t= ^= ^M The omission of the third occurs best upon the arsis, as here on the third beat of the measure, but it must never be lacking on the accent, or thesis. Further exercises may be left to the teacher. Exercises in the Three-voiced Movement to a Given Upper Voice. The following exercise, with the fundamentals indicated, is to be worked out for three voices : C G C — F a d (]7 C -^- -^- -^-_^- The above needs no explanation. 2o6 MANUAL OF HARMONY. The choice of the middle and lower voices will generally depend upon the position of the chords. Thus, in a low position the tenor would be more suitable than the alto ; so, also, can the tenor be taken as the lower voice instead of the bass. The tenor is selected as the middle voice in the following example, as its movement clings more to the bass, while the simple song of the soprano seems more isolated. The former exercise, with a more extended development of the harmony : Qa d G Ert GC dgto^ a e ^ D G7 C 4ii.==S: ^- 412. Treatment. ¥■ » ^^=F^ I -^--^- iiiES 6 ^ "f -«- -(2- -6?-f2- ^^^rf='^^f=f^f^ ■P=t: N.B. In the fifth measure, at N. B., a real ninth suspension appears, through the position of the voices, as a second, and which can occur hut seldom, and only between tenor and bass. It may here be remarked that there cannot be a second-suspension, because the sec- ond results from the inversion of the seventh and must conform to the resolution of the latter, e. g. Or: Inversion. ^^■ E I r 41 Exercise in a middle voice. Tenor. a' A Bb C geO ^«o. H MANUAL OF HARMONY. 207 For an upper voice, the alto is here the most convenient. 4-15. ttsr? i^: ■«> a- i?g^^§^g ^^H §£it 416 The same exercise with the following selection of chords : dg A— ^ Bb G C F B»2 C^ ^ Bb F gC^ d A d • g^ S 417. Treatment. T-r^^ ^f~ -f=-+^ ^H^-^^ i^' 3.bt^_^ _J ! ^ \ -[-- ^-H — h— H ^ 1 (fleft-^^— :i— ^ ^-'-^ e> g» 1 ^ 7 6 pd= 6 -1— T= 6 1 r^i — t>^K-^ ^-^^ ^^- -J— ^'- ^^ i^=i SE ^m PE |£ :H 9- 6 ^ ?^ ^;i The last measure but one shows that even the sixth can form a suspension. For further practice, the exercises which were formerly given for the four-voiced movement can be used. ao8 MANUAL OF HARMONY. CHAPTER XXII. ON THE TWO-VOICED MOVEMENT. The poverty of the two-part phrase from a purely harmonic stand- point, makes it seldom available except in contrapuntal labors, where alone it derives importance from being applied in polyphonic move- ments, for example, in fugues. If, indeed, for simply harmonic use, a metrical and rhythmical variety in the formation of the voices will make the two-voiced movement tolerable, still, the contrapuntal development of the two voices can alone free them from the monot- ony of extended progressions of thirds and sixths, and give that com- pleteness which every polyhonic movement must possess. Necessarily, the omission of one or more intervals will always take place in this movement. With the triads, it will usually be the fifth or the fundamental. When chords of the seventh are used, of course the seventh must not be omitted. Octaves and fifths should rarely be introduced, as they sound too empty. The fourth can only be used in a few cases where the chord of the sixth and fourth would be admissible, or when it takes the place of the chord of the second. (See page 203.) Example. C b^ ^ 418. ^^ 419. ( Treatment r fy ii5) ^ rj JZ. -^- p-^ r—<5> ^^Fl 5 3 6 6 3 6 6 3 <3 3 : II 1 1 'A-x~l\i ' ,. s> --f5> — 1--^<&— G 11 [ n-a-*)^^— 1 II The intervals which have been omitted can be ascertained by comparing the fundamental tones in Ex. 418. Lack of clearness in the harmony will be rare, since each chord explains itself by its con- MANUAL OF HARMONY. 209 nection with the one which precedes and follows it. The same exer- cise with varied harmony: C F— 7 G CG d CCaG C G j2- 420. "^ W- ^1] ^ m- -^^^ i p^= r-=Ff=F :|=p: P: t=t=1=|: Most of the exercises in Part III invade, somewhat, the domain of counterpoint. The only difference is, that here, the harmonies are indicated, and we have only to carry out the leading of the voices accordingly, while in contrapuntal studies, a knowledge of harmony and facility in its use is assumed, so that the selection of the harmo- nies can be left to the choice of the student. These studies may, therefore, be regarded as useful preparatory exercises to those, and will at the same time afford an insight into the relationship between harmony and counterpoint. CHAPTER XXIII. HARMONIC TREATMENT OF A GIVEN VOICE IN MELODIC FORM. By melodic development of a voice is not to be understood here that richer ornamentation shown in Chapter XIX., but through met- rical variety to avoid the simple choral-like progression of our earlier exercises, and thereby afford opportunity for learning to develop the MANUAL OF HARMONY. voices better in the harmonic accompaniment also. The next exer- cise will make this clearer : 422. ^^- ^^ a^^fi—^- -^- ^. ^. The choice of chords will be made at the time of treatment. Al- though the kind of measure chosen will of itself produce a similar melodic leading of the voices to be filled out, still, particular attention must be given to their leading according to the principles developed in the previous chapters, if a free, skillful treatment of them is to be had. The exercise will first be treated in three-part harmony. 423. .^ P 3: ^- T=- ;t==F -I — p e* 'G>-r°- £ 6 98 9i«: 6 6 7 6 4 5 ^<5> :t=t^ This treatment needs no further explanation after the remarks on the three-voiced movement. The harmonic treatment of this melody as a middle voice shows its adaptability, and may be recommended as a useful exercise. To retain the alto voice and obtain a better position for it we trans- pose the melody to F major. iii=_^S^ s=S^ ^f= H=2__^_ 4=1 P=^= canlus firmus. SH ^-&- -f9^-i5>- ^ -|22- -|S2.-^. 1=Ft g|^=£^ I 6 6 7 683 9846 6 987 1^1 '^^ The explanation of the unprepared chord of the sixth and fourth MANUAL OF HARMONY. 211 in the fourth measure, is found in tlie remarks on passhig chords in Chapter XV. It arose accidentally, on account of the progression of the bass by degrees, and stands here in the place of the chord of the second. The treatment of the same cantus jirtnus transferred to the bass : 425. This treatment shows a weak point from the third to the fourth measure, in the harmonizing of the sustained A of the bass. Also the bare fourth in the sixth measure is a very imperfect representative of a chord, unless we regard it as a passing note. If it be desirable to develop the leading of the voices still further, passing and changing notes can be used alternately in the two voices to be added, e. s^. T c./. "^ 'f' r> e> ' '^ 1 _ r^ ^ ' 1 1 f\ ''^'" .^r-. \ r^* l{^-?^~f-[— ^p^h- -^ f p\m f P m^km f [^_^PJ — : L_l_ k-r-hM— P-h^ F+ 6 6 ^7 6 1 m ^ —[- ^V=^=^ I 4-29. Four- voiced treatment. pS - ^ I r ^ g ? ^ 1 ^^'^ . f ^f—f^-r^ ■t=F ^a *E I » )=P=F fe^i^ IS N.B. :r!it &^^^^£S^ 6 4 3 6 ' 8 6 6 6-6 67 43 55 543 867 ^m ^^_^^Tp ^ H ' n!b. MANUAL OF JJARMONY. 213 In the fifth measure at N. B., the skip of the tenor into the seventh is not altogether faultless, because the soprano skips also in parallel motion to the fundamental, G. This can only be excused by the posi- tion of the alto, which holds the connecting tone. In the same measure, appears the chord of the sixth and fourth of the augmented triad, the original fifth of which is prepared. It has here the character of a suspension from below. (See Suspensions, Chapter XII., page 131.) The same cantus Jirmus in the alto, transposed to D major : te ^^ N.B. :^£ te c.f. eee£ »=•! trfta -f3E^E^ iSl iM £ -^- &- it* I S3: ^^q ? J — I- n -x=x Si In the fourth measure suspensions are found in three voices. In the fifth and sixth measures the position of the alto and tenor is not good, because they are more than an octave apart. 214 MANUAL OF HARMONY. Of the remaining treatments, that with the cantus Jirmus in the bass here follows : -(2--&- an^ ^^^-rrrTrr^^ g^S j * ^^- fer^ at \^-f^\ I r ? - 1=t= §ite ^F f^4=J i=4: ^=^ ■^—r^ ^f Pfe^g^ ;i u 1 ^p pEt 6 4 3 ,6 -^— •- EEfE£ 2i6 MANUAL OF HARMONY. The third measure gives opportunity to speak of consecutive octaves and fifths in contrary motiofi. According to the principle laid down heretofore, they are quite as faulty as those in parallel motion, and it is especially the case with the octave progressions that they hamper the free movement of the voices. With the fifth progressions, however, the ill effect is much mitigated by contrary motion, especially those which move towards each other, while those which raow & from each other make the sepa- ration or want of connection moi-e perceptible. (See also Ex. 430 in the sixth and seventh measures, between tenor and bass.) Compare the following examples : f ^h^^i^E^^P^P^g^ An examination of the treatment contained in this chapter will show plainly the melodic development of the voices, and this is the reason for regarding them as contrapuntal labors ; for the essence of counterpoint, as distinguished from the rhythmical harmonic form, requires the freer melodic leading of the voices, but with observance of the harmonic laws which form, so to speak, its innermost principle. In all these examples, even where the voices move in quarter notes, the harmonic ground-work. can be found, and thus they may serve, for the present, to show us the difference between the simply harmonic and contrapuntal treatment of a given voice. The more detailed study of this subject belongs properly to counterpoint itself. CHAPTER XXIV. THE FIVK-VOICKD MOVEMENT. Since the doubling of the intervals of a triad is necessarv even in a four-voiced movement, so also will it be necessary in a greater degree m movements for five or more voices, and even with the chords of the seventh. MANUAL OF HARMONY. 217 In the pure harmonic movement, each voice must preserve its inde- pendence. To accomplish this, the intervals best adapted for doub- ling will be those that admit of a double progression. This can take place, to a certain extent, with each interval of a chord, but the sev- enths are the least adapted for doubling, except, perhaps, where a melodic progression makes it necessary, as for example, in passing. Further remarks follow under the examples given. Exercise. 435. :i±S TTV 7r !t==t r-^-f ^ % In treating this, we may select, according to the position of the voices, either two sopranos, tw^o altos or two tenors. 436. ^ ^ . _^__^___ „ -^y Soprano, Alto I. Alto II. Tenor. pit WE 5B ^SE ^=^ 4 2 3 ii^ '^ ■^ — &- 1 ^ ;b The same exercise differently arranged 4-37. ^ "^ ^ ^ ,^ Soprano I. Soprano II. Alto. Tenor. Bass. U -^ :l==t: ^■ « Szg^ f. iEEE^ p=ffi=^ ^=t f I g - ^ ia *; 4 2 3 i I I rr^^P^ H i8 MANUAL OF HARMONY. That the independence of the voices may be maintained, two voices should not remain stationary upon one tone, or in the octave, if the chords change. In the above example, in the first and second measures, the second soprano and tenor hold the tone C over the bar, but as the harmony does not change, no fault appears, the chord only changing its position. The following passage, however : may be corrected thus : (is ^ -i — g— <&,'g f^ -'9^-^- =F=t= Remark. — This rule, however, admits of frequent exceptions where there are many parts, because other relations then present themselves. That the leading of the voices will allow the leading tone to be doubled, is shown in the third measure of Ex. 437, between the sec- ond soprano and tenor. As in the four-voiced movement, so also in movements for five or more voices, the impossibility of avoiding covered fifths, octaves and unisons will exist in a greater degree. It may be mentioned again, that here also the ojdcr voices must progress in pure relations, and greater freedom be allowed to the middle voices only. The followin (^ 1— f2 ^. P J^=F=^-F=P=^t=t t=f F (=2 <9 ^ <^ — &—y->^ ^3 :t=l= ^ ^^H I (Si e*- X=^ The progressions of covered fifths, octaves and iniisons in this example are indicated by strokes. The open fifth in the eighth meas- ure between the second alto and bass is not to be avoided, since the chord of the diminished seventh can only with difficulty progress other- wise when there are several parts. The first and second alto from the eighth measure could progress thus : 441. < ^ % -P ^- ^ ^ a 220 MANUAL OF HARMONY. That the voices, particularly the middle ones, must often cross each other, is seen in the second and third measures, between the second alto and tenor. For practice in the five-voiced movement, chorals can be used to advantage. The following may be given here : D C D7 G D7 G #3? i=t ^ — — G D7 E7 ^ bo^ E Dt Fl=E^ ^F=t=4 G D — G D7 G Exercises in five or more voices require a simple and natural bass progression, and the less diflficult and artificial it is, the clearer the succession of harmonies will become. This is here all the more important, because with the full chords and the necessitv for the free movement of the voices, very unintelligible progressions can easily arise. The beginning of this exercise here follows : r-r r r r \ r f ^ ei MANUAL OF HARMONY. 221 In the repetition, the following change in the harmony can be made : G G7 C E7 « e a V> e V.l a *— ^ \ 5E =t ^- I r I I -^ 4==t g g=sg^ i-2 f :i=rFy: :S=^ g I :t=bF=p i CHAPTER XXV. THE SIX, SEVEN, AND EIGHT-VOICED MOVEMENT. The necessity of doubling or trebling increases with the number of voices added, and also their independent movement will often require them to cross each other. The simplest harmonic progressions be- come here the principal condition of the possibility of conducting so many voices, and it must be remembered that many chords are not at all suited to this kind of writing, because their intervals require a fixed progression and cannot be doubled, notably, the altered chords and the chord of the diminished seventh. A few progressions of the triad follow here. Progression to the second degree : iced. Five-voiced. ^ 9i I Six-voiced. Seven-voiced. I & -iS- zsz ^ Eight-voiced. i MANUAL OF HARMONY. Progression to the third degree : Four-voiced. Five-voiced. Six-voiced. Seven-voiced. Eight-voiced. m ^^^ SI; ^z. Progression to the fourth degree : Four-voiced. Five-voiced. Six-voiced. i Seven-voiced. Eight-voiced. ^^ =5«? Progression to the fifth degree : Four-voiced. Five-voiced- Six-voiced. Seven -voiced. Eight-voiced. 9t ^i^i=i; We pass over further combinations. It will be very advantageous to try them with all the inversions. As an example in the management of the voices in six parts, the choral under No. 443 is here given : 446. Soprano I & II. Tenor I&II. F=i -7S 1 J_i: x,^- (S- '^^- MANUAL OF HARMONY. 223 -i Jll J ■ ^ ^ ^^ ^=F=f W=^ ^=t= :,=2 — ^ L_LJ L :t=t= te 4 U J— 4- 4 1 V=^ t=F ^^P «=-^ SS ^=X I I - ^ 9 ■ 1 — ^— |!31_| — 1 ' -1 V— L i 1 -^ — $:— -V- 1 I -1 — -L-^^-^- -|2_ 1 6 =pzd — ^ — '1 6 1 ~ — 1 — 6 7 4 3 ...^ h^^ ^ =£ -s^ FE^E^=gE^ -L-J- J V 4-J- i=i p^^"^&s=^i 'I — r — 1 ^t=tf r4^=^ =r:==F f=^ te= ^^^^^^E^ a^ :^=i= » K?^ 13 I I I I P^ :)==t: I I I I ;i==F J_J_ r E^ P« i^^S 224 MANUAL OF HARMONY. i*=»: jJEgE^g^^EE^Jg ^ I I J^j— J-^-4 -gg* ^ - 1^?^ -^ (=2 (2Z- ^^=F Since in polyphonic choral movements, all the voices are not employed at the same time, as in a plain choral treatment, the har- mony often appears in only three or four parts, and is worked up in intensity by the addition of the others. The following examples will explain this kind of chorus movement, and especially serve to show, that suspensions and passing notes can be employed in polyhonic work also, without disadvantage to its clear- ness and comprehensibility. 44-7. Soprano I&II. Tenor I& II. »E^ 5= ^^ =tp=^t 4=-^- U_J- rJc^ -^-T^— ^t? a I g,_ iaE!^ -^- ?^ MANUAL OF HARMONY. 225 J l^. I I :^-=t5=S=l=g=a SB r=^^ X^^^^ 6?:— t-^ ^g g g fg ^ tfefl :^=;^:^=ip=:s: t=^=tti i-^4 J - si 1 =p^ 4-=f= ^ I - i^ u -4= u -^=: 1 1 -^ f— -p — L-i— f? — (2_ -r— — 4- — s^— ^1 -I- — 4 — , —si 1 ~" \ i f H >fLI! 1 =¥= -^ 1 (2. ^ 228 MANUAL OF HARMONY, In polyphonic movements which are divided into two different choirs, the difficulty of this manner of writing is met by making not altogether a tonical^ but often a metrical difference between the voices, where two or more choirs work together. It is always to be presumed, however, that the successions of harmony shall take place in the simplest manner, and never by quick changes. The above is generally to be understood when we speak of twelve or sixteen-part choruses, movements, etc., and only single pieces of Bach are found where eight or more voices, including, however, instrlimental parts, are treated obligato. These hints regarding the polyphonic movement may here suffice, as the rest, with a thorough knowledge of harmony, may be left to personal study. We may remark further, however, that the use of the polyphonic form will be applicable mostly in compositions for choirs. In orchestral works it will not find place, as the taking part by so many instruments of various kinds would lead us to suppose. CHAPTER XXVI. ON THE MUSICAL FORMS OF CLOSE. Several kinds of close have already been mentioned on page 33, and further remarks followed in relation to the authentic close on pages 41 and 56, but throughout the whole treatise there has been no fur- ther opportunity to revert to the subject ; therefore, a fuller explana- tion of these and other forms of close may follow here : The forms of close are divided, first, into the authentic close and the plagal, or plagalic close. The authentic close has the formula V — I, the plagal close IV — I (or in minor, V — i, iv — i), as has been shown before. Both forms are used not only at the end of entire compositions, but also at the close of the principal divisions of the periods and their sections. The more particular discussion of this subject belongs to the doctrine of form. If the plagal close concludes a piece, it seldom stands alone, but MANUAL OF HARMONY. 229 follows the authentic close ; in minor it frequently leads to major, e.g. In this case, as above, it is introduced by means of a modulation. The closes (cadences) are also divided into whole and half closes, or cadences. By the whole cadence is understood the same which is comprehended under the authentic cadences. With the xvhole cadences a distinction is again made between per- fect and imperfect ones. The perfect whole cadences are those in which the bass takes the fundamentals of the dominant and tonic, and the soprano the funda- mental of the tonic, e. g. Not. 45 1. i ^ I 9i=^ i If this is not the case, they are called imperfect, e. g. fe^l s^^ia ) i^=:^ S If the bass progresses from the dominant to another degree, they are called deceptive cadences. 453. m 1=^1=^ :t^ 1 230 MANUAL OF HARMONY. See the examples, pages 91 to 94. The half cadences have the form u hi I — V, e. g. They also consist in this, that the dominant triad completes the phrase. Beside the tonic, chords of other degrees may precede the domi- nant triad in the formation of a half close, e. g. g rz) 1 ^. 1 "l~"S=q ^j ^■"Tl 5 <^ II «J <^ VI Among the half-cadences are also included those closes in the key of the doininafit which are formed by a modulation into the same, not a decisive one through the fundamental position of the dominant harmony of the seventh, but either through its inversions or through the chord of the seventh of the seventh degree, e. g. 456 G: VI1O7 ^^m^^m g: VI1O7 C: V This is the case, hov^^ever, only in relation to the key which has just before been made use of. For the further understanding of these kinds of cadences, compare those which are found in the examples of this book. In No. 388, in the third and fourth measures, a half cadence is found which is formed through II — V, which effects the close of the first section of the whole period ; in the seventh and eighth measures, however, we find a per- fect whole or authentic cadence. In Ex. 393, in the third and fourth measures, is a half cadence formed through I — V, and a perfect -whole., or atithentic cadence in the key of the dominant at the end. (Here, however, there is no half cadence., because the dominant seventh harmony makes the mod- ulation complete.) MANUAL OF HARMONY. 231 In the choral under No. 446, the first strophe ends with an hnper- feet whole cadence, the second with a perfect tvliole cadence, the third with sl half cadence to e minor (iv — V), the fourth with a perfect ivhole cadence in G major, the fifth with a perfect whole cadence in a minor, the sixth with a half cadence in e minor (iv — V) , and the seventh with a perfect whole cadence in G major. The application of the different cadences is easily found in chorals ; for larger compositions they supply the means of boundary and connec- tion of the smaller as well as the larger movements, and should there- fore be used with much care, because upon them, to a great extent, depends the construction of a piece with regard to form. INDEX OF SUBJECTS. Accompaniment, figurated, 198; harmonic accompaniment to a given voice, 166, 189, 209. After-stfikitig oi harmonic tones, 137. Alto, 23; alto notes, alto clef, 128. Anticipation, 136. Arsis, 121, 153, 189. Bass, 23 ; movement, progression of the same, 35, 36, 168, 220. By-tones, harmonic, 144. Cadence, 59, 90; whole, half, 193, 228; perfect, imperfect, 67, 228; in connection with modulation, 163. Cadence formula, 163, 164, 165. Cantus firmus, 209. C-clef, 128. Chorals, as exercises, 191, 220. Chord, 21. Chord-formations, accidental, 1 19. Chords, altered, 45, loi, 115; passing, 153; view of same, 113. " see also Triads, Chords of the Seventh. Chord of the sixth and fourth, 50; the same in the formation of the close, 56; in con- nection with modulation, 158; as passing chord, 154; use of the same, 168. " of the augmented triad, 102, 213 ; of the diminished triad, 170, 203. Chord of the sixth and fifth, 63, 64, 65; the same as suspension, 204; augmented, 109; in connection with modulation, 161. Chord of the second, 64, 66, 67. Chord of the sixth, fourth, and second (see Chord of the Second). Chord of the seventh, 21, 57 ; chord of the dominant seventh, 57,61, 66, 91, 159 ; essen- tial, 69 ; the same in passing, 153. " of the seventh degree in major, 75, 87, 100, 215. " diminished, 84, 88, 96, 100; in connection with modulation, 161 ; in the poly- phonic movement, 219. Chords of the seventh, connection of the same among themselves, 8r ; in connection with chords of other degrees, 90, 96 ; view of the same, 114. Chord of the sixth, 50; augmented, 106. Chord of the thirteenth, 98, loO, loi. Chord of the fourth and third, chord of the sixth, fourth and third, 64, 65, 67. Chord of the eleventh, 90, 98, 100. Chord of four tones, 57 (see Chord of the Seventh). Chromatic alteration, loi. Consonance, 17; complete, incomplete, 17. (233) 234 INDEX. Contrary motion, 26, 1 50. Connection of chords, 25, 81, 90; local, inner, 35. Close, 33 ; authentic, plagal, 33. " see also Cadence, Whole Close, Half Close, Deceptive Cadence. Closing cadence, 59, 90. Closing formula, 41, 163. Cross-relation, unharmonic, 182. Deceptive cadetice, 91. Degrees, diatonic, 13. Digression (see Modulation). Dissonance, 17. Dominant harmony, C-triad, chord of the seventh in connection with modulation, 159. Eleventh, 14. Exercises, for practice of the primary triads in major, 30 ; of all triads in major, 38 ; of the triads in minor, 47 ; of the inversions of the triads, 52 ; of the chord of the dominant seventh, 62 ; of the inversions of the same, 68 ; of the secondary chords of the seventh, 80: of the connection of the chords of the seventh among themselves, 82 ; of the secondary chords of the seventh in minor, 85 ; of the in- versions of the same, 89; of the deceptive cadences, 95; of the secondary chords of the seventh in connection with chords of other degrees or keys, 97 ; of the aug- mented triad, 104; of other altered chords, no; in working out modulation, 117; of the suspensions, 126, 134; of the harmonic accompaniment to a given voice,, 166, 167, 172, 179, 180, 181, 186, 187, 188, 189; in the development of melody,, 192; in the three-voiced movement, 202, 205, 206; of the two-voiced movement^ 208 ; in the harmonic accompaniment to a given voice in melodic development, 209, 215 ; in the five-voiced movement, 217, 220. Fifteenth, 14. Fifth, 13, 22 ; perfect, 15, 16; augmented, 15, 16, 83; diminished, 15, 16, 39, 65; fifth in the chord of the seventh, 61, 77. Fifth-progressions (parallel fifths), 26, 28, 54, 88, 109 ; open, 30, 87 ; covered, 30, 36,. 124, 174, 219; in connection with passing and changing notes, 148; in contrary motion, 216. Figuring, 47, 51, 56, 58, 125, 143. Fourteenth, 14. Fourth, 13; perfect, augmented, diminished, 15, 16; preparation of the perfect fourth 170; the same as chord, 204, 211. Fourth-progressions (fourth parallels) in passing, 150, 151. Formation of the close, 41, 56, 59. Fundamental harmonies, 21 ; chromatic alterations of the same, lOi. Fundame7itaL 21 ; in the chord of the seventh, 60. Half-close (half cadence), 193, 228. Harmony, 21. Harmony, tones foreign to the, 119. Intervals, division of, 17; view of the same, 16, 18; inversion of the same, 18. " see also Omission, Reduplication. Intervals, doctrine of, 13. Interval, 13; major, perfect, 14; minor, augmented, diminished, 15. Interval steps and skips, augmented and diminished, 171. Intervals above, 18. INDEX. 235 Intervals below, 18. Inversion., 50 ; of the triads, 50 ; of the chords of the seventh, 63, 67, 87 (see also In- tervals). Leading tone, 37, 40, 60, 84, 131, 175, 218. Major triad, 22, 70. Melody, its development, 192 ; its rhythmical formation, 193. Middle voices, 23. Minor triad, 22, 34, 70. Modulation, 115 ; means for the same, 156; its extension and completion, 163. Movement, o\\^-\o\CG.A, 198; two- voiced, 208 ; three-voiced, 203; four-voiced, 23; five- voiced, 216; six, seven and eight-voiced, 221. Movement, parallel, contrary, oblique, 26. Ninth, 14; major, minor, 15. Ninth, chord of the, 98, 133, 143. Ninth-suspension, 133. Obliqtfc movement, 26. Octave, 13; perfect, augmented, diminished, 15, 16. Octave-progresstons (octave parallels), 26, 28; open, 30, 124, 148; covered, 30, 36, 56, 93, 174 ; in contrary motion, 216. Omission of intervals, 61, 81, 203, 208. Organ-point, 138. Outer voices, 11. «• Pass, passing notes, 144, 149. Passing chords, 158. Period, 193. Plagal close, 33, 43, 228. Position of the chord, close, open, dispersed, 31, 32, 129. Preparation, of the seventh, 78 ; of the suspension, 120. Prime, 13; perfect, augmented, 15, 16. Primary chord of the seventh, 57, 69. Primary triads, in major, 23, 33 ; in minor, 42. Progression, melodic, unmelodic, 171. " of the secondary chords of the seventh, 73, 81, 90; see also resolution, bass, unison, octave, fifth progressions, etc. ; connection of the chords. Reduplication, of intervals, 25, 41, 51,62, 78, 106, 123, 125, 147, 217, 221. Resolution, of the chord of the dominant seventh, 59, 65 ; of the secondary chords of the seventh (in major), 71; (in minor) 83; of the suspension, 119, 123, 131, 135. Scale (see Triads). Secondary triads., in major, 33 ; in minor, 44. Secondary chords of the seventh, 69, 87, 96. Second, 13; major, minor, augmented, 15, 16. Second-progressions (second parallels), in passing, 150; with changing notes, 1 51. Second, step of the augmented, 46. Sequence, 38. Seventh-progressions (seventh parallels), in passing. 150 ; with changing notes, 151. Seventh, 13; major, minor, diminished, 15, 16; passing, 189; preparation, 78; the same without preparation, 79, 85, 173, 180. Sixth, 13; major, minor, augmented, 15, 16. Signatures, 56. 236 INDEX. Soprano, 23; soprano notes, soprano clef, 128. Stationary voices, 138, 142. Structure, pure harmonic, 24, 152. Style, pure, strict, free, 24 ; pure, 152. Subdominant triad, 23. Suspension, 119, 122; in the bass, 125; from below upwards, 131 ; in several voices, 132, 213. Tenth, 14. Tenor, 23; tenor notes, tenor clef, 128. Thesis, 121, 153. Third, 13, 22 ; major, minor, diminished, 15, 16; in the chord of the seventh, 171, 60, 77; (see Leading Tone). Thirteetith, 14. Thorough-bass notation (see Figuring). Tonic triad, 23, 157. Triad, 21; major, minor, 22 ; dominant triad (in major), 23 ; (in minor), 42 ; tonic triad, 23; (in connection with modulation), 157 ; subdominant triad, 23. " double-diminished, 106; harsh-diminished, 107 ; augmented, 45, 71, 102 ; dimin- ished, 34, 39, 44, 53, 71- Triads of the major scale, 21, 33, 44, 113. " of the minor scale, 42, 44, 49, 113 ; natural connection of the same, 22 ; view of the same, 49, 113. Tritone, 77, 184. Twelfth, 14. Unison, 13. Unison progressions, 28; covered, 206, 178, 218. Voices, movement of the, 26, 59 ; (see Progression, etc.). Voices, compass of the, 128. Voices, relation of the, 128. Voices, outer, 23; middle voices, 23 ; development of the accompanying voices, 198. UNIVERSITY OF CALIFORNIA LIBRARY BERKELEY Return to desk from which borrowed. This book is DUE on the last date stamped below. LD21-100m-9,'48(B399sl6) MT50.R47 1896 C037142172 BtRKfLt Y LIBRAKIIS III CD37142172 ivi21()187 ^/ ^'° THE UNIVERSITY OF CAUFORNIA UBRARY DATE DUE Music Library University of California at Berkeley II