cirx OF Professor John S. Tatlo I ^u essor f.-. .- 4- T , 5. •••* C*« • c*C c • • • • t> ace • • • • • • I c • • • • • SECOND EDITION A COMPLETE SYSTEM OF HARMONY BY H. E. PARKHURST Containing a thorough practical treatment of all chord-formations and connections, an exhaustive analysis of suspension and other auxiliary effects, and a comprehensive discus- sion of organ-point, modulation and cadence, with exercises therein ; constituting a full preparation for Counterpoint. CARL FISCHER, PUBLISHER COOPER SQUARE NEW YORK iRARY o: Bt. _y Copyright 1908 By CARL, FISCHER — NEW YORK International Copyright Secured / JT ^ ^jCC^€^^ CONTENTS, INTRODUCTION— Definitions 5 Part I. THE FUNDAMENTAL CHORDS. PAGE CHAPTER I. —The Common Chord 14 CHAPTER II. —The Secondary Common Chords 23 CHAPTER III. —The Minor Scale and its Triads 35 CHAPTER IV. —The Inversions of the Common Chord .... 45 CHAPTER V. —The Chord of the Seventh 58 CHAPTER VI. —The Inversions of the Dominant-Seventh Chord 65 CHAPTER VII. —Close and Open Position— Concealed Fifths and Octaves — Score — Cross- Relation — Sig-ht-reading 71 CHAPTER VIII.— Secondary Seventh Chords 88 CHAPTER IX. —Inversions of Secondary Seventh Chords.. 100 CHAPTER X. —Seventh Chords Followed by Various Re- solving Chords 104 CHAPTER XI. —Exceptional Modifications in the Resolu- tion of the Seventh 108 CHAPTER XII. —Altered Chords 112 Part II. THE AUXILIARY CHORDS. CHAPTER XIII. —Suspension 128 CHAPTER XIV. — Suspension (concluded) — Anticipation — Syncopation 161 CHAPTER XV. — Auxiliar Tones 178 CHAPTER XVI. —Rhythm— Primary, Secondary and Auxi- liary Chords 194 CHAPTER XVII. —The Organ-Point 209 CHAPTER XVIII.— Modulation 219 CHAPTER XIX. —Modulation (concluded) — Chromatic Chords 236 CHAPTER XX. —Cadences 242 APPENDIX 252 ivi206S63 THK DISTINCTIVE FEATURES OF THIS WORK MAY BE BRIEFLY STATED. ^■■P^HE extended and systematized treatment of the Auxiliary / 1 Chords is prompted by the conviction that a modification ^^^ is sorely needed in the prevalent method of harmonic teaching. The vast majority of pupils, leaving Harmony with little or no drill except in the Fundamental Chords, plunge into Counterpoint and Fugue so ill-prepared for the require- ments of these advanced studies, that their most laborious efforts produce only painfully unmusical results. At present, the pupil sees little relation between his chords of Harmon}- and the chord- formations of actual composition, and this is because he has not been taught how to elaborate his fundamental harmonies with auxiliary effects. The principles of Modulation have been presented in a manner that will, it is hoped, make what is the most subtle feature of com- position more intelligible and attractive to the pupil . If in many text -books the true philosophy of the matter has not been miscon- ceived, it has certainly been strangely misrepresented. Organ-point is generally treated in so superficial a manner, that it will be a surprise to some that it can be reduced to a scientific system which shows it to be amenable to the laws of Harmony, instead of being an authorized license to violate almost all the pre- established requirements of chord progression. Its treatment in this work is the first attempt, so far as the author is aware, to bring under distinct rules this effective species of composition, and to .afiPord to the pupil a method of learning it. Special emphasis, b}^ means of special exercises, has been put npon the need of distinct knowledge of the effect of chords without playing them., — a matter strangely ignored in some text books — the neglect of which makes all study of musical theory absolutely profitless. As a means of bringing the contents of each chapter under distinct review, a Summary is appended, both for self-examination and for the teacher's use. Insufficient drill in elementary harmony — which, as Rhein- berger was wont to remark, is nine- tenths of the whole art— in na small degree accounts for the comparative shallowness of modern composition; and the very best preparation for expressing one's individuality in musical thought is rigid discipline in those funda- mental harmonic principles that yield to no passing fashion, but underlie all thoughtful music, be it classical or ultra-modern . THE AUTHOR New York, July 31^ l9Gi. INTRODUCTION. Definitions. Kvery concussion of air affecting the ear produces sound. Sounds are of two distinct kinds, viz., noise and tone. Single impacts upon the ear, or a series of impacts following more or less rapidly, but irregularly, produce noise; as, a single clap of thunder, or a reverberation of thunder, which is produced by an irregular succession of echoes. A succession of impacts upon the ear, following rapidly and equidistant, produces tone; as, the vibrations of a violin string. Rapidity and equidistance of vibrations are the conditions of tone; i. e., musical sound. The pitch of the tone varies with the rapidity, the lowest distinguishable tone having about i6 vibrations in a sec- ond, and the highest, from 16,000 to 33,000. A single tone is musical, but it is not music; it is the basal atom of music. Music is the intelligent combination of tones. Two sorts of com- bination are possible, viz., successive and simultaneous. Melody. The musical sense of successive single tones is called melody. Beethoven^ Andante Harmony. The musical sense of simultaneous tones is called har)no)i\'. I xe: -o- This latter combination constitutes a chord. Radically distinct, each is the necessary supplement of the other. They are the soul and body of music. Melody without harmony is disembodied spirit. Harmony without melody is lifeless. 6 PARKHURST HARMONY, Simultaneous tones, producing an agreeable effect, constitute a concord or consonance ; producing- a disagreeable effect, a discord or dissonance. Concords are not all equally agreeable, neither are dis- cords all equally disagreeable. (The list of concords — or con- sonances — and discords — or dissonances — will be given later). It may seem incongruous that any effect, in itself disagreeable, should be admissible in music ; it is equally incongruous that salt, by itself utterly distasteful, should be the necessary ingredient of all food. Discordance is simply salt for seasoning. Harmony would be insipid without it. If any one chooses to apply the term dissonance to those harsh effects which are admissible in music, and the term discord to those effects which are too harsh to be serviceable, there is no law against such a classification, nor is there any authority for it, inasmuch as discord (dis-corda) and dissonance (dis-sonans) from their etymo- logy have identically the same meaning. We shall see, later, how the discord is softened or concealed to the degree of being palatable. Harmony. This word, already partially defined, in its relation to melody, is used in three senses, closely allied, yet quite distinct. In the first and most popular sense, harmony is equivalent to concord, — harmonious means the perfectly agreeable, and, the inharmonious involves more or less of discordance. But the musical sense of simultaneous sounds does not limit us to pure concords. There are many chords, tinged more or less with discordance, whose use greatly enhances the aggregate effect of music ; and in a technical sense all combinations of tones, purely concordant or not, which are service- able in the expression of musical sense, are termed harmonies: as when we speak of the ''harmonies" of a composition, meaning the chords. In the third use of the word, Harmony constitutes the first grand division of Musical Theory, and is the subject of the present work. Used in this sense, Harmony is the science of fundamental and auxiliary chords in their individual construction and their proper connection one with another. More briefly expressed, it is the science of the construction and connection of chords. In its three senses Harmony means — concord. " —chord. ** ** — the science of chords. This is the scope of our present work, the foundation of all further theoretical study. It will be well for the pupil to understand the nature and the limits of his present undertaking, that at its conclu- sion he may not be disappointed because he has not learned what INTRODUCTION. 7 lies altogether beyond the province of Harmony. Tones are to the composer what colors are to the painter, and he must first learn the colors, their mixture in single chords, their combination in a flow of harmonies, before he can expect any results that deserve the name of original composition. Harmony, as the science of chords, is often called the grammar of music. But it is more. It is also the spelling book. The several tones represent the letters of the musical language, their combination in chords spells out the zvords, and lastly the proper connection of the chords is analogous to the grammatical construction of language. We shall first have to learn how chords are formed, i. e., spelled, be- fore we can properly connect them. In the definition of melody and harmony it became evident how meaningless the latter is, except as it is animated by the former. But it is to be observed that the part or voice that furnishes the melody (usually the highest part) is also a constituent part of the harmony; that is, the tones of the melody are at the same time elements of the successive chords underlying the melody ; ( for example, the soprano part of "Old Hundred"). But our present purpose will be best at- tained by subordinating, for the time being, the melodic quality of the upper part to its harmonic character, so that throughout Har- mony, and especially at the first, the exercises will have scarcely more than a tinge of melodic effect. But while the highest tone of each chord will be treated primarily as an element of the harmony, the pupil is still to give to the highest part as much of the melodic quality as is consistent with the harmonic requirements. A more free, melodic character in the highest part will follow in due time, and the pupil will then have acquired a correct treatment of the underlying harmony. Intervals. An interval, in music, is the distan ce hetwef>n tw^ toneis. The distance from any tone to the next clearly individual tone above or below is called a^emjtgne, or a half-step ; as, from C to Db. E to F. $ ^ jy A musical sound can indeed be produced between C and Db, but, as relative to these, it has no individuality ; it will be regarded, not as a distinctive tone, but as a defective C (being too high) or a defective Db (being too low). PARKHURST HARMONY. (Note. It is doubtful whether the distance between two clearly distinct tones has ever been less than what is now called a semitone. It is true, that in the Indian music we find the octave divided into 22 parts, instead of 12, as with us, by which they obtain a quarter-tone instead of a semitone as their smallest distance. But this subdivision is purely theoretical, and does not exist in their practice.) The sum of two semitones, as from C to D, or from E to F#, is called a tone or a step. This word tone thus has two meanings: first, that of musical sound ; secondly, that of distance, as the sum of two semitones. This use of the word as a measure of distance is authorized by the word diatonic, in which tone (from the Greeks tonos), has the same significance. This double sense of the word will not be found to involve any ambiguity. For the sake of uniformity, all intervals are reckoned from the lower tone upward, unless otherwise expressly stated. An interval is reckoned on the staff by counting the intervening lines and spaces between the two notes, and adding those on which the notes them- selves are placed. Thus from C to D is called an interval of a second, from C to E a third, etc., as follows : — Second. Third. Fourth. Fifth. Sixth. Seventh. Eighth. i -o^ IE 33: XH "O" The interval has the same name even if either of the tones be raised or lowered by an accidental, thus: ^ Seconds Thirds. Sixths. XE XE 323X -^ -O^ IX -o- -e^ ♦V 4^ Accordingly, intervals of the same name are not always of the same size; and to express the intervals precisely they must have a further designation. The following list presents two sizes of each interval within the limits of an octave, beginning with C : Seconds. Thirds. Fourths. Fifths, minor, major, minor, major, perfect. augmented. perfect. augmented. i m r€T I Sixths ^ w^ XE XH -€>- 1 minor. XE major. XE Sevenths, mmor. major. Octave. perfect. INTRODUCTION. 9 The two sizes differ in each case by a semitone, and in all but two cases the less is called minor, the greater, major. The two excep- tions are in the fourths and fifths, where the terms perfect 2ind aug- mented are used. There is one more augmented interval which must be noticed; viz., the augmented second, thus: Augmented Seconds. ^^^^Inrl ^^J^P This peculiar interval will demand our attention later. Another important interval is a species of a fifth, which is, how- ever, a semitone less than the perfect iifth and is called the dimin- ished fifth , thus : Diminished Fifths. I o^ TSl W lOE Tones identically situated are said to be in unison. i Unisons. I^^o |g*M» ^»^ From any letter to the same letter above is an octave or eighths From C to the second D above is strictly a ninth, but there is such identity in the quality of every tone and that of its octave that for all present harmonic purposes we can reckon this interval as a second; similarly an interval of a tenth is regarded as ^a third, and so on; and however many octaves intervene, the interval is reckoned as^ being within the limits of one octave; thus: _ti. JCL ^ 33: XE -cv -o- Second. Third. Fourth.Fifth.Sixth.Seventh.Eighth, Third, Fifth. Sixth etc. ^^ -^ The following is a list of the most commonly occurring intervals, and the only ones with which the pupil need concern himself at present; YO PARKHURST HARMONY. $ Unison. Seconds. Thirds. Fourths. ^o '.^ :tt^ir4 ^o "im. '^8, "ji;;- 't,^ ix Fifths, diminished, perfect, augmented^ minor. Sixths. major, augmented^ trrr jce xn i Sevenths. Octave, diminished, minor, major, perfect. ^^3 ■r 1F * jce: (For a full list of all intervals see Appendix (A)). A word must be said concerning the proper manner of learning the above intervals. An interval has not been learned when the pupil is merely able to tell how many tones and semitones are comprised within the distance; as, for example, that there are two semitones in a major second, two whole tones in a major third, etc. ; this is mathematically correct, but an utterly inadequate knowledge of the intervals. Again, to see in the interval from C to G, merely a fifth, from the bare computation of lines and spaces, with- out associating with this interval the quality of a perfect fifth, which distinguishes it from every other possible interval — such a process misses entirely the recognition of the most interesting aspect of the interval, its real individuality and character. Thus it means nothing to know that a major third is greater by a semitone than a minor third. The real difference of these two intervals is not in the size, but in the quality of the two kinds of thirds. Play the major third ^^P then depress the E to Eb ^ notice the strong, vigorous, masculine quality of the major, and the weak, almost femi- nine quality of the minor ; compare also the following : $ . » | ff U || » | l ; « By discovering these diverse qualities of the intervals, one comes truly to know them, and only such knowledge can insure success in the study of Harmony, for it is a constant study of combinations of tones. Intervals can be computed, with absolutely no sense of their INTRODUCTION. U effect, and a large proportion of Harmony students are simply computing their intervals ! The result is, that while the exercises are written with some degree of mechanical correctness, they find on completing Harmony that they are confronted by an impenetrable barrier, forbidding any further progress, li they do not then give up the study in disgust, they proceed to "review" by precisely the same process ! It carniot be too strenuously urged upon the pupil to begin this work ^ith the resolve to know the effect of every combination he writes, and to associate it with the writing every time; that is, to imagine the effect constantly, smd to play the exercise only after he has as clear an idea of it as possible, and thus correct his idea of the effect by the actual sound. In this way the study of "Theory" will increase, rather than diminish, in interest. To this end let the pupil resolve to become as independent of the piano as possible, in getting a clear idea of his chords. At each lesson the teacher should play the different intervals, major and minor, and have the pupil name them, so that he will know them by sound, and not merely by sight. As an exercise in the study of intervals, let the pupil analyse the following series of tones, ascertaining the interval from the first to each succeeding, then from the second to each succeeding, then from the third, etc., always reckoning a ninth as a second, as before ex- plained. This will bring to view all of the usual intervals. 11 o ^ ti o ft Q — — xr^eK o o I t o " ^ "^ if o • 1 o After this analysis, go through the series again, finding all the minor seconds, major seconds, minor thirds, major thirds, perfect fourths, etc., throiigh the list of intervals. The Scale. Scala, from which the word scale is derived, means a ladder; and in its application to music it means, literally, any ascending or de- scending series of tones at equal or nearly equal intervals from each other. When the intervals exceed that of a second, the series of tones is called an arpeggio, from arpa, meaning a harp; an arpeggio being such a succession of tones as is most characteristic of the harp. 42 PARKHURST HARMONY. . The scale, in its usual sense, means a series of eight tones, with intervals of a major or minor second (i. e., tones or semitones) be- tween adjacent tones. For the most part the interval between adja- cent tones is a major second, that is, a, whole tone, hence called the diatonic scale ( from the Greek words, dia, and tonos, by means of, or through, whole tones) in which this interval predominates. The Major and Minor Diatonic Scales. The diatonic scale is of two sorts, according to the location of the semitones. These two sorts are called the major and the minor. In the major diatonic scale, with which we have principally to do, the semitones occur between the third and fourth, and between the seventh and eighth tones, thus: 1 1 i/a — 4, — 4 4 — i/g. I jDl XE O 'This is the invariable construction of the major diatonic scale. To become familiar with its formation, let the pupil construct the same scale, beginning upon the following letters of the staff, viz.: G, D, A, E, F, Bb, Kb, Ab, using sharps or ^ats as may be necessary to preserve the correct intervals. The formation of the minor diatonic scale, and the reason for the use of the terms major and minor, will be given in a subseauent chapter. The Chromatic Scale. This is the series of successive semitones or half -steps: j f4iO"ol^o«t|; — ¥T 4> ^ -O L-o — 1 4> — C^ -o- y «» 4> _JJ 4> 4> i> 4> 4> «V 2V Such a difference as is indicated above is called a difference of position. The utility of such variety of position will be seen later. The above example illustrates what is possible in the case of every common chord. Let the pupil write a similar variety of position of the following chords : -o- -o^ XE -€>■ Chord-Connection. The chords of C, F, D and G are each written correctly in the following : i ^^ ^ g w t ZE but if played in succession, it is evident there is no proper connection between them, no natural flow of the harmony ; and our object is, to learn not only the correct formation of each chord, but also their proper connection one with another. For ease of expression, in referring to the several tones of a chord, we shall apply to them the same names as are used in vocal CHAPTER I. 19 harmony, viz : soprano, alto, tenor and bass. This does not, how- ever, involve the necessity of considering the parts as performed by the voice, rather than by any other instrument. Of these parts the highest and lowest are called the outer; the others, the inner or middle voices. Varieties of Motion. Before giving the rules for the proper connection of chords we must speak of the different kinds of motion of the several parts or voices, relatively to each other. There are three kinds of motion possible : Parallel, Voices moving in same direction simultaneously. I ^^ rf=^ xn Contrary, Voices moving in opposite direction simultaneously, $ Uy^ iTTf 3X Oblique, One voice stationary, another moving in either direction. # th rff XE ^^1[JJ | » Of these sorts of motion, contrary is to be preferred. (For the explanation see Appendix (C) ). The two parts most conspicuous in their relation to each other are the outer parts ; contrary motion is therefore to be sought in these parts, where it is not inconsistent with other requirements. Allowable Progression of Each Voice. Our present harmonies and their progressions are the funda- mental ones. Therefore the movement of each voice must be simple. Effect, in its usual sense, must be sacrificed to simplicity. In general the less movement the better, at least for the present. Although we are now dealing with the fundamental harmonies of all music, in- strumental as well as vocal, the student will do well to be governed. 20 PARKHURST HARMONY. in his choice of progressions, by the thought of their being intended for the voice, inasmuch as the easiest vocal progressions are identical with the rnost natural and simple progressions in music universally. The easiest intervals for the voice are the second (major and minor) the third (major and minor) the perfect fourth, the perfect fifth, the sixth (major and minor) and the octave. JDL <^ XE XE ^-4^ ^o^i^*% I Q o- lac ■€>- Any interval larger than a perfect fifth will rarely be used in the present work. The augmented intervals (i.e. augmented second, aug- mented fourth and augmented fifth), are to be invariably avoided. I tF$^ TSL t rc S In general, it is the smaller and the natural intervals of the scale that are to be used. Three Primary Rules of Chord-coxxection. 1st. Lf^there he any tone in common in successive chords, re- tain it in the same voice. ~~ I good. bad. bad. TSl ^ / if « jCE XH «: XE W 3Ci: xn ^ XE g xe: The violation of this rule leads to unnecessary motion of the voices, and a less smooth and flowing progression, as will be seen above. 2nd, Let the moving voices proceed to. the nearest tones in ihe next harmony. ~^ good. bad. good. bad. ^S m XE xr «=^^ XE ^ ± BE xx: xs: XE 3rd. // there he no tone in common in the two chords, let the three upper voices move to the nearest tones in contrary motion to the hass. CHAPTER I. 21 9J good. good. bad. bad. m ^ a: o- ^ TW m 5 XE Not only is contrary motion in itself better than parallel, but it prevents faulty relations between individual voices, which will be noticed later. In the above illustrations some are marked "good," others, ''bad.*' In these and a!! future iUustrations of this sort, the pupil should play the examples, and explain why they are so designated. As a rule pupils pay very little attention to the illustrations. The teacher will do well to enforce this requirement. The Primary Common Chords. The following exercises consist of the various combinations of the Primary Common Chords in different scales, according to the three rules above given. Each exercise is to be written three times, first with the octave of the bass, then with the third, and lastly with the fifth of the chord in soprano in the first chord, the other voices taking the tones of the chord lying nearest the soprano. Care should be taken that the voices do not lie too high on the soprano clef (a common fault with beginners), and never let the soprano be higher than G above the staff. When the bass is low, let the other parts be somewhat lower also; thus the following, though correctly harmonized, has an unmusical effect, owing to the great distance between upper parts and bass. bad. good. a i w m -£i_ « ^ jCE ^ For the success of the pupil in the following and all future exer- cises, it must be reiterated that it is not sufficient that the chord be correctly written on the staff, but the sense of the effect must accom- pany the zcriting. If it cannot be done otherwise, play the exercise 22 PARKHURST HARMONY. through, and then read it and recall the effect. By perseverance in this matter, the abihty of the student will increase as rapidly as the combinations become more difficult. To write an exercise without the sense of the effect is simply senseless. (Each set of exercises will be prefaced by an illustration, show- ing the use of the chords involved.) Illustration. I g 3CX: H ^ H JOL «: W XT « Jan XE P xr m ~rr no zsT All the exercises should be written according to the laws of nota- tion, neatly, and distinctly. Exercises. 2. XH 3x: xn P -o- XE XH XE xn 3. 4. -r\. t» 1 •/• -^ 41 «> - «» *> 4-> O !_<.,> — 1 • " t ^: I o I *M ~i — r~~i r t ~^^ i r^ I ^ O xy- <♦- ^ XE XE XE XE XE -*> XE <^ 9 10. -»): , o -o- t o —f L <> U CY ^^ «> " ^-^ ^-^ 1 «3 <3 o 11. 12. i o -«* ^ XE ■O XE -O^ IE ^V XE XE XT"^ XT O" XE O- CE XT The above exercises are monotonous because they involve only three distinct chords. But facility in these primary progressions makes all others easier. CHAPTER II. 23 Summary. Distinction of independent and dependent chords ; — Formation of the Common Triad ; — The root of the triad ; — Reason for similarity of effect in all common triads : — Two causes of variety in effect of triads; — Major and minor, perfect and diminished triads: — Tonic, dominant and suh-dominant : — Why triads on these three tones are strongest and most important: — Primary and Secondary triads: — Fundamental harmonies four-toned: — The best tone of triad to be doubled : — Position of a chord : — Names applied to the several tones of a chord: — Parallel, contrary and oblique motion: — Which prefer- able: — Which voices most conspicuous: — Best interval-pro p'essions of each voice or part : — The forbidden interval-progressions : — Three Primary Rules for chord-connection. CHAPTER II. The Secondary Common Chords. The Secondary triads of the C-scale are these : VI VII The four-toned harmonies obtained from these triads (by doubhng the root-tone) are to be used in the same manner as the Primary Common Chord. Although these Secondaries are not as important as the Primaries they are all effective (except the one on the 7th of the scale, with a diminished fifth; this will be spoken of later). In the use of these Secondaries we are governed mainly by the Primary Rules of connection before given (on page 20). By following those rules the aggregate effect of the four tones of each chord will be good, although the effect of any two out of the four, considered by themselves, will often be more or less inharmonious. Any such displeasing effect is usually compensated for by the harmony of the full chord ; accordingly the movement of any two of the voices in their relation to each other need not ordinarily be regarded; but there are two exceptions, viz : No two voices can ever move in parallel perfect fifths and octaves. Parallel perfect fifths occur when any two voices, at an interval of. a perfect fifth, moving in the same direction, maintain the same interval of a perfect fifth from each other, thus : I z:6 -^■^ ^^=& t.# 24 PARKHURST HARMONY. They appear in the following fonr-part harmonies, bad. good. bad. good. bad. good. ^ »=^ ^m ^ p Parallel octaves similarly occur when any two voices, at an inter- val of an octave, and moving in the same direction, maintain that same interval from each other, thus: They appear in the following harmonies : bad. good. bad. good. i =^ m -d- -sh i :S| -a- ^ P It will be seen from the above example that contrary motion is an invariable preventive of these forbidden progressions. While they are not likely to occur in the use of our present chords, when the three Primary Rules are followed, there will be danger of their oc- currence when the harmonies are more complicated. The effect of parallel perfect fifths or octaves is always more or less bad, and the foregoing prohibition is the one invariable rule in fundamental harmony. A word as to the reason for the prohibition. Parallel octaves are not allowed because, to obtain the largest effect in the succession of fundamental harmonies, we must have the greatest possible distinctiveness of the parts. This distinctiveness is attainable in three ways ; viz., by distinctiveness of tone, of direc- tion, and of rhythm (See Appendix (C) ). The octave of any tone may be called its higher self. Therefore if two parts move in octaves, the individuality of one of them, as regards both tone, direc- tion and rhythm, is lost in that of the other, and the chords become, for the time being, essentially three-part harmony. For the same CHAPTER II. 25 reason is it even less allowable for any two parts to be in unison in two successive chords ; thus, $ 3CE ^ -^ ^►^ =Sz: oo ^^ xr XE Circumstances will sometimes justify a unison of two parts in a single chord, thus : w f¥^ % zx FS^g^S ZX oo -o- 3X t zc (This will be spoken of again later.) The prohibition of parallel fifths is much harder to explain. Their uniformly bad effect has always been felt by writers upon Harmony, yet no one has succeeded in giving a simple and lucid explanation of the matter. The best that can be offered will certainly be somewhat abstruse, and not being practically nec- essary the pupil will find it stated in the Appendix (D). It will suffice to say here that they are forbidden from the simple fact of their unpleasant effect, which is never entirely concealed by the ad- dition of the remaining tones of the chords. The universality of the prohibition of either parallel fifths or parallel octaves is not be- cause their effect is so much worse than that of many other pro- gressions ; but because in every instance, a certain degree of pos- itively bad effect is evident. The movement of two voices, at other intervals from each other, is often much more objectionable than parallel fifths or octaves. But in respect of all other movements, circumstances so far alter cases, that a movement that is bad in one circumstance is good in another ; whereas parallel fifths and octaves are never so modified by circumstances as to produce a good effect. Let the following exercises, involving the primary and second- ary common chords, be written with a strict observance of the Three Primary Rules. 26 PARKHURST HARMONY. Illustration. I x: P \ fiC l I '^ -fi ^ S ^ ^^ 33r ^sf—a. A better flow of harmony is often obtained by placing the third or £fth of the first chord in the soprano, instead of the octave of the root. If the soprano is to be the third or £fth, it is indicated by a 3 or '5 placed under the first bass note. Otherwise let the soprano be in octave with the bass. This rule must ahvays be carefully observed. Use judgment also as to which third or fifth shall be chosen. The following shows the difference between a poor and a good choice. ^^^' - good. I ft ^ 5^ ^ ?^ tL XT XE XE Exercises. 1. '^ ^ — ^r-a r i r -^ If ^^ If j ^ xn .ix= ^-=^-p — e--J—:^'^-s .-u-^^s^a. 1 ^. rj y....\. . A". \ |J — 1 — 1 [ ti II — \^ — 1 — 1 IT |[ 3^^ «55^ ^ ~^^ ^ TJl S P ^ ^ yif-- irnf ^^ g ) ' < > . ' o s ^^ Ff-tr^N"i^^^^-^-f CHAPTER II. 27 ^ ^ '^ f I '^ J ^ 'fW 3 ^ ^ 10 ^ =551: ^ ^^ I J^^T ^ The Closing Chord of Every Composition. Exery a)mposition closes with the Tonic chord, because this alone, of all the seven chords of the scale, has the nature of complete rest. This terminal effect of the Tonic chord varies somewhat ac- cording to the element of the chord that is in the soprano (octave, third, or fifth from the root), being weakest when the fifth is in soprano : I ^-^ ^ 4 ^: a (^ § ^ JOL stronger with the third in soprano: ^ i ^ i^ Yp r^ § ^ TT jDE ^nd strongest wjth_soprano on the Tonic m w 3 «= XE (The pupil should carefully compare the three effects of the Tonx chord in these three positions, and also examine the closing chord o^ various vocal and instrumental compositions, where he will find that the vast majority close with the Tonic in the highest part, that with comparative in frequency the third, and very rarely the iifth, occurs in the highest part. 28 PARKHURST HARMONY. This matter of the close is discussed more fully in a later chapter under the subject of Cadence). It is better sometimes to violate the Primary Rule of retaining in the same voice the tone common to two chords, when thereby the final chord of an exercise can be brought into a more effective posi- tion for the close, thus : fMn p— -«- bette -js — r. p*= r rq F bettei -^ wM S— -*^ 1— -^ w ^^ U — rr- f =^ -|S> — t^ 1 f=\^ "~¥TI f ... 1 L 1 In any other part of the exercise, the Primary Rule should be followed, in such cases as the above, so as to avoid the effect of a close. When a bass note is repeated in the same measure an octave above or below, the harmony can either be written in whole notes, or, which is often better, a different position can be chosen. In the latter case it is usually preferable that the upper voices should move in contrary motion to the bass, although parallel motion is allowed. I Tf ^ XE ^ O""^ cr i JZ^ f SEESEf p fi^~. —T% ___ rq ♦4! b^ =8= ^ -a — 1 — f — =^ ^ ^ "^ ^ ry • XT ^^=^ 11 ZZJ - s) ,4» r^ hJ d- =d *• : In the following brief exercises, which we will regard as clos- ing fragments, bring the soprano upon the keynote in the final chord. Wf^ 3, (P rp ^==?z ax xi: e m 3CE ^ ^ ? XE CHAPTER IL 29 In the following, bring the soprano upon the third in the final chord. 1. '6. 4. ^ s ^TP rt^tf^i^ The movement of the soprano in the following example, from the leading tone to G (di) , is still more unnatural and offensive than its movement to A (b). i»j a. b ■ffr) o-<-" «^ *): 1 -■ ^3 U fil u -^ M The foregoing progression at (a) which is utterly inadmissible in the soprano, is to be allowed in an inner voice, because less apparent, and is very often desirable, as affording a fuller harmony. ri~li bry-- I -If ). TlT» pin tf >): 1 ^ 1^ ^ "^4^ rz^ Lj-J it uu t> 1-9— J t » This progression (a) is especially desirable at the close of an exercise, in order to have the final chord in full harmony, with soprano on the Tonic. The above descent from the leading tone, when in the middle voice, is to be avoided when the bass also descends, for in this case all the voices descend, thus: 32 PARKHURSr HARROW. g'ood. bad. bad.. better JJL -o- s i ^ -oo i± From the foregoing we deduce the following rule; in the pro- gression from the dominant to the tonic chord, the leading tone can descend a third, when in an inner voice, if the bass ascends: other- wise it must ascend.* The following closing fragments are designed to accustom the pupil to this manner of treating the leading tone. Illustration. % ^ i m :z^m 2Z^ -*>- XE Exercises. j/nrri^rrirJr[ft'i»ii>fML if 4- 5.^ , 6. 7. XE ..■iiiij'lljjl ili' J iirMi'i i rirr i rr|.| | The Diminished Triad, W The triad on the seventh of the scale is different from all the others in having a diminished fifth. In doubling the root-tone for four-part harmony the soprano can take either the octave, third or £fth. ♦Althoujrh this is the usual rule prescribed in text books, the erreat harmonUt Sebastian Bach, is authority, in some of his chorals, for leading all the voicrs i\o\\ n. CHAPTER II. 33 fe^S=tid f^; w bail. XE bad. _Ol_ bad. By doubling the root-tone we have tzco Icadiji^^ tones, so that neither of the above chords is satisfactory. The best of the three is the one with soprano in the third, for this somewhat conceals the octave of the bass, which is in the alto. By doubling the third or the fifth we better ourselves somewhat. i «= m JQL :§: 3x: AX But almost any connection of either of these forms with the other common chords is awkward and displeasing. In whatever connec- tion and in whatever form this chord appears, it bears the stamp of the diminished fifth, which usually prevents its adoption in simple harmonic progressions. The occasional opportunity for its use will be shown later. The Incidental Alteration of the Common Chord. Hitherto we have used only the natural tones of the scale in forming the chords. While the integrity of the scale and the clear- ness of the harmony require that in the main the chords should be thus composed, monotony would inevitably ensue if this rule were invariable. The occasional substitution of an accidental tone for a normal tone does violence neither to the scale nor to the harmony, and casts an agreeably new complexion upon the flow of harmonies. Compare the following : 22: m i zt« xi: « XI 2=5 22: ^ W- M m » m and the third chord will be found more pleasing with the F# than with the normal tone on that degree of the scale. The pupil is not to confound this with modulation ; such a use of accidentals is not modulation, as will be explained later. 34 PARKHURST HARMONY, The subject of Modulation is fully discussed in Chapters XVIII- XIX. Accidentals thus used commonly affect the third in the chord, very rarely the fifth, and when one is placed under a bass-note it is to be understood as belonging to the third from the bass, thus : I m i ^ & xr XE 1^ 3x: n^^ XT ^ ^ X i T The use of accidentals to affect the third is commonly to change a minor third to a major. The following exercises give practice in the use of accidentals. The above example will suffice as an illustration. Exercises. i f ^ XE z. Tx: ^ 2Z 4, XT s T— 1 ^ 22 5 ^ Summary. Secondary triads : — Parallel perfect fifths and octaves : — The way to avoid them : — Reason for bad effect of parallel octaves : — Distinc- tiveness of parts is three-fold: — Successive unisons: — Reason for the invariable prohibition of only parallel perfect fifths and octaves, if they do not produce the worst effect of all progressions: — Rela- tive value of octave, third and fifth in soprano in last chord: — Re- laxing Primary Rule, to bring soprano on the Tonic in last chord : — Procedure when bass moves an octave : — Leading tone : — Exception to third Primary Rule : — Movement from '^leading tone" when in an ^'inner" voice : — proper progression from "leading tone" in different voices, when dominant chord is followed by that of the Tonic — Diminished triad, and doubling its root in four part harmony : — Use of accidentals : — Which element of chord usually affected by them : — Accidentals used to change a minor third to a major. CHAPTER III. 35 CHAPTER III. The Minor Scale and its Triads. The scale heretofore used has been the Diatonic Major Scale. As already remarked, the several tones of this scale constitute a sort of organism, by reason of the internal relation of the tones to each other. But there is still another series of tones which shows itself to be equally an organism, with corresponding relation of the several tones among themselves, and equally melodic, yet with a surprisingly different effect, from the simple fact that the intervals of tones and semitones succeed each other in different order. The Diatonic Major scale of C $ XI- TF^ >o ^> is a sample of the scale thus far used in our work. This can be transformed into another scale, equally coherent, by changing the major third above the Tonic into a minor third, and the 7najor sixth into a minor sixth, thus: I :cF-^ xn o: XE This is not so melodic throughout as the preceding scale, on account of the gap between Ab and B. To avoid this interval of an aug- mented second, the melody, when proceeding by degrees upward from G, takes A, which divides the space between G and B into two equal intervals, thus : unmelodic. melodic. I XE l^O » ^i^ 1., l?o <* IX O ^^ V2 Viz .^.O ^''^ 1 T In connection with harmony it appears as follows : i i t 3X1 ^ ^ i xr bad. ^ ffl good. ^S s H But even as the melodic tone the Aif is not invariably used, for if the 6th degree of the scale is not followed immediately by the 7th, then the 6th deeree will be Ab, thus. 36 PARKHURST HARMONY. ^S i m 3 ? ps ^ 33t -^ i2 xx: 4u ^ S xc XE 3i=:xi We may then regard Ab as the normal tone of this scale, and A^ as the occasional substitute, for the sake of a smoother melody. But as the harmonic tone, i.e., as the root or any element of the chord, the 6th degree must always be Ah, thus : good XE & i 3Jr *« m=^ i & bi d. P ^^ ^=?z jix: 3CE [#=i "fiV ■k- ^k); 1 6 1 ' [■ ^ -4^ bn — c h ' . ?^= & ) G ••■'■ cl — o ** ] This form of the scale I bo t» o i>»" " is accordingly called the harmonic form, and the following, TJ jlQ^lO^^^ ^3r the melodic form. But while the ear is satisfied with the above, as an upward melodic scale, the effect, in reverse direction, is quite in- congruous : I a. bad. good. t^^ 33: «» o « * bo ^ IX " " bo-TT We must therefore have an altered form for the descending scale, which is found above at (b). The necessity of this form is shown, more clearly by combining each of the above forms with harmony : CHAPTER in. 37 I u i^ 'bad. rf *-# f ^ i goodJ r m A g 22: f f We thus have three different forms in our new scale; the h armo nic (ahke up and down), the melodic upzvard, and the melodic downward. harmonic. tf ZTE m XF bo i» OE 17TT- XE^ XT up- melodic. down. ^^=^ ^n xfzzzn iX o 1^ -o- :is^ o 3X XT This new scale, in its collective forms, is called The Diatonic Minor Scale. It is so called because we obtained it by changing the major third and major sixth of our previous scale into minor third and minor sixth. ( Similarly the previous scale takes its name of major from its ^rmjor third and major sixth.) On comparing the major and minor diatonic scales, we are at once impressed with the distinctive character of each. In the German language, which is so apt in the significance of its terms, the major is called hard (Dur), the minor, soft (Moll). The major is vigorous and manly ; the minor feminine and tender ; the one, strong; the other, weak. Moreover the minor scale is proverbially sad, and cannot be joyous. While Milton's L' Allegro is emphatically major, II Penseroso is equally minor ; and yet Handel's "Dead March in Saul" is striking evidence of the capacity of the major scale to express the deepest sadness, for this composition is thoroughly major, containing not even a single minor chord. The tonic and dominant chords comprise the bulk of its contents. The major scale is thus more versatile than the minor in the diversity of its power. But there is a sort of self-possession, a dimly defined hope, in the sorrow of a major composition. The mood of the minor scale is the sadness of despair. Again, looking at these two scales from another point of view, we see that the major is characterized by simplicity ; it is invariable, up and down. The minor is complicated, having three forms. This in- creases the difficulty in its correct use, but at the same time stamps 38 PARKHURST HARMONY. this scale as being richer in its contents than the major, as there are two more tones involved in it. If instead of beginning the minor scale upon C we begin it upon A, and have the successive intervals exactly correspondant v^^ith those in the minor scale of C, in the several forms, v^e obtain the following harmonic and melodic scales of A minor. harmonic. 4% o ^' 331 i» O XE -»/5 ^ -^2 te- up. melodic. down 31: ^ -^ m 3X 3aL -% te- In the harmonic scale tlie semitones occur between the 2d and 3rd, the 5th and 6th, and the 7th and 8th. In the melodic, up, be- tween the 2d and 3rd, and 7th and 8th. In the melodic, down, be- tween the 2d and 3rd, and 5th and 6th. As to the reason for having two forms of the melodic scale, see Appendix (F). It will be seen that the scales of C major and of A minor are closely linked together ; for in beginning the minor scale upon A we find our minor third and minor sixth already prepared to hand. The harmonic form therefore requires only the substitution of G# for G ; the upward melodic, the use of F# and G#, while the dozvn- ward melodic scale comprises the identical tones of the major scale throughout. This degree of identity of the tones, and the consequent identity of form of the triads on A, B, D, and F, If the 7th were to be invariably raised, the accidental could be put into the signature ; but as we have seen, the accidental is omitted in the downward melodic scale, so that the simplest way is that it be always expressed when needed. The first great difficulty in the study of Harmony is in the use of the minor scale. For this reason a full and explicit statement of its construction has been given. To insure a reasonable degree of familarity with its complexities, it is now required of the pupil that, according to the model furnished above in the scale of A minor, he should write all the following minor scales in the harmonic and melodic forms, in the several signatures. ^ >^^i<*it o i i^ri^A \\ h\ , m f -t>- vv-gt.^^ ^ h\\ o \w^ ^ I 55? -€>^ I Write the same in the bass clef : ll" l l*.!"!! | | Hi»»|, l l JAj* ty XT u s ^ & ^^:^ xr XE -^ The purpose of the above exercise will be fully attained only when the effect of each form becomes Hxed in the mind. The pupil can well afford to spend the time necessary for the complete mastery of this scale ; for without it, he will be constantly liable to embarrass- ment and consequent inaccuracy in its use. The Triads of the Minor Scale. The triads of the scale of A minor are as follows : I |.#X U<^§ M: 40 PARKHURST HARMONY. Those on the £rstj fifth and fourth of the scale are the Tonic, Domi- nant, and Subdominant triads, as in the major scale. But only one of them, the Dominant, is a major triad. In addition to major, minor and diminished triads, we here meet with a new form, founded on the third of the scale (C), containing an augmented fifth by reason of the raised 7th (G#). This triad is called the augmented triad. As the 7th of the scale is not invariably raised, the accidental must be indicated when wanted. In the augmented triad it is indicated by prefixing it to the figure 5, placed under the bass note, as that is the interval from the bass. I m i t ^^F^ * XE & XE #5 kl5 A line through a figure is equivalent to a ^ before the figure, thus ^=#5. The dominant chord of the minor scale contains the raised 7th as the third of the chord, and, as already explained, the simple acci- dental, without a figure, is placed under the bass note : I ^m m s its: xn a T In writing the following exercises, place first the octave, then the third, and lastly the fifth in the soprano of the first chord. Illustration. CHAPTER III. 41 1. m Exercises. 2. JOE XE XT ^ -^^ 3x: ^ ^ TJL & 3s: XE 3x: (>. ^ BOl XJl 3i: an -o- 8. E XE S g -O- ^ XE 3CE XE As the raised yth is such a significant tone of the minor scale, in order to impress it upon the mind, let the pupil write out, for him- self, the dominant chord with the necessary accidental in each sig- nature up to ^ * and tes The Augmented Second. The chief difficulty in the use of the minor scale arises from the interval of an augmented second between the 6th and 7th of the scale, A imnor ' ^^ % which is a prohibited interval in all fundamental progression, Q\ving to its difficulty and unnaturalness. The voices must therefore be so disposed that none will be obliged to take this interval. The difficulty occurs chiefly in the connection of the chords on the 5th and 6th of the scale, thus: 42 PARKHURST HARMONY. The above faults are avoided by the following progression : i ^ m XE XH XH m TF 3CE ■^~r This is the only progression possible in the combination of these two chords. In such combination neither the root nor the Hfth in the chord on the 6th of the scale can be doubled. The procedure in the connection of these two chords is expressed in the following law : We must invariahly double the third in the chord on the 6th of the minor scale, when that chord is preceded or follozved by the dominant chord. This doubling can be either in unison or in octave, thus: I unison. unison. octave. unison. unison. octavo. XE XE SE m ^ m ^ XE m TSST m^m XBX XJ ■^^ m -o- XE XE XE jCE XE X£ T The difficulty in the connection of these two chords, and the sin- gle solution of the difficulty, must be clearly understood, as the fre- quent embarrassment in the writing of exercises in the minor scale will be found to center in this very point. The following exercises will give facility in the combination of these chords. Illustration. m m i SSI ^1 M 33C ^8^ ^r m ^ m XE J Let attention always be given to the position of the iirst chord of each exercise, as indicated by the figuring. Carelessness in this re- spect is certainly inexcusable. CHAPTER III. 43 Exercises. 2. m ■ J M J I'r.WhJ ^ fO r - ^ r. C * -O— >):l4Mrf irfi ^^ q17 3X1 ^ 6. xx: -o- 7. s 8. .3 ^ ^^ 3X *>:l\^irr' 10. fe fe# ^ XE -^ f-^ ^^ 13. ^s m 14. 15. 3 3X 16. m ^ -G- ^ a XE ^ 1 In the connection of the chords on the 2nd and 5th of the minor scale, the rule of retaining in the same voice the tone in common rnust be violated in order to avoid the progression of an augmented second, thus: As seen above, the^nly way to avoid the fault is to have all the upper voices descend, even though the bass descend. The following fragments introduce this difficulty, and also the preceding, in differ- ent scales. Illustration. m ^ xx: -^ zz: m i 44 PARKHURST HARMONY. Exercises. ^2. s. , 4. ■ 7^' If I ii y i Jf i "i i «/j i . i ,i i ° i i»iWifrii g'i"ii^'vjirf;rr i i f ■c*- g> '^z There are two diminished triads in the minor scale, on the 2nd and on the 7th degrees, in A minor W F^=^ irH- — i» instead of only one, as in the major scale. The resources ot the minor scale are not to be judged by the use of the sim- ple chords thus far presented, for after deducting the three chords, on the 2nd, 3rd and 7th of the scale, in A minor ^5 which arc less effective because of the diminished fifth in two of therri^ and the augmented fifth in the third, we have only four remaining. But it will be none the less advantageous for the pupil to work out the following exercises, with a strict observance of all the foregoing rules. As a precaution, look through each bass, before writing the harmony, to see if the 5th and 6th of the scale are in immediate connection, so as to double the third in the chord on the 6th. Illustration. ^^ j4#dE * m It5 ? m f XE CHAPTER IV. 4S Exercises. a ^^;nfL-lNlr- m 2. «5? e ^ 22 -« H& 3. , xz: -«— «^ ' \ rJ ^ I ^^T t. | | .j | ..-^4^ ^^^H^i — p-'^'-T' — J — —^ \ {' \P — ht-i If y '^i ^ rji [ N J ir J u 1 1^^ ujioj m *^ 22== = :^ f ^^^ Summary. How the major scale is transformed to the minor: — ^Why the minor is less melodic than the major: — How the minor scale is made melodic: — The three forms of the minor scale: — Points of con- trast in the major and minor scales: — Why the A minor scale is called the "relative minor" of C major : — Interval between keynotes of every major scale and its relative minor: — Signature of every minor scale : — Why the accidental that produces the "leading tone" in the minor scale is not expressed in its signature : — Classification of triads in minor scale: — How the raised fifth in the augmented triad is indicated : — How the alteration of the third in a chord is indicated : — Chief difficulty in use of minor scale : — Why augmented second is prohibited: — In the connection of what chords the aug- mented second is most likely to occur : — In such connection what law to be followed : — Rule in the connection of chords on the 2nd and 5th of the scale. CHAPTER IV. The Inversions of the Common Chord. Hitherto we have used our chords with the root of each in the bass. This is the most simple and obvious arrangement of the tones, and chords in this form are said to be in the fundamental position. But we can form a re-arrangement of the tones (for example, in the chord of C), wherein not the root but the third is in the bass; and 46 PARKHURST HARMONY. still again, a second re-arrangement wherein the fifth is in the bass , thus: m XE ?^ ^ fundamental position. m xr ^ third in bass. 33: xr ^ fifth in bas; XE The fundamental form and the two re-arrangements are still radi- cally the same ; that is, they all have the same root, C : but with this radical resemblance, they yet produce quite different effects from each other. These re-arrangements of the chord are called its in- versions. That in which the third is in the bass I m » xx is called the first inversion, that with the fifth in the bass is called the second inversion. 8: ^ The use of these derived chords affords great variety in the employment of the common chords. Each inversion will be examined separately. The First Inversion. In this chord, as in the fundamental form, to obtain four-part harmony, we must double either the root, third or fifth of the triad, thus: ^ good, less good. g^^- XE -€>- root doubled m XE XE « third doubled. XE XE -€>- fifth doubled. XE By a comparison of these several forms, and still more by ex- tended experience, it will be found fnostjatisfactgryjo double eith^ CHAPTER IV. 47 the root or the fifth, and (except under certain circumstances) least desirable to double the third, i. e., the bass. An explanation must now be given of the figures hereafter to be found under bass notes. The full figuring of a chord is the set of figures placed under a bass note, indicating the intervals of the sev- eral notes from the bass. Thus the full figuring of the chord of C, in fundamental position, i p ^ IS To simplify the matter, it is agreed among harmonists that when there is no figuring with a bass note, it shall be understood that 5 J i.e., the common chord in fundamental position, is intended ; and when it is necessary to indicate a common chord by figures, the full set is abbreviated to one or two of them as the case may be. This will be understood later. The full figuring of the first inver- sion i m i XE 3x: 3CE -€3- jcx: g is 6 or 6 when the third is not doubled ; this is usually abbreviated to 6, which, placed under a bass note, indicates the first inversion of a common chord. This means that the root is a third below the bass note. The procedure in such case is, find the third below the bass note ; this is the root ; find the elements of the common chord on the root, doubling the root or the fifth as the location of the voices in the preceding chord may require. Because of the figuring, this inver- sion is called The Chord of the Sixth. To become familiar with the process above given, construct the following chords, in each case doubling first the root, then the fifth. Until we reach the subject of ''Open Position," (Chap. VII) the three upper voices are not to exceed the limits of one octave; that is, the tenor cannot be more than an octave from the soprano. 48 PARKHURST HARMONY. In chords of the sixth the soprano and tenor will often be just an octave, as in the above example. i XE 33: -*> -o- -€>- XE 33E 6 6 6 6 6^ 6 Whether the root or the £fth is to be doubled, depends upon the connection ; the doubling should be such as involves the simplest progression from the previous chord, thus: m good. m s TV 5» — 6 « XT less good*, XE 3 good ? — r bad In the following chords of the sixth, the root is to be doubled. Exercises. 3. . 4. ^^^rirn.>i i nrriwi i J i jji»i i <>j i Jf4"p ^a 36"^ — 3 6\ — "a '^5 ' " I ' b' " ^3'tf ^ '^" In the following chords of the sixth, the fifth is to be doubled. m z. Exercises. 3. 4 "ImVfX) ^ 3' 6 XE xx XE 5 6*^ 6^ 3 $ 6 When the tone that is doubled in the chord of the sixth appears in the following chord, let it usually he retained in that voice which will cause the other voices to move contrary to the bass, thus: s i B m H XE -O- « 2Z2 ^ 22 good less good. good. less good. good m XE XE XE 6 6 6 6 B The melodic effect of the soprano must often determine the doubling. In the following exercises the pupil is to use his own judgment in doubling the root or fifth, observing the same rules for the close and smooth connection of chords as were followed in all previous exercises. But it is to be observed that the "Three Primary Rules" for the connection of chords have their most particular application in the use of the chords in fundamental position. They CHAPTER IV. 49 are very often, but not so invariably, applicable in the use of inver- sions. The pupil must therefore rely a little more upon his own dis- cretion, aiming constantly to secure the smoothest progression of the harmony, and the most melodic effect of the soprano. Illustration. ipiti' ±i ^—r 6 S^ XE t ^ ■^rit IS — 73 ^ 221 ^ XE O " 5^ 6 "^ Exercises. ^) \ r -f-'^-H^-'' r P - 1 1 1 — r-H ii 3 'e 6 6 ^ J c ' " -*?^ — —\^--f^^-'-^-p — -d— r--T — tM — II ^ i i-iJl-^rifi i[^-^ N jMj^^zJ^ s ^^^ ^ 3X 3 * 6 J» 6 Hf g ;^=F jE g 331 1 5 6 6. ^ ^ f ^ ^ C "^^ — .^ — XE zt:^ 7. . ZL » i: . g «* HCT *>=^ J!rr irnff^ i rrirJMy B Doubling the Bass Note. For ease and smoothness of progression, especially when two or more chords of the sixth occur in succession, it is often desirable to double the bass note, thus: 50 I PARKHURST HARMONY b. ij i E f^r P g xs: « XE ^ 9~r « g i xs: S ft I 6 6 6 6 5 (In the second measure of (b) the common chord following the chord of the sixth is indicated simply by a 5 ) . According as the triad from which the chord of the sixth is de- rived is major or minor, the bass note in the chord of the sixth will be a major or a minor third above the root. If it be a minor third the effect of doubling it is much better than when it is a major third ; and when minor, no particular pains need be taken to avoid its doubling. Indeed it is sometimes better to double it for variety. Ob- serve this doubling in the above illustration. good 2 / good. good. g ^ — t ?=i TZ. W} t 6 ^ 6 6^ 6 '« mi. ara mi. ^i^d mi. 3ra If the bass note be a major third from the root, it can be satis- factorily doubled when the voice that doubles passes diatonically through the octave of the bass, to the next degree. In such case the effect is good. (See above at (a) and (b) .) The foregoing constitute the two chief exceptions to the rule against doubling the bass in chords of the sixth. In the following chords of the sixth, sometimes the root or fifth is to be doubled, and sometimes the bass note (the third), according to the rules given above. These exercises require careful study in order to become familar with the varied treatment of this chord, which requires more care than any other chord in Harmony. As the variety of chords increases, there will be increasing opportunity for individual judgment and taste ; therefore let not the pupil fail of constantly having the sense of the effect, as he writes the exercise, playing it over after writing, to correct any erroneous impression. CHAPTER IV. Illustration. 51 i5 5^ 3f==:S: ^ s Ztl^ xz: 6 •6 6 6 6 Exercises. i s Hi 1 'ft ifi =22 -rw XE 6 6 ^^ ?^7— - m 6 6 6 5 4. i XX ^ i ^ £KM^ XE -t 3 6^6 i g ^ 2t^ XE st:5^ 6 '6 6 6 6 The justification of doubling the bass when it is a major third, is found in the smoothness of progression, and in the fact that the part that doubles the bass has a decided melodic movement, from which it cannot be turned aside for the sake of avoiding the doubling. Doubling in Unison. In a succession of chords of the sixth, it is often advisable to bring two voices into unison, as in the following. m <5}©- s zz:'7~prxi:i!g S S ===?^^ s: S ^ good. bad. ^xi=:z2 G 6 6 6 n:=z2 good, P bad. zzz ISl -€^ 6 6 52 PARKHURST HARMONY. At (a) it is bad to double the ''leading tone", which leaves as the best alternative the bringing of soprano and alto into unison. At (b) the avoidance of parallel octaves or a bad doubling of the bass (a major third from the root) is also by means of a unison. This unison of two voices is a most convenient device for avoiding faulty progressions, and should be kept in mind. To become familar with this disposition of the voices, let two of them be brought into unison as often as possible in the following exercises, only not in two suc- cessive chords. Illustration. i fUj4ip-|lji ^E Xil -c^ 2za ^ ■&- m J3L TSl 6 Q ^ ^ Exercises. 6 6 ^u^ i XE 36 6 6 ^. i ^ 33: 6 5 6 e^ ^ n &-^ m 22=1^ -O- 6 6 m ^ ^m ^ -o- $ ^ In the chord of the sixth on the second of the scale, either the bass note (the third) or the fifth must be doubled, and not the roj^^ which is in this case the "leading tone". foot."" root. 8rd i M 5th Srd ith 5t^ bad. bad. i good. good. good. good. good. m f f m r' \r r 6 6 '6 6 '6 6 '6 6 6 6 "6 In accordance with the above, harmonize each of the following fragments tzvice, first with the bass note doubled, then with the fifth. CHAPTER IV. 53 ^ m\h(f \ \¥Mkni{r\\^'^UiKfm 6 6 6^6 6 6 6 6 "6 6 .6 6 The diminished triad (on the 7th of the scale), which we found so unserviceable in the fundamental position, is quite effective and finds its principal use in its first inversion, the above chord of the sixth on the 2nd of the scale. There are unusual difficulties in the diversified use of the chord of the sixth, and the pupil is advised carefully to study the various points above noted, that he may be able, in all variety of circum- stances, properly to use this chord, which, all in all, is the most diM- cult chord in Harmony. The Second Inversion. i xz: «^ i fundamental postion. m XE XE ^ second inversion. XE By putting the fifth of the chord in the bass we obtain a new harmony, and yet radically the same as the fundamental position and the first inversion, as the root is identical. As in the first inversion, so here, we can double either the root, third or fifth. best. I xc , root doubled. m XE H third doubled. XE XE «=§= -e^ fifth doubled. XE=inzi3: It is by far the most satisfactory to double the fifth (i.e. the bass), both in itself considered, and as securing a smoother progression to the next chord ; and for the present we will consider this the only allowable tone to double. The full figuring of this chord, I " t* ^=^ m XEXE ^ 5 4 4 54 PARKHURST HARMONY. is 6 which is usually abbreviated to J. From the figuring it gets the name of Chord of the Sixth-and-Fourth. The procedure in writing every such chord is, reckon down a fifth from the bass note ; this gives the root ; determine the elements of the common chord on this root, and place them in the upper voices,^ doubling the fifth (i.e. the bass note). It should be distinctly understood that figures always indicate the intervals of the upper voices from the bass note, and never from the root. This mistake is often made by pupils. Thus in the above example, 6 means a sixth from G, which is E, 4 means a fourth from G, which is C, and G-C-E are all the diverse elements of the C-chord, in the form of the second inversion. The most common use of this inversion is in connection with the common chord founded upon the same bass tone : # m s «5pa^ 35: XE T^ 6 5 4 3 In such case the figures J must be followed by figures that repre- sent the common chord in fundamental position, either I or 5, or 3. When the third in the second chord is to be affected by an accidental, the accidental alone is sufficient to represent the second chord. If the bass moves an octave in the last half of the measure, no figure is necessary over the second bass note. (This is all illustrated in the above examples.) The chord of the sixth-and-fourth is sometimes followed by a chord of the sixth on the next degree above. ^m w m CHAPTER IV, It can be preceded by various chords, 55 m m ax m XE b 6 5 4 ^*^ ^ ?: 2 ^ ^— i ^:f XE 6 ^ r i ^ xi: 4 No difficulty will be found in the writing of this chord, if the previous general rules are followed. Illustration. ||E H#fH ^ s 3X XE ^ g -5©- «=; i XE 6 3 4 B^ (5 5 4 Exercises. ^^>^- i-p4f-4 is— f-^ £ XE 3 6 6 ^^ i IE H, ^ o I /^ ^ f XE n 6 3 6 6 4 3 6 3. 4 6 6 4 s J l J i MJiJ -^ i^a IT 6 e XE -6—8- rr i PJUHrJ p TSZ g* r J |o 5. 3 6 5 4 ?l 6 6 it 6 4 6 6 6 6 # 4 4 I EOE XE ^^ Sf <2 3 -^ ^ 6 5 6 5 6 jg- 4 JJ XT 4 ;^ 56 PARKHURST HARMONY. 6. i 22: 7. ^ ? XE 6 4 3 s f f f :^=? jCE 6 4 3 8. :5F m ¥ jCE 6 ^ 6 6 4 3 The rule to retain a tone in common in the same voice does not necessarily apply when a fundamental chord is in immediate con- nection with one of its inversions. In such case, the two chords are radically the same, and there is no effect of disconnection if the voices change their position. The principle is the same as in the case where the bass moves an octave, and the other voices can change their position (see page 28). Thus in the middle of the second exer- cise above, a better effect is secured by changing the position as fol- lows, m «5i=^ 5 instead of ^^ ^ 3X « XT The only chord of the sixth-and-fourth thus far used has been that whose bass was the dominant, i.e., the second inversion of the tonic chord. This is the most common, but others can be used with no more difficulty, and with good effect. XlL t!. C. pp » ^ XE XHX ^ 9 <*- xi: m xn XE -^ 6. 3 4 ,e CHAPTER IV, 5i The same rules govern the progression as heretofore. When any interval from the bass except the third is to be affected by an accidental, the accidental is placed before the figure expressing the interval, as b6, ^^. As an exception to this rule, a ^ belonging to any figure (except 3) is indicated by a line through the figure (as at c, above), while a b or 'i is placed before, as at (d). By some harmo- nists the accidental is placed (with less propriety) after the figure, 6^ 5#. The figuring is also sometimes found above the bass note, which is not advisable, as it interferes with the tenor when placed on the bass clef. Illustration. fe ZS12 3CKZ m XE f XT f 3CE 3 4 ^ ^ H .4 When there are two tones in common in two adjacent chords, retain that one which will secure the best melody, and the best posi- tion of the voices, thus : not. ^ ^^ ^ m XE m T7 ^ XE Exercises. s ^ 'XSL ^^^ f- XE 6 4 3 m ^ — 4 3 i 551 xc -6 4 3 ^' A 6 6 4 3 ^ -^'rrji r -cv 4 3 g 5. 3 6 6 r 6^ ^ XE 5 6 XE 3 4 g rj 6 6 6 ^r-27- -t^ 58 PARKHURST HARMONY. ^ & :3Ds: f XE -e>- 5 6 S 6 4 t « .-^ ,,, — XE ^ xn ^ 4 a XE ^ 4 ^ i 6 4 -i -^ ^ XE ^ 6 6 4 a 6 6 G .4 it Summary. Meaning of "fundamental position" of a chord : — Two inversions ©f a common chord :— What should be doubled in first inversion :— meaning of figures under bass notes: — Full figuring of commdn chord:— Full figuring of first inversion: — Its abbreviation: — ^The procedure in writing chord of the sixth :— Whether root or fifth shall be doubled :— Which doubled tone to retain in next chord : — Primary Rules less applicable in inversions : — Two exceptions, allowing bass to be doubled : — Doubling in unison : — Doubling in sixth-chord on second of the scale: — Chief use of tnaa on seventh degree of the scale :— Doubling in second inversion:— Full figuring, and its ab- breviation : — Procedure in writing chord of sixth-and-fourth : — ^^Fig- nres express intervals from what :— Meaning of ^ 5 or J ^ or 6 #. — Moving all the voices when the fundamental position and inversion are in connection : — Meaning of accidental before a figure, and of a line through a figure :— Procedure when there are two tones in common in successive chords. CHAPTER V. The Chord of the Seventh. We now come to the second elementary chord in Harmony, called the chord of the seventh. s^ fi=ft in reality an outgrowth of the common triad, formed by adding to it the third above the fifth, that is, the seventh above the root; hence called, the chord of the seventh. There is a peculiarity of this seventh, which distinguishes it from every other tone in the chord, and stamps a new quality upon all the chords of the seventh ; viz., a strong and constant tendency to CHAPTER V. 5% lead downward one degree. This tendency determines the progres- sion of the voice containing the seventh, and thus in a degree con ■ ditions the next chord. This can be illustrated by the seventh and the root, omitting the other tones of the chord. ^ This inherent drawing of the seventh introduces a new quality into our chords, illustrated in a degree by the leading tone of the scale, and binds together the harmony more closely than could be the case in the use of only common chords. The Resolution of the Seventh. The seventh, in its discordance which, if long continued, is in- tolerable to the ear, finds a point of rest in the tone below. This leading downward is called the resolution of the seventh, and the following chord is called its resolving chord, and the tone below the seventh its resolving tone. The peculiarity of the seventh, stated above, gives rise to the law The seventh must always be resolved, and in the same voice. As the seventh can be added to every triad, we shall have seven chords of the seventh in the scale : C Major. Primary and Secondary Seventh-Chords. The seventh-chord by far most effective and most frequently used is the one founded on the fifth of the scale, hence called the domi- nant-seventh-chord. This is so pre-eminent above all the others r\' to be the one primary seventh-chord, and the remaining six are tht^ secondary seventh-chords. The Dominant-Seventh-Chord. m In distinction from the common chord it will be observed that every seventh-chord has four instead of three diverse tones ; hence the seventh-chord requires no doubling in four-part harmony. The dominant-seventh-chord can appear in the following posi- tions : 60 PARKHURST HARMONY. I «^ g W^ joe: m 3X i> it The most common use of this chord is in connection with the tonic chord, which resolves the seventh of the dominant, and affords an easy progression of the other voices : I 30: B^=«^ m jx. xn The seventh must descend (to E) ; the third (leading-tone) must ascend ( being in soprano) ; the fifth (D) has no decided tendency Hke the seventh and the third (leading tone), and is to move in that direction which will result in the fullest harmony. The bass can descend a fifth or ascend a fourth, to tonic. If other positions be chosen for the upper voices the progression of the seventh remains the same, that of the fifth and third may vary: ^ ^ ^=aE S=5 8 — ^ttt t. ^^ nsS: JtX. " «> ^ 30: XE XH XE 3x: 33: The third, the leading tone, when an inner voice, may descend if the bass ascends, as in the common chord. These diflFerent pro- gressions should be carefully studied, that the diflference may be clearly seen. In accordance with the above, harmonize the following, with the third, the fifth, and the seventh successively, in the soprano, notic- ing the motion of the bass, as that controls the motion of the third (except when the third is in soprano). (The chord of the seventh is indicated by the single figure 7, unless other of the intervals are to be affected by accidentals.) 1. 2. . 3.. _ 4. ,. _ 5. m t f I" ll^ii r \fW~[ U B XE XE 'H^ I " 1 jO- S ^ ^ XE S CHAPTER v. t?J Although every seventh-chord, in itself considered, sounds better when all four diverse tones are heard, ease and smoothness of pro- gression, and the better effect of future harmonies, often make it advisable to double the root (no other tone can be doubled except sometimes a minor third), thereby sacrificmj:_either^the^ tjiir^^ the fifth. F?=^ N-^ ri — t ^^ -H-4t — j9 1 -»-H t4= good. ^ ^ — 5 — bad. ^^- — O ^ bad. -f _5 ^__ good. -J^ 1 7 i> LL h 1" ? 4> 4- 7 ti 7 ^ It is much better to sacrifice the fifth than the third, as at (b) ; consequently, In the seventh-chord y when the root is doubled, omit the fifth. At the close of an exercise that position of the dominant-seventh- chord (which usually precedes the final chord) is preferable which will bring the soprano upon the tonic in the final chord, as this se- cures the most complete effect of a close ; accordingly in the follow- ing example, (a) and (b) are preferable to (c) and (d) for a closing effect. 0. ^ d. m m H 3x: 3z: good. ^r « -O- 3^ good. ^ less good. "ST least good. 3x: For this reason the following progression at (a) is better at the close, although it involves more motion, whereas the progression at (b) is better at any other point of the exercise : s i b. 3CE ^ t5>- S -^ The effect is generally better to descend than to asce^^d to the seventh, eren though it involve parallel motion in all voice^i. 6?. PARKHURST HARMONY. The combination of the complete seventh-chord and the incom- plete tonic chord is more musical than that of the incomplete seventh- chord and the complete tonic chord, even at the close of an exer- cise, thus : better. ifihz- j ^ i XE 33r ^ -~s^ — incomplete. incomplete. complete complete. XE XE jDE jKH 6 7 67 4 4 It is evident that in a work like this only the most general state- ments can be made. The pupil must seek to obtain the best efTects, not by slavishly following the rules, but by consulting to a degree his own taste, thus quickening his musical sense. An exercise may be correctly written, and yet produce a monotonous impression. This is generally caused by too little motion in the soprano, thus : better. I 3X W^ « «a- iS ^^ ^r W^ ■si-zf- m jS 3H XE ^6 7 6 7 In working out the following exercises, the seventh-chord having been written, the first thing to do in the following chord is, to write the note that resolves the seventh in the same voice in zvhich the seventh occurs, then move the other voices to their proper places. Illustration. m ^ ^ ixr: 2=12 Z?=^ «: :gr-" ■6f- -&- % jCE tr: % 3 CHAPTER v. Exercises. 63 § xc 3 6 7 6 6 4 3 XE 3 6 4 6 6 ^1> I J I I ilJ J F I f ^ k^ r 4. fi tt 6 ^ iss: -^TJ T-^ i^if 5. 6 7 4 -o- XE f iS>— ^ 6^ 6 7 6 7 6. -^ f 33C XE Ff=ff 4 3 6 4 ^ 6 7 4 f i zz -^ 6 '6 4 7 ^^ ^^ S t5« «• jS. 5 B 0. »^ i ^ 7 H 7 -»- 4 -o- "B 6 # 6 ^ XE ^ XE 2Z XH 6 6 4 ;i 6 7 4 The Dominant-Seventh in the Minor Scale. in A minor. ^ ^^^^ m m «M> iJ^gr ^==« ^^ O S XE XE XX XE XE XE XX >v4» *In this measure write two positions of the same chord, to as to maintain the movement in half-notes. ^ PARKHURST HARMONY, As will be seen above, the progressions are identical with those of the dominant-seventh in the major scale, and require no further -explanation. Illustration. m Wf XE § «5F 7 ' tf XE 22 *t n ^^ « 6 5 f ' (It is best that the voice having the 8 should take the 7, as in the last measure but one of the illustration.) Exercises. :««: i p i p \ f' r ^ XH 6 4 j* 8 7 *ir !!■> -o- 6/6\ -%- 5V5^ 4 a 3 Jr\2) 2 The dominant-seventh has three inversions. The first, formed by putting the third in the bass, has for its full figuring 5 , abbrevi- ated to |, hence called The Chord of the Sixth-anekFifth. In the different positions as follows : in C major in A minor XT ^ «: B^ no o -«*• i « 3?o; -«»- ■ O o ^o " ^ -!■> t> xx: XE The process in writing a chord of the sixth-and-fifth is, ^rj/ y?na //»^ roo^ (a third below the bass note) ; on the root construct a sev- enth-chord, so disposing the notes that the voices will move properly from the preceding chord. As a preliminary, write the following chords of the sixth-and-Hfth in the different positions : 66 PARKHURST HARIl/iONY First inversion of dominant-seventh in major scales. ^^ " Ph^ W^^Mihk^m .. Whhh M m s JDE S 3x: r i ,o ii n," 4fe fe^ XE XE First inversion of dominant-seventh in minor scales. prjjo| | i>i|.jiVhl|i/)>,jlu i oik^^y^^oll^ ttKmi: The second inversion, formed by putting the fifth in the bass, has for its full figuring 4^ abbreviated to ^, hence called The Chord of the Fourth-and-Third. In its different positions as follows : in C major I tj: 30^: ^^^=^ 5 xy m ■^ in A minor #Ro#8 jt JOSS g«jffo*> «»■ § 4 8 The process in writing this chord is, find the root (a fifth below the bass note) ; on the root construct a seventh-chord, disposing the notes as the previous chord requires. Write the following chords of the fourth-and-third, in the different positions : Second inversion of dominant-seventh in major scales. 'r>^KA\h- \\ hL M-\\W..\\m^ X3E ^:? S ^ g ^ jci: 4 3 CHAPTER VL Second inversion of dominant-seventh in minor scales. 67 jer ^ J^ j^ J^ &■ ^ q6 -6- 4 3 4 3 -6- 4 3 1 3 XE 3 The third inversion, formed by putting the seventh in the bass, has for its full figuring 4 abbreviated to 2, hence called The Chord of the Second. In its different positions as follows: in C major i r^ » V o § Xft. 8 8 « "O" ■o- in A minor I iB^ <>8 {ts-m- The process in writing this chord is, first find the root, (a seventh below the bass note) ; on the root construct a seventh-chord, dispos- ing the notes as the previous chord requires. Write the following chords of the second, in the different positions : Third inversion of dominant-seventh in major scales . ^y-^..\\\:'\mK pfy° p,i^^^ * ^^ *5F m XE 2FF Tn ^ a ^ S 17-rr Jtxi: ^^ ^ 2 2 2 2 Third inversion of dominant-seventh in minor scales. ^ i, .> \\U P i ? -^ XH ^''<^ rrhv ^^m 2 4- 2 A- 2 2 'I 68 PARKHURST HARMONY. It wijl assist the memory to notice that the figures follow in regu- lar order from 7 downward, thus, fundamental form 7 first inversion 6 second ** | third " 2 The figuring of the inversions must be well memorised, to pre- vent any confusion among themselves, and to keep them distinct from the inversions of the common chord. The common chord with its inversions, and the seventh-chord with its inversions can be compared as follows: m -*>- m 4 « €^ « ^ That tone v/hich in the fundamental position is the seventh has precisely the same tendency to lead downward in all the inversions. Accordingly we speak of that tone which is seventh in the funda- mental position as still the seventh, whatever the inversion. Thus in the following four chords F is equally the seventh in all of them. i ^ a^ -CV: «^ XT m and the resolution of that tone is the first thing to be attended to in the following chord. B is also called the third in all of them, and has a constant tendency (as leading tone) upward to C. Similarly G is the root, and D is the fifth in them all. This uniform method of designating the tones of the chord serves to keep constantly in mind the derivative nature of these new harmonies, and simplifies the progression of the voices, by finding them so largely the same as in the fundamental form. In the fundamental form we frequently find it necessary to double the bass and to sacrifice the fifth (rarely the third). In the inversions there is no doubling, consequently no sacrifice of any element of the chord. Each inversion must contain all four elements of the chord. CHAPTER VI. 69 From the foregoing we are now able properly to resolve all three inversions. The various positions of the three upper voices can cause no difficulty when the true character of these chords is under- stood. Dominant-Seventh Inversions in C major. -o- g ^ xr XE « XE — =: ^^- "or § 5F r <» -o- XE XE 6 2 6 Dominant-Seventh Inversions in A minor. ^^ o t ^^ 1^ X3: ^ ■<€!€> ^ XE ==xi: ^^ -^ 3CE XE XE 6 5 XE xx: 1¥ ^—^ 2 j6- 4 3 K *^ i4- 2 (Let it be remembered that figures express the intervals from the actual bass, not from the root,) Although it is generally better to descend to the seventh. m H m XE ^ better. ijpP= XX 8 7 8 7 yet it is sometimes better to ascend, when a decidedly melodic move- ment can thereby be attained, thus: ^M S i V " i XX S| 6 6 4 5 70 PARKHURST HARMONY. Illustration. 3^ u a3=t z? 25=5 -«*■ m "t 6 7 XE Exercises. 551 i f XE 5 6 2. i ^izz g f xk: ^-^ ^ 2 6 3. m ^v 22 f -O- 8 7 Is 6 4 7 ^ f -e^ 6 2.6 m 8 7 35: 6 7 4 ''M: i Jj i f[ i iii i i- g 6 Te" 5 -e- 6 3 6 8. 5 ^^fc m 6 7 6 6 4 ^ 6 '6 "4 4 3 o: ft 7 i A^ '6 ^=22 ^^ 4 41 CHAPTER Vll. 71 9. 51l=fi 32 6 -^ *' O- 6 7 4 3 « 10. m ^ f yfe 6 ^ 4 3_ 4 1 i i ^ EXE 12. 6 6 2 6 4 6 7 o It »^ ■^ xr 1^ 3 6 Summary Name of first inversion of a seventh-chord, its full figuring and abbreviation: — Procedure in writing chord of sixth-and-fifth : — Name of second inversion, full figuring and abbreviation: — Pro- cedure in writing it: — Name of third inversion, full figuring and abbreviation : — Procedure in wTiting it : — Order of figures, from fundamental to third inversion : — The same tone to be regarded as seventh, in fundamental position and in all inversions: — The law in all inversions as regards doubling: — Sometimes ascend to seventh for melodic efifect. CHAPTER VII. Close and Open Position. Concealed Fifths and Octaves. Score. Cross-Relatiox. Sight-Reading. Thus far all our exercises have been written with the three upper parts as closely together as possible. As a result these three voices have always been ivithin the limits of an octave. m M=^ u, r- ■- -9— i? — t- -^o — 4» ^ 7 Chords written in this manner are said to be in close position, which is the easiest manner of writing for the beginner. But it is evident that a permanent limitation of these three voices to the compass of an octave would eventually produce monotony, and the best effect can often be secured only by spreadin^^ tJiese voices, and the harmony 72 PARKHURST HARMONY. is said to be in open position when the three upper voices do not fall within the limit of an octave, thus : I I m 9-^ a XE m 6 7 (It will be seen that the above harmony is identical with the pre- ceding example, the only difference being that the voices are spread). The octave is the boundary line between close and open position,, and soprano and tenor being in octave we may call the position either close or open. It is to be understood that the alto must always lie between soprano and tenor: — that is, the parts are not to cross each other. An octave or less between soprano and tenor makes close position. An octave or more between soprano and tenor makes open position. The acquirement of facility in open position, and at the same time a review of the subject up to this point, is the object of the following sets of exercises, covering the several points. Attention must be called to two matters : first, it is never allowable for any two adjacent voices, except the tenor and bass, to be distant from each other more than an octaz^e, as it invariably pro- duces a thinness of effect, which is never agreeable, thus: £ft- m K. ^ m bad. ax XE gooct. This prohibition does not avail in the case of tenor and bass, but it is better even in this case that the interval should not too largely exceed an octave. ^ 3 ^ i g XT n better. (2_ I -€V- IDT Secondly, the pupil must be on his guard against parallel fifths, which are more likely to occur in open than in close position. Thus the following, in close position, CHAPTER VIL 73 ¥ zz: ^ XEDE 3x: 6 when put into open position, as at (a), shows parallel fifths ; it must therefore be arranged as at (b). a. b. i m &. 331 XE m XE= 3s: Two voices can move diatonically from a perfect to a diminished fifth, but not from a diminished to a perfect fifth, thus: Xi. -o- -€>- :£t -o^ JQL H -O^ good; -Ci- j5I good « 1 .^fc^ ^ J J-r^ I , J 'J" XE ^ZSTL 351 -C^ -O- O- i:i better. bad. '6 I4 XE 1 '4 6 ^ ^ XE XH The progression from a diminished to a perfect fifth is neverthe- less sometimes so inconspicuous as to be used even by good writers, especially when it occurs between alto and tenor, thus. F^ 2-" [-.r^ y — — ^ but in general, the prohibition is valid. 74 PARKHURST HARMONY. Note. A word of explanation in regard to the coriect notation of exercises in open position. The stem of a note should be so placed as to bring it, as much as possible, upon the staff. If the note be above the middle line, the stem should be turned down, if belozv the middle line, it should be turned up. If two or more notes average above the middle, and are joined by one stem, it should be turned down ; if they average below the middle, it should be turned up. m ^ g ^Eip^ ?= In "close position," the three upper voices are commonly joined by one stem, on the soprano staff. But in "open position," soprano and alto are written on the upper staff, and the tenor is commonly placed on the bass staff. In this case, each pair of voices can be united by a single stem, as above, or each voice can have a separate stem, in which case the soprano and tenor stems must be turned up, the alto and bass stems turned down, thus : s u ± i W fi" Pf F3 i ^ JJ i m % g XE 2=22 F T5- The same laws prevail in the connection of chords in open as in close position. Let the illustrations be carefully examined. Primary Common Chords. Illustration. I#=f^ Ip P 1 'J 4> t4= ^- — — 9 — 5> — -€»- ^ r 1^ *» or last two chords thus. i XE m XE XE Major. m CHAPTER VII Exercises. 2. 75 ^ an 22 3X 3 XC g ^ XE «^ ^ 5. m 6. 7. 2z^ 6^^ -6 "Minor, 1. «F 3. P^ P33 S S=a XE XT 3 4 5 « ^^ rj g ^ r 'm' iJj n 8. K.Jl rJli J ^ & m s^«^ 5 ? '^ ^ 3 I, Concealed Fifths and Octaves. Before proceeding further in exercises in open position, it is desirable to explain a progression which is of frequent occurrence, under some circumstances productive of one of the worst effects in Harmony, under others, perfectly permissible. This progression is that of a concealed fifth or a concealed octave. (The fifths here spoken of are only the perfect fifths). A concealed Hfth occurs if two voices, at any other interval than a fifth, progress in parallel motion to a perfect fifth, thus: i^^ ^S^^ r—i» l8 *y 1 ** ^ "cr 3X xn xy- XE ^€> XT— -^ § ^ V — o -- 3CE3XI ^^ 3D|g;=^ Qq lf> XE add voice above. add voice below. Let the pupil find all the concealed fifths and octaves in the fol- lowing, comparing each pair of voices. |i|.(:i.ijiJriiTir[irpJ.iiijij ^ = E-5=^ = E^-:5^^=c^^5=^^=t^l There is perhaps nothing in Harmony in regard to which it is more difficult to give rules than concerning concealed fifths and octaves. Certain it is that text-books and teachers in general make too much ado over them, so that they become a perfect bugbear to the pupil. The difficulty of the case is, that while many of these concealed fifths and octaves are inadmissible, a large number of others are admissible, and even unavoidable, and it is impossible to make any plain and simple classification of the good and the bad. After all that shall be said, much must still be left to the musical CHAPTER VII. 17 instinct to determine the propriety or impropriety in many individual cases. The usual explanation of their bad effect is as follows ; when a voice moves by a skip, the intervening tones are more or less faintly suggested. Thus in the following, concealed fifths- a. b. c. d. e. ^^ - <^ -4^ xi: « XI Oi» I JKT^ ^ -^>- XH 8: XE OC^ xr^ O . ^<; Srcfi £2. » o: -€>■ XE TOE ■^^ The most detailed classification that could possibly be made would still require many exceptions, and be all too burdensome to the memory. To simplify the law to practical limits it may be stated as follows : Concealed fifths and octaves are most to be avoided between the outer voices, but are allowable in the case of any two voices, when either of the tzvo moves only one degree (best of all zvhen the single degree is a semitone), thus: or in the case of the tzvo inner voices zvhen both skip, the combined progression of all four voices being good. The above rule is the best general statement of the case. But it is not offered as being infallible ; it only admits of fewer excep- tions than any other. The proper observance of the Three Primary Rules for chord-connection, and particularly contrary motion be- tween the three upper voices and the bass, will largely eliminate the objectionable cases. There are two exceptions to the general rule that require notice. CHAPTER Vn. 79 First : Concealed fifths and octaves, in which both voices skip, can occur even between the outer voices, when the progression of the harmony is from one position to another of the same chord, or from an inversion to its fundamental, or vice versa, thus : «y-^ o -^ ^ 1^^ - ^ 3x: ^>- xn o o o c» «: » o U» fg xr W XE fi: ^ SA ii_ XKX <> €f XE XE XE ;r ;z: <^^ 4 — 6 - 4 - 6 7 5 Second : Concealed octaves, in which one voice moves only one - pp=« iCEEt P s ^ firn-T r xr 6 4 3 CHAPTER VII. 8? An incomplete chord (as in the 6th measure) can be allowed when a much smoother progression of the voices is thereby at- tained. (Similarly in exercise (2) at *.) Exercises. 'k Open position. ')-.! h M.l i zznie ^ 3X 6 6 4 3 m^ 3. i *^ uj i fi; i JjMfii; i ^ ^ i 33: 3 TTg 4 ^ ^^ -o- 6^ 4 l» C3 I3 The Dominant-Seventh Chord. No further illustration of open position is necessary, Exercises. Open position . 1. ^ 3L ax 6, if o 3n: XE 31: o ** xs: 1 xn XE -€>- Xfe. .Ol i -o- « 1 o ^3L The last example, written in these clefs, appears thus : m t 49 — &■ g <9 r. ll*^a p p r^ r -'H^ — " — f '^ji 1 r 1 — ^ ■ 1 W^ -o- Exercises in score. Close position. 1. ga^ ist:^ 64^6^ «^^ Ji 6 'ft fci:^ -€V 06 6 2 ^ 4 "5. 6 ' ' e'e^e '« 4 87 g ^ ? zz 3. 66 6'6 6 i 64 ^4 8 326 6-8 7 4- Zj'\, \' ^ \^ ^ 6 yj f \ ^ ^ 6""^ ^ 7 64 ^^ "Of- 4. Open position ^ JJli rl o § g I r J 3 « 6 •6 4 4 3 6. Open position. f 7 4 g ZZII ^ f ►o- % ^6 -€> «f « 6 6 It 7 4 CHAPTER VII. 85 Cross-Relation . A very unmusical effect is often produced when any two voices, one in one chord, and the other in the next succeeding chord, take different tones on the same degree of the scale. ^ ^W W i t 1 7$i^: ■€>■ J Such cases as the foregoing are inadmissible from the evident an- tagonism of the voices. When different tones on the same degree of the scale occur in successive chords, the effect is always good if they occur in the same voice, thus: i w -e>- s m When the two tones thus occur in the same voice, a cross-relation existing at the same time in another voice is generally not objec- tionable , thus : m r ^ ^ ^ t 2302 M / g m g There are some cases in which both voices move one or more degrees, and still the antagonism in the cross-relation is so slight as to be unobjectionable. Such cases are therefore admissible , thus: E «=; t-rr g 7 4): r f i <^r r \>-9- ^ S: Cross-relation is not, therefore, invariably prohibited. Each case must be judged on its own merits. It is usually admissible 86 PARKHURST HARMONY. when one of the two voices takes the two tones (as explained above), and is least objectionable when the tones are of so short duration that the antagonism is least emphasized. X Occasionally an unpleasant effect is traceable to a cross-relation existing between two voices not in successive chords, but with one or more intervening chords, thus : i J 3CZ AA ^^m ^ ^ 31: A^ .S3l m The only unpleasant cross-relation that can arise between any of the natural tones of the scale, is that which comes from using the fourth and the seventh of the scale (major or minor) in success- sive chords: major minor. major. minor, bad. better.best. bad. better, best. bad. This interval, an augmented fourth (also called Tritone, because the sum of three whole tones), can be used in cross-relation, except where it becomes too evident, as In the examples marked "bad"; that is, in general, between the outer voices. Sigiit-Reading. A student may have learned all the details of chord formation and connection, and at the end, be quite unable practically to make any use of his knowledge. The majority of Harmony students, after two years' study, cannot sit down at the piano and properly connect half a dozen simple chords. This is the result of that same separation of theory and practice that has largely prevailed hitherto in the study of a foreign language, wherein the pupil, after months and even years of study, cannot speak the simplest sentences, al- though he has become fully initiated into all the mysteries of de- clension, conjugation and syntax. CHAPTER VIl. 87 • Tlie Harmony student will see the chords in a new light when, with the bass given, he plays the harmonies, according to the rules already familiar to him, without first writing them. This process gives in a short time a practical fluency which years of mere exer- cise-writing can never afford. We will call this process improvising the harmony, or sight- reading, being, as it is, the first step in the art of true improvisation, i. e., with no bass being prescribed. Exercises of this sort, begin- ning with the very simplest, will from this point on be interspersed with the usual work of the student, and it is urged upon the pupil not to forego the advantage to be derived therefrom. Even if he aspire to be only a harmonist, and not a composer, this practical use of chords will be of incalculable benefit. The procedure in the use of these exercises is as follows: Play the first bass note and the three other tones of the chord, with the octave, third or fifth in soprano, according to the figure, then deter- mine the letters of the next chord, moving the voices according to the rules in writing, being governed mainly by the Three Primary Rules, With patience and care the pupil will at length be able to im- provise with the same correctness with which he would write. Avoid placing the soprano above the staff, as the effect of the harmony is shrill and disagreeable when it lies so high. (In the first set of exercises let each be played in three positions of the first chord, i. e., with octave, then third, then fifth, in soprano, as in illustration.) Illustration. Sight-reading. 2. m XE o !<> xx: XE n 13: <> 'o 3. m m ■^>- 3X XE xx: XE XE XE -O- "CE 'y4 " I €>- XE XX -O- XE XE ■€>- s 7. § 4 V. o ^ o- KE €>^ XE XI XE XE- 10. 0[ ^h\ — ho^ p -o XE xr €V 88 PARKHURST HARMONY. (The teacher should require the pupil to play these exercises at the lesson. They should be played slowly and practiced sufficient- ly to insure their being played smoothly and accurately. For the present they are to be played in close position.) Summary. Close position: — Open position: — Boundary line between the two: — Allowable interval between adjacent voices: — Proper and improper succession of perfect and diminished fifths: — Definition of concealed fifths and octaves: — Difficulty of rules in the matter: — Explanation of bad effect: — Objection to the explanation: — ^When more and when less conspicuous: — Rule concerning them: — Best method to avoid them : — Two exceptions to rule : — Concealed unisons when allowed : — Writing in score : — How tenor is written : — Cross- relation : — ^When admissible. CHAPTER VHI. SECONDARY SEVENTH-CHORDS. All the seventh-chords in the scale, excepting the dominant- seventh, are called secondary seventh-chords. The reason for this will appear later. ki i '"^^i One of the commonest uses of the dominant-seventh is in con- nection with the tonic chord: -^ "^^ i Y " m In this formula the bass ascends a fourth or descends a fifth, and the progression of the other voices has already become familar to the pupil. On account of this familiarity, the secondary seventh- chords are at first made to progress similarly, although it will be found in a subsequent chapter that we are by no means confined to this progression. The tendency of the seventh in all seventh-chords CHAPTER VIII. 89 is invariably downzvard, even though the seventh of the chord be the leading-tone of the scale : 4 " » ^ In the dominant-seventh chord, the third is the leading-tone, and has a natural upward leading : I o <> ^=^ ^ but in the secondary seventh chords, the third has no such quality, and has greater freedom in its progression : I fulua ^ ^ XE ^ XE The foregoing formula for the resolution of the seventh chord (i. e., in which the bass ascends a fourth or descends a fifth, and the other voices progress accordingly) is common in all the secondary seventh-chords except two, viz., that on the fourth of the scale, I ^ s -o- 5=SF g M^-^ -ii. -^ where the progression of the bass is objectionable, and also results in the unsatisfactory common chord on the seventh of the scale ^ and the one on the seventh of the scale. ^ ^^ XT m 331 fvhich is not objectionable like the preceding, but is far less usual 90 PARKHURST HARMONY. than that progression in which the bass moves onl\ one degree to the tonic , thus : b. c. i V good bad ^¥r XE O- JOL :n: -€>- XK (The progression at (b) is bad, because of parallel fifths ; the effect at (c) is good, notwithstanding the concealed octave, which comes out so prominently. We have also at (c) the doubling of the iifth, which is allowable in this connection.) The resolution of the secondary seventh-chords will not be diffi- cult after the foregoing explanations, but attention will be neces- sary to feel the exact effect of each, they being different from each other, and from the dominant-seventh, as regards their constitution of major or minor third, perfect or diminished fifth, major or minor seventh. The Preparation of the Seventh. A discord which is altogether too harsh when it enters abruptly, often becomes serviceable when the ear has been somewhat prepared for it, whereby the harshness is in a measure softened. Thus the discord at (a) enters abruptly, and is intolerable, but at (b) the ear is prepared somewhat for the effect, and the same interval becomes allowable : b I f ' r I' " r ^ f Illustrated in four-part harmony thus : not prepared. prepared. not prepared i4-tj J 1 1 g 1 j J II H^ 1 u From the above examples it is seen that the ear is prepared for the discordant effect by hearing that tone which forms the discordant interval in the preceding chord, and in the same voice. The neces- sity of the tone being in the same voice is seen in the last example above, where the identical tone is heard, first in the alto, then in the CHAF1Ek///f. 91 soprano, but the ear is not thereby prepared. (In usual phrase, the tone is said to be "prepared"; but to state it exactly, it is the ear.) The effect of the dominant-seventh without preparation is satis- factory, but the secondary sevenths in general being more harsh, need preparation. Exactly why this distinction exists is not easy to explain, but the fact is evident, and needs no argument. We have then the following rule : The seventh, in secondary-seventh chords, must be prepared by appearing in the preceding chord atid in the same voice. The followin£>- illustrates the preparation, in different voices, of the several secondary-sevenths : (In the seventh-chord on the seventh of the scale (as in the last example) that position is far better in which the seventh from the root is in the soprano: (a) is better than (b) or (c). Tlicre is less need of preparing this than any other of the secondary sevenths, as the effect is less harsh. I *R= Illustration. g ^ 1 ^ g i -g^ t^^^i dfAfim % f t 7 92 PARKHURST HARMONY, Exercises. 1. g zz: m I TH ^' ^ 'f , XE 3 6 '7 « ?. r; P f T7 — n5^ 2 6 7 T~^ 8. r ^^ 4 1 =*Wt f=Ft '2 Cfi -ts>- N=^ _ — f-fs-j-is^ HI W 6 7 -4-^ 7 ^ LS '^erg'si; 1 L«_1J s 3 f 7^ 67 5. 2 6 ^ i g XH 6. 7 8 7 Tjr m ^j r^ -i» f 11^ T^ 6 4 7; ^ i ^ O- «>-" 8. 5 6 7 gp=g i s zz=e ^ n: ys 6 9. open portion. 6 ^ 8 7 »=<> JLJ J P \ !' rl Pi '6 6 '6 -3)- 6 5 5 7 « 10. open position? ^ s ^ xnm M Series of Seventh-Chords. The resolution of the seventh-chord has heretofore been a com- mon chord, on the fourth above, or fifth below. But it can as well l)e a seventh-chord, which in turn may be resolved by still another seventh-chord , thus : M t^ ^ ^ ^sw=^ xx: 4 pTjjTy or 55i={^ 1 ^ ^ 77 7 fi 7 -iS—K 111 Xfl 33: jce: CHAPTER VIII. 93 No difficulty is involved in the substitution of a seventh-chord for the common chord, but it will be observed that the third of each sez'enth-chord (as above) becomes the seventh of the next chord, and therefore remains stationary ; also that by adopting the simplest progression of the voices the fifth is omitted in each alternate chord; irom which we derive the following rule : In a succession of seventh-chords in the fundamental position omit the Afth in each alternate chord. Exercises. 1. ^\' n •l* -A y rJ -^ r) -fe! A\-. 2-^ w 7 7 7 7 7 7 7 6 ^ 1, 1 u ^^ F^ A2L g :^. 6 6 ^^ ^ ' 6 6 ' 6 7 f2 ^ 677 g O- 67 777777 67 5. Frf=] P=t=i ff=^ -f-f- 1 ^1 3 6 1 6 7 7 j=^ 6 * -Al L^ ^ ^7-|» s J I.J ^ 1^^ f ^ A a la -^^ ^ 7: open position. « I 9 '6 i J '^ 1^^ rJ If j 1 ^^ j N J I.J g ^ 5 ¥ 8. open position ^ "5" 777777 77 Secondary Seventh-Chords in Minor. Their use is more limited, owing to the awkward progression in- volved through the raised 7th (G# in A minor). Three are service- able, on the 2nd, 3rd and 7th of the scale. 7 ^ ^ 7 94 PARKHURST HARMONY. 2nd 3rd on 7th iiB:4?^f?si^:?^ti2;rti 3XCC ^ TF ^«: ^^ L^. it o ^Itfito |i t^ ^w 33E XE XE 3X n i 1 i 1 7 7 7 7 Those on the 2nd and 3rd require no special mention ; that on the yth is a new and important chord, known as The Chord of the Diminished Seventh. a*^ — _ .A ^ ^ w -♦>- -€»- XH bad. good. ^ o: fe^ bad. good. bad. good. 7 -5^ 7 7 7 -7 7 The usual progression (into the chord on the fourth above (G#-C) is impossible, as the progression of the bass is not allowable, and the chord on the third of the minor scale (with an augmented fifth) is not satisfactory. The progression of the bass is therefore one degree upward, (as in the seventh-chord on the seventh of the major scale), and the third must not be allowed to move in fifths with the seventh as at (a) above. The Diminished Seventh, the softest of all sevenths, needs no preparation. There are three sizes of the seventh-interval; major, minor and diminished, $ -o- ^ and they are harsh in proportion to their size. Write the following diminished seventh-chords, in different podf- tions, also in close and open position, and resolve properly ; 7'^ 8-ii"»c\\\\ 8 XE -•» — ► W=ff i # better £C XIL better. •4^ XE Illustration. '-&- -o- "^ 7 a ^ =2 z:sc=3 «>^ «==^ t:^ 4>^ *^ f fczi XE 7 Exercises. 1. ^ r i i''iiJ 1 '^ 1 °. if^ 36 7^ 2. 7 ^ XE 3. s ^ ^^ ^^^ -2; — fi^ 3 6 "T"^ s^^^^^^ 6 -6^ 4 it rr-t©- ^ 3 i 6 7 19 r ^—-&- \ \ \\ ? \^-A 6 4-61 67 o- 6. 6 7 « 4 % ^ ^ 2 JgfJ 1 ^ ft) H >. - «- 3 6-6^ ^ 6 4 3 "y- open position. ^ I 5 4 i , ^ ^3 ^- open, position. ^S ^ 'uj '^j y^ ^ tT 6 8 7 4 i 96 PARKHURST HARMONY. A more musicianly effect is obtained by holding over the tone; instead of repeating it, when it belongs to the same voice in two or more successive chords. This is illustrated in the first two meas- ures of the first of the above exercises in open position. i * ^ ^=f^=H 3CE ^ f jh: 31 ^ bettelr. J2. i r ■A- "6 3 Two EXCEPTIONS TO THE RULE THAT SECONDARY-SEVENTHS MUST BE PREPARED. First exception : When the secondary-seventh chord, by the use ■of accidentals, takes the form of a dominant-seventh-chord ; i. e., has a major third, perfect iifth and minor seventh; thus : _ bad. good- ood. / ^ 'I lU Mill II I, Every chord that is altered in this way is, in fact, a dominant- seventh chord of some scale, but as used above is only a secondary- seventh chord altered to that form, there being no actual change of scale. Such a free entrance of the seventh as the above will however be comparatively infrequent, as the simplest harmonic progression will usually involve preparation, thus: m I XE 7 i Second exception: When one of the voices moves diatonically through the sez'enth, in the unaccented part of the measure, thus: F^ S /^ ^ CHAPTER Vni. rU h^T- 97 #= ^ ^ :s:?= _ -^ Nf^ rfti r4 1 -X- tf -^ 1 «» i> 4> ?s| 8 7 87 87 87 87 (Note. The matter of accent is fully explained in Chapter XVI.) This use of the seventh will be referred to again under the sub- ject of passing tones, (Chap. XV.) and may be designated as the passing seventh. It is found frequently in the inversions, as well as in the fundamental form , thus : . isj- inv. 2pdinv. 3rd inv. feF^ ^ " |o U>— Iq- I o se w Al n &-r. 46 26- '6- -6- 3 5 5 5 TH 6 - 5 4 8 7 3 As the above example shows, when the passing seventh occurs in the bass, it results in a chord of the second, and can be so figured ; but it is usual in such case simply to put a dash ( — ) under the seventh, which always means that the other voices are to continue the harmony of the previous chord. This does not mean that the other voices must remain immovable, but if they move, it must be to tones of the same harmony, thus: ^ \ ; }hVm^ \ ^^.m -o^ 9, l < ^ |fe -7: ^^ ^y 33: '^ § I s ^^m 3X O 6'- 6 if- 6 9-6?-6 5 5 5 Write the following fragments, changing the position of the har mony in the second chord of each : close position. open position. m -z^ ^Try % i'^l\J\m^\ 2:^ TSL 8-6 - 6 6 8-6 The harmony in such cases is to be changed chiefly for the sake of securing a better location of the voices, or to avoid monotony. 98 PARKHURST HARMONY. The pupil must use his own judgment as to whether the voices should move, or sustain the tones of the previous chord. Paral- lel motion of all voices is here allowable, as on page 56. Illustration. ^^^ fc^3#ato r prrM'f r^ff r "^ 3-66 7 56'78-77'-6 XE 20? 7 7 Exercises. 2f— -TV 1. ^ 4 1: » r^ ^ .3. 8« 43 e "^ ^ -T^ff \\p \ ii <> — 1-^ ^ SP ^ zang: tl7 ^5» ^iT^ 6 6 6 T~6" 3 . ope n position m a ^ ■«=»- ^ 3X 6 8 7 -? 67 4 6 7 8-7 4. open position V I P \?r J m fS fJ -^ 6 ^^ 8 7 &-HV Tir S 5ii 5. close position, ^^ xn 22 k!6 6 67 6. ^^ T^. n ^\ s ^V H tf-K»- 7, 5 87 6 8 7 ' 6 8 '^ ^ *f P /v <^ . 4- ^ l« W ^»-7: 30: *> 35e 6 '7 87 '**" iJ 6 4 8. , in sco^e.3 W-|^ 6 "'I, iijr iii,i^ijiiii,iii,ijij II 5 !< ^-f - <> -(. ,i57 CHAPTER VIII. 90 Sight-Reading. Primary and secondary common chords. ^ MajoViicale. i 1 '^ Ir J l f J 1^^ ^ r: — (^ 30E J rJ zzz=z:rz:±z I ±11: = : — ?:>— :zzzrii-p— izuzcr 3. S H i [ rii ^^ iN^i^ir ir ^ i^^r -0-" ^M ^ ■*♦- f-^ i^j ,j ^p j m 5. see page 29. I II Ml, lull "^ -^>- ^ ^ P^^^ 7.Minorscalc.8. ^ ^ to. 1 ? fe!^ m 2t^ tTjt ^ 11, 3— -ho f- 12. see page 42 g; f g r II I If (: XE 18. 14. ^ 5K i M(;fir(aMirf;irjiMiJii. ^^ 5' ? 15. i ^ /•s -f9- ^ «v <9^'-T&Q- z^r^^^--E. zz^xazz ^ 'Y '^ ^ r T 3 r Chords and their connections are not mastered till they can be fluently improvised in the above manner. Effort in this direction will be found to repay far better than the mere writing. The minor scale presents peculiar difficulties, and a review of Chapter III is advisable. Summary. Secondary-seventh-chords: — The usual progression of seventh- chord on 7th degree of scale : — How the discord of the seventh is 100 PARKHURST HARMONY. "prepared": — Need of preparation in secondary-seventh chords: — Procedure in a series of seventh-chords : — Use of secondary-seventh chords in minor scale : — Peculiarity of seventh-chord on 7th degree of minor scale : — How it differs from others in regard to progres- sion and preparation : — Three sizes of the seventh-interval, and their degrees of harshness: — First exception to the rule of preparing secondary sevenths: — What is the "dominant-seventh form:" — Second exception to the rule of preparation: — Meaning of a dash under bass note: — Changing position of upper voices, and parallel motion in all voices, when "passing seventh" occurs in bass. CHAPTER IX. The Inversions of the Secondary-Seventh Chords. These inversions are formed in precisely the same way as those of the dominant-seventh, and need no special explanation, as the several elements have the same progressions as in the fundamental position. In the seventh-chord on the seventh of the scale, both major and minor, in which the root has a progression of one degree upward (to the Tonic), care must be taken to avoid parallel fifths in the first and second inversions, just as in the fundamental position. Major scale. ^S ^m SfcS = 3^ baJ. good. good. bad. good good. bad. ^m (9 — n ^ ^=7 g IB — fe ts*— " 5 ^ rp — --5 fjr Minor scale i HH j> iP =i^=^ bad. good. bad. good. bad m good. J J IJ J m A- « '4 5 5 CHAPTER IX. 101. The third inversion of eax:h of these chords Major scale. . Minor scale ^ « ±: ^^ i "TT -2 5" 4 4 4 can seldom be used with the resolution into the ^ chord, and it is to be observed in general, regarding inversions of the secondary- seventh chords, that they are not as uniformly effective as those of the dominant-seventh chord, and the position of the three upper voices needs to be chosen more carefully. In reality, a large propor- tion of all secondary-seventh chords, fundamental and in inversion, that are practically used, are altered into the "dominant-seventh form/' Illustration. i i'hih^k\l^p^^\l^^h'}' ^ =yF^ t s J* II .ji lyju.JiJi » , ••• I " Exercises. m m i 1 3 16 't t m WW T-T i5~^ — nrr 5 m t ^ \rj 6 ' 6 6 7 ' Q ^ I I f i i -i ;' I f 3: # 77-1^ ^^ i S ZI3I2Z &=IZZ ^ ^izi xn 6 ^T"^ 5. t^ o *):, a o 5- if ^ ,r; p — — H y > g 1 — 6 1 jLl_y3 o ^ — if — w 3 6 3 \-'— T^ 6 ^ 1 (5l — 1 ^3^ '-or" 102 PARKHURST HARMONY, ». ^s ^g* i^ j g * ^ ^6 6 'U 5 ^3 g i S ^ ^ F5 r^ xx tS'-sHS^ 3# ^ 8. open position. -^ 7 mr. ^@ *>^ m XE IT «5 <^-U 8 7 8 7 ^' open position. 6 '6 '6 6 4 5 ^T *mHJ I "JN 7 I^? 6 4 7 i^ 6 4 3 I in 10. ii 567 -6 7 7 7 7 '^'■"l![ i r i ff;l | fJJIyjJjJ llAlllUl I I 5 4 er^ 5 4 i Sight-Reading. With first inversion of common chord. ^ i xr TIMS' 2^ « § zz Xfl -z; ^ 6 ^ m f zz: ^ 2Z 3 it V ■ ( 9 § t ^3 "cr 5. g ^ 3Cf: % t 6 T Let the basses of the following exercise be correctly figured, so as to express all that is involved in the harmony of each chord. This is just the reverse of all the foregoing exercises, in which the figured bass is given, from which the harmony is to be determined. CHAPTER IX. -A. 103 K^'f ^'fiiiJ jj^iff|iiiijj I J I . If riif If^ 3 ^^ ^^m ^ 1^ ^ *#*^ • • g ^ g ^ ^ j^|MHljJ■■ili l ■^li.^iJ lJ^Jll m ^ P^ 15^— U 4jl^^, i j i/"V-^ I iri j i i^j-^^ i i jJ i p^ * aac f ^^P^^^^^ ^^ 2EP ^ P ^^"'^1- jljj^r'i P r r ' -^f^i'-^ S *t f ? ^ r ij ^r Mi:± It would be well for the teacher to write additional exercises like the foregoing, to be figured by the pupil. Summary. Formation and progression of inversions of secondary-seventh chords : — Caution in progression from seventh chord on 7th degree 104 PARKHURST HARMONY, of major or minor scale, in fundamental or inverted form: — Inef- fectiveness of most secondary-seventh chord inversions, and need of care in position of upper voices : — Frequency of ''dominant-seventh form'' in secondary-seventh chords. CHAPTER X. Seventh-Chords Followed by Various Resolving Chords. The essential thing in the progression from a seventh-chord is that the seventh descend one degree. The resolving chord hereto- fore used has always been the common chord (or seventh-chord), founded on the fourth degree above, or the fifth degree below the root of the seventh-chord to be resolved , thus : iUi^-l 53 m w^ m rz. The one exception thus far has been the seventh-chord on the seventh of the scale, major and minor, the root of which moved one degree upward. But any chord, having a close harmonic connection, and allowing of the proper resolution of the seventh, may also be used, what- ever the root-progressions. The various chords that can follow the seventh-chord may be divided into two classes : 1st, those in which the bass moves: 2nd, those in which the bass is stationary. CHAPTER X. 105 First Class. (a) Bass moving one degree: (major or minor second). ^M^ 53^ mEi m sm ^w J. i i^ m § ^z^-.is:^ ^rs m. 5.6^3 435 5 It often happens that a progression that is inadmissible in one position of the upper voices is allowable in another position , thus : bad. good. i (b) Bass ascending an augmented Prime. m i ^0 m VI — ^- Second Class. Bass stationary. With stationary bass, the resolving chord can take the form of any one of the five chord-inversions, viz., 6, J, e^ 4^ 2, thus : i m E TTO Til r. 3X "tM «^ :gr •^^^ ^ >^-7:^ ^ -«^ ^ XE fc33: :ii: 33: 3x: IE o* 7 6 1 A ^ 4 2 5 With stationary bass, the seventh-chord, ivlicn itself an inversion, most naturally resolves into a higher inversion of another seventh- chord , thus : 06 PARKHURST HARMONY. 4 'J :J° I J ;^ 3 ^ _«JL fetJ S ^ Y o 5 3 "6 — sr 5 -6- 4 3 The form of resolution used in the preceding chapter may be called the fundamental, as it is certainly the more conventional reso- lution. The several resolutions offered in the present chapter afford a great and pleasing variety in the harmonic coloring ; but the par- ticular situation must determine the fitness of each and all of them. As the harmonies become richer, and the chord-connections more in- tricate, it will not be amiss again to remind the pupil that his success depends more and more upon his having a clear sense of each har- mony, and of its flow into the following. If any example or exer- cise cannot be thus heard in the mind, it should be played over, until the pupil, without playing, can recall the whole effect. Illustration. 23C3= 23=33 jMm^ jijpfi^rf ifl SXi «i^ i ■^ — r i ^$ 'HS^-i©- A TXH 3V 'ea'e'ie e'?'^ ^ ' « 'h "2 'e l^, " g^ Exercises. ^ ^ ^ 'J lis ZZ y ^^^^^^ i JJ '6 '6 '4 6 y '6 _ffl- 7^ t 3 6687 5 S 9^W^ 3-66 7 « ^^ :oi4 3 .^ . ^A ^ ; 8 7 2=-P— S^ JV 6 f^« *~ cr 5 T ^^ ft 2 6 "i « -| 6 m f J , I . v ^-f hJ^-n'^^ ^4f-j -*»- CHAPTER X. 107 5. ^^ i ^3=1 IZ. m .5 6 7 ^ 6- 3 t "^ 2 L i^ -cv ^ ^ — 8 7 6 8 7 5 -«>- p sp <^ g> t 7 ^ 6 6^ S. open position. 1 XII 33E -€> -O «V rj2 zzig XX ^S^:3ci t^f 5 8^r2 6 3 :?" ^ 66 4 6467 53 87 SiGTTT-RE NDING. With second inversion of common chord. ? 1. ra: xr FT <^ ^ -S^ 3a: z. 3. 3 ' I O- irrr 4 3 4 3 s '5 '6 ^ ' 6 5 ♦^ ^ 'T^^^g^ &^ ^ 6 *^ ^ 6 5 4 3 i i^i^ XE ^ XE 6 5 6 4 3 ^ — '^ 6 5 4 3 5. 3 i^ XE 4 "cr ^" — — y r ' » _ > ' * u xr 17 4 jr r^ It is a very interesting and profitable exercise for one pupil to play an exercise slowly, and another, by listening, to determine and name the successive chords ; indicating them either by the letter of the root, or its degree in the scale. When it is impracticable for two pupils to practice this together, the teacher should make it a part of the lesson-exercise. 108 PARKHURST HARMONY. The very simplest exercises (involving only the primary common chords) should be first used in this way, and other chords added by degrees. Summary. The essential thing in progression from a seventh-chord :— The resolving chord heretofore used, with one exception: — What other chords can be used to follow a seventh : — How classified. CHAPTER XL Exceptional Modifications in the Resolution of the Seventh. While the fact remains that the seventh demands the degree below for its resolving tone, it is possible, without doing violence to this inherent quality and demand of the seventh, to introduce some modifications in the chord-progressions, which prevent the monotony of invariable uniformity. These modifications may be classified thus: 1st. Delaying the resolution. 2nd. Moving up from the seventh and resolving in an under -voice. Each of these modifications will be variously illustrated. The pupil should carefully study the examples of the second class es- pecially, as it is generally impossible in a figured bass to compel the unusual progression ; in most cases it being possible so to har- monize as to avoid it entirely. 1st. Delaying the resolution. This can be done in two ways : First, by moving the voices from one position of a seventh-chord to another position of the same chord, or by the use of successive inversions of the same chord, thus: J i ^. h ^ J XE & ^=^ 11 ^ 3X XIJ The mark x shows the transference of the seventh from one voice to another. Naturally the resolution follows in the voice that last contained the seventh. Secondly, by so moving the other voices that the original seventh appears as another interval in one or more chords before the reso- CHAPTER XL 10^ lution. The resolution may appear in the same voice as the original seventh, or, if the tone that is the original seventh be transposed^ the resolution may also be , thus : i XE i ^ ■^ ■€*■ ^ ^ r=Tt f^4f^ M 3nE 3X 5 «: i -<=^ i XE 6 « " I ? ' • § ^ T FT A + indicates the original seventh; a * indicates the resolving tone. Another way of delaying the resolution will be explained under Suspension. 2nd. Moving up from the seventh, and bringing the resolution into the bass. The bass itself can ascend or descend to the resolving tone, ia the two following ways : fj:^. b. "Z -^ 6 3 6, -' <5 Resolving into unison, as at (a), is admissible, but is more harsh than resolving into octave, as at (1)). This substitutionary resolution in another voice can occur only in the bass, because that voice is so prominent as to give the resolu- tion with nearly the same force. The following, with the resolution substituted in the alto or tenor, are not satisfactory. ^^ » ^ pen ^ 33: * XE 110 PARKHURST HARMONY. An imperfect fifth can follow a perfect fifth, but not vice versa; accordingly the progression at (a) is inadmissible, but correct at (b). ^ b.-f good. good bad. s: bad f JQl p bad good. m f JOE T In regard to the case at (b) it should be observed that the sub- stitutionary resolution in the bass is seldom satisfactory when the seventh has occurred in the soprano, but is quite adequate when it is in alto or tenor. The reason is, that the seventh is most conspic- uous in the soprano, and the resolution must be equally emphatic by occurring in the same voice. A voice giving the seventh of the chord may, before resolution, pass to another tone of the same harmony, and sooner or later the seventh be resolved in the same voice, or in another voice, thus: $ ^. ^— xg -^ IDL XE XH XE -€♦- xs: XE XC -^ jfy -^ 5 5 S ^ i The greatest deviation from the simple and normal resolution of the seventh is that in which the voice containing the seventh moves, together with other of the voices, to an entirely different harmony ; while the resolution occurs later, either in the same voice, or in another one , thus : ^Jr-JUJ j^ ^^^^^ImpMS ^f^^ — '74 K kfl « '4 i :?2: ^-yr (> - 4 ^ 5 4 5 3 •> * i!5 All the essential deviations from the strict and immediate reso- lution of the seventh are exhibited in the foregoing examples, which CHAPTER XL 111 should be carefully studied that they may be understood in the har- monic analysis of music, and that the pupil may himself introduce them as occasion offers. Such treatment of the seventh will ever remain exceptional, and finds its justification chiefly in the more melodic character of the voice containing the seventh, and in the de- mand for variety of effect. The following exercises afford fre- quent opportunity for this treatment of the seventh. Let the pupil avail himself of each opportunity, that he may gain practical fa- miliarity with the subject. Illustration. ^ — -^ >5 — 6 7 4 3 Exercises. Ii7 i. m mn^ SH 3: -^ z±±^ 2.' ^' I ''' I H^ m i '^ iC ^M ^i ig^^J »' rt 3. § »i;. '6 j9 J r P r^ J J J * » n: :fcfc= 4 3 Z 4 3 7^^ § ^35 ;;^fep I i ■€>= 5^ «=Z^ ''^ hi 4 4 4 8 7 ^61,7 4 5. open position. ^1 « ^ § ^ S XH 33: ^-^ — h« 6 b 4 ^ 7 6 fcl6 ^68 4 4 3 I j? !,5 4 4 3 6. open position S td '4 6 35 7. open position. ^^^^tF tR fi r/ L r :/^i t 6 ^i \? • ^ 37 — tr: i ^B^ fF 4 3 4 B 7 ' 6 14- 5 4 2 O — '6 8 7 5 i 112 PARKHURST HARMONY. The foregoing is perhaps the hardest set of exercises thus far/ and requires careful attention to introduce effectively the unusual progression of the seventh. Sight-reading. With common chords and their inversions, major and minor. 1. ^ xn f ^ ICE 43 -3^-^ 656 43 6 6 § ^ ^ XE ^ --^ ' W ' " IT m n m -o- T^ 4. 2Z ^^^ « 6 6 IT Summary. Two ways of modifying the progression from a seventh-chord: — Two ways of delaying the resolution: — In which voice only the substituted resolution can occur, and why : — Why bass is inadequate as substitute for resolution of a seventh in soprano: — This excep- tional resolution of the seventh is justified by what ? CHAPTER XII. Altered Chords. One or more notes of our two elementary chords (the common chord, and the seventh-chord) may be affected by accidentals. In many instances, such an alteration will result only in a different variety of the same chord, such as we are already familiar with, as changing a major chord into a minor, or vice versa. I =^m fe m In other cases, the accidental converts the chord into some- thing radically different, so that the notation is faulty as expressing the intended effect ; thus CHAPTER XIL 113 when used to express i M UL $ ♦>■ ff is incorrect. In still other cases, the accidentals so distort the chord as to dis- qualify it for a fundamental harmony; thus: I * wm After eliminating all the alterations of fundamental harmonies, as above described, there remain five accidentally altered forms of chords which are characteristic and serviceable, the dis- cussion of which will complete our treatment of fundamental har- monies. Of the three ways above mentioned of altering chords by acci- dentals, the first re-forms the chords, the second de-forms them, and the third, now to be spoken of more fully, trans-forms them. 1st. The Augmented Triad. |tf^l<^Hl^§ We are already familiar with this chord, as the triad on the third of the minor scale ; but it is more common and serviceable in the major scale, on the first, fourth and fifth of the scale, as above. The augmented interval is commonly introduced as a "passing note" , thus : 1. 3. r I 3 i m m s s XE -^ XT XE isr. 3a: In all minor triads, the effect of the augmented fifth will be found to be like that of a minor sixth, hence not characteristic , thus : I ^ means, ]\4 PARKHURST HARMONY, It is the fact of the augmented being usually preceded, as above^ by the perfect fifth (with the elimination of what would be the "leading tone'' of a minor scale) that makes this chord commonly used in the major rather than in the minor scale. This chord can also be used in the two inversions, of which the first is the better : 1. 2. ^m o — XEzzgng:^ XL 3. IS 11 Hgji^, 9: 8 h5i -^^<^" - » O II 11 ZJOOi 0||0 4> m ]£ ^m «€>- 3tt: it 4 - j* 5 4 - il 4 By the addition of the seventh to these three augmented triads we obtain the following : hi \^^\\f I'lp T ") *^ s ^ XE -O- xx: "T" <^5 j»5 The first and second, which are secondary-seventh chords, are not effective in the inversions ; but the third (the dominant-seventh with augmented fifth) is good in all the inversions, but best of all in the first and third. '$Ji l^i llLj ^^ f^=^ S*: a. Wl Xfl 5 — n- 3 - 22 Care must always be taken that the augmented fifth and the sez'enth shall resolve into octave, as at (a), and not into unison, as at (b). CHAPTER XII. Exercises. 115 xt ^^ (9 P- i xx: ^ 3X 5 -&- — ^ 4 3 B rt 5 6 « 4 3 5 4 7 ^^ xx: -€♦- xr -€^ 3DC -€V xmz H'Er5-&-3|t5-5r6::7 66 -. .3. * 4 ' -€♦- -^ Ijd I ^ - cz: 3tE: -€>- -^-5^ 6 — ■ 6 5 ■ 7 6 " '^ 6 — ■ B 7" 4 3 ^5 4 S -^ ♦* 3 J 5 ^ H»- v'k'' j iJi t J i t s ^5= zz <3- ^ \ tl 'tt H7 5 S 4 - B 6 3 - 5 5 r>. open position. ** ^^P i^zizzzj^ ;. fj a ^ ^ if f ^1 ■f4 .3 li5 5 4 Si(>H r-K'i:ADIXG. Jf^/Z/i dominant-scrcnth chord. 1. ':^: J I (' fJ I ^S 22—-:^ e*^ ^ 2. F^ ^ ^ 3X ^ 17"^ ' — ^-15 B5 7 ' I — e^B-Vl5=± _ 4 3 ^ 4 ^ 3. H^ — ^— fri 3 r-^ 4- F^^ ^-^ 7 ^ f> — ^^_5_^ «■ 7 --1 Write the three augmented triads in the keys of G, D, A, F, Bb a.rJ Eb. Write the dominant-seventh chord with augmented fifth in the same keys. Write the three inversions of the above seventh-chords. rnd. The Chord of the Augmented Sixth. i w^ !I6 PARKHURST HARMONY, By taking any minor triad with a perfect fifth, and raising the root a semitone, we obtain a combination which is ineffective in the fundamental position, but of great use in the first inversion, which is called the chord of the augmented sixth (as illustrated above). Not every sharped sixth is an augmented sixth. A sharped minor sixth becomes a major sixth, I xr » XE » -€¥- €^ EEtM to: S==iS fe but a sharped major sixth becomes an augmented sixth. Every minor triad, in the first inversion, affords a major sixth, there- fore by raising the root of any minor triad we get, in the first inversion, an augmented sixth. This is the result of "inversion," which is fully explained in the Appendix (G). '"''■«^ s a lO. «^ a in G. ff Iff ^ XE S 6 The inevitable progression of every augmented sixth is upward a minor second (i. e., a semitone). This is as invariable as the reso- lution of a seventh downward one degree. Yet in absolute dis- tance an augmented sixth is the same as a minor seventh. This variable requirement of the same interval under dift'erent circum- stances is treated of more at length in the Appendix (H). All of the minor triads can be thus treated, but only those with a perfect fifth afford a perfectly satisfactory combination, like the above. With a diminished fifth, the effect is not good. ^^^ A peculiarity of the chord of the augmented sixth is, that only the third from the bass (the fifth from the root) can be doubled, as it is the only one having a double progression; thus, t sfe ^ ^ pleasing and quite un- usual : CHAPTER XII. 119 ? 3X -O m 33: T^ 15^ ^ # « -4ir 5 7 tl5 ^6^ 5 a ^^ 6 7 All the facts concerning the chord of the augmented sixth- and- afth have been illustrated by the use of a single chord of that sort. But as stated at the beginning, any minor triad with perfect fifth, its root raised a semitone and the seventh added, will give us the same effect in its first inversion. Every scale has three minor triads with perfect fifth, viz., on the second, third and sixth of the scale, illustrated in the C-scale thus : ^ ^§ g Raising the root, adding the seventh, taking the first inversion, and resolving according to the usual method, the procedure in the case of each of these is as follows: i^ps XE xs: * o -o- XE 8^^ JDE 13: ~o~ or _o_ m 3ci: -^ XE i 5 4 3 3. fr"-^ \hH xr XE i 5^^ « -o- ii: -6- 5 or J2 XE XE XE ¥ 5 #5 5 3 ^ ff^* itfy; -cv « XE XE ^^ >« JOL xs: rrr ii S XE ZDl -O- XE ^ 6 ■ -fir -«r -ft- -5- 5 4 # 5 1 # 120 FARKHURST HARMONY. Let the pupil take the triads on the second, third and sixth of each of the following scales (G, D, F, Bb), develop the chord of the augmented sixth-and-Hfth, with its resolution, and place underneath the proper figuring, as in the above example. Only by such a pro- cess can complete mastery of this chord be obtained. Exercises. # *l^ -*>^ J3L 6 ^ 4 2 6 -6- m 1 -4T It W* £ 4 $ i 35: 5 4 ^ § ^ -o- ^ 3t TIT 5 .11 ll6 4 5 3 4 4. § rzB: s zz 6 BT^ 5 « 5. 5 4 2 P a ^5 — lF-% XE A 87 i 6 ft 6" ^ 6 5 4 ^ n In the last illustration, three chords of the augmented sixth-and- £fth are exhibited, derived from three minor triads of the C-major scale; but no one of them resolves into an unequivocal C major chord, and the second and third have a resolving chord that is thor- oughly foreign to C-major as to be unsuitable for that scale. The first of the three will be seen to resolve into the dominant of the relative minor scale. m ICEZZZXE 3tr JOL -CV^ m s -€>- -6- 5 XE and usually finds employment in this connection. The other two similarly resolve into what may be taken as the dominant of a minor scale, but very remote from C-major; and thus this chord of the augmented sixth-and-Hfth, serving as a connecting link between re- mote scales, is frequently used in modulation (See Chap. XVIII). CHAPTER XIL 12t 4th. The Chord of the Augmented Sixth- Fourth-and-Third. The chord of the seventh on the seventh degree of the scale, with its third raised, gives us the following: ^3 r^ tftr^H ^^' - '^''^"" '^^"^ ^^^' s 7 7 o . o m -^ xn 31: 4 3 4 3 It will be observed that this chord is formed on the remaining minor triad, the other three being used in forming the chord of the augmented sixth-and-Hfth. Of these forms only the second inversion, the chord of the aug- mented sixth- f our th-and-third, is practicable, but this is pleasingly characteristic and effective. It differs not at all in its construction JFrom an ordinary chord of the fourth-and-third (second inversion), except that the sixth from the bass is augmented instead of being major or minor, and the resolution is strictly regular. But there is ia combination of intervals in this chord which distinguishes it from every other, and it should be studied until it can be readily distin- guished from the ordinary fourth-and-third chord. To this end let i^he pupil develop this chord after the manner of the above illustra- tion, on the seventh degree of the different major scales, and resolve it, noticing that in the resolution the 5th (i. e., the bass) and the 7th descend a minor second (a semitone), and the 3rd (which is the augmented sixth; from the bass) ascends Or minor second, while the root remains stationar}\ The two chords, the augmented sixth-and-Hfth, and the aug- mented sixth-fourth-and-third, are so nearly alike in sound to the unpracticed ear, and yet so radically different in their construction, that it is well to bring them into comparison in the following manner: ^^ XE 33: 33: 35: ^V i ^^ 33L ^^ ^ •¥- 3X -fr rt 5 -fr 5 4 # 4 3 122 PARKHURST HARMONY. The two chords above differ only in one tone, and the ultimate resolution of the two is the same, but the root of the first is D, and the root of the second is B. In the following exercises let the pupil determine which of the sixth' f our th-and-third chords have an augmented sixth, and which of them have only a major sixth. Exercises. 5 5S: o- 131 2. f 'i 6 r ' U \Ar 4 i m 3 fi -fS- 30r 1 -€»- r. ^ ' **_ ' ^ 3 - open position 7— T 3. 6T ^^ S E=3Z 4 *^ 3 4 g I / - J gHi g jH 5 # 4. ^ open, position. ^pr-15 i pep XE :si: ^«>^ ^ -tir « 5 4 4 3 ^ ^ 4 8 -«>■ -«>- 54 <» 4 3 3 ^ ^ -tt- K 1/7 '■ fi" 4 tf 5th. The Diminished Triad with Major Third. I ^ m. XE This is not of service in four-part harmony, as neither of the intervals admits of two progressions, and therefore cannot be doubled ; and in three-part harmony it is of use only when the voices are dispersed in this manner, I «♦- CHAPTER XII. 123 Its use can be illustrated thus : ^ XE i ^^=g ^8r 4 XT 6 1^ 6 If -^ 5 The following- will assist the memory in regard to these difficult ■"altered chords." Every triad in the major scale is at the foundation of an "altered ■chord." From the three major triads (on ist, 4th and 5th degrees). we get the chords with augmented fifth ; from the four minor triads (on 2d, 3rd, 6th and 7th degrees) we get the chords with aug- mented sixth; using the first three for the chords of augmented 3txth, and of augmented sixth-and-Hfth, and the remaining one (on the 7th degree) for the chord of augmented sixth-fourth-and-third, thus: 4 ^ i: |«»R- I a n «' y i t f- ^ | | »| T I 1 f For an explanation of the method of determining how a g^ven distance is to be named, as for example an augmented sixth or a minor seventh, an augmented fourth or a diminished fifth, etc., see Appendix (I). Beyond these five incidental re-formations of our two elementary harmonies (the common chord and the seventh-chord) there are no others that are to be ranked among the fundamental harmonies. And in regard even to these five "altered chords," which are cer- tainly striking in their effect, it should be observed that the substan- tial merit of any composition depends not to any great degree upon the startling effect of strange harmonies, but mainly upon the ar- tistic use of the simple and familiar chords. Chords are the words of music, and the deepest thoughts of any language find their best expression in the simplest terms of that language. It is however incumbent upon the author of such a treatise as this to acquaint the pupil with all his w^orking material, that he may be fully equipped for every emergency. At the same time this is a 124 PARKHURST HARMONY. most opportune occasion for reminding the prospective composer of a fact he can never afford to forget, namely, that when an author can find nothing new and true to say, he only cheapens his art by resort- ing to the startling. After the foregoing study of all the fundamental chords the pupil is in a position to appreciate the classification of those chords into the independent and the dependent, as made upon page 14. The common chords in general constitute the independent chords, as in- volving no definitely fixed progression. This is pre-eminently true of the fundamental position and the first inversion of the common chords ; whereas the second inversion, the J chord, by reason of the interval of the fourth which it contains, has in it something of the quality of a discord, and is thus followed most naturally and commonly by the third (as it were, the resolving tone of the fourth). The second inversion of the common chord is certainly the least in- dependent, and is closely allied to the dependent chords, which have inherently a fixed progression, and comprise the seventh-chords (fundamental and inverted) and the altered chords. In other words, the independent chords are the concordant, the dependent chords are the discordant. Summary. Three ways in which chords are altered by accidentals: — How many characteristically altered chords: — The terms that character- ize the three sorts of altered chords : — Formation of the augmented triad: — Where it occurs in the minor scale: — On which degrees of the major scale serviceable: — In what way augmented interval is commonly introduced : — Effect of augmented fifth in minor triads: — Use of augmented triads in inversions : — Addition of seventh to the three augmented triads: — Comparative effectiveness of these three seventh-chords in their inversions: — Formation of augmented sixth chord: — Distinction between sharped sixth and augmented sixth: — Invariable progression of augmented sixth: — Which of the minor triads can be used to form augmented sixth chords : — Which interval only can be doubled, and why : — ^^Formation of augmented sixth-and- fifth chord: — Problem in its resolution: — Solution of problem: — The natural interval of progression of each voice, moving from this chord: — Which of the triads of the scale can be used to form this chord: — Comparison of the three sixth-and-fifth chords of a scale, as r^.gards the relation of the resolving chords to the scale : — A serviceable chord for modulation: — Formation of augmented sixth- fourth-and-third chord : — Diminished triad with major third, when serviceable: — The seven successive triads of the scale at the CHAPTER XII. \T^ foundation- of what "altered chords" : — The merit of a composition dependent chiefly upon what: — Meaning of independent and de- pendent, as applied to chords, and what chords are comprised in each class. Figure the basses of the following Exercises. fl^^^^^ I" i|i iii'ii" 'yi-ix p ^ .;-'ij f" i rJiiMr i ;f ^ M I iii iriTiiif I \\\ \v\^\ Ti i 'Jj||ii.jt'Jiij m r* Wf XT i w ^^ i=t ^^ p ff i' iiii ' iJ J iJJUi^iiJ ^ jJ'V^i'rr'rrir lJ-^ m^ ^rr'r rr ' r rr ' i' '^"^fff | '-lH-|r'VMJ,ll''ll(^ JiJjJiMJj J ■^•>f frri»f r^ | |.^7^l^''^ l ^'^r^i-J^tP 126 PARKHURST HARMONY. 9. i v^'' j|tfMf^HW^rrr(',irff'^ 10. fe s F^ f rff r ':;^^,i;,,.,fj'j;.g.*ii 'Mr I r r «r »r jA^^^^ ^ y't'T )' rU.J ^^ 2z: V27 PART II. ':he auxiliary chords. The chords which have thus far engaged our attention are the /nost important, as being the fundamental harmonies. They consti- tute the harmonic basis of all musical composition. They are the skeleton, solid and substantial, by whose firm continuity the whole structure is made coherent. But while in rare instances a whole composition (but of necessity very brief) may be developed out of these fundamental harmonies — as hymn tunes in choral style, like "Old Hundred" — the outlines of such a form of composition are evi- dently too rigid and angular for prolonged use. While "fundamen- tal harmonies" — the bone and sinew of the composition — can never relegate their peculiar functions in what may be called the anatomy of music, it is no disparagement of their importance that they must be clothed upon, to insure a becoming grace. To afford lowing outlines, as well as infinite variety, where else we should be soon op- pressed with an ungainly and repulsive austerity and endless mon- otony, is the function of the Auxiliary Chords, forming the rounded fleshly covering that gives constant proof of, yet at the same time gracefully conceals, the skeleton beneath. It is like the drapery that takes form from the very figure it hides. These auxiliary effects may be classed as follows : 1. Auxiliary Chords. (a) Suspension chords. (b) Auxiliary Chords, other than "suspension chords,"' to be described hereafter in detail. 2. AuxiLiAR Tones, of various sorts, and known as passing tones, appogiaturas, grace notes, etc. A so-called "auxiliary chord" is usually a combination of tones belonging to a "fundamental chord" with other tones foreign to that chord, so that we can speak of the e?itire combination as an auxiliary chord, or speak only of those single tones in the combina- tion which are foreign to the fundamental chord, in that case call- ing them auxiliary tones. Thus we can call the following harmony an auxiliary chord, or speak of the soprano (d) as an auxiliary tone combined with the common chord of C. 1 2^5 PARKHURST HARMONY. i ^ 4 ): The foregoing furnish all the Accessory Harmonies wherewith the Fundamental Harmonies may be embellished ; and the knowledge of both sorts, Fundamental and Accessory, makes possible the full analysis of all chords. The several accessory effects given above must now be studied separately. CHAPTER XIII. Suspension. Hitherto the movement of all the voices from one chord to the next has been simultaneous. But under certain conditions one or more of the voices can be delayed on their tones in the first chord, while the remaining voices move to their places in the following chord. The result is a mixed chord ; i. e., it is a combination of tones of which one part belongs to one chord, and the other part to the other chord. The tones that are thus held over from the pre- vious chord are said to be suspended. In the following, ^ 58; XF 3£ « ^ 3r instead of having the soprano move to B at the beginning of the second measure, it can delay upon C until the last half of the second measure, thus: i ^ m XT Vy^S s xz: The pupil must clearly distinguish between suspension and mere retention of a tone. Two chords often have a tone in common, which is then simply retained, and belongs as much to the second chord as vto the first. Thus G, in the above example, is common to all three •chords ; but C, in the first half of the second measure, does not be- CHAPTER XIIL 129 long to the second measure (which belongs to the chord of G) and is foreign to the prevaiHng harmony. The proper tone of the har- mony for soprano is B. The characteristic quahty of a suspension, making it effective, is the discordant relation of the suspended tone to the true harmony of the measure. There are three sorts of resolution, according to the movement of the voice from the suspended tone to the next, viz., (i) Resolution downward. (2) Resolution upward. (In these two sorts the voice moves by one diatonic de- gree down or up.) (3) Free resolution (to be explained later). (i) Resolution downwaeld. This method of resolution, in which the suspended tone leads to the next degree below, is by far the most common, as it is the inherent tendency of every discordant tone to lead downward to a concord. In the second sort of suspension we shall find that other considerations are involved, which counterbalance the natural down- ward tendency, and induce an upward movement. By the very nature of the case, the suspended tone is heard in the previous chord ; it is therefore prepared, and the natural law of discords requires also that it be resolved by leading downward one degree. The simple law of suspension is — Every suspension must be prepared and resolved, and in the same voice. ' Inasmuch as any tone of a chord can be suspended, if it can only be properly resolved in the next chord, it follows, inversely, that we can have a suspension above each component tone of a chord, pro- vided that the tone above it belongs to the previous chord. Thus we can have a suspension above the 8th, or the 5th, or the 3rd, or the ist (i. e., the bass tone) ; or, in other words, we may have a suspen- sion of the ninth, of the sixth, of the fourth, and of the second, as follows: 33: W=f ^ ^ 9th 6th XT 4th 2nd 3 ^ 33: XE XE -9 — w -V 7 W 4 5 a 3 130 PARKHURST HARMONY. Of course, some suspensions are more effective and more fre- quently employed than others, but it is our present purpose to dis- cover all possible suspensions, and in regard to those that appear least serviceable, there are circumstances that may justify and even require their use. As before remarked, the characteristic feature of a suspension is its discordance with the prevailing harmony. But in the suspension of the sixth. ^ r ^ 3x: 6 5 the suspended tone does not produce that effect, and the combination may be analyzed as simply a chord of the sixth followed by a com- mon chord on the same bass tone. Any isolated case like the above would more naturally be treated, not as a suspension, but as a verit- able sixth-chord ; but when it occurs in a series of suspensions, the most intelligent analysis would find a suspension in this chord also. Thus in the following, ^^i i'iUliJ 2Z ^ ■o- xz: -o- xr XE IB — 5" r^ — 3- it is plain that the ruling harmony of each measure is that which is formed in the last half of each measure, and by omitting the suspen- sion, the fundamental harmony is as follows: $ ^=f=a m -*>- §-mj^^_Ui ^ xz: xn -•V- xin 6 6 so that in the second and fourth measures we should properly treat the sixth as a suspension. We shall find other instances of concord- CHAPTER XIII. 131 ant suspension, where we must judge by the circumstances whether it be a genuine suspension. We will now treat of each suspension singly. Suspension of the Ninth. This can occur in cither of the three upper voices, thus : ^^ ^S xr zz: f «^ -*»- XE XE XE "sr It will be found more satisfactory in soprano or alto than in tenor, for the reason that the discordance, being between the suspended tone and the bass, is not so conspicuous when one or more tones, in concordant relation to the bass, intervene between the discordant tones, which draw the attention from the discordance. When the suspension is in the tenor, there can be no intervening tone to soften the effect. Heretofore no distinction has been made between the ninth and tlie second, and essentially they are the same. But by the remove of one or more octaves the harshness of the discord is mitigated — di- luted by the distance. The suspension of a second, resolving into unison, like the following m ^ -♦>■ xz: rfT m XE g ^E>- is not endurable. The same objection exists to a similar suspension in the tenor, P XE M ^J«i but in less degree, because the combination, being at a lower pitch, is less shrill. While unsatisfactory if it resolves into unison, such a suspension of the second in the tenor is admissible, if the bass 32 PARKHURST HARMONY. moves away from the tone into which the tenor resolves, thus M -€>- ^ S The figuring of the suspension of the ninth, with its resolution. The procedure in writing 9 8 is usually 9 8, abbreviated from 5 - this chord is: First Hud the ninth above the bass, put it in the same voice in which that tone occurred in the preceding chord, then put in the third and the fifth of the chord that is founded on the bass tone. Illustration. bd.MT^^ijL., JTiJ SI j^^l^ij 1SZJS ^ T^ 98 6 98 6 98 87 98 7 5. \>b. Exercises. 7 8 6 9 s.-^ xr « 1. 17 ' 6 — te-7 § ' 9^8'»' Xfl ^-^ t> 5 9 8 2. yf 3D[ XE « 7 .9 8 6- 9 S 6 6 t> *> l»5 9 87 s 8- open position. i ^ XE jDE « I «' 6 98 g 9 8 6 4. open position. w ^^^m t T 98 4 3^ a ' o XT 6 5. close position 64 9 8^ 98 m 5^ 1^ fc '6 l» XE « 87 XE - rf "5—^ -T~cr T 4 CHAPTER XIII. 135 Exi-:Reisi:s. ^ l, ts ^ s P -O^ ^ 8 7 9 H 7 t> 2. open position. jDC ^^^=22 ST 8 "7 6 Xfl XE 1^ «r^ 3. close position. -W^ F~8r 7~15" m -^ 3z: zz: -g-7 g~7 9^76 4. open position.. 6 8 7 i XH XE 3 XE 6 7 6 6 - b b o^ iS _ 5 4 8 7 6 g ; o — 6 .8 7 m 5. open position :tli ^ f 4 3 xi: 7^ 6 6 6 7 6. open position. xn ^ ^m XE ( g Pig F6 7 B 'id Ijl 6 ^6 y 8 '6 5^ 4 6 5 4 7 SUSTM'XSION- OF THE NiNTH IN SeCOND TxVERSION i JtjJ ii JtJj «^ « «ir XE i^i^ g XE -w-^ XE "6~^ 5 4 XE "6 ^ 5 4 f XE 5 4 This is a very common and effective suspension. As in the chord of J, it is better to double the fifth (i. e., the bass tone), the same holds good when the suspension of the ninth is introduced into this chord, as in the example above. The doubling- of the root in the chord of J is usually to be avoided, as harsh ; m *v. *> 4 § 36 PARKHURST HARMONY, but the melodic progression of the voices sometimes makes it de- sirable, as in the following: Similarly, the doubling of the root in this chord of | with a sus- pension of the ninth is still more harsh, as the suspension and its resolving tone (an octave distanct) are heard simultaneously; I ib^^ -€>- m XE 6— :zr 5 C 4. but melodic considerations can also make this desirable: i w 33r JDL -€^ ^ 6 - 5 4 7 - 4 3 The figuring of the suspension of the ninth, in the second in- version, is 6^ which is to be carefully distinguished from our previ- ous I, which signifies the first inversion of a seventh-chord; for the analysis of our present combination shows it to be a common chord, with the root a fifth below, and with a foreign element (the sus- pended tone) in it. Inasmuch as we shall find several other sus- pension-chords, whose figuring is identical with that of some of the chords already learned in Part I (the fundamental harmonies), but utterly different in their nature and progression, it is in general inadvisable to name the suspension-chords from their figuring. There are only three exceptions to this : — the suspension of the ninth and suspension of the fourth, in their fundamental position, are called the chord of the ninth, and chord of the fourth. Also the suspension of the fourth in the bass is called the chord of the CHAPTER Kill. 137 Hfth-and'second.. The remaining suspension chords are indicated by giving the name of the suspension as in its fundamental position, and adding the inversion as the case may he. The suspensions thus far considered are therefore named as follows: Chord of the Ninth. i ^ ^ ^^ Suspension of the Ninth, First Inversion, I ^^B ^7~6" xr 7 6 6 Suspension of the Ninth, Second Inversion. I J tJ -I I J I J -i C ^ XE 6 - 5 4 XE 6 - 5 4 This manner of naming them affords the only complete analysis of the chords, and is by far the simplest. With the figures | ~ the suspension of the ninth, second inversion, can be written in either of the above given forms, al- though there is no figure to account for C in tenor of second form. But in writing this C, although not expressed in the figuring, we are not at all violating the nature of the chord. Intelligent harmoniz- ing must rise above the mere matliematical calculation, and grasp the inner nature and spirit of the chords. 138 PARKHURST HARMONY. Illustration. il T,W^i | ,j-' i vJi ' J | J ^ fffr" ■f^j.rf 8=* _i — t 1 1„ m ■o- 3z: XE g XT T^ IT 2~^K^ •3 B 6 - 5 4 Exercises. ^ zzz:^ ^ ^6~^ 9 8 6 - 9 8 W i> 5 T^Y £ XE 3 3. ' t ~7~W 2 6 ^ XH 3 ^ 6 54 8 7 s 22=^ s — ^ 5 4 ^»- 5. open position 6 7 4 ^ ^ *f ^ y « t -^ — 9 8 ^ "5 6. open and close 8 7 ^ XE zz=?z a -^>- 5 '^7 ' « H ' 7 « ■ 9 8 ' g e ^^ « '7 ^ s^ XE 4 ^ « 7 4 3 S 8. open position, in score. i « «7 5 f? 98 6 98 7 5 ^ 6 987 ^6 ^?^.^ 67 6 5 XT 987 The suspension is merely a rf 3 6 5 5. m m t5 4 ' I3 7 7 3 6 6 6 7 4 Suspension of the Sixth. Fundamental position. ij^^J^ IE 1?!^ ^ XF~ ~6~T ^:^ XE 40 PARKHURST HARMONY. In its construction this does not differ at all from a chord of the ^ixth, and not being a discordant suspension, will be regarded as a suspension only in a series of such chords, thus: *fs i^ 'li ni ni h^ ^ ^ JOL XE XE 6 5 4, 3 4 3 The ruling harmony of each measure is #'roN§iyi§ H i XE XE XE This chord needs no special illustration nor exercises. First inversion. ^ i^^-S- m XE m p 3nr XE t i f x6 - 4^3 In its construction this does not differ at all from a chord of the sixth-and-fourth. and will therefore be regarded as a suspension only in a series of such chords. No special illustration nor exercises are necessary. Secoond inversion. r 1.— I I ^ xe: XE ^^=^=^-^ ^ « 4*: 8 -€>- * 3 % - 9 The figuring of this chord is 6 but the pupil must be careful not to call it a suspension of the ninth, although the suspended tone is a ninth from the bass, but should recognize in it the suspension of the sixth, in the second inversion. CHAPTER XIIL 141 Suspension of the Sixth. Suspension of the Sixth, first inversion. Suspension of the Sixth, second inversion. m T ^ th 3 IZZ 6 5 ^ XE ^ -', 'V /J ^^ ^ 1 '■^ --«- <* — p _l 1 6 - 4 3 Illustration. 9 8 6 4 ^. pTi,-iT^i|.. | jT^-' ^^ -€>- TT fe^ zz: H JCE -^ xi: 9 8 8 7 6 - 4 - 6 9 8 6 5 8 7 Exercises. f. jCE 2=^ XE XE 3 6 6- 5 4 2. 4 - 8 7 S XE " J g r ^ ^ ^ ^ 46 67 67986 3 5 3. open position. T8 87 3 5 4 7 3 6^f S 4. close position. 6- 87 XF 5 4 3 5. 7 6 ^^ — ^ ^ m 5 6 x> — 5 -* 8 7 *: IE ^ Xf — 3 7 8 6 9 8 T "Or 721 i i ^i^ XE V y 4- 7. 6 - 4 - 1 3 9 8 98 f XE ^=3 22 XE 3 '6 6 - Ji- 6 5 4 2 7t 6 6 5 6 4 7 it 42 PARKHURSr HARMONY. Sight-reading. Open position. xc § 77— P i XE 8^ ^6 2. 4 1 ^ ^^ S ^ 22 3. V 1 •o- f jCE 8 7 s ^ ^ 73 <9- XH 3 2 6 Suspension of the Fourth. Fundamental position. I XE JT f ^r " -r" r ^ 3cs: 5 - 4 » m XE 5 - ♦ 3' The full figuring of this suspension with its resolution is usually abbreviated to 4 3. It is usually better not to have this suspension and its resolving tone (even an octave distant) heard simultaneously. U «>--o- ^¥r 9ZXE: 6 4 8 5 But when there is a whole tone, instead of a half tone, between the degrees of the scale on which the suspension and its resolution occur (so that the fourth and third of the chord arc in a less harsh relation to each other), CHAPTER XIII. 143 I ^J J II ^^J J -&- ^^ XE bad. 4 3 ~ry 4 3 and when, in addition, there is an evident melodic progression in two voices, in contrary motion, such an effect is admissible, thus : ^^ i Illustration. ^^ -O- 31: xn -€> XJ^ #=t3 ^ § 1©- <^ -<^^ — "y fe-W^t^ ax -3 O" i 4 8 6 « 5 -€>- Exercises. 4 3 7 xs: TT— r!g XE XE 30: 2. 43 98 43 9 8 4 .3 98 S^bI? 3 ^S i nzz^^zsi ^=jd ^—d 4 3 6 6 3. - 6 6 6- XT .5^ 437 i ll, a

' o " ^ 'O 3 436436 987 6 51)6 -6 J36 667" 4. open position m i XX «tzs XX XX -e>- 5 4 3 2 6 n \ %'^ 4 3 9 8 8 7 XX 5. close position; in score. 144 PARKHURST HARMONY, Sight-reading. 1. o#p|r^llPr;^ w 1SW9 ISZI^ 7 6 7 ^ f «^=^=*5=^ ^^p ^c-zz -€>- ki5 T^ 6^ — 7 3 5it> 4 t g XE ri i fjij i ^=0: O" 76 « 5 ' I 3 4 3- First Inversion. 6-flr 1 ^i 7 6 3 7 6 4 - 146 PARKHURST HARMONY. Sight-reading. Open position. m 3a: t9 (9 ICE 2. 7 6 8 7 5 2 6 8 7 ^ m 3X «>- ^ 4^ "65 7 ^^ W = i^ «■ k;5 4 3 3. m ^ 1 i 5 6 8 7 6 5 87 Ty Suspension in the Bass. Thus far every suspension has occurred in the three upper parts^ but it can be introduced equally well into the bass, provided the sus- pended tone be properly prepared and resolved. This affords opportunity for three suspensions in the bass, one of which is among the most common and effective of suspensions, while the other two are suited only to peculiar circumstances, and rarely occur. These three suspensions are derived, like all the foregoing, from the fun- damental position and two inversions of the common chord. Suspension of the Second (in the bass.) The first form is harsh, because the suspension (D) and its resolving tone (C, an octave distant) are heard simultaneously. The second form is better, doubling the third (E), instead of the root (C). No figuring is needed under the resolving note, as it is the root of the common chord. The student cannot fail to understand this suspension, if he will compare it with the progres- sion in the first two chords given above. This suspension rarely occurs except in a series of suspensions in the bass. CHAPTER XIII . Illustration. 147 I ^pi §=«=iJ r ?r^ ^^^^^^s m jlTr^rr an i ^ -€>■ 1^ 5 4 8 7 6 4 ^5 4 3 Exercises. si s ^=H= ? 7~^ fczzi * — 3 * S xc ^ -€^ 8 7 r^ ^ 22 IT « -€»- 5 6 4 3 3=^=^ 6 5 ^ 1^ I BE *J I 67 4 8 4. open position. 6 - -o- -o^ ^ XE I -7~Tr 5 4 3 3 4 This will be a concordant or a discordant suspension, according to the element of the chord that is doubled. If the fifth be doubled, as at (a), it is discordant, but if the root or third be doubled, as at (b) and (c), it will be concordant. (We are here speaking, of course, of the root, third and fifth in the resolving chord, which is the ruling harmony of the measure, although it is fully expressed only in the last half of the measure). This suspension seldom oc- curs except in a series, and whether tlic concordant or the discorfl CHAPTER XIII. 149 ant form should be adopted, depends largely upon the melodic pro- gression in the other pars, thus: b. i xr xn 3X g m Tn XE « ^ -o- XE js: -€^ ^ vrT^t i The above examples strikingly illustrate how imperfectly the mere figuring expresses the true nature of a chord. Thus in the 7 first example, the first chord of the third measure is figured s. Now it is in the nature of a genuine seventh-chord for the seventh to move toward the bass. But in this case, being a suspension, it is plainly in the nature of the bass to move away from the seventh ; yet the two chords have precisely the same figures. Again, in the second example, the first chord of the third measure is figured ^, In its construction it is a common chord, in its nature it is plainly a sus- pension, and thus the (apparently) seventh-chord in the first ex- ample, and the (apparently) common chord in the second example, are in their nature identical! In the concordant form of this suspension, as the figuring is |, it is unnecessary to express it, as will be seen in the following: Illustration. i XJl H xx: XE H -O- xi: -^rt- xx: XE ^p^ Xe fe£ a XE f XE -5—6- 2 ■3" t;7 When the suspension is in the bass, its harmony, being the same as that of the succeeding bass note, may be expressed by a diagonal dash, pointing forward to the following harmony, which is also to be its own, thus : $ 3: XE -e»- XE XT" ZXEI XE XE O 1 ( 9 t 150 PARKHURST HARMONY. Exercises. 1. ^ ^x J ^# r ^ — H f- — P-^ ' — ^- — ' — ^-^'^l ^

r f i-i ^ ^m W7 4 -^ Mi-J ^ -€>- -t trr 22 xi: ^r^ 6 5 1} - T ^ * zz: 3X xz: 5-&- 5 1^5 ll> 5-er 'ff 4 7 We have now treated of all the single suspensions possible in the common chord and its inversions. We have next to consider Suspension in the Chord of the Seventh. The most satisfactory of all suspensions are those in the seventh- chord, by reason of the greater richness of harmony, which softens, without effacing, the discordance of the suspension. All the possible seventh-chord suspensions will be presented, but briefly; as no new difficulties are involved. The dominant-seventh chord will be used in illustration, as the most common and satis- factory. (While all the secondary-seventh chords are ''fundamental chords", and as such may have their several tones suspended in a following chord, it will be found that the seventh interval itself of any secondary seventh chord (either in fundamental or inverted form), is too harsh to admit of the delay in its resolution, and cannot in general be suspended ; but any other tone of such a chord can be suspended. On the other hand, the seventh interval of a dominant- seventh, or of a secondary-seventh "in dominant-seventh form", can be suspended, thus : I * ^ood. s ^ £ good. bad? XE 152 PARKHURST HARMONY. -€>- bad. § bad. * XT good. i xc « - 5 - 4 3 The harshness of any discord is softened by quickly passing from it, and the above that are marked *'bad" may be allowable when the notes are quarters or eighths, instead of halves. Such effects will be considered later, under the subject of auxiliary tones, Chap. XV. Suspension of the Ninth. Fundamental position. I s TfQ- H &z^ xw b. W XE 33E II — w 7 - It will be remembered that in the seventh-chord the root is often doubled, and the fifth omitted (as above (a) ). This affords oppor- tunity for the suspension of the ninth, in connection with the sev- enth (as above (b) ). The third can be omitted, instead of the fifth, but this should not be done when it can be avoided. First inversion. I l^ i m It will be seen that this results in a chord of the seventh on B, and being resolved similarly, it will be regarded as a suspension only when occurrmg in a series. Second inversion. I s m CHAPTER XIII. 153 This results in a first inversion of a seventh-chord on B, resolves similarly, and needs no special comment. Third inversion. ^ w m ■? — 3- This results in a second inversion of a seventh-chord on B, re- solves similarly, and needs no special comment. In the above set of suspensions, the first, called the chord of the ninth and seventh, alone requires practice. Illustration. — r — c) o — A ^ P g I ^ —r, _CV ^ !z=e ■*>- I t TH -WW 7 - 5 4 3 9 8 7 -■ i Exercises. 8H7 m t 8 '; ' " Xfl s ^ h 98 '2. open position q 4 3 3ce: t XE 1 XE 3. 7 - g-B 4 3 9 8 TP 9 87 m. XE 31: ^ 9 8 7 6 -(r- 4 - 5 4 3 Suspension of the Eighth. ■WW 7 J I i -O- ^^ ^ : r<> r " g ^^f fundamental. is> inversion. 2nd inversion. 3rd inversion. ^ XE XE -o- -O- 5 154 PARKHURST HARMONY. The suspension of the perfect eighth, resolving into the seventh, presents again the anomaly of the common chord in the aspect of a suspension, and it would certainly never be classed as such, except in such connection as the following i m MLlilAiU£ nzz XI- JDL «^ -€>- ^ xs: <^ \^^ i xx: XE where the ruling harmonies of the measures are as follows : I ^ «^ x^: ^ § 5i? JCk. -€>- ?ut by the use of the diminished eighth, 4> I - 8 7 we get an unequivocal suspension above the seventh ; but it is too harsh for frequent use. Suspension of the Sixth. Fundamental position. m xn J /' fi XE 7 - ft 5 In the common chord this suspension lacks the discordant quality, which is here furnished by the seventh (F) in its relation to the sixth (E). CHAPTER XIII. 155 t'lrst inversion Second inversion: ^ -p^ y " — 1» — 6 - 5 - 4 8 >J J II ^ J T^J J bad. I good. «1^ 1 tl JlX. 4 - 8 - This is not good in four-part harmony, but good in five-part. Third inversion : I -pis-- » V P I o 6 7 6 4 4 1 2 - Let the pupil indicate all the sixth-suspensions in the following t 4|,TlA^J ^dJM.^^.'lTd^l:J,^l- ll J » xz: i JJ i «F XE XE XE 3Ct rt 6 - Is 9 8 7 - 7 6 A- - 2 - 7 6 6 156 m PARKHURST HARMONY. Exercises. xn i Xfl o^ ^ 6 5 ^ ^ 6 9 8 76 W ^7 '3 6 4 3 I I '6 is- 6 I ^ ^ 3 6 3- open position. # 2 -^ 6 8 7 -^- 3 1^6 4. close position. XE 6 - 4 3 5 7 - 6 5 ^^3 6 65 4 3 ^ 5=31 fei 9 8 7 7 6 i 33r -C^ i 5. 6 5 6- 98 li 8 7 <^ g -^ xi: -€>- id 3 6 T^ y^ 6l6¥ tJ6 4 - 4 - (>5 ^ 2 - 4 7 The pupil should examine each suspension in the foregoing and subsequent exercises, and give its exact name, according to the previously given method (page 137). Faithful practice of this sort will give a mastery of the subject. Sight-reading. ^ If r ir H 8 I? « ^ XE jE ? 9 8 '7 5 7-5 5. open position. 6 b5 98 6 4 4 37 ■5ar ^ BX ^6 7^ 6 an -^ 9 8 7 6 -f- 4 - 5 4 3 - 4 # ^.-, ^ -6- ^4 3 Suspension in the bass. Fundamental position. ii^i €^^ a. 1 6 2 7 6 7 7 6 3 \n o»e form (without doubling the root) equivalent to a chord of CHAPTER Kill. 59 the second, as at (a). The other form (b) is rarely serviceable in four-part harmony. First inversion: very good. Second inversion: good. Third inversion: m -^ ^ vr rr>f 6 5 4, 3 3 i S: -o- ^ recognizable as a suspension only in a series. Exercises. y % rJ ^ 331 Tr 6 - 5 4 ^^ 3 6 5 & 7 - 4 3 2 6 -6r 8t!7 6 7 m :kji XE -^ ^8 4 ? 4 3 -jr lijO PARKHURST HARMONY, 4. open position. m n^i T-^^ i 5. close, position. 6 -6- ft 7 J ^T--0 ^ ff^PTSf 54 4 3 9 87 Summary. Necessity of auxiliary chords: — Classification of auxiliary effects : — Definition of Suspension : — The characteristic quality of a suspension : — Three sorts of suspension : — The law of suspension : — What suspensions are possible in the common chord: — Why sus- pension of the sixth is more naturally regarded as a fundamental chord of the sixth: — Suspension of ninth most efifective in which voices : — Distinction between ninth and second : — Suspension of sec- ond in tenor : — Figuring of suspension of ninth, and its resolution : — Procedure in writing this chord : — Suspension of ninth in first inver- sion, in two forms, and figuring of each : — In one of its forms equiv- alent to what chord : — Suspension of ninth in second inversion, and its figuring: — This chord equivalent to what fundamental chord: — Proper method of designating a suspension-chord : — What suspen- sions are to be avoided : — Suspension of sixth in first Inversion equiv- alent to what fundamental chord : — Suspension of sixth in second in- version how figured : — Suspension of fourth how figured : — When can its resolution (an octave distant) be heard simultaneously with the suspension: — First inversion with resolution how figured: — Second inversion with resolution how figured: — Suspension of sec- ond in bass, in two forms: — Suspension of fourth in bass how fig- nred : — Suspension of sixth in bass in two forms : — In the discordant form equivalent to what fundamental chord: — Tie not essential to suspension : — Relative length of preparation and suspension : — Sus- pension in chord of the seventh : — When can a suspension be pre- pared by a seventh : — Suspension of ninth in seventh-chord how fig- ured: — Three inversions of same equivalent to what fundamental chords: — Suspension of eighth (perfect: and diminished) : — Suspen- sion of sixth, fundamental and inverted, how figured: — Suspension of fourth, fundamental and inverted, how figured: — Suspensions m bass, in fundamental and inverted chords, how figured. CHAPTER XIV. 161 CHAPTER XIV. Suspension (concluded). Anticipation. Syncopation. We have now passed in review cz'cry possible single suspension; that is, in a single voice. But it is feasible to have suspension in more than one voice at a time, and we proceed to show what is possible in this direction. Suspension in two Voices. In the nature of the case, the suspended voice moves after tiie others, that is, alone. If two voices are suspended, they must move together. Therefore any two voices, capable of proper resolution, can be simultaneously suspended, provided that they stand in con- cordant relation, so that their progression into the resolution will be agreeable. The following makes this plain : c. d. ^^fc^-JiJji i M 2±:^ Xfl «-z: fi W rP \ r j ^ o W r P \ r pg ^ '^l^ l l:£^ rf jingle, single. double. bad. good. bad. § IE jSH m 6 9 8 6 4 3 5 5 9 8 6 9 8^ 98 43 5 43 ^65 The concordant relation is necessary, because the two suspended voices are so conspicuous in their motion ; as will be seen in the example, the intervals of thirds and sixths are much more har- monious than fourths; and our double suspensions are generally limited to those in which the interval is a third or a sixth. in thirds: ^ ^ -3^ XE iSh-r. xx: ■o^ in sixths : F* ^ — n9 n rr — V -J G ] G ^ 1 p |*> 9 1 i^ r i^ H -j- —\ o «Jfe :162 PARKHURST HARMONY. Double suspensions, with the interval of a third or sixth between the tones, are very effective in the chord of the seventh, and involve no new principle, thus : M U *^ S: i :^S m p^ft i'S-rMP-tiKi: 9-^^ •^^77 TSL i-ij fe« m i IX z::?z pT^ EXEKCISKS. m XE 30E -^ 22 9 8 9 8 7 6 7 - 9 8 76 76 4 65 4JJ 3 - 3 - 4 3 98 43 8 7 ^ 32 ft fclZ -O^ I I 2 6 3. 5 4 3 3 2 XT 8 7 ^m |9— r ^ XE -O- -O- IE XH 3 9 8 6 !4^ 6 l;7 9 -4. 764 2 4 9 8 7 -6r j,7 . |6 5 4 ^ a ^ I « -^ ¥^ XE XE 1 5. open pos n position. ' I 9 8 9 6 4 U ^ ^ 76 7 - 4 - 6 5 ^ ^ o- 3CE JX fczi "? 9^ 7 6 7 4 -# 57654 65 > 4 6. open position, * ^ 3 ^6 67 XT s m g jy S XE 6 4 A- ^^ U- 6 — '6 ^ 3 3 2 2 3 4 2 3 3 81^7 6 7 Suspension in Three Voices. The usual method of employing suspension in three voices will be explained later. It is of rare occurrence, and is illustrated as iollows : I ^ Jfe m XKE XT CHAPTER XIV. 63 Exercises. 1. & -€V ics: 5t|7 2. 9 8 ll4 3 9» 7 6 54 a7 4 9 § 4 3 ITT 4<^ 9 87 7 6 - 98 7 6 4 3 9Er 7 6 5 4 7 -6r 5 4 3 - %} 9 8 7 *> 4 3 8 7 XE ^ 3cs: m ii 3 6 7 Resolution of the Suspension into Another Chord. Hitherto the resolution has been into the same chord, that is, the unsuspended voices did not leave their tones until the suspen- sion was resolved. But it is possible for the unsuspended voices also to move simultaneously with the suspended voice, so that, while the resolution is precisely the same as before, the harmony of the re- solving chord is quite different, thus: 9 » This can always be done, provided the resolving tone is an ele- ment of the new chord, and the other progressions are correct. The harmony is richer by this method, inasmuch as the effect of three chords is compressed into tzvo, (as above). Such progressions are at first more difficult for the pupil, and it is indispensable that he should clearly see the suspension in the first chord, and its resolution in the second. To this end let the following example be carefully studied, in which each suspension has several resolutions. 164 PARKHURST HARMONY. §^ 4th 9 6 I 9th & 4th in bass. m^ T-jr. 3^ ^ «-z 5^-^ ^ ^^nci ^ s M ^^ ^ cv 4 7 4 -^ 4 3 I ' I 'I 7 4 4 3 6 ^ 5 4 4 3 In the same manner as the resolution of the seventh is occasion- ally delayed (chapter XI), so that of the suspension may be delayed, by introducing a chord in which the suspended tone is continued, but becomes (i) a different suspension, and is then resolved, or (2) the seventh of a fundamental chord, and resolves, or (3) a concordant element of a fundamental chord. S^ 1. i 1. ^ ^^ u 41 -O- IX H s 301 9 4 f XE 4 3 ry -*v I f I f r ^^'^ 2. I f tf ^ I * -S: 3X i ff i 3x: sh-*' I 4 6 5 3. ^^ ^1^^^ J i ^ 9 % 4 3 [ o 3: i XE 3x: CHAPTER XIV. 165 One way of delaying the resolution of the seventh is by intro- ducing a chord in which the seventh becomes a suspension, and as such is resolved. This would oftener occur in chords of the dominant-seventh or of dominant-seventh form, than in the pure secondary-sev- enth chords. This method of delaying the resolution of the sev- enth could not be mentioned in Chapter XI, as the nature of sus- pension was not yet explained. Hitherto the resolving chord has afforded the true fundamental harmony involved in the suspension-chord. But this will not be the case when the suspension resolves into a nezv harmony. To de- termine the fundamental harmony of the suspension-chord, it will now be necessary to combine the resolving tone with the other tones heard simultaneously with the suspension. In the case of the sus- pension of the ninth, in second inversion, when figured |, there will be a danger of misinterpreting it as a fundamental chord, viz., the first inversion of a seventh-chord. As a suspension the bass must he doubled; as a seventh-chord inversion there must he no doubling, and the chord must therefore be interpreted and formed according to the requirements of the situation. But ^ followed by J com- monly means a suspension-chord. In the case of the full figuring 6 there can of course be no ambiguity. Exercises. zzz:^ s ^m XE -<& 9 7 5 6 4 ^ g XE . i 'J i 'J xs: 3 6 6 ^ 7 li 166 PARKHURST HARMONY. 4. m ^ W ^ zz 6 7 5 5. 6 r ^ ^ 2 ^ 9 6 6 7 4 3 6 87 5 *>lI> J I P^ i * zz: r^-t^ "^i^^W^ 4 7 6. open position. ITT 5 6 7 6 7 s S s ^ p «HJ^ «^-« •'4 7 7. open position. .9 1,7 » l>5 6 6 4-87 kl 5 3 - ^ ^^FM? . ^ ^-z^ t o % o 7 9 4 17 9 ^6 8 7 6*7 Delaying the resolution. 8. J f^lffhp ' J \Wj ^ (^ t9-^ ?2: 9. 5 '6 9-2645^ DO o 43 ^ 4,'6^^ 2l»5 4 <^ 3 6 6^ 4 ^ K Q lA Irr >nZ^7I 6 '4. ^ Q tt 1-7 Q ft 9. fi / ti. Q O a V *-* 5 9 '6 '7 '6J4-6 6 '4 '7 9 6 1,7 9 8 2 64 6 98 6 7^'^' 7 4 2 5 '4 43 3 7^54 10. i 4 v.. a ; p i r^ s ^^M^ n: zt±^ ^ 98-e- 6 6-4 3- 3 r j gl I g| _L -6^ 6 9:^ ^ n7 11 5 49l>766 26 4-5 xr s ^ 1 It is an interesting exercise for the pupil to choose for himself the harmony that shall accompany a given suspension. Thus, sup- posing the following notes represent the preparation, suspension and resolution in the soprano I ^ then the first chord must contain D as an element of the harmony, CHAPTER XIV. 167 and the chord of the next measure must be such that D and C will be a suspension and resolution, thus: ^ m m 9 S We have here a suspension of the ninth. By changing the harmony we can have a suspension of the sixth or of the fourth, thus : m ff -€*- § ^ TT ^ 4 3 A little practice will make one quite adept in the selection of proper harmonies, and make the whole subject of suspension more clear. The following- fragments are to be treated in this way, letting the given part appear in tne soprano, and then transposing the parts, so that the same suspension shall appear in the alto and then in the tenor; thus, I I in soprano. in alto. in tenor. E £ ^ let the pupil adopt whichever suspension occurs to him, and more than one if possible. It can only be successful when the pupil clear- ly hears the effect in his mind. The teacher can protract this exer- cise when desirable, and much depends upon him to make it interest- ing. Exercises. inc. L — ^1 I iL inG. ^ r^^J I I t n,| J^ t l Jl'^ -"ll 'H '' ^# ^ -^ ^=jd A variation from the usual direct progression to the resolution is that wherein tl'-e suspension-tone is shortened, and a harmonic tone 168 PARKHURST HARMONY. (either below or above) intervenes between the suspension and the resolution, thus: t^i^i-^Wji^liWlM, I »F= g M> II IZ XE i-Jji § JOE ^ XH ^ff xn f XE TT j | jJ.ii>!7J,^J | | JTJj b. JC& T § ^ XJl 1 xi: xn m 3' 3 9 8 6 6 This is analogous to the movement of a voice from the seventh to another harmonic tone before resolution. "Open position" is more favorable for this freer movement of the voice, as a unison is less likely to occur, and yet the latter is not reprehensible (as at (a) and (b) ). The effectiveness of such a movement of the voice must be determined in each individual case. When the suspension-chord resolves into another chord, the harmonic tone to be chosen belongs, of course, to the suspension-chord. Harmonize the following in half notes, and then insert harmonic notes. Exercises. i m ijL_ O , ^ m n XE -CV 6 1*8 7 6 -# >. 4-4 open position. 3 7 t> « - 7 - 54 4 ;i 1 m -o- 5? -^ ^ 7 6 4 6 3 8'. open position, 4 - 4 3 i t: s ^ i m 4. close position. 9 6 I? 87 9 s c»- I -€^- 3 ^Te 5 ^ 7H q I*% I^> |o = xn ^p xx: m XE This often accounts for the upward leading of the seventh in the unusual progression of that dissonance. (Exercises later.) (3) Free Resolution. The two foregoing sorts of suspension are alike in this respect^ that the suspended tone leads by one degree, either up or down. This strictness of resolution (by a single degree), is sometimes re- laxed, when, a movement in suspension having been established, either the exact repetition of a phrase, or else a sequence, calls the suspended voice by a skip to its original position in the harmony, thus: ^ 22 exact repetition 3 ::^ P^^ 11^. Sequence. The repetition of a musical phrase, at successively higher or lower intervals, constitutes a sequence. The phrase may be of any length, usually short, and either a single part, or harmonized in any number of parts, thus: CHAPTER XI y. \7f I ZX] Xfj ^►^ 330 ^ J^rnp i PTlrBp^ ^ ^^ The several voices of the harmony naturally partake of the sequence character. In the practical use of sequence the given phrase rarely occurs more than three times, as, if more extended, it becomes monotonous. The pupil can now understand the use of "free resolution" in a sequence, thus: I ^ €=5 — - a c 3 sks W -sfe- t;:i ^^^ »|j,y pppf it p'p^i i ^^ rTfC^ri ^Sg Furthermore, in the course of "strict resolution" an occasional "free resolution" can occur, when the skip is made to reach a tone essential to good harmony, thus: a. I '>- ! (' r Tr iiJ-f b. :y g ^ 172 PARKHURST HARMONY. The harshness thereby resulting, as at (a), is skilfully avoided, without losing the force of the suspension, by inserting a "rest", as at (b). This device is of frequent occurrence. Let the following exercises be first written, and then introduce suspension throughout the bass by beginning the bass on the second beat, thus ; I ± -&■ ^ ^ p then let the pupil note the examples of each of the three sorts of resolution. It will be observed that the third sort is of rare occur- rence as compared with the others. W ^tt mmm\\ny^ ^ 2. 1 i zz: i xr F=^ ^^ 3 6 8. 8 4 3 m ^^ fW 36 6 6 4. ■6 6 4 5 -6r S iL#ii^);' i rJ Ui i ^Jj^jMi i j «>-^ 5. g VfVU^VKH^^^^ SA- 6-^ 4 7 Re-write these exercises, and put the soprano into suspension throughout. Such a prolonged series of suspensions would usually occur either in soprano or in bass. An effective use of all three sorts of suspension is found in octave passages, where the absence of harmony largely prevents dissonance, thus: CHAPTER XIV. 173 le m^a Figure the basses of the following exercises, and analyze all the suspensions. ^ — i-j^ ^^ JAA -U- lA rr'r rr'r ^^ ^ § 5=F an i jj^^jjjj|jM ^^ ^ f=p r r TTT ^ jU^J4rii=i=i33ii^ rr'r r '^-r^ f i *=i=i I fet Lj. ft'-r i| f 8 y*f-f r'p-p ^ s p p^ 2Z ^- g-f -^ -^ ^i JtJ J J 'ri''' T r'irn r-TT ^ ifr j^ry^f irfg 3CE Mr r ir f 174 PARKHURST HARMONY. i^bfef i (! nrm XSi. PTf |n|U| j jjj | j .^ l i, i j j,^ J J J mJ ^ i ¥ i f TIT rfY''r'rr'r l |''il'^' l fe wt F ifffyifFf f^y i f'rf i " ii 6. r rmhUf^i^M'fiX /^ i l^l^ j pfflf f i® i IC3C ? ^=p In the first measure of the sixth exercise, the third beat may perplex the pupil P m in deciding whether the figuring shall be 7 or ^, i.e., whether the ^ 2 interval between bass and tenor shall be expressed by 9 or by 2. As similar cases are likely to occur, the distinction between a ninth and a second needs to be a little more fully explained. Essentially, a ninth and a second are alike, and ordinarily all intervals are reckoned as being within the limits of an octave. In the case of every discord the ear demands a compensation by having CHAPTER XIV. 175 the two voices in discord move into concordant relation, generally by the upper or the lower voice moving down one degree. In the case of a second, resolving into unison, there cannot be said to be a concordance compensating for the discord, as when a ninth resolves into an eighth, i ^^ U I 2 i 9 8 9 8 and even the latter hardly affords adequate compensation. Accord- ingl}^ in such a resolution as in the last example, figured 9 8, more than an octave must intervene between the voices, that the resolution may be into an octave, and not into unison. But where the lower voice moves away from the upper (as at (b) above), the concord- ance is secured without the octave distance, and such an interval would be called a second. Anticipation. The exact opposite of suspension occurs, when the voice, instead of delaying upon a tone of the previous harmony, anticipates its tone in the following harmony, by taking it before the other voices move. In Anticipation as in Suspension, the voice thus moving usually does so by a single degree, up or down, and rarely by a skip. In the following exercises let the anticipation be introduced in three ways ; ist, in bass ; 2d, in soprano ; 3rd, in the three upper parts simultaneously, each exercise being first simply harmonized. The first four measures of the first exercise are here given in all the ways, as illustration. 176 PARKHURST HARMONY, a. pil \ ii \ llf \ f]!ti .iliir^ f l |-:(g anticipation in bass. nticipation in soprano. ^ f i r r r J \?i rJ J ^ \UMJaL i fif 'ZTh P ^=^ ^ anticipation in sop. alto and tenor. ^ m f ir I- Exercises. g c: S ft 1^ ■g I .; ^ i j ^ niz^^ xi: '4 6 '6 t> 6 ? 6 ^ 5 6 6 7 4 ^ 0:fl P f J \r)r^ If ^ I JJ LJ ^ 1 ^ i 6 ^ ^ ^^ 6 6 3. * a I ' I^^ 22 * 5 6 -e- y*^ r r irr^ li'„ wi Ufv^ ^^ It will be readily seen that such an auxiliar tone cannot be used as the preparation of a suspension, thus ; ^ IE ^r* c> -^> ax «IP^ ■^ o- ff and it may be said, in general, that the preparation of a suspension must he a fundamental-harmonic tone. More noticeable are auxiliar tones of the next class : 2d. Those which occur diatonically (sometimes chromatic-ally) on the accented parts of the measure, and simultaneously with the harmonic tones, thus : i r|jJJJ | 3 . i 1 tj J i i i ^. ^ '1 Ff m s Still more conspicuous are 3rd. Those which appear by a leap, 0)i the unaccented part of the measure; in which case they must move by a degree up or down to a harmonic tone, thus : ^% n ^^ T 3X W -«»- ■o^ ¥ JCE. XE XE i xs: ^ The abrupt effect of these tones entering by a leap must be coun- terbalanced by a shorter duration of the tone. CHAP J IR XV. tdi And the last class of auxiliar tones are 4th. Those which appear by a leap on the accented parts of the measure, thus : l Vr ^lT ^i;r ^ ^^ I xx: sx: ? XE In this case, when the auxihar tone is below the harmonic tone, it is better to be distant only a minor second, using an accidental if necessary ; when above the harmonic tone, it can be at an interval of either a minor or a major second, according to the location in the scale. This is because a dissonance naturally leads downward, and if it is to lead upward, it will do so more easily if its motion is only a semitone. The foregoing classification of auxiliar tones will be easily re- membered when stated thus : (i) unaccented, diatonic or chromatic (2) accented, *' "' " (3) unaccented, by a leap (4) accented '* '' " and successively more conspicuous in this order. Such auxiliar tones as are marked x in the following example may be called auxiliars of the ist class, but they are not, strictly speaking, passing tones, as the harmonic tones between which they stand are identical : £jT] s^nv I ^7T] P an f r « i jCE XE Still, being diatonic and unaccented, they belong properly to the 1st class. Let the pupil assign each of the following auxiliar tones to the proper class. The notes not marked are all harmonic notes. 182 PARKHURST HARMONY. 1 X X X X #V^ f._.^ f ^ i ^r^i^^ ' P^ ^ m ^ As a rule, the auxiliar tone leads at once to the harmonic tone; but two auxiliar tones can be used together zi'lien both lead naturally to the same harmonic tone, thus: I s« T ffi 3 X X ^ m -o- An auxiliar tone can be inserted between a suspension and its resolution, similarly to a harmonic tone (see page iio), when the auxiliar tone leads diatonicaUy to the resolution: i^ ^ iTe-^ll^fl'^^J^^ ^f^^^ ■i^ -9- ix a m 3Sl m n: Also an auxiliar and a harmonic toiu can be conjointly inserted before the resolution, or even two auxiliar with the harmonic tone, when necessary in order to reach the resolution diatonically : r CHAPTER XV. .183 P ^^ ^ -8 H ^,^^ ^ ff^ ^±8i: ^-J ijii^Jji B TSr 42. m ^m p XXE f ixe: ST When two voices move diatonically in sixths or thirds as follows, ^ f f F I f J a XE ^ JDL ^ XE xs: XJr it is a simple case of "passing tones" in each voice. But as an in- strumental effect, a single part or instrument may take all the above tones, thus, I ^^ r fTjjjj ji ^S- xr TT] JTTl j J i> ^ in which not the adjacent but the alternate tones are thought of, in their relation to each other. It is a double melodic progression, and such a part may be called a compound part. In the several cases before mentioned, the foreign tone was one degree distant from the harmonic tone that followed it. A less frequent use of the foreign tone is that in which it is one degree 184 PARKHURST HARMONY, distant from the harmonic tone that precedes, and is followed by a skip to another liarmonic tone, thus: i i J Mi t XE » «^ 3^ ^v- ^ 3X XH X X F^m^=i^ ?V X X i "•J^JTJ] ^^ HgTffM-^ rC»- xr X X X X XX i X X J^^M i h f> 1> Progressions similar to the last illustration (b) are not so un- common. The close diatonic relation to the preceding harmonic or passing tone seems to be the justification of this sort of foreign tone. A slight variation of the above is where the foreign tone is repeated, which sometimes has the effect of a suspension prepared by a foreign tone, and is admissible only in the more rapid move- ment of quarter, eighth, or sixteenth notes. It is like a prolonged single auxiliar, or like two auxiliar tones drifting to the same harmonic tone. p fefeiS xf: tt -♦*- i 4 1: * 5 XE XE f I f ^M XE XE i CHAPTER XV. 185 Grace notes and Appogiaturas ^';i Yfn-H p ^ \ as i i are simply auxiliar tones of very short duration, used according to the previous rules. The foregoing, together with Anticipation and Suspension, ex- plains all the varieties of foreign or auxiliar tones. The following exercises are designed to give a practical acquaintance with the sev- eral varieties, and are preceded by a few special suggestions. In the use of passing tones it is better to move away from a unison than into unison, thus : good bad, m i The reason seems to be that the ear requires to be compensated for a discord between two voices by a harmony of the same voices, which it fails to get when the voices proceed to a unison. Except in rapid movement, the harmonic tone into which an aux* iliar tone leads should not be heard in any other voice simultaneously with the auxiliar tone, except at an interval of one or more octaves ; and even then it is not well to have the third in the chord heard at the same time with the auxiliar tone adjacent, excepting when the third is in the bass, i.e., in a chord of the sixth. jj„ j | i ^ jjj| | 4 .utd ^ bad. good. bad. good. :r ,. I lf f a i p 301: With a rapid movement, and especially with fuller harmony (fre- quently in instrumental music) this prohibition is not enforced. 186 PARKhURST HARMONY $ 8 ^ We are not limited to single auxiliar tones. They may occur in two or more voices, and produce a great enrichment of the harmony. They may be in parallel or in contrary motion, and of the several varieties of auxiliar tones simultaneously. ^ p \>{' II (i i ^i' I I p j*. -i-^-^ in two voices. £ £ in three voices. m i e i4-^ i^r i ^ I I ^) i I J"J in four voices. i ^ In the above examples the foreign tones are all "passing tones." It is more usual to combine a ''passing tone" in one voice with a foreign tone of another variety in another voice, thus: I i ± Tm i f 9 Jjiir'tit-f J 4 S f The use of "harmonic tones", in which any voice passes from one tone of a chord to another tone of the same chord, either singly or combined with other harmonic or foreign tones in other voices, is alwavs admissible, thus : CHAPTER XV, 187 ^ r^ SS=^ ^^ XE -O- i P XE n sy rf^^— 'fi'- f ' f '^ g^J^J'Jl^Pj XE The combinations are endless which are thus attainable by the use of harmonic and auxiliar tones. The simplest flow of harmonies can thus be amplified into the most elaborate and masterly composi- tion, which will yet be readily understood by the listener, because all this elaborateness is as it were merely a beautiful veil which only half conceals the simple underlying harmonies. Thus the above examples rest upon the following simple chords: a. .1 b. ^N J c. ^^ xc XE «±# ^ i ^ XH ^ XE ^^6 16 6 ^'6 The {nteUigibility of an elaborate composition is proportional to the simplicity of its fundamental harmonies. This is strikingly illustrated in the opening eight measures of the last movement of Beethoven's Sonata Op. 2y, No. 2, the first six measures containing only three different basal harmonies, and all the tones being "har- monic," without a single ''auxiliar." Presto agitato. ^^^^^^P ^H^^'^^^H ^ ^ XE m 186 mm. FARKHURST HARMONY, ^ ^^ g^to 9^ $y gff^CT^^^^^i ^ I J iJ ii I M s ^ ^ TCE g^ 3 SE 6 x6 5 This matter of fundamental harmonic simpHcity will be alluded to again later. The following exercises are first to be harmonized simply, as heretofore, and then made more elaborate by the use of auxiliar tones. Let all the exercises first be written with only the embellish- ment of passing tones, in whatever voice eflfective, and let them also CHAPTER XV. 189 h?. introduced in the bass. Then re-write all the exercises, using the :iuxiliar tones of the 2d, 3d, and 4th sorts wherever possible, hut only "where the effect is made more musical thereby, and noticing carefully which sort of auxiliar tones is used each time. Be careful that the embellishment he not confined to any one voice, but distrib- nted among them all. Attention must also be given to the following : Uniformity in the Rhythmical Movement. Every composition, and these exercises as well, must have a cer- tain uniformity in the rythmical movement. Thus, if the movement be mainly in half notes, the steady current of this movement would be much disturbed by having, now and then, a whole measure filled with eighth notes, thus : S3L, ^y^ i ^A-^ -&- xe: ;y> 1,1 1„ |.. 1,^1 ^^^ ff TF There is no regular flow in the foregoing, because the different currents, in half, quarter, and eighth notes, conflict with each other. It would be better as follows : JQL If the current start in quarter notes, this movement must pre- dominate throughout, with only very occasional half or eighth notes , thus : ^m « iiiiji ^^ ^ jCfc- XI. PF^F i ^ 190 PARKHURST HARMONY. -# f P £ sw a ^ * -e- 6 3 6 6 9 8 6 -6- 3, 5 ^^^ « ^ 3 5-fr g I'e P^ffr ' 87 ^ 6-43 « 8*7 ''"'^'Jyj^"''i,^f^^^ 6^6 ^ .^ ^ 4 5. m i -k^ a TT €^-€f- 22=03 ,6 B7'6 i,t> a 6 87 4 6. 3 6 H 6 1,4 'e 2 7 V6 6, ^ ^ 'I ?6 6,6 4 ts o ^ 5 8 7 7. open position i IE KZ 5 ir 6 4 3 -6- 4 3 -6- |i 4 3 192 PARKHURST HARMONY. 8. opeir position. Mu-w niM^^m M- 9. close position. -rf ''' 6? i- l-p-n i- » ^*S ^ f^eW. Wa^ Trie 3 7 « 10. M^ zc ■^►— u — c^ .\a I, 11, c 5^6 6 -t 6 ■« tl5 7 •? "7 1^ 6 4 ^ ^ S 5 9 6 4 7 12. ^ j^LdX # 5 ^ 5 ix: 6 67 4 m. open position. # ^ 47 14. close position. S ^ 5t 4 > g 9 6 6*6 9865 4 j» The above exercises admit of great variety in the harmonizing, so that each can be written in several ways. The pupil is advised to exercise all his ingenuity in the use of foreign and harmonic tones in the different voices, with suspensions, so as to acquire a fluent use of elaborate and yet natural harmonies. If further exercises are de- sired, the pupil can make use of any of the basses previously given in this work. Open position will be found far more favorable for the free movement of the inner voices, and the judicious alternation of close and open position will secure the most satisfactory musical results. CHAPTER XV. 193 Sight-reading. Open position SS ^7 t> ^^ -«^ 5 6 fio 2. m 22=:^ XE 6 «8T 5 3 7 -6r 4 8 3. yir~g 1 (9 »5-t5^ 4» Ip r; '8 7' 4 ^*- va: -wy 5 8 7 8 7 ^LU-a gC|g ^ f 4 5 Parallel Perfect Fifths. The progression of parallel perfect fifths, which is invariably prohibited in fundamental harmonies, is occasionally admissible when one or both of the tones forming them are auxiliary and of short duration, the effect in such case being so transient and inci- dental as to be hardly appreciable, while the avoidance of them might be at the expense of a smooth and natural progression of the voices , thus : 4J^iiWi^ | by#¥ p b. Lj4giLJ ^=^ ^ i 4 -J. m \f — ^ Summary. Auxiliar tones; unprepared auxiliar tones classified into (i) un- accented diatonic, (2) accented diatonic, (3) unaccented skipping, and (4) accented skipping: — Preparation of suspension must be what: — Two auxiliar tones in succession: — Suspension followed by auxiliar tone : — Meaning of a "compound part" : — An auxiliar tone having its relation to a preceding harmonic tone : — Grace notes and appogiatures : — Moving from, not toward, a unison : — An auxiliar 194 PARKHURST HARMONY. and its following harmonic tone not to be heard simultaneously: — Auxiliars in two or more voices : — Harmonic tones how used : — Uni- formity of rhythmical movement: — Allowable parallel perfect fifths. CHAPTER XVI. Rhythm. Primary, Sfxoxdary. and Auxiliary Chords. Rhythm is accentuation occurring at equal inten'aJs. Tt is the pulse or beat of music. The interval between any pulse ■and the next succeeding pulse is measured off by what is termed in music ''the measure ;'' the pulse or beat occurring at the beginning of each measure. The interval of time between two successive pulses may be long or short, but it must in general be uniform, throughout the given composition. A 'Svhole note" , A as its name implies, normally fills the measure, /j kCj * - ^ - "i. e., expresses the duration from one pulse or «/ emphasis to the next. But the emphasis, strictly speaking, can be made apparent only by the contrast of emphasized and unemphasized tones. If two whole tones succeed each other, A i the beginning of each measure has an emphasis, but it can be made apparent only by intermediate tones receiving no accent ; thus, A A i &-&■ There are two generic sorts of rhythm, the double and the triple rhythm, according as one or tzvo subordinate beats occur between the accents ; the first called double, because every second beat is ac- cented ; the other called triple, because every third beat is ac- cented. The following illustrates triple rhythm: A A , i ^ O^^G The varieties of double rhythm are expressed by the following" figures; | (or t) \, \ (or C) J, J. The varieties of triple rhythm by the following figures ; 3 3 3 6 9 12 6 2 4 8 8 8 8 4* Compound rhythm is that wherein the double and the triple rhythm are contained within the same measure. Thus a passage in 8' ^8 ^^ 4 ^^^yt^"*"! involves both the double and the triple accent . CHAPTER XVI. 195 ^^^^^^^ ^^ ^ ? If a measure be filled by two equal chords the first will be ac- cented, the second unaccented. By virtue of the accent, the first chord acquires greater importance than the second, and makes a stronger impression upon the mind. This can be illustrated by play- ing the following series of accented and unaccented chords, and after- ward playing only the accented chords, which will be found to convey largely the musical idea of the whole : i .^i jif g - ; I a ' I W I ^ u 13 n: ^ «5^ i ^ XE ■j* .. - --=-^^-^-=— iJ-^--7; - g - -^-^ ij—ii — r f -(-— ^ — 1 '^-—\ The same thing is true in triple time, though less markedly, since Tjy playing only the accented chords, tivo are omitted for every one that is played. J' a J JU.. Y^-r. J 1 »■ —m- J - J , ^-»-| -4»J5-3 1 r— r 1 .i r«— ^iH 1 2 ^'iJjfJI o- 1 11 'i U 1 :i The foregoing examples illustrate the fact that even fundamental harmonies are not equally important. As indicating the relative im- portance of the accented and the unaccented fundamental chords, the former are called the primary, the latter the secondary harmonies of the measure. 196 PARKHURST HARMONY. Passing Chords. The term "passing- chord" has no precise limits of definition. It is appHed in general to all unaccented chords in which some or all of the voices move by one degree (diatonically) from one accented chord to another. The term would also be applied where, in a series of passing chords, one of the same sort occurs on the accented part of the measure; as those marked "^ in (c) and (d). Passing Chords are of Three Distinct Sorts. 1st. Fundamental harmonies, with a regular progression as such; illustrated above by all the passing chords in (a) and (b). 2d. Those in the form of fundamental harmonies, but zvithout the proper progression as such. As in the first measure of (c) and (d), with the normal progression as follows: ^ ^F|^-^ 3^ ^-^ proper progression of chord of the second. X 22 similar instance. W^ ^ -e>- 2 Such chords, though having the form of fundamental harmonies, have not their force, but are of the same nature as Auxiliary chords explained below. CHAPTER XVL 97 3rd. Aiixiliary chords This term is applied to all harmonies in which one or more voices contain unprepared atixiliar tones. (When the auxiliar tones are prepared, the chords are called "suspensions.") When the unprepared auxiliar tones are also passing tones, there result passmg chords of the 3rd sort. The three sorts of passing chords are illustrated thus : ffi^i-a- l lLU * i - ii -U i 'l'' jOl. IX ^ fT TT IX first sort. , second sort. m -o- xs: 6 2 6 7 The above choras of the second and third sort may be analyzed either as auxiliary passi)ig chords, or as fundamental chords with passing tones. Another sort of auxiliary chord frequently used is that in which the auxiliar tones are not passing tones, but are taken by a skip, as already explained in the chapter on auxiliar tones ; or the two sorts may be combined in the same chord. Let the pupil closely examine the following-, and determine the fundamental and auxiliary chords, and the different sort of auxiliar tones. _,« . Li i-A ^ V The Harmonic Support of a Melody. In the definitions of the Introduction, the distinction between melody and harmony was shown. The two are radically different, and can be to a considerable degree separated from each other, hut not entirely. In a succession of chords there may be nothing apparent that seems worthy the name of melody, yet doubtless there cannot 198 PARKHURST HARMONY. be even the simplest succession of connected chords in which the experienced ear cannot detect at least a faint quality of melody, either in one part or another. The utter divorcement of melody from harmony seems impossible. But how is it when a melody is per- formed which is absolutely free from all harmonic accompaniment? Do we then have melody alone, pure and simple? No, for in such case the melody is the audible edge of an inaudible harmony. Melody is linked into harmony, and, in its performance, drags the harmony more or less distinctly through the mind. When a well known melody whose harmony is familiar is performed, the associ- ated harmony is quite clear in the mind of the hearer. In a melodic passage like the following, I ^^ XE the intelligent musician will find that he is accompanying the melody with a delicate, filmy, harmonic support, like this, for example : i J J J j ij J J J s^ 3X -^ 3x: ^ XE XE XE There are four ways of determining such unexpressed attend- ant harmonies : I St. By the tones of the melody itself, when they are all, or nearly all, elements of the underlying harmony, thus : i^^ ^ 4 )1 _ I [o I -^ — —L.^ 1 J rriri[j:£;JiTiTj ^ t m X i XE CHAPTER XVI. 199 2(1. By the metrical recjnirenients of a composition when de- manding the cadence-formula (see Chap. XTX.)., as at the end of a composition (as in last measure at x). 3rd. By the last expressed harmony, when the tones of the mel- ody are not conspicuously foreign to it, thus : ^ r:\ ]7TJ^ /C\ ^ J i ■5i W=^ g *~« /C\ m «> ^ (This shows how the same melodic passage may rest on entirely different harmonies). 4th. By the laics of natural selection, according to which the melody will be supported at the most important points by the prim- ary chords ; elsewhere, by harmonies that are simple and closely con- nected, thus : m m m W¥ m ^ ^ 5X p xt rr g ^ ^= ~rT H -O- icr n i> XT ^ -€>■ rs: XE 3CE I IV In analysis, the ist and 3rd methods will cover most of the cases of unharmonized melody. Octave passages are seldom so prolonged as to require more than two or three unexpressed har- monies. An isolated note is either a harmonic or an auxiliar note, accord- ing to circumstaT'ces, thus : tf=FH I 3X -O- harmonic. auxiliary. m JOE XE i 200 PARKHURST HARMONY. Defective Harmonies. Not infrequently one or two elements of the chord are unex~ pressed, as in duet and trio passages, where the circumstances of the case must determine the full harmony. m b.' «z=a z C? • — KT tenor omitted. ' y-H' J \p ^? TW IDC -«*- '••^'r':i | JJL i iV.^ -o- ^s alto omitted. I . M & M #ii & (The voice omitted in (a) and (c) is supplied in (b) and (d). The harmonic analysis of duets and trios will show that the omitted parts are expressed in the accompaniment. In the first of the following exercises a single voice is omitted, and in the later ones, two voices. They afford opportunity for the exercise of all that has been thus far learned in Harmony, and de- mand careful study. Let them first be filled out so that the har- monies shall be the "fundamental chords", and afterward let the added parts and also the original parts be moderately embellished with suspensions, passing tones, etc. Each exercise will admit of more or less variety in fundamental harmonies and embellishment, and the pupil is advised to write each one in as many different ways as possible, using ''open" and ''close" position in each exercise, and alternating as the case requires. Exercises in Defective Harmonies. If the following exercises prove too difficult for the pupil, let thein be reserved for the "review" (see page 251). After completing the harmony in each exercise, let the chords be analvzed CHAPTER XVI. 201 1. supply tenor in 1-3, * ^ m Z2==«CIS f 9-9^ Tt^ ■■wT \U' ^m rr'r^r'rrir 2. jn'f-MJ.iNJ i a fi > g ' fi ) iS TT ^ r ' r^i' ir^J|°<^r I r ^1^^ l^ 8. ■] ,1 i j J ij i Hr ip T- 331 ^=T= xr >L It ^ r 5 1 ] m' <> \% '^A-t^ lo^ 'i^^ 14^ ' ^> ^ .fc^;^ 1 1 ^•''" 'l-r'' '° '" '^ '"" I ^ji supply alto in 4-6 ^ ^ <5^-^d ^ iJi^ii^^ .^-=^.^i.Jj ^>^g" | » | o \[' P\r xi_ ^ xn -€>- i °- I J ,J I J J^r^i 1 ^-^ iJfe ^^^ r J ^ 1 C E ^^ ^M ^ ^ 4t^ ^^ -c^ 33: X5~ 202 PARKHURST HARMONY. 6. lMt±±AaU - J I J -I 'I [ -O- W A ^^ ^ ,,] J ^ .^^ i XE fTT XE lij|t|^J ^h^ H J ^ |.) J <© ^ XE g^ ^i i « ^ ^^iJ J -*>- M r f r-i^ i 7. supply soprano in 7-9. ^ rr^^ -o- 'ii ji yj ^^ 1 Ff?3fT^EpF?f3f pzi:& xn i rifM" li^r r K iO- # ^e- -€>- J^^K J ^ m 12. jJj^^j^ l "- |o JMM ^ ^ : . 1. a X»^ J3L ^ 13. supply alto and tenor in 13 -18. supply hr^jyylyU ^ fe?^ j^ii o rj ^^- ^ # ^ 1X< ^^ f r 14 1 ^a .J ,- ! 1 1 -h- 1 J J J \ ' * i— — 5^ /J ^;^- * ^ ^ ] 1-^ ^^ o — P ' Le. -t— r ^ l^^ ''^ ^ |j-i-^ r^-^^j|j- 332 P ? izz-r-w -j^-P-^f^ p' f r ^ f lo. r xr: P Jl.!-ilJJJj|J^ I ''^ki •'^ I JJ ^''■''(- I rJf'r ] g-1^ # p^ ^",JJ,jJJ , J-^JyJJj|-;jj|jJg^J^JJjj ^^-i^ irr r irrrr i r . VMfffrir ^2= 204 PARKHURST HARMONY. 17. i y — q ^ J | J .M 1^ -M^ s 1^ ^ sac 300 r r V r r ^ 18, I JJJ | ,UJ J I J. JM^M^ ?>'"j,rfi' I' irrrfrrr ^ u ,, i > -'■ i'ljj i .i.j,] ijjjj m I g ^ I ^rrr r TN' 'f r r 19. supply soprano and tenor in 19-20. ^ N-^-H'-^H^fVf-' rr r Vrr rr m H^7— ^ r'rr Tj^ ifyi^-i^-^rr^ t f Tj .JO. ^^^^M^i' f Vi'^^rA^^ ' i'r '-' i CHAPTER XV 1. 21. supply alto and bass in 21-22. 205 ^S.«J ^J ^ i ^ s ■g— ?: jj^J jjjjJJU JQ_ ^ if i'i I ' 'i ' M I J^JJJ O- Xi_ J^j ,f,^ ^^ ,1>JJ jiJ j S S XE 22. ¥''J i Jj i ,i. ii „ i j i .i,i^^^^ TE ^ =U: i^^ J^^i i J ^ ^sr supply soprano and after. ^ . fr i f'r i ^" i - iii ' , ; ,i '." i l^ X3l -O 24. ZKX ^ Slow Progression of Fundamental Chords. There are limits in the rapidity with which fundamental chords can follow each other, with ease and satisfaction to the mind. While these limits are not mathematically precise, there is a wonderful con- currence of opinion which forbids that the elementary chords should follow each other, on the one hand, too slowly, or on the other hand, too rapidly. In the former case the fundamental movement is too monotonous; in the latter case the mind is required to exert itself unduly to grasp the movement. The normal tempo of the elementary chords is one of the requisite qualities of a successful performance. 206 PARKHURST HARMONY, Ease of comprehension of a musical production depends upon the moderate movement of its fundamental harmonies, and their natural connection. These conditions being complied with, it matters little how rapidly the individual tones and chords succeed each other. Multiplication of "harmonic tones" or the reiteration of the self- same harmony creates no new harmonic effort for the mind, and auxiliar tones and chords, in proper subordination to the fundamental chords, do not obscure the transparency of the harmonic frame- work. As regards the multiplication of ''harmonic tones," no better illustration of this truth can be given than one that has already been -cited, viz., the opening measures of the last movement of Beethoven's "Moonlight Sonata" See page 187). Fine illustrations of a clear and simple harmonic basis, yet ex- hibiting great elaborateness by means of harmonic and auxiliary tones, is found in J. S. Bach's organ preludes. The use of harmonic and auxiliar tones in the bass, as is so characteristic in Bach, gives an appearance of far greater harmonic complexity than really ex- ists. Compare the following, from one of the above named com- positions, with the subjoined "harmonic basis". I ,, nnnJTn h^^ h-M ^' W ^^^ S f- rf i CHAPTER XVl. 207 I *^ ^ -G^^ I fa S 3* S> S» 5^ = t-i I g ^ i zi p^ ai ^ p 8 iT i <: jmj?Ti^.;^^J7n ^ * « * S ? *i ^ f * i w^ ^ j^jJlsm^ ri^iil F^ f=c p r s ^ ^ j.4--tj-u-4^m j ^F,r- m h^ w ^m m ^= 210 PARKHURST HARMONY. In order thoroughly to understand the development of an organ- point, let us take the following example of basal harmonies : The above are all fundamental harmonies, except the two chords marked x, which are auxiliary. If the harmonies at this point had been abbreviated thus, / : ' 1 J11H 1 ..1 f s xf: the auxiliary chords would have been in their normal subordinate relation to the fundamental chords, and the A in tenor and F# in alto would appear plainly as passing tones, and D in soprano would be an anticipation. Compare the original and the abbreviation care- fully, and the essential likeness at once appears. In the original the auxiliary effects are, so to speak, magnified by longer duration. This magnifying of auxiliary chords is legitimate as a counterpoise to the prolonged assertion of the fundamental G-chord zvhich is maintained by the continuance of the pedal-note through eight measures, so that in the aggregate the fundamental and auxiliary chords still main- tain their normal relation. In other words, the gravitation of the harmonies, through all the organ-point, is to the G-chord, which justifies what w^ould otherwise be a disproportion of auxiliary effects. In the same way other parts of the organ-point may be embellished with auxiliary chords such as, in other circumstances, would be out of proportion, as in the following: 1^ -,-) iff^i ^i >T^ 4'' hi '1 1 - 1 ■■ 1 ^ >)■ ' 1 =i= — 1 1 1^. Lo Lo — J-o — L^* — Lo ^ ' » CHAPTER XVII. 21 Ordinarily the chords marked x would be expressed in quarter or eighth notes ; but whoever feels the magnifying of the entire effect, and liears the G-chord, sounding through it all, will consent to the prolongation of the auxiliary chord. The above harmony can be maintained, and yet made less angular by the use of passing and harmonic tones, thus : i iC;i.-Jc:>L^t=:;J-L-U nrrrfTU^fzrrnf «*f E xn It is well understood that auxiliary chords are tributary or grav- itating to fundamental chords, as seen in the foregoing illustration in half notes. But in the last illustration (in quarter notes) we find chords (marked x) which gravitate to the auxiliary; these are really sub-auxiliary , and this is precisely what we should expect ; for when auxiliary chords are advanced to the duration of fundamental chords, there would naturally spring up a class of chords that would occupy a correspondingly subordinate position. We shall sometimes find such sub-auxiliary chords in a passage that would not be called an organ-point, but all such cases will have more or less of the quality of the "organ-point." The above can be still furtlier elaborated, which will increase the auxiliar and sub-auxiliar effects : \ll r r i - If f r ■V" — 2 — w — 1 f — s~ f%=— — ^ -r^£-f-»- ^4=. H ' -r-#— ^ o X X )t X X ^ X Lo o X Lmmi ^ 212 PARKHURST HARMONY. ox o X#X |»XO*tA OXX ^ ♦i^ -^ The above is partially analyzed, as follows: o means fundamental chord X means auxiliar chord, # means sub-auxiliar chord. The pupil should study the above sufficiently to recognize the drift of sub-auxiliar chords to auxiliar chords, and of auxiliar to fundamental chords. This relation of the different sorts of chords, and the immediate and ultimate gravitaion of all harmonies, can be exhibited in a tab- ular view, as follows : GRAVITATION of sub-auxiliary to auxiliary chords. Hs r^^gi-_ A I Jf r1 J ■ I , X <^ X <^ X . X I X mmmms^Y' err 5Ttx ' ^x x^x m r r ,ii^jj|j..... ^T^ I cv ^ ^^^^ of auxiliary to fundamental (seventh and common) chords. i^ fl^fQj^ J-^^^ Jjj^OfiJS XE 1 ^S f I o » Xfl CHAPTER XVII. of seventh and common chords to common chords. > * >:.b« 5 ^i^ ?^^ XXIM zz:3t^ gl ' - ' -l- - pj^ fl" f -^ CHAPTER XVlll. 219 M XT f5^ 2 "li^^c ^ ^►^ Xli M g g 31: JCE nr ^-^ I Hh [H^ipifiito rirVf i i|f ri4Jr ^^ S #3^ -O- ^ ^^ S22 -^ i |€t ^ ^S ^ ^9G- ^^ I ^ J4^ J y a 31: ^ 2=^ m I a ^ s ^ ^^ 1^-77 ' i Mf h J J l pf' l f' zz: ^ ^^4fff]fWj sg ix: CHAPTER XVIII. Modulation. The intelligibility of a musical composition requires that the scale he evident in which it is composed. A scale is adopted by the listener, (unconsciously indeed) at the beginning of the piece, and the harmonies must so proceed that the same scale is clearly main- tained, or that the mind, without too much effort and suspense, shall be able to assign the harmonies to a new scale. The possibility of maintaining the old, or of adopting a new scale, lies in the pre-em- inent significance and importance of certain harmonies of the scale. By previous examination of the several tones of the scale it has been seen that they are not a mere series of tones, distinguishable from each other only in pitch, but that they have inherent individu- alities in their own quality or coloring, and are linked together by evident tendencies of motion, which give to the entire scale the char- acter of an organism. The two chief tones of the scale were seen to be the Tonic and the Dominant, which may be called the focal points of the scale. This quality of Tonic and Dominant is absolutely independent of pitch, and is reflected from any tones that occupy these respective positions in a diatonic scale — reflected from them, ^hen held in a certain light, precisely as a particular color gleams 220 PARKHURST HARMONY. from a diamond when turned to the proper angle. Thus the one tone G *: b* S has the quality of the Dominant in the key of C, the quality of the Tonic in the key of G, and the quality of the "leading tone" (the seventh) in the key of Ab. And similarly every tone may thus be made to reflect the quality of every degree in the scale. What is true of Tonic and Dominant, as regards their importance, is equally true of the common chords founded upon them. They are the predominant harmonies of the scale, occupying the significant points in the series of harmonies, and toward them the other har- monies gravitate. This is simply a statement of facts in the case, capable of verification by the analysis of all w^ell composed music. The pre-eminence of the tonic and dominant harmonies is also plain- ly evident by their greater frequency than that of any other chords in the scale. To become convinced of this double pre-eminence, of position and of frequency, let the pupil analyze the first part of dif- ferent compositions, say fifteen or twenty measures, or as far as the original scale of the composition is plainly maintained. To illustrate the method of analysis we will use the first eight measures of the Adagio of Beethoven's piano Sonata, Op. lo. No. i. kK^ I J "J^lp^ c\^ m rr r- ^ ^n'-i>ig i 7 «=^ Fundamental harmonies. ^ i ^ itJ^ ^ ^ 3 ^ 6 rt- CHAPTER XVIII. also the first eight measures of his Sonata, Op. 2, No. 3. Allegro con brio 221 ^ rviic^iu cun orio. , . ^ -Q. r g - ' Fundamental harmonies. ^s -^^ ^ ? E 6 6 5 This exercise of analysis should be practised in the case of sim- ilar passages, which the teacher can select. The most important positions for chords to occupy are the open- ing and closing of the entire composition, and of its sections and periods, also the accented parts of the measures. The dominant chord follows long after the tonic chord in impor- tance ; and the subdominant chord is much less important than the dominant. While these three, collectively, have a pre-eminence over all the other chords of the scale, which warrants the common classi- fication into Primary and Secondary, it will be found that the main- tenance of the existing scale is effected almost entirely by the pre- eminence of the tonic and dominant, and chiefly by that of the tonic. So long as this pre-eminence is maintained the mind retains the original scale, and when the normal relation of principal and sub- ordinate chords is altered, the mind, sometimes at once, oftener gradually, renounces the old scale and adopts a new one. This sub- stitution of a new scale is called Modulation. The assertion of the scale ordinarily occurs in the very first chord, and the scale being adopted, no change occurs until it is felt that the tonic chord of that scale is not receiving its due emphasis, and the mind casts about to 222 PARKHURST HARMONY, determine in what scale the normal relations of the chords will be restored. It should be remarked at this point that the only possible method of explaining Modulation is to make it evident to the student what his own mental processes are in this proceeding. Modulation is a spontaneous act of the mind in each individual listener. He cannot be compelled by another, he cannot even compel himself at any given point, to modulate. It must be a spontaneous operation .induced by his musical sense of the harmonies in their relations to each other. And any one fully understands modulation just as soon as he clearly sees how his own mind acts in the process. For this reason it is imperative that every statement here made should be fully verified by the student, by examining himself to find whether he act- ually does what is here asserted. The following passage would be judged by the eye alone to be in the key of C, as there is no signature ; but judged by the ear, which knows no signature, the first chord , suggests the G-scale, and the whole passage lies consistently in that scale, because of the prevalence of the primary chords of the scale, and especially because of the emphasis and frequency of the G-chord. And yet every chord of it belongs equally to the C-scale. If a piece opens as follows: Allegro the first scale suggested is the G- Scale, but if played allegro, this first thought is dissipated by the emphasis that falls upon the C-chord in the second and third measures, which would be an unusual chord to emphasize as the subdominant of G. Yet in this example every chord belongs equally to the G-scale. The foregoing shows that any CHAPTER XVIIL 223 passage of music is in reality in that scale in which the ear interprets it to be, independent of any and all signatures. Suppose a principal section of a composition in the key of C ends with a complete cadence thus, ¥ r fH 5Z: 3X « /Cs ^m thereupon follows trrHtr fnTf^ m. J r i fr.fff ¥ ^ The musical nonsense of beginning a new division of the piece with a chord so subordinate as that of the subdominant, induces the mind instantly to adopt the new scale of F, and to read the pas- j^ge in that scale, although it contains not a single chord foreign to the old C-scale. F now takes the coloring of the tonic, and C that of the dominant. ;.• Thus far we have said nothing of accidentals as a means of mod- ulation, for WQ have used none. The common fallacy of supposing that modulation hinges upon the use of tones foreign to the scale is sufficiently exposed in the foregoing. The absence of accidentals cannot prevent a modulation, nor their presence cause one. Modula- tion can be effected instantly and easily without them, and on the other hand they can be introduced numerously without our feeling any inclination to change the scale, thus: ti^^' h i 'i'^^ ifc=# ^ 5 t ^'^S^lF^ • This is not saying that accidentals are not frequently of very great assistance in effecting a modulation, nor that the chords in the above example that contain them do not offer especially favorable points at which the mind cottld be diverged into a new scale. But 224 PARKHURST HARMONY, they are futile in themselves to accomplish the work. The musical sense must first require a new key note for the re-establishment of the normal relations of principal and subordinate tones and chords, before a modulation can take place. Suppose we have the following progressions, 1. ^m f ? r m i f 1=^ have we modulated into the key of G? Each one must study his own feelings to determine. If one person says he has utterly given up the C-scale, and adopted the G-Scale, then for him it is a complete modulation. If another says he looks upon the F# as a substitute for F (producing the more agreeable major chord of D) and that he regards G as still the dominant, then for him it is no modulation. If followed immediately by this phrase, ^4-iJJj4^ i r^ ^^^ i ^ which plainly lies in the C-scale, and the two passages are per- formed continuously, doubtless almost every one will read the first •as lying in the C-scale, with the simple substitution of F# for F. But if the first phrase be continued thus, m I u * XlL P^ r f rr -O- TT XE «^ W ^ the above, being read more easily in G, will react upon the closing part of the first phrase, and influence one to the adoption of the G- scale. That is to say, the closing part of the first phrase is ambigu- ous, and ambiguous phrases arc usually interpreted in the light of what follows. This ambiguity of a phrase (as regards its key) is one reason why the first hearing of a composition is more difficult CHAPTER XVllL 21^ than the second. When once famiUar with the piece, the mind knows where to fix its modulations. It is easier to modulate into the subdominant than into the dominant, (for example from C into F, than from C into G). For if the G-chord is emphasized, it may still be the emphasis natural to the dominant, but the emphasis of the F-chord (a comparatively subordinate chord in the C-scale) so disarranges the normal relations in the C-scale that F is very readily accepted as a new tonic. Comparatively speaking, all such suspense of the mind is of in- frequent occurrence, and of short duration, and familiarity with the composition results in assigning definitely to one scale or another many of those passages which at first hearing were ambiguous. Still, there is an exhilaration in such suspense when the mind is not thereby overtaxed, whicli is one of the many devices in the compos- er's art for preventing monotony. Tlie readiness or aversion of the mind to interpret an ambiguous passage in a new scale depends greatly upon a circumstance which must be spoken of. At the beginning of a piece one expects a clear announcement and somewhat prolonged maintenance of the scale, and very early in the composition any modulation is distasteful, as it evidently mars the unity of it ; but after a time the original scale be- comes monotonous, and then a new one is as refreshing as before it was repellant. The mind also becomes quickened in its action, as the piece continues, just as it does under any sort of exertion of its powers ; and in this condition modulations can be effected with ease and delight, which otherwise would be laborious and painful. And in the climax of vigorous activity the mind can flit from scale to scale with most extraordinary facility. We now proceed to speak of the different sorts of modulation, as a preparation for the pupil's own practice of the art. Scales may be classified, as regards their relation to each other, into allied and foreign scales. This is for convenience, and not strictly accurate, as it. suggests a radical distinction that does not exist, for nearly all the scales commonly spoken of as foreign to each other really possess various degrees of alliance. The alliance of scales consists in their having tones in common, and to a degree the greater the number of tones in common, the closer the alliance. Thus the scales of G major and F major are the most closely allied to C major, as the tones of each of them are the same as those of C, with one exception. The scale of D has two tones different from that of C. A has three tones, etc., until finally the scales of C and CS have not a single tone in common. Also those scales that have the most 226 PARKHURST HARMONY. tones in common have several fundamental harmonies in common (compare those of C and G), while the less closely allied scales have only single tones in common. As regards modulation into ''foreign" scales, the different de- grees of alliance counts for little or nothing, it being as easy to pass from the key of C to that of Db (these two scales having only two tones in common) as from C to D, which have five tones in common. The scales of the dominant and subdominant of any key, to- gether with the relative major or minor (as the case may be) of that key, are commonly known as "the related scales" of that key. Thus the "related scales" of C major are, A minor, G major and F major. The related scales of C minor are Eb major, G minor and F minor. (Let the pupil name the "related scales" of several different keys, major and minor). 1st. Modulation into the relative major or minor (as from C major to A minor, or vice versa). These two scales are so nearly allied that without effort one i> able to hold both in the mind simultaneously. Their relation is much closer than exists in the case of any other scales. This closeness of relation is well illustrated by the fact that the syllables of the major scale (Do, Re, Mi, etc.) are retained for the same tones of the rela- tive minor, so that the key note and the dominant of A minor are called "La" and "Mi", instead of Do and Sol. This is the case in the so-called "moveable-Do-system," — the only sensible system, by the way — wherein the key note of every major scale is called "Do," and the fifth of the scale "Sol," etc. Of course, in the "immovable- Do-system," (in which C is always called "Do," D "Re," E "Mi" and so on, whatever the scale may be), the retention of the same syllables in the minor scale that are applied to the same tones of the relative major scale does not so signify the close relation of the two scales. The transition from a major to its relative minor, or vice versa, is well nigh imperceptible. Thus G#, the characteristic tone of A minor, may be regarded as an incidental substitute for G in the scale of C, and the following chords, * t. m ^ m if occurring in a passage evidently in A minor, would be regarded as the common chords on the 4th, 5th and 6th of that scale; but if the CHAPTER XVlll. 227 context was in C major, they would be thought to He on the 2d, 3rd and 4th of that scale, with the use of G# to produce the stronger major chord of E. As a matter of fact, the relative major and minor scales so melt into each other that it is impossible to use the term Modulation in respect of these scales, as signifying as much as where there is a more radical and unequivocal reconstruc- tion of the scale. The close alliance of these scales makes it possible for the major and minor complexion in faint degree to sweep in rapid alternation over the harmonies, like lights and shadows over a landscape, and the mind is not confused by the labor of a new scale- construction. Where one rhythmical division of a composition ends plainly in major or minor, and the next begins with the relative minor or major, there is a definiteness in the assertion of the new "mode" or quality that would be characterized as a genuine modu- lation. The full adjustment of the matter must be found by each student through the examination of his own feelings, as he listens to the alternation of these scales. The interplay of major and minor is perhaps most frequently illustrated in chorals, which it is advis- able for the student carefully to study, and then compose simple modulations of the same sort. 26.. Modulation into the other "related'' {dominant and sub- dominant) scales. A great many of the so-called modulations into the dominant and sub-dominant keys are in reality not so. A modulation is completely wrought in the mind only when a new tonic is indisputably necessary for understanding the harmonies. But the harmonies of the domin- ant and sub-dominant, and especially the former, having already fre- quent occurrence in the old scale, and thus capable of ambiguity, longer time is often necessary to give that unequivocal pre-eminence to either of these chords that shall lead the mind to a full modulation. Accordingly the precise point of modulation into these scales is very often indeterminate, and different minds will modulate at different points. The difference must be recognized between the mere sug- gestion of a new scale and its full acceptance, and there can be all degrees of emphasis in the suggestion, prior to its acceptance. A tonic-chord is emphasized not only by its own use, but by the use of its dominant-seventh chord, whose resolution is so naturally into the tonic-chord that one seems to hear the latter by anticipation, — a prophecy of the tonic in the dominant-seventh. Thus 228 PARKHURST HARMONY. ^^ 30L the first chord, on D, suggests the following G-chord, and so empha- sizes it, and similarly the C-chord gives emphasis to the chord on F, by its almost inevitable resolution into that chord. Advantage is taken of this fact to emphasize the chord which it is desired shall be taken as the new tonic-chord, by having that chord precede which shall find its most natural resolution in the new tonic-chord ; that is, the dominant-seventh chord of the new scale. Thus we see how the accidental (F# in the first case, B^ in the second) helps to the emphasis of the following chord, and thus assists the modulation, while powerless of itself to cause it. The modulation at this point is as yet only suggested, even if the harmonies move slowly, and the emphasis of the new tonic-chord must be followed up, to eflfect a complete change of scale ; and at what point the ambiguity ceases, it may be very difficult, and perhaps impossible to tell , thus : to be played slowly. i *v m XE -ey- XE 33: ^ JOE « m -^^ ^ -o^ 33r XT ^T" m ^^,0 A^ XX. -t^ XE -O- <">- XE ~r¥~ -€V ft=^ Aft tft A> fS=q 15- <> fS=i —^ 4> <*■ ii — J *^ 1 ^ ** t> 4T L-o 4> ^—4 Where similar harmonies follow each other rapidly there may be scarcely the suggestion of modulation, and if the sequel is continued in the old key, the mind, when it has become familiar with the music, will maintain the original scale, amid all the accidentals which, under other circumstances, would help to suggest a new scale. This IS one of the ways in which a person understands a composition better on second hearing — he has learned how to interpret some pas- sages which, as regards the scale, are ambiguous, and is helped in reading them by a knowledge of the sequel. If, as sometimes hap- CHAPTER XVllI. 219 pens, a passage will give equal sense in the original and in the new scale, one person may read it in the new, another in tlie old ; that is, one modulates, the other does not. Sometimes by a slight alteration, a passage that belonged plainly to the original scale can be read in the new scale, when that scale has become estab- lished in the mind, and a peculiar effect of identity and difference is produced , thus : irt C. - - .t inG. ^^^^^^g * i ^^■Mt-± -t ht^^ ^^fS^Jl^ i ;i ^ffl Let the pupil at this point continue his study of modulation in simple vocal and instrumental compositions, with special reference to the modulations into the dominant and sub-dominant of the original key, observing how they are sometimes instantaneous, some- times gradual : and then let him connect simple chords in such man ner as to bring him from his original scale into its dominant or sub-dominant. His first eft'orts may be crude, but with continued practice he will rapidly acquire the technique of the art. 3rd. Modulation into the more remote scales. Modulation into the "remote" scales is much less frequent, but far more striking and beautiful, when properly introduced. As in such modulation there will be none of that ambiguity such as we find in going from tonic to dominant, there will be little or no diffi- culty in obliterating the old scale and establishing the new one, and in this respect this class of modulations is the easiest. On the other hand it is at the same time difficult to make a satisfactory modulation of this sort, for the reason that, the old scale being obliterated be- fore the new one is established, the harmonies during the suspense must with special consistency and musical effect cling to each other, and so like a bridge bear the hearer over to the firm ground of a newly established scale. Such a modulation may be attained more or less quickly, according to the wish of the composer and the re- quirements of the situation ; either 1st, Instantaneously, I ^ jj !« ii^'-'-i i ^ s s -€»- 230 PARKHURST HARMONY. which is technically called a "transition," and occurs most frequent- ly in passing from any major scale to that which lies a major third belozv (as in the example), and is most conclusive when the "transi- tion" occurs at the beginning of a new rhythmical division of the composition ; or, 2d, by means of one intermediate chord (often the dominant- seventh chord of the new scale). ^^ ^ Db Dt ^ m m tiF acy— Jz m '>' . ] rf\T * i 3X o- As a most serviceable intermediate chord we can avail ourselves of either of the chords containing an augmented sixth (the aug- mented sixths the augmented sixth-and-fifth, and the augmented sixth-fourth-and-third), as the resolution of these chords brings us to a harmony which can readily be interpreted as the tonic harmony (often in the second inversion, as a J chord) of a new scale. The pupil is advised to make a careful review of the chords con- taining the augmented sixth, and he will find that those founded on the third and on the sixth of the scale, which are unser- viceable when the composition is to remain in the old scale, are very valuable as a means of modulating into foreign scales. But it is to be observed .that when we modulate (as said above) by means of on£ chord, although the harmony following that chord is very naturally accepted as the tonic or dominant harmony of the new scale, yet the new scale is not so absolutely unequivocal, that violence is done to the feelings if the following harmonies bring us out into still another scale. The use of the several chords containing an augmented sixth m effecting modulation is illustrated in the following: from C major to A minor. C major to B minor. --^*3 — 'HH— ;iz^:z:#==fe=i%| 4 ^^-^4f ^ ^ — ' — 1 — 1 — ■ 1 1 p h«4 CHAPTER XVllL 231 C major to E minor. C major to B major ^ i <^ f-fp f zt ^ H PB= ^ XE XH -O- 5 The modulation is effected at the ^ chord into which the aug-- niented chord resolves. If the pupil plays the examples slozvly and attentively, he will feel the root of the chord to be the tonic, and the hass to be the dominant, of the new scale. By giving to this resolving J chord a major third (instead of a minor as above), we modulate instantly into the major scales founded upon the same letters , thus : into A major. i \ i h XE XE W XE -^ ^ i m ^ XE into B major. m ^ ^m i i jA j}i j^ ') " 1^ There are still other modulations through the intervention of a single chord : to F minor. I #; re 1 ^ p^ 232 PARKHURST HARMONY. toE minor. F^f«; P X » xs: i to Et major. to E major. i xc lg #^ ^rrs^ ^ XT m: m r i f r 3X The above modulations are not all equally successful in fully es- tablishing the new scale. A modulation that is attempted with the intervention of only one chord is always more successful with a slo7v movement of the chords, as the mind thus has time to prepare for the change of scale. The reiteration of the intermediate chord, either identically the same, or with more or less change in the posi- tion of the voices, will usually make the modulation perfect; thus, the last of the above examples can be in this manner prolonged, yet without using any essentially new harmonies, and the modulation in- to E will be unequivocal , as follows : ^ xx. i i xr Any modulation which would appear hasty if the intermediate chord were at once followed by the new tonic harmony, can be made satisfactory by this method of reiteration and delay, and the pupil is advised to practice the art of prolonging the modulating chord, by changing the position of the several voices, with special attention to the melodic character of the soprano, which will divert attention from the sameness of the harmony. 3rd. Modulation by means of more than one chord. No new principle is herein involved. Instead of accepting the next chord following the first foreign chord as the tonic or dominant of the new scale, the composer does not settle upon that key, but in- troduces one or more chords wliich compel the hearer to gravitate CHAPTER XVllL 233 into a different scale from the one first suggested. Thus there may be a mere glancing at different scales, fully accepting only the last one into which the foreign chords lead, or sometimes there may be a distinct modulation into a new scale, followed immediately by a distinct modulation into still another. Circumstances must deter- mine the propriety of this prolonged suspense and special effort of the mind. What would prove a shock to the feelings near the beginning of a composition, is often a pleasurable sensation after- ward, to relieve the monotony. In many cases it will remain an open question whether there be several distinct modulations, or whether a number of new scales have been only more or less strongly sug- gested. The following examples will suffice to illustrate this last sort of modulation. to Fj^ nfiinor. I i U b. to D major. u ^ ^m XE ^? ^ a^i 2SS w-1 ?^^ ^ ^ m \?p \) f j rf¥ V-W ^> l#p \ to C^ minor. i^ c. -o- XE i ^ ^ M W 4^ ^^ V=\ m y^ i ^»\^ ¥ f tec d. to D minor. to E\> minor. M fjfjf -^ s m :#^ o ^ feM «■ -^ ^ ^ tJ U g m -o- y-i;^> feg *^*s^ p^ Izo: ^^^r^ "jiz: xm ^^p- WDE. 234 PARKHURST HARMONY. Enharmonic Change. In the second measure of the foregoing ilkistrations (a) and (b), the tone that is expressed by Ab in alto is continued in the next measure, but thcie expressed by G#. This is for the sake of having the notation express to the eye the proper relation of the tone in the chord to which it belongs; The harmony of the third measure is a common chord founded upon C#, the fifth of which chord is G#, not Ab. Such a change is called enharmonic change, and may occur in several voices simultaneously, thus; It is an interesting fact that even after a new scale has been per- fectly established, and the old one apparently forgotten, there is still a lingering memory of it in the mind, so that it is easier to re- assert the old scale again than to pass into any other. In accord with this fact is the requirement that in general a composition should end in the same scale in which it began, to maintain the proper unity of the composition ; and yet, between the beginning and the end, the mind may have perfectly established itself in a dozen different scales. Probably the simplest, least obtrusive, and most successful method of passing into a remote scale is by changing the third in the triad from major to minor, or from minor to major, in a succession of slow harmonies, thus : to AV major. to G minor. k> rWi^ i M -^ l^j. i'-^ ^'^g I '-n lt.-§ l^'-L^ 4-r^-^ ^S ODE O i 4»— i i¥ I \, km II *» I *M «» iX to D minor. CHAPTER XVIII. 233 I M ^m IT -Tf C» ff W m XE xr By progressing slowly the mind easily adopts the new scale, but if the harmonies follow rapidly the modulation is too abrupt. This change is best made in the tonic-chord of the first scale, but it can also be made in the dominant and sub-dominant chords. If the pupil has had little or no practice in modulating, he is advised to find his modulations on the piano, starting with the key of C, and wan- dering off into other scales without predetermination as to the scale into which he will come out. Having found a good modulation from C into any other scale, let him then use the same formula in modula- ting from G and from other scales. This is exceedingly good prac- tice, and he will soon modulate as readily from any scale as from C. In connection with his own efforts in modulation, the pupil should also study the works of the best composers, to cultivate his taste for the finest methods of introducing new scales. Summary. The intelligibility of music requires what : — The predominant tones and chords of a scale: — The most important positions for chords to occupy : — How a scale is maintained : — Adoption of a new scale caused by what, and called what : — Modulation not dependent upon accidentals : — How ambiguous phrases are usually interpreted : — Why easier to modulate into sub-dominant than into dominant : — In what parts of a composition one has aversion and inclination for modulating: — Meaning of "allied" and ** foreign," as applied to scales : — Which are called "allied" or "related" : — Close relation of major and its relative minor : — Why the precise point of modulation into the dominant or sub-dominant is so often indeterminate: — A scale can be suggested without being adopted : — Why it is both easier and more difficult to modulate into the "remote" scales : — The most frequent case of "transition" : — W^hat chords especially serviceable in modulation : — Enharmonic change : — The old scale not utterly oblit- erated :— Modulation by changing major chord to minor, or viee versa. 36 PARKHURST HARMONY. CHAPTER XIX. Modulation (concluded). Chromatic Chords. The varieties of modulation are inexhaustible, and a critical taste will reject all such as are crude and mechanical. The finest of all cannot be realized in a detached passage of three or four meas- ures. Their appropriateness is recognized, and their beauty en- hanced, by the circumstances under which they occur. The art of changing the scale is one that requires long and patient practice, as it admits of the greatest skill and delicacy. Its mastery can be anticipated only after the pupil has carried his studies far beyond the province of Harmony. The difficulties of the subject must be an incentive, not a discouragement, to the cultivation of a refined taste for this most subtle fruit of the composer's skill. Formulae of modulation are of little worth; at best they only illustrate the method and principle, and help the student to acquire the technique and spirit, of the art. The following illustrate the method of passing from C major to every other major scale, and from A minor to every other minor scale. After playing them attentively, let them be transposed, by be- ginning upon other major and minor scales. The analysis of modu- lations in standard compositions is also excellent and interesting discipline. But above all the student is urged to develop his own power, in the discovery of other progressions whereby to reach related and remote scales. Six diatonic major modulations from C major. ^^^ ^-J.i 1(11 C toE. -p u . . . fd . K-J 1, J ffi H; «* ? ^ f ^y I CtoGUor F^) M Cto At, =^ xr <» m «^ ^ XE PR XH 1^1^^ |bJHu ,i,¥>ij^i'n | | fY | ¥'!r|-^ g C to Bb. A ,!,„ iij 4^ i r"^ '^r^f l^k J rr^r " g ¥ b r^ P Six diatonic minor modulations from A minol*. y " ^.- A to c. ft J'l i Vi i ,. i iVi i ,.^^i#4 ^^ w ^m * 238 PARKHURST HARMONY. A to D: ^ m iil^ XH f ^ s 4 v r - ' i9- XE f^ 22 A to E: p ^ P i If ^ AtoF j ^ jTrl ' J I 3a: f^ ^ 'iTfT i r i i /? P- XJ" Five chromatic minor modulations from A minor. AtoBK . I AtoC#. m #R^ ^^ ^fe ni(tij#^ fe Jf::^=:S: n !» Bf2 « t >o II I *^r I $° ijg C to El.. Mi^ I 'xiwjh^N^^M^^ Ato F^: «1F IX ^ i 331 zt^ A to G;t V Hf l l -l I J » ') j ig — r - ^ (^ 1^ ;o- CHAPTER XIX. 239 ^A very peculiar chromatic series of chords, favorable for modu- lation, is that in which the bass is a continuous downward chromatic scale, while the three upper parts alternately move in an ascending chromatic scale, the entire series consisting of the three chords, J, 2, 7, repeated over and over. Each chord can be the initial one for a modulation. Let the pupil determine into what scales he can pass from the several chords. U) (2) (3) (4) (5) (6) (7) (8) (9) ^^^f^rWW etc. .v"j r'r fitf^jiiJ >%ii,.)^jyj ji^ A quick transition from scale to scale is sometimes desirable, as in a sprightly movement like the following: in F major in F minor. in A\> major in A\> minor. ^w A slow harmonic movement, more or less elaborated, pro- longs the passage into the new scale in a very effective manner, as in the following, where we pass from the key of C to that of Ab, the modulation being complete, although we have only reached the dominant seventh of the new scale. Indeed, the tonic chord of the new scale must, as a rule, be avoided until the scale is fully estab- lished. I Allegro ?=^ -^ spg^ ^ 7 ? F f 240 PARKHURST HARMONY. In the following, modulation is instantly induced by the fact that the mind regards the first chord of the second and of the third phrase as standing in the same scale-relation as the first chord of the first phrase. Hence Ab minor and E minor are at once regarded as keynotes of new scales. By successive modulations into the dominant, one can pass through the entire circle of scales, coming back to the original key. As examples of this sort of exercise see Beethoven's "Two Pre- ludes," Op. 39. The first part of No. 2 is as follows : — ^^g ^ F l^fl^f n f j^,j|j-_j> m r<--T m i m ^ CHAPTER XIX, 241 ^ uAimi ^ ^f PTtf s ^ m k g *^:g I* I ? ^ P ud ^^ ^ fp^ 'y-h^y^ u ^^ e ^ 5 ^ ^^W ^^ jtAJJ*^ a ^ ip^- ^ ¥^ etc. tt ^ ^ ^ s Such a form of composition cannot be a great work of art, but it is a profitable exercise for the student. In some chromatic progressions one may lose, for a time, all idea of a scale, and at any point a scale may be established. Such suspension of all scale relation, however, can be only of rare occur- rence and of brief duration. :.in7\\^,^m ,i ^^, P ! ^ f-ff l» 242 PARKHURST HARMONY. Without producing a modulation, it is possible to use all varieties of chromatically altered chords, as follows: — ^ ^^ -J J w^-^H^ t\>f\h fpf I 'lf r 't fflr ? Let the pupil acquire all the skill possible in forming elaborately chromatic chords. Improvisation will lead to the discovery of many beautiful and striking effects. But it is an embellishment that is to be used with great discretion. Excess makes a composition florid,! [but weak and diffuse. Strength of musical thought, as of all other thought, has simplicity as a main clement, and the enduring music of the world shows a masterly preponderance of the simplest harmonies. Learn to use chromatics — then learn to avoid them! yC CHAPTER XX. Cadences. A "cadence" is a point of rest. The word means, Hterally, a "falling," and in its technical use involves the idea of the "gravita- tion of chords" to that one in the scale upon which the mind can completely rest, i. e., the tonic chord. The most complete cadence therefore consists of the tonic chord, emphasized by being preceded by. that chord which leads most naturally into the tonic, and thus as it were expresses it by anticipation ; i. e., the dominant chord. With the seventh added (forming the dominant-seventh chord) the resolution into the tonic is more emphatic, and the formula for the most perfect cadence possible is as follows: a; Complete cadence, i 3 XH -cv m 3nE Not a cadence, ^0 CHAPTER XX. 243 The essentials for the completeness of this cadence are that the tonic chord shall occur in the accented part of the measure (com- pare the above (a) and (b)), that each chord shall be in its funda- mental position, and that the tonic chord shall have the tonic in the soprano. The Authentic Cadence. Any dominant or dominant-seventh chord (unaccented), fol- lowed by the accented tonic chord, constitute? what is called the "authentic cadence/' This is in several varieties . thus : i 5 XE 3DE S -O- complete incomplete, incomplete. inc. ■^►- mc. XE XE C. H 3a: ^ 23 -€>- 3? tt -O- ^ XT inc. inc. TT inc, ■ST inc, 3lSL XE XE XE f 6 6 That is, any deviation of either chord from the formula ex- pressed above (viz., the dominant or dominant-seventh chord, in fundamental position, followed by the accented tonic chord in fun- damental position with the tonic in soprano) is still an authentic cadence, but is called incomplete, and the aforesaid formula is called the complete authentic cadence. The above will suffice for the general classification of the Au- thentic cadences ; but it is to be observed that the more we depart from the formula of the most perfect cadence, the less of a feeling of cadence (i. e., a point of rest) there will be. Thus there is very little of the cadence-feeling- when the tonic chord is expressed in its first inversion (as at (a),, (b) and (c) above), and such a use of the chords would hardly ever occur, where the effect of a cadence is required. When the tonic chord is expressed in its second immersion (as at (d) and (e) ). there is absolutely no cadence feeling, as the J chord can never be a point of rest. To be serviceable as an '"incomplete cadence" the tonic chord is almost Z44 PARKHURST HARMONY, invariably in its fundamental position. The desirability of having different degrees of completeness in the cadence-feeling will be ex- plained later. The Plagal Cadence. The unaccented sub-dominant chord, followed by the accented tonic chord, is called the Plagal cadence : I 3x: ic ^ ^ ^ ■«»- ve ^ 1 ^ XH xr 3nr (These are all Plagal cadences, and the distinction of "complete" and "incomplete" is not so important as in the authentic cadences, but both chords are usually in fundamental position.) This cadence, as the close of a composition, is rarely used alone, but is generally preceded by the authentic cadence , thus : ^^ -r%- XE & anthentic xn plagal. XE XH XH — o — This is also called the "Amen cadence," as it is the one commonly used for the "Amen" after the last verse of Church hymns. The Half Cadence. This occurs when the dominant, instead of the tonic chord, is placed in the accented part of the measure, and is preceded either by the tonic chord, or by any other that naturally leads into the dominant, thus: CHAPTER XX. 245 We can rest on the dominant chord longer than on any other, except the tonic ; and that form of the half cadence will give the strongest feeling of cadence, in which the dominant chord is pre- ceded by such a chord as leads most evidently into the dominant, that is, when preceded by its ozi'ji dominant or dominant-seventh chord, as at (a), (b), (c) and (d). This is not a modulation, as has been explained in the preceding chapter, but a casual use of the ac- cidental, which of itself cannot produce a change of scale. The Deceptive Cadence. This is produced when the unaccented dominant chord is fol- lowed by any other than the tonic chord ; thus : f^ l » U l » ^ f TJ ZZ XE JOE r This is called a "deceptive" cadence, because the tonic chord is the one that most naturally follows the dominant, and the above progressions are somewhat unexpected. Yet the unexpected is not necessarily the unsatisfactory, but often, on that very account, the more pleasing. In addition to all the foregoing cadences, a certain degree of the cadence-feeling can be produced by the use of any common chord in the scale, when preceded by a chord that leads strongly into it. b. -o- H H S « bad. good. bad good. ^^ F^ -o- m c. d. e. XE 351 3x: m-. bad. good. ^^ f good. good, -^ f XE ^ XE In (a) and (b) the final chord is emphasized in being preceded by a chord that almost inevitably leads into it, and thus a degree of 246 PARKHURST HARMONY. cadence-feeling is created. A major scale and its "relative minor," and vice versa, He so closely together in the mind, that the passage from one to the other involves no effort, and (c), (d) and> (e) may- be felt, (c) as an authentic, (d) a half, and (e) a deceptive cadence, in A minor. Below are presented all the different kinds of cadences. Cadences in C Majok Dominant-Tonic . H ffiB m 3CE 3X H ^ ^ o g ^ ** II eP ^ <^ complete. com plete. ? Subdominant -Tonic H acE XE ^ 5 « ^ % ■9- -*»- 1!W=» § 3JE XE 3Ci: ^ Dominant S « « ^^^ XT »'^ ^ "cy •o" ^ XX XE Xfl § 4 3 f Dominant — ^ h"> 1 1 ^ ffi > H XT -^^ ^ 3i: -o- -€V ^ CHAPTER XX. 247 i s «: 3 ?gff^^^ BF Jri" ii r r 1 n^T i €> xs: .< ie:3 6 7 6 7 The last three may he regarded as respectively authentic, half, and deceptive cadences in the scale of A minor. Cadences ik A Mikor. Dominant -Tonic. s m s n 33 XT XS <^ -*> dS' IE cojfiplete. *^ com m -e>- ^ plete. XI n 4 1> 6 i Subdomin ant -Tonic. s XE 3X g ^ f f 331 xs: XE XE Dominant, i ^Iro Ihj U^ II;: ^ t«^i^g-4|« ^ W^rr XT TT, ^ 33r=::^ ^^ 5 r ' r Dominant -~ m XKE -€>■ XE XT M m s 248 PARKHURST HARMONY, I i I? XE ^ s= -cv jdc ^^ iM ^ o « ^ 4 The last two are inconsistent with the scale, inasmuch as the "lead- ing tone" (G#) is sacrificed. Nevertheless they can be used in a composi- tion in this scale, and may be regarded as, respectively, a half, and an authentic cadence in C major. The practical use of cadences will be best understood by first understanding that a musical composition is not a constant and unin- terrupted succession of harmonies, from beginning to end, like the in- cessant flow of a stream. A musical composition is an orderly suc- cession of different musical ideas, variously related to each other, conjoined, and yet to a degree disjoined. It is analogous to a liter- ary composition, the several thoughts of which are also variously related to each other, conjoined, and yet to a degree disjoined. Thus the literary composition, taken first in its entirety, at once falls into a certain number of chapters. Each chapter has its subordinate divisions in the form of sections, or paragraphs, and within each paragraph every complete idea takes the form of a sentence. Last- ly each sentence is usually so complex as to contain a greater or less number of those ultimate organic fragments of an idea, each of which is called a phrase or clause. Thus we find that the grand idea, expressed by the entire com- position, literary or musical, is minutely subdivided ; and the mind, in the conception or in the reading of the work, finds a point of rest in the progressive development of the idea, wherever it finds a distinct, although it may be a very minute, completion of that idea, in any of its most subordinate details. Thus the mind is frequently finding the cadence throughout the entire composition. And the cadences, or points of rest successively sought and gained, are al- ways commensurate, in their duration or intensity, with the relative importance of the fragmentary ideas to the grand idea. The marks ©f punctuation — the period, colon, semicolon, comma — in a measure express to the eye the relative duration of the rest or cadence. Ab- solute rest, with no eflFo/t of the mind beyond, can come only with the completion of the work. This absolute rest is found only in the •'complete authentic cadence," the ''full period" of the whole idea. CHAPTER XX. 249 The foregoing cadences are very unequal in the degree of the cadence-feeling excited by them, and are thus adequate to the var- ious demands for cadence in the development of the musical idea. It is not to be supposed that the various chord-connections in the foregoing list of cadences always produce the cadence feeling. Many of them are used frequently without any sense of a cadence. The rhythmical structure of the composition in a degree creates the de- mand for a cadence at certain points, and the inherent cadence qual- ity of certain chord-progressions thus re-inforced by the rhythmical demands creates the sense of cadence in the mind. That is to say, the cadence-form and the rhythmical movement are conjointly operative in producing the sense of a point of rest. For example, the domi- nant chord occurring in the beginning of a measure, and preceded by v^^hatsoever chord, cannot invariably create the cadence feeling, and yet such a chord-progression constitutes the ''half cadence'' formula. But if the rhythmical structure demands a cadence, the above formula is at once felt to be a point of rest. The rhythmical movement and the cadence formula must conspire together. And the less of the in- herent cadence quality there be in any chord-progression, the more is the rhythm determinative of the sense of cadence in that progression. The mutual interaction of the rhythm and the ca- dence formula can be learned only by practice. But the foregoing table of cadence formulae should be carefully studied, as only in these formulae does there exist any of the inherent cadence quality. The pupil is also urged, after mastering the above table, to study chorals, which more clearly illustrate the doctrine of cadence than any other form of composition. Each line of a choral closes with one or another of the cadence forms, and the success of a choral de- pends in no small degree upon their judicious alternation. Other kinds of composition can also be studied in respect of the use of cadences, but this presupposes some knowledge of the art of con- structing a composition, which is learned by the study of "musical form." As the concluding exercise of this chapter, let the pupil write examples of all the different kinds of cadence in several different keys, major and minor. Summary. Meaning of cadence: — The formula of the most complete ca- dence: — Authentic cadence, complete and incomplete: — Plagal ca- dence: — Its use with authentic cadence: — The half cadence: — The most complete half cadence : — The deceptive cadence : — Why so called : — Analogy between a musical and a literary composition :— 250 PARKHURST HARMONY, Where does a cadence occur in both forms of composition : — Intensity of a cadence commensurate with what: — Cadence feeUng not alv/ays produced by cadence formula : — What must co-operate with the cadence formula to produce the cadence feehng: — The use of ca- dence in the choral. In conclusion, a few words as to the treatment, in the foregoing work, of the voices or parts, as compared with their treatment in practical compositions, vocal and instrumental, such as solos, duets, trios, choruses, sonatas, symphonies, etc. The divergence of such works from the form of all exercises in this book is so great as to induce the feeling in many minds that there can be little or no relation between the one and the other, and the undeniably good ef- fect resulting from the violation of certain rules that are invariably insisted upon in a text-book of Harmony (such as the use of octave passages) tends to weaken one's faith in the validity of such rules. The confusion all arises from a mistaken idea as to the real scope of "Harmony," and the legitimate application of its rules. The essentials of harmony are taught therein, but not the numberless de- tails of effect which in their place are legitimate and necessary. The foregoing work teaches only how to secure the fullest harmonic effect with four voices. But there are many other effects highly de- sirable in music beside the *' fullest harmonic effect of four voices." The prolonged use of four parts in this manner would soon become extremely monotonous. For variety of effect and relief to the mind, the four parts must sometimes be treated differently, and sometimes a less, and sometimes a greater num- ber of parts must be used. The greatest aggregate of musical effect is secured by proper variety and alternation of means. So that there is an important place for unisons and octaves, for solo, duet, and trio, for full chords and for absolute silence, as well as for the "fullest harmonic effect of four voices." The acomplished composer must be familiar with every device that shall enhance the effect of melody and harmony, with every grouping of the tone-colors, with all lights and shadows that shall help to realize the tone-picture. In view of such a goal, the work accom- plished by a "text-book of Harmony" seems almost insignificant. In one sense it is. But the essential principles of all harmonic combina- tion — the most important thing of all — are therein learned, and the student now stands one step beyond the threshold of the art. Before proceeding to the next department of theoretical study — that of Counterpoint — it is in most cases very advisable for the CONCLUSION. 251 student to make a thorough review of the entire subject of Har- mony. By so doing, he will be amply rewarded in the more complete understanding of all the fundamental and auxiliary chords, in their construction and connection, which is the requisite preparation for success in musical composition. In making a review, it will only be necessary to write so many of the exercises in each section as will give proof that the subject- matter is fully mastered ; and it will be much more profitable to use the basses as exercises in **sight-reading," for this will give a mas- tery of the chords such as can never be attained by merely writing them. In the review, it will be found that the sense of the chords can be imagined much more easily and accurately than before; and, as a final word of counsel, the pupil is urged to cultivate still more as- siduously this power of knowing the effect of chords without playing them ; for without it, any satisfactory progress beyond the province of Harmony is impossible. 25? PARKHURST HARMONY, APPENDIX, The discussion of questions having a purely theoretical interest, and without any practical application, in the study of Harmony, does not properly belong to the body of such a work as this, and has therefore been reserved for the Appendix. Other questions, of un- doubted value to the more advanced harmonist, but of doubtful utility to the beginner, also find here their solution. (A) Full List of Intervals. r T^^ — I 1 perfect,or unison tiut ^ir.e nted m ajor Seconds. * minor augmented !<->. T3r ^ Kf ' Thirds. " Fourths. » major min o r diminished perfect augmented diminished tf" \^^** * ^ o- f XE i Fifths. " Sixths. ^ perfect augmented diminished major minor augmented S irrr jo: ' Sevenths. '^ Octaves. major minor diminished perfect augmented dittiinished XT aac [XE f $ Ninths. ' major. minor. Tenth. Eleventh. o — i Twelfth. Thirteenth. Fo">-te«ith. Fiftee^h. APPENDIX. 23J»i Perfect intervals. Prime. ± 1 Fourth. Fifth. Octave. ^ i •!> Cl Q 4> o 1 Major intervals. Second. Third. Sixth. Seventh. Ninth. -€>- XE ^^^ Minor interv^als. Second. Third. Sixth. Seventh, Ninth. ^ ^ trrr Augmented intervals. Prime. Second. ^ Fourth. Fifth. Sixth ^ ^ Diminished intervals. I Third Fourth. Fifth. Seventh. Octave ^ €V * XH r^^ — ^ f For all simple harmonic purposes the intervals of a ninth, tenth, etc., are the same as a second, third, etc., and are commonly so named. In "Suspension" the ninth is distinguished from the second, and in the later study of counterpoint, the tenth and twelfth are sometimes distinguished from the third and fifth. But with these slight exceptions all intervals are reckoned as within the limits of an octave. (B) Reason for the General Use of Four-Part Harmony. As the fundamental combination of tones in Harmony is the "common triad," it might be supposed that our elementary chords would be "three-part harmony." This is not the case. The deter- mining factor in this matter is the consideration that such a number of parts will inevitably be adopted for general use in both vocal and instrumental music as will afford the most satisfying fulness of harmony, combined with the requisite simplicity and transpar- ency of the chords, and distinctness of -the individual parts. The aiumber of parts in the chord can be increased indefinitely, but ?^4 PARKHURST HARMONY. beyond a certain point such increase tends to produce fulsome harmonies, and a sacrifice of simpHcity and distinctness. A reduction, beyond a certain point, in the number of parts, on the other hand, makes the harmonies thin, and the remaining parts correspondingly obstrusivc. The oppressive richness of full chords is replaced by an equally oppressive poverty of scant harmonies, and what was before well-rounded, through the abundance of the parts, becomes angular through their scarcity. In view of all the requirements, the most satisfying eflfects are produced by four-toned harmony. This is not to the exclusion of five, six, seven, and eight-part harmony, on the one side, or of three and two-part, on the other side, but in the nature of things four is the normal number. Even in the florid harmonies of orches- tral music, we find a substratum of four parts, giving the basal chords on which the elaborate superstructure rests. Our vocal music is not in four parts because we have soprano, alto, tenor and bass. On the contrary, the Creator has furnished us with this fourfold pitch and quality of the human voice to meet the harmonic require- ments of our nature. And in instrumental music the acme of pure harmonic enjoyment is found in the "string quartet." : (C) Wherein the Distinctiveness of the Parts Consists. One of the satisfying elements of harmony is the distinctive- ness of the several parts. This distinctiveness is three- fold, viz., dis- tinctiveness oi pitch, of direction of movement, and of rhythm. Suppose the bass and tenor are as follows : oo £ XKE OO OO There is here no distinctiveness at all. The voices are in unison. The tone is stronger, but the two individualities are merged into one. But in the following, P :«: Jt there is the first element of distinctiveness, that of pitch, but their movement and rhythm are alike. In the following, ^ ^ 77 .^ ft APPENDIX. 255 the two voices assert their individuahty still more by unlikeness in their direction of movement ; and in the following. we find the three elements of distinctiveness combined, viz., pitch, direction of movement, and rhythm. Only in these three ways can the different voices or parts assert their individuality.* In the exer- cises of Harmony, and in the choral style of composition, the individ- uality of the voices is almost exclusively confined to pitch and di- rection of movement, with little variety of rhythm. The highest voice alone is treated as a melody, and the under voices have little more than harmonic significance. The fugue, on the other hand, is the highest form of harmonic writing, because each voice is treated melodically, and in addition to the individuality of pitch and direc- tion of movement, is also as rhythmically distinct as possible. (D) The Rel\son for the Prohibitiox of Parallel Perfect Fifths. The objectionableness of parallel perfect -fifths is evident, but har- monists have ever found it impossible to understand and state clearly the reason for the objection. The following statement does not pretend to be original, or less abstruse than previous efforts of other writers. Every chord in fundamental position has its boundary line or circle expressed by its root and fifth. The proper connection of chords requires a sort of resolution or floi^' of one chord into the next; but when any two voices express the fundamental and fifth in two successive chords, the boundary circle of each chord seems rigidly maintained, the harmonies are in contact, but they do not coalesce , thus : 4 d{ I [§ s ^ «: S ■a FO- i XE *This is presupposing- the same quality or tone-color in the parts or voices. Variety in this respect affords another valuable element of distinctiveness, to be sure, but we are here con- cerned only with the elements involved in harmonic structure. ^56 PARKHURST HARMONY. In seventh-chords, the occurrence of successive perfect -fifths be- tween any two voices, even though one of the fifths intervene be- tween other than the root and fifth of the chord, will also prevent the coalescence of the chords , thus : « pp In the diminished fifth there is not the same effect of a boundary circle, and it can be made to follozv a perfect fifth (a) ; yet the eflPect is not good if it precede the perfect fifth (b) ; still the progression from diminished to perfect fifth is by some good writers allowed .between the inner parts (c). I i b. ^^ s -€>- ^ goad, bad. tolerab i PP ICE i 6: tolerable. The foregoing statement concerning parallel fifths is far from conclusive. This is frankly confessed. The designation of the root and fifth as the ''boundary circle" of the chord is somewhat fanci- ful. The exact truth of the matter eludes our grasp. We wait for some more discerning eye to detect it. But the foregoing state- ment expresses enough truth to put one upon the track of more "truth than he can define in language, and however vague or er- roneous our explanation of the matter may be, the sense of the lack - XE "cr As before remarked, their relations in the harmony may entirely change the leading quality of all the tones. (F) Reason for the Two Forms of the Melodic Minor Scale. I XE XE Upward . Downward. iX m The difference is comprised within the upper four tones. I and arises from the preponderating importance of the "leading tone" in the upward scale, and of the minor sixth in the downward scale, both of which tones are essential to the complete satisfaction of the Minor scale, but on account of the gap between them i one is sacrificed to the other, so as to secure a more melodic pro- 258 PARKHURST HARMONY. session, by the avoidance of an augmented second, and by a more equable division of the distance from E to G#, and from A down to F, in having two successive intervals of a whole tone each, rather than a half tone followed by a tone and a half, thus : V 1V2 better. i/^ iIa better. i f It remains to be considered why the minor sixth is sacrificed to the major seventh in the upward, and not in the downward scale; and why the major seventh is sacrificed to the minor sixth in the downward, and not in the upward scale, so that the following forms are unsatisfactory: ^^ ' ^^ ** o » _ 1 if o although they are quite as melodic as the same scales in reverse order. The two distinguishing characteristics of the Minor scale are the minor third, and the minor sixth, and both of these intervals must be maintained to preserve the consistent minor quality of this scale. But the stability of any scale depends primarily upon main- taining the pre-eminence of the Tonic of that scale; and that pre- eminence is largely secured by the emphasis it acquires from the tnajor seventh of the scale in its leading quality, finding its "rest" in the tone to which it points, that is, the Tonic. Therefore when we pass from the seventh to the eighth we have impaired the integrity of the scale, unless we find that emphasis of the eighth which comes from the "leading" quality of the major seventh, which helps to as- sert the eighth as a Tonic. If then the minor sixth, which is a char- acteristic of the minor scale, comes in conflict with the major seventh (for the minor seventh never "leads"), then the minor sixth must be in a measure subordinated to the major seventh, and the €ar accepts the major sixth, when the seventh is to be followed by the Tonic. This accounts for the major sixth in the ascending scale. But when the movement is downward from the Tonic, and thus there is no demand for that quality in the seventh that shall "lead" to the Tonic, the necessity of the minor sixth outweighs the demand for a major seventh, and the latter is sacrificed to the former. The true minor scale is the harmonic form. The major sixth and the minor seventh, that are found in the melodic forms, occur •only as the result of compromise. The various subordinations of the APPENDIX. 259 sixth to the seventh and of the seventh to the sixtJi are illustrated in the following : ff^-f^m ^^m mm iJP But with all this apparent sacrifice of minor sixth and of major seventh, it is to be observed that it is never as the true harmonic tone that the major sixth or the minor seventh occurs, but only in the inconspicuous manner of a "passing" or "auxiliary" tone (see Chap. XV). The incongruity of using them as harmonic tones is seen in the following: X '^Cf^f^US XE ^ g ^ f 3x: ' 1 1 ' "^ H ' "—^ — * The incongruity of associating the major sixth and the minor third is plainly felt in playing the following, especially if the two intervals are emphasized : i ^ It seems inconsistent that the same incongruity is not felt in the ascending melodic scale. It certainly is not, and the reason is doubtless in the fact that in the upward scale the gravitation is strongly toward the Tonic, and the mind instinctively accepts the major sixth as a temporary compromise to the "leading tone," and lays little stress upon its major quality. In the foregoing downward scale, however, there is a plain assertion of the A-major scale until we reach C, which as a minor third, is a flat contradiction to A- major. (G) Inversion. The inversion of a voice is its transposition to the other side of an accompanying voice. The most common interval of transposition 260 PARKHURST HARMONY. is the octave, but any other interval can also be used. In all the following illustrations, the octave (which means one, two or any number of octaves) is the interval of transposition, unless other- wise specified. The following shows the inversion of the lower voice above the upper, and of the upper below the lower : s ^ l "\' Hi;/" XX o\o It will be seen that the resulting interval between the voices is the same, whether the lower or the upper voice be inverted. The following shows the result of inverting the upper or the lower of two voices standing at the successive intervals of the dia- tonic scale : 3 A W^ >) . A l ^) yW 5 'F=^ ^ £1. ^ ) fM^Mm t (K (o^> t^**» XE 6 "CT" 7 6 The original and resulting intervals are expressed by the follow- ing series of numbers : 12345678 87654321 thus a prime becomes an octave; a second becomes a seventh; a third a sixth, etc., and the sum of the original and inverted inter- vals is always 9. Thus the larger the original interval, the smaller will be the inverted interval, and vice versa; also the larger size of one interval inverts into the smaller size of the other ; hence a major interval inverts into a minor, and a minor into a major, and a di- minished into an augmented. Major into Minor, and vice versa. minor. ,7 maior. mmor. ^"^j^i- *"*"ui. , n^ajor. minor, n^a^r. minor. ^^ ^^^ L ^ \.L ^ minor, maior. minor, major, minor.- maior. 'minQr, majot^ «5 ^fT" 7 7 minor, major. 6 major APPENDIX. 261 Augmented into Diminished^ and vice versa. I aug. i ^ "I 2 i 8 dim. 4 aug. 5 15 — dim. diin. 5 dim. (.3 , ^ aug. 6 aug. ^ o: dim. 4 XE 5 dim. dim. 5 aug. dim. tf 'ci' htf»^^ I (tf"!^^ I '■g**'^^^ j 4 dim 4 aug. 3 dim. aug. T aug. It is evident that unless the two voices are within an octave of each other, the transposition of either of them by a single octave will not result in an inversion : 4 °f "■! °-f I t) -o ^ ^^ thus a ninth becomes a second; a tenth, a third, etc., and the result- ing interval is essentially the same. But if the voice be transposed two or more octaves, an inversion is secured, and the resulting inter- vals are either identically or essentially the same as when either of the voices, within the limits of an octave from the other, is trans- posed a single octave ; thus : Transposed Transposed Transposed one octave, two octaves, three octaves. In all the above inversions the upper intervals are either abso- lutely or essentially thirds, and the lower intervals are either abso- lutely or essentially sixths. So that what may be called the octave inversion invariably produces such an interval as, in its relation to the original interval, is expressed by the same number as if the voices were within an octave, and inverted by an octave. The ociave does not invariably become a prime by inversion, but the prime always inverts to the octave (one or more octaves). The octave may invert to an octave ; thus : 262 PARKHURST HARMONY. octave to prime. prime to octave . The transposition from octave to unison, and from unison to octave, necessarily ranks as an inversion, yet without being a transfer from one side to the other, and is devoid of that essential harmonic change of relation between the voices that results from all the other inversions. Besides the octave-inversion, it is possible to invert by any other interval, either less or greater than the octave. Of all other in- versions the commonest in use are the inversions of the tenth and the twelfth, thus : inversion 6f the tenth. inversion df the twelfth. -if ^-fc «» , _^ 4« O *' n r» ** ^ r^ *» " Tm r* •» ^^ c^ *» ^^ vV r» ** ^ -^ -€^ -O- -O- -O- -«--€> -»► -O- -^ -€^-^ -O- -^ -^ -^ h-r^. ^ «» *> <-» ** •^ r^ *» *^ -■•^ «» *^ ■ The explanation of inversion properly belongs to the subject of Harmony as it relates to certain harmonic relations of tones; but the application of inversion belongs only to the higher forms of musical composition. Yet as a matter of interest to the student, and to give him a better understanding of the subject, the use of inversion will be briefly explained. Suppose we have a short melodic phrase in one voice, like the following : i ^^^ Xfl ^ -o- to which we wish to add an accompanying voice, thus : '^WW'f"'''^^'' -'^'r If this accompanying part be written according to certain laws that pertain to this sort of composition, it can serve not only to ac- company the first voice in its present position, but also if one or the other of the two voices be inverted throughout by an octave, thus: APPENDIX. 263 this secures new harmonic effects throughout, while the voices them- selves are identically the same. This is one of the arts of the com- poser for gaining nezv effects with old material; that is, securing unity and variety, th^ two fundamental requisites of every com- lX)sition. The foregoing sufficiently explains the purpose of inversion, whether by the octave, which is the most common, or by any other interval. (H) The Tdextitv axd the Difference of Aug^iexted Sixth AND Minor Seventh. chord of aug. sixth, chord of dominant a^g. sixth. minor seventh, wiih resolution, seventh, with resolution, i: avg.sixin t 3z: XE izxz: #» s m xn o: s I chord of aug. sixth and fifth, with resolution. chord of dominant ;eyenth,with resolution. i I *8 CE €>- B -v^ — The ear knows nothing of sharps, flats, or naturals. These si^iis are simply devices of Notation, so as to express precisely to the eye the relation and interval of tones, as the relation and interval exist to the ear. What we may call the physical distance of D# from F (as above) is precisely the same (for all practical purposes) as the distance of Eb from F. But under some circumstances the ear rec- ognizes this interval as an augmented sixth, and under other circum- stances as a minor seventh, and according as it is felt to be the one or the other, the following progression is thereby determined. This progression differs radically in the two cases, for it is in the nature of an augmented sixth to lead up a miiior second (i. e., a semitone), and it is in the nature of every seventh to lead doz^'u one degree (which may be either a major or a minor second). The normal resolution of all discords may he said to b? down- ward, however inexplicable the fact may be. This is amply illus- trated in the *'sus})ension-chords," wherein one sees the constant drawing of the ninth down to the eighth, of the sixth to the fifth, of the fourth to the third, and. in the commonest of all discords, of the 264 PARKHURST HARMONY. seventh to the sixth. A strong counterbalancing consideration must therefore exist in that interval which would ordinarily be regarded as a minor seventh, neutralizing the natural tendency, and leading from the discordant tone upward; in which circumstance the interval is felt to be a sixth (of the augmented sort), rather than a seventh. The exceptional treatment of this discord is explained by saying, that the mind constantly recognizes the fact that the coherence and musical sense of successive chords depend largely upon their Hoiving in one and the same scale, or only from one scale to another wherein the modulation shall not sever the coherence. In the following progression the chords cohere in the same scale, when the discordant D# leads up to E. J m xy t £ J[|-|,iU g ^ -^ « 6 -e- a \^ The same discord, regarded as a seventh, involves in its natural resolution a chord that is out of all coherence with the preceding chords, and necessitates a modulation that is utterly forced and un- natural. ^ iti -t> i m -« ; <^ 6 1.7 If the passage were in the key of Bb, it would be equally incom- patible with the scale to lead up from the discordant tone, as at (a), which would now be construed as a seventh, and resolve as at (b). X ^ 2 m XX. APPENDIX. 265 To state the matter briefly, the foregoing discord is naturally re- garded as a minor seventh, but wherever such interpretation leads to an incoherence of the chords, and to a forced modulation, the mind construes the discord as a sixth (of the augmented sort). A cir- cumstance which often makes it easier to construe this as an aug- mented sixth is the fact that the melody frequently leads up to it, and what we may call a melodic momentum in a measure predetermines the upward resolution. This is only one instance of the mental process of determining the nature of an interval according to the situation in which it occurs. Thus the interval which under some circumstances is a major second, under others is a diminished third; what is sometimes an augmented second is at other times a minor third; what is sometimes a major third is at other times a diminished fourth, etc. The following table presents the various equivalent intervals. I diminished major second. third. ir aug^. second. minor third. ^^ s \ >\>K>^ ^ O- diminished ' ' diminished ^ major third. fourth. aug. fourth. fifth. 1^ * €>- IE ' aug. fifth. mino r sixth. ' ' aug. sixth. ^ a: t minor seventh. major* seventh. diminished eighth. ^ EE -fJT (I) The Essential Principle of Notation. The chapter on "altered chords" brings to our notice certain in- tervals that are ambiguous, i.e., dependent upon circumstances to determine their name. Thus the distance which in some cases is an augmented fifth, is in other cases a minor sixth. The distance of an augmented sixth is often a minor seventh. (For a full list of the equivalent, and therefore ambiguous intervals, see Appendix (H) ). The question is often asked, why a given interval is expressed in no- tation as it is, and the answer commonly given is, ''to conform to the 266 PARKHURST HARMONY. principles of Notation;" which leaves the enquirer no wiser than before, but inspires within him a proper awe in view of the mysteri- ous "principles of Notation." There is but one essential principle of Notation, and that a simple one, viz., to express the relations of tones to the eye exactly as they exist to the ear. In determining intervals between tones, the ear moves along the steps of the diatonic scale. These steps of the scale are expressed to the eye by the lines and spaces of the staff, and there must be as many intervening lines and spaces as there are intervening steps of the scale. To illustrate this, suppose two tones are heard, which we will call C — F#, « 3 4 I * and supposing the scale of G to be already established in the mind, the ear moves in that scale through tones which we call D and E, so that the interval is expressed in notation, c — d — e — f#, a fourth. But again, supposing the scale of Db to be already in the mind, then the ear will move in that scale, and the interval is expressed in notation thus, c — db — eb — f — gb, a iifth. 3 4 tl 2 3 4 This illustrates the one essential principle of Notation. The real relation is that which the ear hears, and the notation is accurate when the eye sees as the ear hears. 14 DAY USE RETURN TO DESK FROM WHICH BORROWED MUSIC LIBRARY This book is due on the last date stamped below, or on thejfete to which renewed. re subject to immediate recalL jnii p w 'JAN 20 1972 NOV R1973 iiiM fi 1976 JUll U io< v^ ,P.To!ifo^T|l'1.3. .^^^S^&... MT50.P27 1908 iVi206963 THE UNIVERSITY OF CALIFORNIA UBRARY DATE DUE Music Library University of California at Berkeley , ,,, ,:\m. i!;:M:.:iil:|||!!ll!li I I'll iilii llii mm m !i ,'i!;l^ 'lii'i m \\l\mi