Music Lib. o o 1 D = — — CD • JZ 1 51 ===== i> P*B 3D — g < 1 91 — — -n = :t> 1 2m — — ^H o ■ : < THE LIBRARY OF THE UNIVERSITY OE CALIFORNIA LOS ANGELES ® ilium Practical Harmony HomerA.Norris Part I ■BHHml L P- n MUSIC oU LIBRARY V.l Southern Branch of the University of California music ~ Los Angeles LIBRARY Form L-l MT50 Practical Harmony A COMPREHENSIVE SYSTEM OF MUSICAL THEORY ON A FRENCH BASIS BY HOMER A. NORRIS Part I. Consonance Part II. Dissonance Part III. Key to Harmony PHILADELPHIA THEODORE PRESSER CO. 4-o-a ^b^> Copyright, 1894, BY H. B. Stevens Company Boston Copyright secured in England Copyright transferred, 1903, to Theo. Presser / MUSIC f.lBRARY H7^f PREFACE. » The author has endeavored to prepare a text-book on harmony, based on the principles of the most eminent French theorists and composers, which shall enable the student to analyze with ease and clearness the most complex musical compositions of the modern school, and which shall also stimulate the musical instincts of those who are endowed with the gift for composition. It is justly urged against the average text-book on harmony, that it is either too elementary or too scientific. If too elementary, it leaves the pupil uninformed regarding much that he will meet in the works of the masters, and it usually contains detail which fatigues and discourages. If, on the other hand, the book sets out with details of the laws of acoustics, it appeals more to the mathe- matician than to the musician : the theoretical is developed at the expense of the practical, and neither artistic intelligence nor mu- sical sentiment is quickened. Whatever may be proved by such mathematical calculation, it has little or nothing to do with aes- thetics which is constantly changing. Our modern musical system is based on what is both natural and artificial ; it has been accepted, and our musical habits, so to speak, and much that we call musical instinct, are the result. New musical effects come, we suspect, as a spontaneous discovery, rather than as a result of patient scientific investigation. For this reason, in all matters having to do with tho artistic and the aesthetic, practice should precede theory. The study of harmony can be made, and should be made, not a drudgery, but a delight ; and the French methods have been chosen as a basis for this book, because they present theories in an attrac- tive, as well as in a practical manner. The Frenchman is instinctively an artist. The beautiful appeal;- to him irresistibly, and his feeling for the narrow line that separates the commonplace from the purely artistic is sensitively keen. One proof of this may he found in the many beautiful examples by eminent French composers and theorists, written expressly for this (iii) i v PREFACE. book, and which appear in Part II. If one were not told, one would not suspect that they were "harmony-exercises." The laws governing key-relationship and all that should be understood by tonality — that element of modern music which is of the very first importance — have been emphasized. A text-book cf to-day should make it clear that Wagner, Brahms, Leoncavallo, and Bruneau are as truly in key as is Mozart. It is believed that this can be most speedily and most safely accomplished by first demonstrating all possible uses of the diatonic triads. So far as the author knows, there is no book published in this country which reduces the so-called "•Augmented Sixth" chords, the stumbling block of all harmony students, to altered Dominant Seventh chords. He feels certain that with this system they will be readily recognized, and what is of the greatest importance, that their tonal relationship will be apparent. Moreover, by this method the works of the masters can be analyzed much more easily and clearly. The svstem of a figured bass has been adhered to in the opening chapters, in order that the pupil, before being thrown wholly on his own resources, may gain a certain facility in correct writing. Terms in common usage have been employed wherever possible. The chapters are divided in keeping with the subjects discussed ; the length of the lessons must be left to the discretion of the student or of the teacher. A small pamphlet, intended for teachers, and containing all the exercises, with the harmonies of the composei*s, is issued separately. The author desires to express his appreciation of the warm words of encouragement, and of the suggestions sent from time to time during the writing of this book, by his Paris teachers : Messieurs Theodore Dubois, Eugene Gigout, Alexandre Guilmant and Benjamin Godard. He also acknowledges his indebtedness to the various text-books used at the Paris Conservatorv, and notably to the Treatise by Reber, with the accompanying "Notes et Etudes" by Theodore Dubois. The author claims little or nothing that is new ; the book is rather a compilation or condensation of that which he believes to be the best. It is hoped that among the really good books on this subject it will find a welcome place and add something which, may be of use to the modern student. m Uoston, August, j8yj. THE AUTHOR. CONTENTS. PART I. CONSONANCE. Chapter 1 page i Note. — Intervals, — Inversion of Intervals, — Classification of Inter- vals, — Exercises, — Suggestions. Chapter II. page 8 The Major Mode, — Chords, — Triads, — Part-writing, — Melodic Progression, — Harmonic Progression, — Consecutive Octaves and Fifths, — The Tritone, — .Sequence, — RulesTor harmonizing Basses, — Suggestions, — Exercises, — Additional Exercises. Chapter III. page 23 The Minor Mode, — Melodic and Harmonic Progression in the Minor Mode, — The Augmented Second, — Suggestions, — Exercises, — Addi- tional Exercises. Chapter IV. PAGE 29 Chord-relation, — Harmonizing Melodies in the Major Mode, — Sug- gestions, — Harmonizing Melodies in the Minor Mode. Chapter V. page 34 Figuring of the Bass, — Open Harmony, — Exercises. Chapter VI. PAGK j, Chords, — The First Inversion, — Exercises, — Note concerning the Study of Counterpoint. Chapter VII page 44 Chords, — The Second Inversion, — Observations concerning the Terms Consonance, and Dissonance. (v) v j CONTENTS. Chapter VIII. pagb 54 Form, — The Phrase, — The Period, — Cadence, — Exercises. Chapter IX. page 59 Modulation, — Tonal Relation, — Modulations of the First Order, — Exercises, — Modulations of the Second Order, — Modulations to Re- mote Keys, — Passing Modulations, — Exercises, — Harmonic Se- quence, — Exercises, — Tonal Sequence, — Exercises. Chapter X. page f& Resume. Notation, — Chromatic Scale, — The Ecclesiastical Scales,— Chords, — Triads, — Melodic Progression, — Omission of Voices, — Consecutive Fifths and Octaves, — Hidden Fifths, — The Tritone, — The Augmented Second, — Tonality, — Form, — The First Inver- sion, — Modulation. PRACTICAL HARMONY. PART I. CONSONANCE. CHAPTER I. Note. The only elementary knowledge of music presupposed is that necessary to sing or to play, unaided, a written melody of the simplest order. INTERVALS. The distance from one note to another is called an ititerval. Intervals are reckoned upwards, and are measured by the number of degrees they occupy. By degrees is understood the lines and spaces of the staff - '. The interval at a, in example i, is a fourth; from C to F, inclu- sive, there are four degrees. The interval at b is a sixth, and that at c a ninth. Ex. 1 I W =t -%,& ^&-*& -& m -&- - 1 Third. Inversion of third. PRACTICAL HARMONY. e All intervals, except those called perfect, change their character by inversion: major intervals become minor., and vice versa; the diminished become augmented, and vice versa. The perfect fourth and perfect fifth are the only intervals that remain the same when inverted, and this is one reason why they are called perfect. The unison by inversion becomes a perfect octave, and is also classed a perfect interval. A few theorists name the perfect intervals major. As they stand in the regular order of the major scale the_y are certainly major, but they alone remain unchanged by inversion, and for this reason, as well as for others that will appear later, it is better to give them a more specific name. Moreover, these inter- vals are termed perfect by the more prominent theorists, and it is always best to follow tradition unless some great advantage is gained by a change. CLASSIFICATION OF INTERVALS. There are certain intervals which at once please the ear and give a sense of repose or finality. The most important are the fifth and octave which are termed in musical theory the perfect consonances. The next in importance are the major and minor thirds and sixths , these are termed the imperfect consonances. The interval of the fourth is classed by the best theorists a mixed or neutral interval ; it is sometimes consonant, sometimes dissonant, according to the position it holds. Theoretically it may be con- sidered a perfect consonance, but musically never, because few intervals give a less sense of repose or finality than the fourth. At one time it was considered one of the most perfect of intervals, later as a dissonance. This suggested that it might be either one or the other according to conditions, and so it is now named a mixed interval. This will be more fully explained in the chapter on the inversion of chords. In writing ascending passages of half-steps it is correct, as a gen. eral ride, to use sharps, as at a in example 14; in descending pas* sages it is correct, as a general rule, to use flats, as at b. Ex. 14 6 PRACTICAL HAKMOXY. Played on a piano or organ the QJ at a gives precisely the same sound as the Di? at b , but played on a violin or any instrument that gives a pure scale, the CJJ is higher. For this reason sharps natu- rally ascend and flats descend. From C to Q% is called a large half- step, from C to Di? a small half-step. In other words, a chromatic semitone forms a large half-step, a diatonic semitone a small half- step. EXERCISES. Copy the following notes on a staff* and above each write the in- terval called for. i Chromatic Diatonic Enharmonic Small Large Unison. Aug. prime, semitone, semitone, interval. half-step, half-step. _£k_ ^m ■$z: g Major second. Minor second. Aug. second. Major third. Minor third. ~w&* Aug. third. Diminished third. Perfect fourth. Aug. fourth. Dim. fourth. Effi -te- -«s>- I Doubly-aug fourth. Perfect fifth. Dim. fifth. Aug. fifth. Doubly-dim. fifth. - =i= =l=iE===l c- -\>zr Major sixth. Minor sixth. Aug. sixth. Dim. sixth. Major seventh. Il^^l! << Minor seventh. Dim. seventh. Perfect octave. Dim. octave. 3£: $ Aug. octave. Major ninth. Z&r Minor ninth. & Aug. ninth. I I PRACTICAL HARMONY. 7 JVbte. The diminished fourth and fifth are often called i?nper- fect intervals, to distinguish them from the perfect. The terms imperfect and diminished are synonymous in speaking of the fourth, fifth, and octave. SUGGESTIONS. The student is urged at this point to name the intervals in any standard piece of music. For this exercise nothing could be more exhaustive than the overture to Wagner's Tristan and Isolda, which may be found in inexpensive edition at any music store. This exercise is for the eye only, and it is the teacher's duty to see that the ear is likewise trained, for it is of the greatest impor- tance that the student realize at the beginning that he should hear as well as see. One of the most practical exercises is for the teacher to play or sing a melody which the pupil should notate on black-board or music paper. It is best to play or singthe melody slowlv, and with as little accent as possible ; in this way it becomes a valuable exer- cise in rhythm. Unless the pupil has absolute pitch, it will he found necessary at first to name the key in which the melody is played or sung. It is best to play a short phrase three times, with a slight pause between the first two hearings, but connecting the phrase the third time to the succeeding phrase. The pupil should notate all of the phrase he can hear before the third repetition. After the whole has been notated, the teacher should play it through slowlv, the pupil correcting the errors as best he can. With a few exceptions this exercise will be found discouraging to the student at the beginning; a few lessons will show surprising results, and later he will realize the great advantage of such an acquisition. Another useful exercise is for the student to write any intervals he may choose. The teacher may play them either correctly or not, and the student must decide whether or not they are played as written. For all work of this character the black-board is more useful than music-paper. The pupil will save much time if he will acquire the following method of notating : In making a whole note draw the upper half from right to left: •^ N , then add the lower half from right to left: PRACTICAL HARMONY. O. In making a half note a stem only need be added: J. This method not only insures greater facility of execution but elegance of notation. Whenever a single note stands above the third line the stem should extend downwards : :L ^— • Whenever a note stands below the third line the stem should extend upwards CHAPTER II. SCALES. THE MAJOR MODE. TRIADS. PART-WRITING. MELODIC PROGRESSION. HARMONIC PROGRESSION. CONSECUTIVE OCTAVES AND FIFTHS. THE TRITONE. SEQUENCE The form of the major scale as used to-day has remained fixed foi about two centuries. It consists of a succession of major and minor seconds, the lattei coming only between the third and fourth, and the seventh and eighth degrees of the scale. A scale with the above succession of intervals is said to be in the major mode, and diatonic. Ex. 1 5. I m -^r-*^ 2 - ~&- /»?- —& Unless the student is thoroughly familiar with all the major scales he should now write one from each of the following notes : C, G, D, A, E, B, F#, Gtf, Cb, Gb, Db, Ab Eb, Bb, and F. Place no sharps or flats at the beginning of any scale, but insert them, wherever necessary, preserving the same order of intervals as is given in Ex. i 5. CHORDS. By the word chord is meant the simultaneous sounding of differ- ent tones. Chords are built by taking any note and adding above it a succes- sion of thirds. The lowest note is called the root or fundamental PRACTICAL HARMONY. In example 16, G being the lowest note, and those above formed in a series of thirds, G is the root or fundamental of each chord. Ex. 16. i -s>- ^ i -- 1 To find the root of any chord, arrange the notes so that they be- come a succession of thirds ; the lowest note will always be the root or fundamental. In example 17, E is not the root of the chord at a, because the interval from the second note of the chord, G, to the next, C, is not a third but a fourth. Rearrange these notes, as at <$, in a series of thirds, and the root is found to be C. a. b. Ex. 17 i J2- % -<§— -&- Chords are reckoned in this way containing three, four, and five notes ; those of more than five notes, or aggregations that cannot be readjusted in thirds, will be explained later. EXERCISES. Name the roots of the following chords : Ex. 18. <&— o TT <"> m -O.- r> -&- -0- jO- -G>- J2- sr Sr m % 1 j , 1 1 - & -a- -<2- =^ fcg 9 — — 1— ?h V I TRIADS. A chord formed of three notes is named a triad. This chord forms the basis of all musical composition, and for that reason will be used exclusively in Part I. of this book. Triads, like intervals, are either major, minor, diminished, or aug- mented. A triad may be formecton any degree of the scale. IO PR A C TIC A L HA RMONY. Each triad is formed by adding a third and a fifth to any note taken as a root ; the distance of these upper notes from the ix>ot de- termines the character of the triad; i.e., whether it be major, minor, diminished, or augmented. A major third and perfect fifth form a major triad. A minor third and perfect fifth form a minor triad, l A minor third and diminished fifth form a diminished triad. A major third and augmented fifth form an augmented triad. Roman numerals beneath chords show upon which degree of the scale they are founded. The different kinds of triads are usually dis- tinguished in this way : large numerals denote major triads, small numerals denote minor triads. A zero (o) by the side of a small numeral denotes a diminished triad, and the plus sign (x) denotes an augmented triad. The different kinds of triads found in the major scale would be distinguished by Roman numerals as follows : Ex. 19. Major. Minor. Minor. Major. Major. Minor. Dim. '7S~ II ^ -&- I £2- -3- -- -G>- -O- VFifth doubled VThird doubled. Y--V- % - -<&- —&- -O- -&>- -- ■& fj -&- --&- -<2- sr o -O.- :i-! II The leading-tone is rarely doubled unless belonging to a chord formed on the third degree of the scale : Ex. 25- It sometimes becomes necessary to omit one of the notes oi a chord. In elementary harmony the fifth is the only note that may be omitted. MELODIC PROGRESSION. The progression of a voice from one tone to another is called a melodic step. A sufficient number form a melody, air, or song. The best and really only thing theory can do to aid one to melodic writing is to point out progressions which are disagreeable to the ear or difficult of intonation. PR AC TIC A L HA RMON Y. 13 The melodic intervals permitted are : all the major and minor in- tervals to and inclusive of the minor sixth, the chromatic interval, and the octave. The major sixth, minor seventh, and all the diminished and aug- mented intervals are forbidden, with the exception of the diminished fifth which is permitted when the second note is leading-tone, moving up one half-step, as at a, or the same interval inverted, with the upper note moving dozen one half-step, as at b. The two are often combined, as at c. Ex. 26. ft. -&■ -&- =t -z^- -&- I -&- WE*l -&- J -&- jQ.- I The leading-tone, so called on account of its strong melodic ten- dency to lead to the tonic, may move to other degrees of the scale under conditions like the following : If the second chord does not contain the tonic, as at a, the leading-tone may skip. If the leading- tone does not belong to the chord of the dominant, as at b, or if it does belong to the dominant, but is placed in an intermediate voice, as at — £*- f=t= -«- ±=rt <-^-^-»# - l5>- ^ R 2 -* II THE WATCH ON THE RHINE. i — H l^-H— a — 1—4- \- -^-0- ^4=i m—m- t r ^m =p^ -> 0^0 d.d f j » &-\ & U ^ 00 m=^ -p-*- a rRA C TIC A L HARMONY. 15 It is a mistake to think, as many do, that all the beautiful melo- dies of the great composers came to them suddenly, as inspiration, and that they were written as first conceived and never changed. Nearly all of Beethoven's melodies are rhythmical, simple, and nat- ural in intervals and modulation, yet no composer spent more time in changing, polishing, and perfecting his melodies than did he. HARMONIC PROGRESSION. Here, as in the rules for melodic progression, all that can be done is to point out as clearly as possible those harmonic progres- sions which are repugnant to the ear and have been avoided by all the masters. If striking exceptions are found in the works of these great composers, one may be sure that these masters first knew the value of the rule before they disregarded it. Those who know most about such matters agree that the best way to study any form of ait is by absorption. The student will save much time and labor if he will follow the advice of his teacher, taking a great deal for granted. It is not wise to experiment on matters already solved by others. He will later fully appreciate and understand present restrictions. But the teacher should explain as clearly as possible, and es- peciallv by appealing to the musical instinct, why one progression is forbidden, another permitted. In connecting the different triads in a satisfactory succession, either of three movements may be used. When voices rise or fall simultaneously, as at a, example 2S, the motion is said to be parallel, or similar. When one voice rises while another falls, as at b, the motion is said to be contrary. When one voice remains stationary while another rises or falls, as at c, the motion is said to be oblique. Ex. 28. dri^-JrdrdrJ 1 ^> I « PS * Contrary motion is preferable to cither oblique or parallel. By its use the parts gain individuality, and many progressions which are considered taultv are avoided. i6 PRACTICAL HARMONY. CONSECUTIVE FIFTHS AND OCTAVES. If the student will play the following melody with an added part five notes below, he will find it most disagr.eeaLle. Ex. 29. *-> -*- • i i i d=±b=t J ■ft r r Till i/i ^ Nor will he find it more acceptable, but rather worse, if the mel- ody be doubled one octave lower. Ex. 30. S 9 —m — m — m — V& — etc. Consecutive fifths or octaves like the above, either by parallel or contrary motion, are forbidden. Fifths by Fifths by Octaves by Octaves by parallel motion, contrary motion, parallel motion, contrary motion. ( S=s^h=^= =^h=^~ =?- =i= =s= Ex. 3 There are other successions which taken alone are nearly as un- satisfactory as fifths, as, for example, a succession of fourths: Ex. 32. ^ <5>- '& ^ -&- -&- -&■ -G>- sr jO- - i But the preceding may be made very musical by the addition of another interval : Ex. 33. r=2$-- jGL- rs -d- & -&.- -- .a.- -&- -&- While the bad effect of consecutive fifths is rarely bettered by any arrangement of the voices. Consecutive unisons^ either by parallel or contrary motion, are forbidden : PRACTICAL HARMONY. Parallel motion. Contrary motion. l 7 Ex. 34. *> re -a. re (2- i -&- m -<2- -jO.- -~ 1 This succession, when heard under certain conditions, produces one of the worst possible effects, and for this reason was called the diabolus in musica by the old school of Italian musicians. \\ hen the chords of the dominant and sub-dominant are heard in succession, with the leading-tone in the soprano followed by tonic, the two notes of the tritone are heard, first in the soprano, then in the bass. Ex.36. This harsh effect is called the false relation of the tritof?e, and should be avoided by placing the leading-tone in an intermediate voice. Ex. 37. SEQUENCE. A sequence is a symmetrica] repetition of a melodic or harmonic figure. Ex. 38. Melodic. 4— -El t"^J\{^..;\. .:..;!! ^. t$ PRACTICAL HARMONY. Harmonic. Ex. 39. In the above harmonic sequences the same bass is harmonized three ways. In each all voices move regularly in exact sequence. But tin's is not always necessary, nor need the responsive figure always be exactly reproduced. In sequence, the ear being gratified by a regularly recurring rhythmic figure, certain progressions which would otherwise be considered faulty are permissible. Note. It is not expected that the student will memorize or even understand all the rules and accompanying illustrations in this chap- ter. They are placed here more for future reference than present study, and he will better appreciate them after writing the succeed- ing exercises. The foregoing illustrations are condensed for convenient reference into the following RULES FOR HARMONIZING BASSES. MAJOR MODE. I.- If no figure stands over the first bass note, begin the exer- cise with the octave of that note in soprano, placing the other notes of the triad in the nearest position underneath. A 3 or 5 signifies that the soprano is to begin with the interval indicated. This ap- plies to the first chord only. II. If a chord contains notes that were in the preceding chord, they should be retained in the same voices. This rule may be lisregarded under the following conditions: When the bass moves from the second note of the scale to the dominant, as at a ; when the second chord is a repetition of the pre- ceding chord, as at /> ; and in sequence, as at c. b. Ex. 40. -I- A~Z iz=iiiiz=| e -&- >)■■ eI^USS PR A C TIC A L HA RMONY. 19 III. If there are no notes alike in consecutive chords, move the soprano, alto, and tenor in contrary motion to the bass. IV. Consecutive fifths and octaves are forbidden. V. Allow no voice to progress any augmented or diminished interval except the augmented prime — chromatic interval — and the diminished fifth, as in example 26. VI. In the succession V, IV, do not allow the relation of the tritone between soprano and bass. ( See examples 36 and 37.) VII. Double the leading-tone rarely except in sequence. SUGGESTIONS. Choose positions neither too high nor too low. — Do not pass the limits in example 20; the extremes should be of short duration. — As a rule, double the root in preference to any other interval. — Con- trarv motion is stronger than either parallel or oblique. — With a bass moving sequentially, seek a corresponding svmmetrv in the other voices. — Although not invariably to be observed, it is usually best to close an exercise with the soprano ending on tonic, pre- ceded by leading-tone. Note. Particular attention is called to the fact that when the bass moves from the second degree of the scale up to the dominant, it is often best to move the three upper voices in contrary motion to the bass. See first exception to Rule II. Also when the bass moves from the dominant to the sixth, it is often best to double the third of the chord on the sixth degree. This is especially true if the chord on the dominant has its third — leading-rone — in soprano. Not. Ex. 41. % -72- -TOT -1& & -& -&- II II A careful observance of the preceding suggestions will save the student much labor and needless confusion when he comes to exer- cises in the minor mode. In the following exercises a soprano, alto, and tenor are tc be added to the given bass, according to foregoing rules. In harmo- nizing these basses no instrument should be used. The key- board should not be touched until the exercises are finished. 20 PRACTICAL HARMONY. A>. 1. 2. §» ^ "Z7- -- -- o -»: ^ II wi>. Mi^ ,§>_ -S'- -02- ■sf — Si" 5fr. -02- -i r -«>- ?=F ■5 1 - ^ EEEEEEE 1 ■ «- 4. PS -I 02- ^=p: -s>- F 4= -««- ^ =t "Sr II /'. '■ g» i 0= 5* H :»: o =t -g* — «s>- "25" 3 6. ©feg^E -- ^ =j -=3 02- -& — -P — g*- (=2 &- t- II -t5>- B\>. 7. 8. 9. §» -s>- P 'ST 27" -&- & I f ^-£ » 1 O p=±=t^ ^g— f 2 -- ^— hs< — - ^- c? I 2-E§i»: 3 -02- ^b. t± £ o -02- -4- -&- o \\ 13 liil=Ei^S^ -<5>- ^R=fF^ 5»-^-^ 1 PR A C TIC A L HA RMONY. 21 After these basses have been harmonized they should be played ; whenever a succession is unsatisfactory it is possible that a rule has been violated. If a passage could be written in either of two ways, each apparently correct, write the form preferred in large notes, and the other possible disposition in small notes. After the exer- cises have been corrected in this way by the student, with the aid of an instrument, he should listen to them while played bv another. Without looking either at the keyboard or the music he should name the major — principal — triads whenever they occur. As soon as these can be readily distinguished the minor chords should be named in like manner. This exercise stimulates the musical in- stinct and should be followed throughout the book. It is recommended that the preceding exercises be corrected be- fore the following additional basses are harmonized. The lessons should all be written in ink, and the pupil should come to his les- son prepared to play them in the key in which they are written, and also to transpose and play them in the keys indicated by a capital letter at the right of each bass. This practice of transposing the lessons should be continued in keys selected by the teacher. ADDITIONAL EXERCISES. The following basses are to be harmonized according to previous rules. The repetition of notes, irregular rhythms, and generally light character of these exercises are purposely introduced ; it is one one of the aims of this book to lead the student bevond the writinsr of monotonous psalm-tunes. Although the succeeding exercises are instrumental rather than vocal, all previous rules regarding the tieing over of notes common to consecutive chords should be strictly fol- lowed. Whenever rests occur, as in exercise 5, the voices should move to the next chord in as strict accordance to rule as though there were no rests. As a general thing it is best to tie over a note which will bring contrary motion ; this rule may often be disre- garded in progressions like the following, when the outside voices move in thirds. Ex. 42. I % J i o ¥ 1 i I " V !! 22 PR AC TIC A L HA RAW A Y. EXERCISES. Allegretto. 8 1. l§gfe 00 c- 1-0, -0- -&- -_i_. ! — |-F-# -- =9 1— H ^h^ -0-&— --i^n^f-^z ^EB^ =ft sr^* tt £ ^ II 2 ^ig3 4=*E^ Eg* = ^=g=j^^Ej=^EJ =fc JL-P—& S3£ _^ — „ — - =P=3Z^T -• I * — ^=^~ zjr =5=?= 1 Andante. ■Cl-?- *r8 • * 8 - @SP=^iE* -i l_ V- P-'-r0-±-P-^ • f±±3? 1=1 :=±l2:$3 • — P- 0^~t- 3 * -i — -&- ■#-=— F- t== s Allegretto. 3 4. 8^ ra^qzcnL^ ■I M .- ^ e hb=h^±hd tt Vr"hr~fi . #d!=t H iz±atz: ia Lightly. P 3 ta^=*=#^ : -s>- f— Z-0— *- — 9 * . »-r- ^-H^a PP jsh. N ' -L^_ P3 9b X—B -Sr .. i^mm ~zt-r I PR A C TIC A L HA RMONY. 23 CHAPTER III. SCALES. THE MINOR MODE. MELODIC AND HARMONIC PROGRESSIONS IN THE MINOR MODE. THE AUGMENTED SECOND. The two scales employed in modern music are the major and minor. Each major scale has an accompanying or related minor scale, called its relative minor. It is customary to use capital letters in designating the major keys ; small letters the minor. Ex. 43. C (Major). a (Minor). The relative minor of any major scale has for its starting-point, or tonic, the third note of the descending major scale, and its sig- nature is the same as the major to which it is so closely related. The relative minor of C would be a ; that of G, e ; and that of F, d. A major and its relative minor are said to be related, because they look and sound much alike. The major scale of C is formed as at I. in example 4-4 i on e of the earliest forms of its relative minor, a, stood as at II. : II. Ex. 44. * 3=± P^ :«=; I This form was in use long before our major scale. It has under- gone various transformations, which would here be confusing and valueless. The form used to-day in elementary harmony, and for that reason called the harmonic minor scale, stands as at II. in the preceding example, with its seventh note chromatically raised. Harmonic Minor Scale of a. Ex .'45.fi 1=4 -tr ~* ill 24 PR AC TIC A L HA RMONY. The harmonic minor scale, then, is found by taking the third note of the descending major scale for a tonic, and chromatically raising its seventh note. This seventh was raised to gain a leading-tone and to secure a dominant chord in minor the same as in major. A chord on the fifth degree in any minor key without this leading-tone would be dis- appointing and produce no satisfying clocr. Ex. 46. I -<9- - I 1 II PRACTICAL HARMONY. In the major mode it is often well to double the third on the sixth degree. In the minor mode the third on the sixth degree must al- ways be doubled when preceded by the fifth degree, to avoid the augmented second. Ex. 49. V VI V VI V VI The third doubled in the octave, as at a in preceding example, is always preferable to the unison, as at b. This unison between soprano and alto weakens the harmony, and should not be used when another disposition is possible, unless coming on an unaccented part of a measure, as at a in following example, or at the close of a musical phrase, as at b. Even in the latter it is generally better to allow the leading-tone to descend, as at c, in order to gain a full chord at the close. a. b. c. Ex. 50, 1 m 3 i ~ 83T~ a r fH S& m cc -gf>- -&- & £2_ II -G.- Cf & a.- -!S>- II The unison is least objectionable between inside voices, and is best introduced on the weak part of the measure. The different kinds of triads in the minor mode are as follows: Minor, Dim. Aug. Minor. Major. Major. Dim. Ex. 51 . I -3- i _ 11° iikS 3 g 19 III* "SP- IV 19 m *> s> -<52— -n3- -62 SS ^^ r w^ VI VII' For the present the diminished chord on the leading-tone, and the augmented triad on the third degree will not be used. Reasons for this will begiven later. The diminished triad on the second degree will be of frequent use. The principal chords oi the minor mode are the same as those of the major, and all that is written regarding them there is equally applicable here. 36 PRACTICAL HARMONY. Whenever a sharp, flat, or natural, stands over a bass note -with- out a figure by its side, as at a, example 52, it signifies that the third note from the bass is to be chromatically changed. A figure by the side of a chromatic sign calls for the corresponding interval from its bass to be altered. See />. Ex. 52. A chromatic sign once used to change a note, will effect all other notes in that measure that are on the same degree. ADDITIONAL RULES FOR HARMONIZING BASSES. MINOR MODE. I. Whenever the bass moves from the fifth to the sixth degree of the scale, or vice versa, double the third of the chord on the sixth degree. II. Whenever the bass moves from the second degree of the scale up to the fifth degree, move the three upper voices in contrary motion. Xotc. The early musicians, as a rule, made the final chord of any piece of music major, even though the mode were minor. Such concluding chords should not be looked upon as changes of key or modulations, hut rather as a change otform from the minor triad to the major. PAL7.STRINA. Ex. 53. \J " "" f ^ £ 1^— 9V 5 - -v 1 • 1 " m ^—] ^ 5 * &— — - — H These early writers looked upon the minor third in a triad as an imperfect or artificial interval, and consequently rarely used it in a concluding chord. This concluding optional major third will oc- casionally be found in the succeeding exercises ; it will be designated by the necessary sharp or flat enclosed in parenthesis, as in examples 2 and 3 in Additional Exercises. PRACTICAL HARMONY. *7 SUGGESTIONS. Carefully reread the rules and accompanying Suggestions at close of Chapter II. The student will do well to look the basses through before harmonizing them, noting those places where the bass moves either from V to VI, or VI to V, or from n to V. After marking the places where these successions occur, again read the two additional rules for harmonizing basses in the minor mode. ■&- EXERCISES. G>- i l. §3 4-z? -h- -- *> -C2-- i 2 - EiSs HE =r r=^ •r 2 s< -7zr jS.- 3. SHE -&- -|— j2- -^> "»- I -^- - f. I 4. zgifcrffigEgzi —2 -s 1 - s>- =t -- -<2- Z?" "Z7- I * -f" -<2- 4 <5^-r ^_ =4 -zsf i e. b ^b o r_i E* X ^- 151= •g-ii-^-r-^--^ ^r^FT f^g-r ■sr; D 7. 8. F F—f :t: «<— «?-= -—\ II tSgPKE D -<3L b5z±lr§^±t ^_ n ^i_ J 9 - ^ISEE * ■'" a ^. a a ^gg^f a ft -*?- ■o- ^wef^ l^ES a -> ^ ^ i 2S 1 1. PRACTICAL HARMONY. a -s>-. b „. SSfeS $ ££*=£: P ■F *s?-^ ^=P= -P gg$ ^rfr-yrP 2 - 12. t2^i^ jS2- -s^— -S>- =f=tt ■&=x -- 13. iip^ii -(2— 4- -(2- -,-(2- t=^ -&»- ;i;i «. is?- e ^. ADDITIONAL EXERCISES. The following exercises, corresponding to the Additional Exercises in Chapter II., should be harmonized after the preceding exercises have been corrected. 1. o : B B •- B B a t 2- E§3fe*fe^EpEf =^=Ft - d=^^i=i « — m-i -tS- =t=m izzsit -«>- ^ ; ■5 1 4. ^iSifizpzz^:^ *. i==£ f -*-3— * - m I*** &-*- -H *rV-*r 1=f **-=!-* ^^r II EXERCISES. The student should now compose several short basses in both the major and minor modes. The arrangement of all like work must be left to the discretion of the teacher. This original work is of the greatest importance, and should be insisted on at each lessor. r/iA C J JCA L II A KMONX. ** CHAPTER IV. CHORD RELATION. HARMONIZING MELODIES The relative good or bad effect of a chord depends much upor preceding and succeeding chords. The same chord, placed undei different conditions, produces wholly opposite effects. This is st true that a triad heard under changed conditions so changes in char- acter, that to the inexperienced ear it is unrecognizable. A chore which, preceded by certain other chords sounds very disagreeable, may become under other conditions one of the most agreeable. The truth of this may be in a measure realized by playing the following illustrations, which contain precisely the same chords : Ex. 54. 19- HiB Sir II m §fc§ I -&- V- 1 £>- r> II That at a is almost intolerable, while that at b is acceptable. The chord on the leading-tone, marked x, is unpleasant at the 1 ?st when coming in the major key with its root doubled, and for that reason has not been used. This same chord in the minor mode is full of character and beauty. Ex. 55. 3° PRACTICAL HARMONY. When one hears an isolated consonant chord, the ear immedi- ately accepts it as a tonic. If there are several chords in succession the ear is not satisfied until the tonic is again heard. Ex. 56. At a, example 56, there is no satisfactory close ; at fr, the same suc- cession with the tonic added is complete and satisfies the ear. For this reason it is generally best to begin and close a piece of music with the chord of the tonic. In a series of chords there are three chords which must be more frequently heard than others in order to make the tonality and mode decisive. These are the tonic, dominant, and sub-dominant. A suc- cession which did not contain more of these principal triads than the secondary triads, would be indecisive and lack tonal force. Their excessive use produces monotony ; their good effect is height- ened bv the judicious intermixture of chords on the other degrees. Composers give as delicate attention to chord-succession as paint- ers do to the mixing of colors. The chords of the tonic, dominant, and sub-dominant have the strongest tonal force ; next to these in tonal force are the chords formed on the sixth and second degrees ; the latter should neither be too frequent nor too prolonged. The chord on the third degree in the major mode is weak, tonally, and should be more rarely in- troduced. The augmented triad on the third degree of the minor mode, as well as the diminished on the leading-tone of either mode, are not to be used. HARMONIZING MELODIES. THE MAJOR MODE. In the following exercises a soprano is given, to which alto, tenor, and bass are to be added. The rules given for chord progression in the harmonizing of basses apply here. A soprano note could be harmonized as either the root, rRA C T1CAL HA RMONY 3* third, or fifth of a chord. For example, C could be either the root of a chord, as at a, the third of a chord, as at 6, or the fifth, as at c. Ex. 57. b. ~Z7- -&- -G>- ~or -&- . — &- &- 1:1 SUGGESTIONS. Besrin each exercise with tonic and close with same. — The inter- vening chords should consist largely of the three principal triads. — . The chords on the second and sixth are of frequent occurrence. — The chord on the third degree should rarely be used except when followed either by the sub-dominant or the sixth. Ex. 58. A r- — V /" ^N u yr ^ e> - f\ & & Z? II w ■ft ~& Zr -&- m --&- -ts>- I — &- z? 1 A chord maybe built on any note of the scale except the leading- tone. — It will be found best to first compose a bass, then add the in- termediate parts. — The harmony should change with each soprano note, and the root of each chord must be in the bass. — Never move from the fourth degree to the third degree. — (See note Ex. 59.) Never move from the fifth degree to the fourth degree, with the soprano moving from leading-tone to tonic. Note. The progression from the fourth degree to the third degree produces the false relation of the tritone. Ex. 59. r#~ II w II ■ tr ^. ^ —&— O 1 3 2 PRACTICAL HARMONY. Note. When first attempted, the harmonizing of melodies is exceedingly difficult. The following exercises should bere written till satisfactory to the teacher. With the average pupil, two or three or perhaps more lessons should be spent on this chapter. Not more than eight melodies should be harmonized before the teacher corrects them. The practice of transposing should be con tinued. 1. MELODIES. THE MAJOR MODE. er^t r> d: •rizfci -s>- 0^ 0-0 B. 8 2. = 7f: (T ^= g ■&—&- ■f^-e- I 3. -*mm :i E^. -• > d •- ■73- 0—0- *$=$=*$=* • 4. atS H~ i • * tri e £ ±*g£ts!: si Sfc^f^ F 0000 *=± II It «-*+*•! * J-J =+ -<&— 6. ITl^ ■ 0^-0-0 ^4 d=p=tr=|: *b. FffM4^MI A - * G. F ffi^S3jrT=tJT :: l= ^ 7. 8. »^^ d \d. +■ j: #b. -(=- 1 PR A C TIC A L HA KMONY. 33 9. fc^^ m fr-fr ^ 1 ! f | F j22_ -P= #- t5> — *— m — • fe^l 10. tet «g -& — «> -I— MM -f52— «>- >5 -i5>- 5*— - P—<9- I 1 1 - eV =?w^r* . £? —— & ~- — H 1(1 ) — ^ P V — s> — a ' — — 1 — ,9 — --^— u 12 zta=«=4 iSbtfc*: — «»— * — *- 4 — 1-4 -z?- II i= 13. 14. 15. ^E -&- » # F -«a_ -- M= II S A\>. £%£=£ t—m—t M=t=c ^-= — <&- 1 tf H ' ' ?=g = -- "Z?" -<©— Gt>. 25 II MELODIES. THE MINOR MODE. I m -* — * %&-* m — * — # .$* -25*- i g^ 2. II =fc —I I- e). J. © (»)2= 3- : ^ ^ z^8. »• • ^ \> l u 4. feI££H*»: :S3 c-> (O -> o &* & 34 PRACTICAL HARMONY. 5. to iWEStg tad ft- •Td— d — !- •jj£ &s>- =t -g^-gH -g* ! Jl 1= H --^^ (5) ife^pgi^^^^ ?d==H CHAPTER V FIGURING OF THE BASS. OPEN HARMONY. In order to indicate as clearly as possible the position which the notes forming a harmony are to occupy, figures are placed either above or below the bass. The figures indicate the relative position of the upper three voices above the bass. The figures | would signify that an octave of the bass should be in the soprano, a fifth from the bass should be in the alto, and a third from the bass should be in the tenor. (See a, example 6o.) It must be understood that these three upper voices may occupy any octave above the bass, provided the voices do not pass the limits given in Chapter II. The figures f would signify that a third from the bass should be in the soprano," a fifth from the bass in the alto, and an octave from the bass in the tenor. (See b.) Ex. 60. ^ -<2- -- 8 j2- b. JO- -G>- -G>- 3 5 8 fl II It is often desirable to move one voice of a chord while the others remain stationary. This may be indicated by changing the figures according to the interval desired, and by drawing a horizontal line after those figures, the corresponding notes of which are to remain stationary. PRACTICAL HAKMOXY. 35 Ex.61 a. | . rfr^r* — — n 1 1 — i h C. ( &£ sJ ~+- 1 — -g : 1 g : ^ 1 IMJ Z r2 & s? • & ' 3 8 5 3 -<&-. 3 5 8 5 3 J. 1 ■ UP 5 3 5 3 5 8 5 8 1 8 3 1 , 8 J ~ Of f Bi3— = -— -- P* H 1 S n a • s> • « • i « • ii V £ 1 ii Such changes are often made to gain rhythmic or melodic variety, or both. A horizontal line over different bass notes signifies that the harmony over the first bass note is to be continued. In such a case the upper three notes may remain stationary, as at a in the following illustration, or the position — not the harmony — may be changed, as at b. Ex. 62. ± :± :=!: m A horizontal line drawn through a figure signifies that the cor- responding interval should be diminished. Ex. 63. -TO- :i=h ^m Consecutive octaves and fifths which result from a change of posi- tion of a chord, are permissible. Ex. 64. 36 PRACTICAL HARMONY. It often occurs that a change of position does not correct what would otherwise be consecutive octaves or fifths. Ex. 65. The consecutive octaves at a and c are hardly more disagreeable than those at b and d. The change of position, coming on the weak part of the measure, does not destroy the effect of the octaves. The same is relatively true of the fifths at e andjf, and of the octaves and fifths at g and h. Experience and instinct are the best guides regarding progressions like the preceding, because the part of measure on which the chord occurs, as well as the relative length of the different positions, greatly influence the character of the successions. OPEN HARMONY. When the soprano, alto, and tenor lie close together, as at a, example 66, the harmony is said to be in close position. When the voices are so disposed that the soprano, transposed one octave lower, comes between the alto and tenor, or the tenor, placed one octave higher, comes between the soprano and alto, as at b, the harmony is said to be in open position or open harmony. a. b. Ex. 66. - — &- -J5L- -fi. ^> — a~ -O.. .£2.- -— h -G>- -— =* 9 4- 6k- -f~ -<9- ±^* : i|— S 1 - -«> — -GL—\ -iZ- T -■&- -X &h-e\- * N -I *, r -<9- -&- ■^ - -*9- 1-&- r n=2- -(S 1 - -S>- :£: r I The two examples above contain the same harmony ; the one at b is much the richer, and the alto and tenor voices lie more in their normal positions. In the following exercises the position of the voices in the first chord is indicated. After the first chord the voices should move to the nearest position of the next chord, according to previous rules. it often occurs that an exercise beginning in open harmony win end in close harmony, and vice versa. In many of the following exercises the second and sometimes the third note under which a horizontal line is drawn, is a note foreign to the harmonv. Ex. 68, 1 \ -&- <9- -&- jO- I Se|e£ -s>- 3 2 .G-±- A. -f&- ^ -&- \ All notes foreign to the harmony are called " ■passing-notes;'* they must be approached and left diatonically, i.e., they must never be skipped to or from. But if the note or notes belong to the harmony, they may be approached or left by a skip. ~\ 1- Ex. 69. IS jO.- o> m=k & *=}-- ii 4 $ "5°> 3§ PRACTICAL HARMONY. Passing-notes may be employed in the different voices, if by so doing rhythmical or melodic interest is gained. The following frag- ment: 70. 9. — would be correct, harmonized as follows : But it would be more interesting with passing-notes, either in the tenor : I «== & -0- -&-. atzt f^i=f r -- -&- o ^ ^5-^=2- 75H-- ■g?— » 3. IWf^ ■*-*- 3=E vS>— r^ g=^ =j *£t* [I 8 5 3 3 — 8 5 4. iBzdtti-^i H=fe 3 8 8 5 5 3 -&- p=r=^ S3 J*** £=* ;^— •- i 5. i^z-fc^tozj^z^: - — P-b -4 ^ * | T - CHAPTER VI. CHORDS. THE FIRST INVERSION. Many of the preceding exercises have necessarily been more or less dry and uninteresting on account of the chords all standing in what is called their fundamental position. When the root of a chord is in the bass, the chord is said to be in its fundamental position. When any note not the root of a chord is in the bass, the chord is said to be inverted. When the third of a chord is in the bass, the chord stands in what is called its first inversion. d-O PR A C TIC A L HA RMON Y. At a in the following example, the chord is in its fundamental position ; at b, the same chord is in its first inversion. b. Ex. 9- ^ At b in the preceding example, there is a figure 6 over the bass note. This shows that the root of the chord, C, stands above the bass note. Whenever a 6 stands over a bass note it signifies that this note is the third of a chord ; the chord of which this bass note is the third should be written. If a C were given with a 6 over it the chord of A would be required ; a 6 over F would call for the chord of D, etc. All that was written regarding the doubling of the third in Chap- ter II. should now be reread ; it is particularly applicable here. Whenever the third is in an outside voice — soprano or bass — it is more prominent than when in an inside voice. For this reason it should rarely appear in soprano and bass at the same time. At a in example J2, the third coming in outside parts is so strong that little else is heard. Occasionally, in order to gain a better melody or rhythm, the third may be doubled in outside parts, as at b or c. At the second measure of the example at <~, the third is best doubled. As was explained in Chapter II., it is often well to double the third when it is one of the principal notes of the scale. !x. 72. The first inversion of a chord is so soft and pleasing that many progressions which are harsh and disagreeable in their fundamental position become wholly satisfactory when in this first inversion. It was for this reason that the study of triads in the root position, was made as exhaustive and exacting as possible. If the preceding PRACTICAL HARMONY. 4-1 exercises were so arefully written as to be to a degree satisfactory, it will now be possible to gain far more agreeable results with the use of the first inversion. This is an important point to keep in mind when harmonizing melodies. Parallel motion, even in four voices, is often possible when mov- ing to a first inversion. Ex. 73. I i OBSERVATIONS. In chords of the sixth, as in chords in the fundamental position, it is usually best to double the root — The third may be doubled if it is one of the principal notes of the scale, or to gain a more melo- dious leading of the parts. — In successive chords of the sixth, with the bass moving diatonically, the third may be doubled in alternate chords. The diminished triad on the second degree of the minor scale usually appears as a chord of the sixth with the third doubled. Consecutive fifths are permitted between inside voices if the second fifth is diminished. Ex. 74. PS -&■ 49- 6 *-i & r (2 Jg: i ^ II 6 6 6 (2- . 3 & 1 <> ■-&■ II 1 %Ep " 6 6,, -r>5 -=—r-& & i'PP o> 6 , 6 _ -w 42 PRACTICAL HARMONY. 3. : m -G>- &- 6 tf -«>- g^j g^^^g|a^^^3i^ [| 5. » :tfct 3 fcfc F^i X=- 6 6 6 t 3Edw& -•-(- *M: SpT ^M\ .SEE 6 6 6 6 _(2- 4= -«>— ±4= ^i A H -•-•- o ^ I .Stftf note. 65 7. £ »£££ 4=ti i9- :t==l P 6 65 6 6 65 ^2- -(^ m 3 — 5 # 8 — * s. ESStefe 9-B|g^ : ^ -f=2- ±±zz= -<2- J] 10. I * 8 6 3» :p: 36 f e 36 J 3 F ^W i ^M==t=l d e 56 « s» Sit B Note to the teacher. If the preceding lessons have been thoroughly mastered, it is very desirabre that the pupil should begin the study of strict counterpoint. If undertaken at this period the student will use all the music material he has acquired, and the study will prove less irksome than it would later on, when he would find it neces- sary to begin again, and with irritating and apparently senseless restrictions. Harmony and counterpoint are not different studies but different departments of one great study; the former treats more specifically of the structure of chords, the latter of melodic invention. Nothing will so speedily give the student an accurate working-knowledge of triads, in their root position and first inver- Note. 63, 65, 56, 01^6, signify that two chords are to be written over one bass note. The 6 stands for first inversi^ the other figure for root position. In such a case the 3d ( the bass note ) is usually doubled fft the 6th chord. PRACTICAL HARMONY. 43 sion, as the study of strict counterpoint. There is no reason why it should not be taken up now, and be carried on hand in hand with harmony. It would be preferable in conjunction with this text-book, to use the treatise on strict counterpoint, viz. " The Art of Counterpoint," by the author of Practical Harmony. In harmonizing the following melodies the rules given in Chapter IV. should be followed. SUGGESTIONS. The chord on the strongly-accented part of a measure should rarely be the same as the chord on the weak part of the preced- ing measure. A chord on the weak accent anticipating the strong accent, robs the latter of much of the emphasis which should belong to the first count. It is not necessary to change the harmony with each melodic note. The bass may remain stationary : or may pass from fundamental to first inversion, or vice versa. 1 \ u In choosing between open or close harmony, select that which will keep the voices in their normal position. Open harmony is usually preferable. ( See Chapter V. ) The third of a minor triad is often doubled. ( See Ex. 73. ) MELODIES. I. i t§m T-^r~^ — &t± -£?- 5 'V -<2- n QpJ iJ^JfeN^^^M ^i^H 44 PR A C TIC A L HA RMONY. fa is -&- &±?=± ±=fz 4= t — 1= c rtr~ - I 5. U y,^4e) f^ B -#-(S2- Ip=^ r«-fi? F^g- P -5>- g^ .52- I 8 BE^ sea m^g =j=ptt= ■F-i- I CHAPTER VII. CHORDS. THE SECOND INVERSION. The second inversion is obtained by placing the fifth of a chord in the bass. In this position the notes above the bass form the intervals of a fourth and a sixth, and for this reason the second inversion is com- monly called the six-four chord. The triad of C in its three positions should be figured as below : Ex. 75. Root position. Fi rst inversion. Second inversion. / / 1-1 ( / r? o 72^ 1 ( \ 1-2 n 1 V * % & M «_ 8 5 or 8 -- 6 6 f 9 c l| II When different chords are to be placed over an unchanged bass note, each chord should have its special figuring. Ex. 76 \ 3: -9r- «- a -£v- 6 6 4 g£| ^ I i PRACTICAL HARMOXY. 45 In a case like the preceding, each chord has an equal part of the value of the hass note. It often occurs that the general rhythmic character of the piece demands an unequal value of the notes. Figuring like that in example 76 could, among other ways, be varied as follows : Ex. 77. Figuring like the preceding is vague, at the best, and the choice ol the length of the notes must depend largely on the taste of the pupil. The second inversion, far from having the sweetness of the first, has a character which, if not hard, is at least very bright and dominating. There is an imperious tonal force about this posi- tion of the chord that is so strong that the root generally gives the effect of a tonic. This is especially true if it is introduced on the strongly-accented part of a measure. For this reason its use is subject to certain conditions ; for, if introduced carelessly on any note of the scale, there would result the effect of constant mod- ulation, or at least of wavering tonality. On account of its power- ful tonal force, its use is largely confined to the three principal triads. When introduced on a secondary triad, especially if it comes on the accented part of the measure, it gives the less important triad undue prominence. From the foregoing, it will be readily under- stood why this six-four chord is best used on a tonic. Play the following examples from " Lohengrin " and note the dom- inating, imperious effect produced by the six-four chord. Ex.78 1 I !'' '-- : o £3 3 I s > 5 d&£ 6 4 O 3 s> • -- m m <> % 'be* 1—4- >• c* ;-> o> a i II bo *» o II 4 6 PR AC TIC A L HA KMONY. The six-four chord, although constantly used by modern musi* cians, is subject to peculiar conditions. No other chord demands more delicate handling, nor is there one that is more abused. The laws governing its use are among the most important in musical composition. In every six-four chord in a major key — except that of which the root is the leading-tqyie — there will be found the interval of a per- fect fourth between the bass and one of the upper notes. Whenever a six-four chord is introduced on any note except a tonic, one of the notes forming this perfect fourth must have appeared in the preceding chord. When a note has thus appeared in the pre- ceding chord it is said to be prepared. If a six-four chord were to be written on C it should enter in one of the following ways : b. Ex. 79. s- -&- -&- sr 4 6 4 -&- ~0~ C -a. II In a six-four chord, on C, the-two notes forming the perfect fourth *tre C and F. One of these notes is prepared in each of the above example:) ; at a the F is prepared, at b the C is prepared. In the chord following the six-four chord, one of the notes form- ing the perfect fourth should remain stationary ; the other should descend. This is called its resolution. b. Ex, SG. At tf, ir. the preceding example, the fourth is prepared in the bass and resolved in the soprano; at b the fourth is prepared and resolved in the tenor. It should be clearly understood that either one of the notes form- ing a perfect fourth maybe prepared, and that this preparation need PRACTICAL HARMONY. 47 occur onlv when the fourth is formed between the bass and an upper voice, and may be dispensed with entirely when the root of the chord is a tonic. In harmonizing' a six-four chord it is best to double the fifth of the chord, — that is, the bass note. Ex. 81 ■i -SM- 1 6 -&=*: 1 The fundamental, when doubled, produces a good effect in pas- sages like the following, where the fundamental forms a part of the succeeding chord. Ex. 82. If, however, the fundamental of the six-four chord does not appear in the chord folio-wing the six-four chord, it is better not to double the fundamental. -!— r— 4 - Ex. 83. As was stated at the beginning of this chapter, any chord in its second inversion, entering without preparation of its fourth, will produce a modulation. From this it will be understood why the second inversion on a tonic needs no preparation in either major or minor. A six-four chord on a tonic only strengthens its own 48 PR A CTICAL HA RMON Y. tonality. This chord on a tonic should always be attacked on the strongly accented part of the measure. Ex. 84. I s~ ?z -<9— 6 4 -iS>- -<5>- -TZT =1= — «- -&- 1 -- -£2.- I I When a six-four chord is preceded by another position of the same chord it needs no preparation, as at a ; when succeeded by another position of the same chord it needs no resolution, as at b : Ex. 85. Successive six-four chords are permissible only when one is built on a diminished triad ; this fourth needs no preparation. The fol- lowing would be practicable in the minor mode. Ex. 86. y c =£ -&- s< ty ~ s>~ 6 4 --SI- o III (S-- -25*- -S? 6 4 t "25" -(2- "2?" II Whenever a six-four chord is built on the second degree of a minor scale, as at example 86, the bass note should not be doubled. Although the second inversion is best when used on the principal triads, it may occasionally be introduced on other degrees on the un- acce nted part of the measure. Here it will not have too great tonal PR A C TIC A L HA KMONY. 49 importance, ing chord. In such instances it has more the character of a pass- On second degree. On third degree. Ex. 87. ± w- -- On sixth degree. /* N_ =2: II -&- 6 4 6 t 9* c> --&- -72~ G>- & f> II In each of the six-four chords in example 87, o?ie of the notes forming the perfect fourth is both prepared and resolved, as explained in examples 79 and So. OBSERVATIONS. When musicians speak of a dissonance they do not necessarily mean a discordant, inharmonious combination of sounds. A dis- sonance is a chord that is not accepted by the ear as final ; it must be followed by another chord. Dissonances may resolve into other dissonances, and indeed, it is a marked characteristic of the modern school of chromatic harmony that they do so resolve; but, unless thev eventually arrive and repose on a consonance there is no satis- fying close. The following successions, although harmonious and agreeable, are dissonances. No ear with the slightest musical instinct could be content with an ending on any one of them. Ex. 88. Ex. 89. x: S§dE8?£s£Bi= *£ &zx 1 i^zte: <2_t:J&22_t| -3* -49- -s>- ^i=^=fe=Ei«==^^^^^^ JZ- -«> -&■ 4*2- ? b* m YVagnkr. fi o z > 8a - •-. Jr. fe 3* -P- H- 8* &• ^ £ 5 t ?o Bs ^ i - ^p^E^|fe%i • tt* r -4^ r > 5° PRACTICAL HARMONY. The following, on the contrary, are consonances, and any one heard alone would be accepted by the ear as final. a. Ex.90. JO.- -GL- -O.- -&- -&- -&- -O- The difference, then, between a dissonance and aconsonance is this : a dissonance, though oftentimes more harmonious and satisfying than a consonance, must be followed by another chord, while a consonance, taken as an isolated chord, will be accepted by the ear as final. The best effects are those in which there is a judicious use both of consonances and dissonances. Ex. 91 \ \ i£g \ kJ- Wagner. &=P&# r-%=^r • ^ w^m PRACTICAL HARMONY. 5* The chord following' a dissonance is called its resolution. When dealing with dissonances as explained in Part II., it will be found that the school resolution of any dissonance, demands that the dissonant note shall progress down to the next degree of the scale. The six-four chord, although not properly a dissonance, has this characteristic of all dissonances : it will not be accepted by the ear as final. The regular resolution of the dissonant note, the fourth — espe- cially if it be used on a tonic where it has the most character — ■ follows that of all dissonances and should descend to the next degree of the scale. Ex. 92. All that was written in Chapter I. regarding the interval of the fourth as having, at certain times, the character of a consonance, at other times that of a dissonance, for which reason it is called a mixed, or neutral interval, will now be better understood : when the interval of the fourth comes between two of the three higher voices, as at a in example 93, it is consonant ; but when it comes between the bass and any higher voice, as at b, it is dissonant. .a. b. Ex. 93, f as: ^ -£•-_ 6 t -<2- [' !. -7S~^r- r> -f7* -&- -<&- II 6 ■I 6 1 n A clear understanding of the preceding will be of great service to the student when he begins to write strict counterpoint. The most frequent exceptions to the preceding rules regarding the six-four chord, are included under the following irregular resolutions. I. Either one of the two notes forming a perfect fourth, instead 52 FRA C TIC A L HA RMONY. of descending, may remain stationary and form a part of the succeed* ing chord : Ex. 94. IT. A fourth, instead of descending, may ascend chromatically Ex. 95. 6 I -<&- ^H -- s>- -G>- ~K>- -&- -#?- m 6 4 A chromatic change of the fourth, like the above, always im- plies a change of key. » The resolution of the fourth is often dispensed with by the best writers, when coming on a tonic in successions like the following: Ex. 96. But all such progressions are usually followed by harmonies which may follow the six-four chord ; and they should be looked upon as interrupted resolutions of this first chord. Many of these "observations" will not find their application till later. It is not expected that they shall be fully understood at this period, but if they have been carefully read the student will be well-prepared for the study of dissonances as they are treated in Chapter XI. The figures % followed by a 3 or a 5, or either of the chromatic PR A C TIC A L HA RMON Y. 53 signs t3, £, signify that two chords should be written over the same bass note ; the bass note is always the root of the second chord. S s <■- Ex. 97. i 9i «=: -(9 — & &— 6 3 or 5 4 -N S~ -^j— ttST — a^ — ^~ g 3£ . Ill] I * 6 4 : Efc IJ EXERCISES. '•E§S: 6 6 6 6 6 — (22- 6 4 3 -- -s>- -a- 6 Q __f2- •-> B 4 -S>— P O -« — a 5 (2- -(9- 6 4 ^> ^ IJ 5 6 6 6 6 6 8 4,643 ) - , ,- f- m 646 ,643 6 6 . 8 4 8 6 4 J 6 6 3 6 4 4 6.|: 3gEgEEm > i 54 PRACTICAL HARMONY. m$± -.|fe 6 6 34 u ~tS>- -e2- s>- -G> - I $6 4 3 6 6 - it 6 4 6 4 -- -(9- -S>- m - -&- 6 6 6 435 643 43 8 6-, 5 3,4 4-*» 3 5 06 3 1— h -l— r — 1 CHAPTER VIII. FORM. THE PHRASE. THE PERIOD. CADENCE. Form, in music, is the means by which the composer gains unity and symmetrical proportions; it is the frame in which the musical picture is placed. Music without rhythmic order, melodic and harmonic relationship — without form — would be unintelligible and monotonous. As form is the outward expression of the thought, there can be as many forms as there are varying: thoughts. There are certain orders of musical form which are more symmetrica) and gratifying than others : these have been so perfected by the great masters that they are almost universally accepted as the best mode of expression. The best examples of form are to be found in what is called "abso- lute " or "abstract" music, in contradistinction to what is known as "programme" music. The smallest succession of notes, which, taken alone, forms a satis- fying musical thought is called a Phrase. The length of the phrase varies according to the length of the thought to be expressed ; but the most commonly used is that of four measures. Beethoven. Ex. 98. ! I COTS % BdL^ztpzezrJi: t % :p~rS r~ TSTT *1 rn PRACTICAL HARMONY. 55 It should be noticed that in the preceding example the rhythm of the third and fourth measures differs from that of the first and second, and that the four measures are necessary to complete the full thought. A passage of four measures, in which the third and fourth are but repetitions of the first and second, does not form a four- measure phrase, but is called a Double Section. If the third and fourth measures are but rhythmical repetitions of the first and second measures, the passage is still called a Double Section. Ex. 99. =#4=j i &- =1 m Ex.100.: tJ Beethoven. -4 iF^f^^>=^^=:J^5 5s^ ifcz^ m The distinguishing characteristic, then, of a four-measure phrase is, that the four measures are indispensable for the expression of a musical thought. The Period consists of two phrases of equal length. As a rule there is enough similarity in the two phrases to show that the second is responsive to the first, although the second is usually more emphatic and final. Beethoven. :x. 101. < 9^^ 4 -*-^ 55 #.-• \ ? *. ? fi- A ^»* f- #■ -f- v[=:i ^-'-^- E E3:-a= : E^| =£ Ec-c : E E=p =E E-E * E E 1 =3 1 I =^S ■• & -zl^+ UZ» p-±. -• ^ ••* *- *-#■ £ • F=F -x FiF = r-=T=t=pl m When one speaks of a period one means the period of eight measures, similar in construction to the preceding. There should be *6 PRACTICAL HARMONY. enough melodic and harmonic order in the period to form by itse I a complete musical sentence. There are other periods of different lengths but they are nearly always qualified, as, for example, "six- measure period, " " seven-measure period, " " ten-measure period." Without such qualification the period of eight measures is under- stood. CADENCES. A cadence is the close, more or less definite, of a musical thought. It is to music what punctuation is to prosody ; it divides the thought and gives the proper emphasis. The Authentic Cadence is the strongest. It is formed by the chord of the dominant followed by the tonic ; the latter chord must always fall on the accented part of the measure. The following- are forms of the authentic cadence : Ex. 102. \ 3i |3?fe|33i^|^#=f| "Z7 ^ ^ J2- •*- _£Z^€l -£&*- 6 6 4 _(S2_- -O- -&■&■ -O.. -72~ I Illustrations I and II, with the root of each chord in the bass and with the soprano ending on the tonic, -are termed the Perfect Authentic Cadence. The same harmony, but with either the soprano ending on a note other than the tonic, or either or both chords inverted, are termed the Imperfect Authentic Cadence. See III, IV, V, VI, and VII in preceding example. The Plagal Cadence, consisting of the subdominant followed by the tonic is particularly agreeable when following the Authentic. Ex. 103 Authentic Cadence. Plagal Cadence. jy II ' e* ' — S> " J 6 4 cv ^ II * I- II s a. *3 &■ II 1 1 The Plagal Cadence may be used without being preceded by the Authentic PRACTICAL HARMONY. 5? The Half Cadence, as its name suggests, marks a short rest; it usually comes between the members of a phrase or period. T 1 ^ half cadence is usually made on the dominant, preceded bv any other chord. Ex. 104. -9—4 I— J- -- I -4- "25!- — I- -m- -25!~ II -S>- p3EEEf 6 I ]| The Deceptive Cadence — sometimes called the false, inter r up ted, or broken cadence — consists of the dominant followed b] any degree of the scale except the tonic. It is often followed b» another degree of the same scale, sometimes by a change of key. Ex. 105 i II & ~N /-~ I -&^- -&— |— F— <9-\- ~-SL— H - "25^ 3^: _ z?- rte- The character of a cadence depends largely upon what has precedei it. The authentic cadence is most frequently preceded by a si* four chord on the tonic. This use of the six-four chord is the mosl common and the best. Ex. 106 I -s S N S" -4-4, - l . f g-p,^ . 4 s!tI- -V s - &- -4 -«4-5) 2 <> St+- &-;\ J >G> 1 -W~\<>-0 L | 1 L £?-'-#- L ' L -!£i l T , A^-r- r4- ii EXERCISES. 1. Compose a short bass in C, ending with Perfect AuthentM Cadence. 2. Compose a short bass in i/', ending with Imperfect Authentic Cadence. 5S PRACTICAL HARMONY. 3. Compose a short bass in A, ending with Plagal Cadence. 4. Compose a bass, longer than the preceding, in A b, dividing it with the Half Cadence, and closing it with the Perfect Authentic followed by the Plagal. ■ ^. Compose a bass in d according to the formula in No. 4. Before harmonizing the succeeding melodies, the student should read again all that was written in Chapter II. regarding melodic and harmonic progressions, as well as the " suggestions" at the close of Chapter IV. The chapter on the second inversion should also be re-read. This done the student should divide the following melodies into phrases, seeking that cadence for the close of a phrase which his musical instinct tells him is best adapted to its character. After the cadences have been decided, the other harmonies of the phrase will more naturally suggest themselves. The second inversion is a most important factor in the cadences; it makes them emphatic and final. (See Ex. 106.) Although it is not absolutely indispensable, it should be employed whenever the nature of the phrase permits it. As its use is somewhat diffi- cult, it should be seldom introduced except in cadences, and then under the conditions recommended in this and the preceding chapters. Whenever the nature of the melody permits, change the harmony with each note. Sometimes it will be best to retain one harmony during two, or perhaps three notes. In this the pupil must follow his musical instinct. EXERCISES. =1 itait I -EE£=t ^ ■*—&■ fe=f P= ■& — &T ■&- =£ -m-ji- —T^- o 2. 1 -*>- -G>- -Q.- -&- l t5'- -- I PRACTICAL HARMONY. 59 ~&- T- ■&- &---& ^P© II 6. -f 2 — - - g) — &- ■&—&- -&- -&- -&- &—& ^stitS^i T=t II CHAPTER IX. MODULATION. TONAL RELATION. MODULATIONS OF THE FIRST ORDER. EXERCISES. MODULATIONS OF THE SECOND ORDER. MODULATIONS TO REMOTE KEYS. PASSING MODULATIONS. HAR- MONIC SEQUENCE. Modulation is the art of moving from one key to another. If a composition of more than a few phrases in length were to remain in one key the monotony would be wearisome. Digressions from the original key are made, to gain variety. The possibilities in modula- tion are probably limitless. From Mozart to Brahms there has been a constantly widening latitude. Art is progressive ; that which to-day seems impossible, may to-morrow be accepted. Hence, it is wiser to say what one may do, rather than what one may not do. The mo6t helpful theory is that which enables one to analyze, under- stand, and better appreciate the compositions of acknowledged masters. The question ought not to be " Is tins passage in Bach, Beethoven, Schumann, or Wagner, wrong?" but rather, "Should not the old system, which cannot account tor the new effect, be modi- fied .' " Practice should precede theory, and one function of a new text-book is to adapt the old rule so that it shall include the latest discovery of a great composer. It should be understood clearly that modulation is the method we employ to get to a new key; it is the process and nol the result ; it is the means by which the change is effected and nol the key into which we pass. A sudden change of key dot's not necessarily So PRACTICAL HARMONY. include a modulation. If the chords of C and Gb were heard suc- cessively : Ex. 107 I jffi- i 1&- & 1 there would be no modulation, only a brusque, unsatisfactory leap from one key to another. If the two keys were united by a succession of chords having one or more notes in common, the progression could legitimately # be called a modulation: Ex. 10S. - u l?-z?- g>— ftg*- £2_ fr gl k =fc £ » ill I It will be seen, later, that it is not always necessary to have a note common to successive chords. One should realize that the same rules apply to harmonies in different keys, as to harmonies remaining in one key, and that sat- isfying modulations are governed by intelligible melodic movement of the different voices. With a clear appreciation of the principles of tonal relation, it will nearly always be possible to understand the effects of agreeable modulations, even of those which seem intricate and remote. Whatever means one may employ to effect a modulation, there is really but one principle to be kept in mind: destroy the tonality of the old key, and prepare the ear to receive the new. Whether the modulation shall be brusque and startling, or well-prepared and gradual, depends wholly upon the effect desired. TONAL RELATION. CLOSELY RELATED KEYS. Keys are said to be related when they look and sound alike. PA A C TIC A L II A RMONY. 6l The keys most nearly related are those whose signatures are the same, and those whose signatures contain one sharp or one flat more, or less. The nearest related keys to C arc its minor, a ; its dominant, G; and the relative minor of G, r; its subdominant, F; and the relative minor of F, d. They may be represented by the next five ascending notes of the scale : Ex. 109. Nearest related keys to C. d. e. F. G. a. -&- This is relatively true of all major scales. Minor keys have equally five related keys which are represented by reversing the order and descending five notes of the scale : Ex. 1 10. Nearest related keys to a. G. F. e. J. C. II The nearest kevs, then, to any major, are its dominant, its sub- dominant, and the relative minors of these three keys. The nearest related kevs to any minor are its dominant and sub- dominant minors, and the relative majors of these three keys. The tonal relation existing: between more remote kevs will be explained later. MODULATION. Continued. A modulation is effected by introducing notes characteristic of the key to which wc are going, but foreign to the key we are leaving. Two chords at least are indispensable to determine a key. The phrase at a in the succeeding example, is presumably in C; by the introduction of g#, as at /;, the key is probably in a: Ex. 1 1 1 62 PR A C TIC A L HA RAW NY. If, in successive chords, a note common to each chord is to be raised or lowered, the alteration should be effected chromatically, i.e., the change should be made melodicallv or in the same voice. Ex. 112 -AL iS2_ — a — \ I H&— — ^ — II XT — & 1 — — jSL. -H 5' — a — a II S 1 When a note first appears in one voice, followed by another voice taking this note chromatically altered, there results a harsh effect known as "false-relation," or "cross-relation." Ex. 1 13. The disagreeable effect of a "false-relation" may be realized by playing the following in quick succession : Ex. 1 14, 9- F :p=-= m There are certain " false-relations "occurring between the bass and an intermediate part which are not disagreeable. Experience can best determine the limit of such progressions. Among those most frequently found in the writings of acknowledged masters are the following : Ex. 1 1 5. yiEi&j 3= EgE p= bg^i 1^0 PR A C TIC A L HA RMONY. 63 The preceding example at b can hardly be called a "false-rela- tion," because, although this relation exists between the bass and alto, the alteration really occurs in the same voice, i.e., the alto. The skip of the diminished fourth at a, example 115, calls for the explanation, that, in modulations, more liberty is allowed in the progression of the parts. This is especially true of the bass. In modulations, when the bass moves to the leading-tone of the new- key, many intervals which would otherwise be difficult, are easy of intonation and therefore permissible : Ex. 1 16. I Dim. fifth. Dim. fourth. Aug. fourth. Aug. second. As a rule it is better not to double a note which is to be chro- matically altered : Ex. 1 17. I y S3 /T " fv\ « v 7 % l) ' & ■" c^* II y. X 1 J <3 JK 5 1 w - II nor, as a rule, will the interposition of one intermediate chord destroy the effect of a " false-relation : " Ex. 1 18. This relation, however, coming between the last chord of one 6i PRACTICAL HARMONY. phrase and thejirst chord of a succeeding phrase, is permissible. The following examples are taken from Bach : Ex. 119 W -(St- ^=g w- 7 ?~ yx~&~ £i (2 (2 , fZ , O.- 9% jg jg- -- 1 sa± i$2l=^: -- r y. ~ s» — I The note to be chromatically altered may be doubled in pro- gressions like the following, where there is strong contrary motion. Ex. 120. I -&L W- --m- -(&- i -&- -(2- I The note chromatically altered should rarely be doubled, unless moved to by contrary motion : :x. i2i./ ( Bad Good. 5WJ.3 \^<2- H?2- ■*- —& — — Z? _ -0- II -iS 1 - l§3 PRACTICAL HARMONY. 65 The regular or most natural resolution of a note chromatically raised, is to the note a semitone above : Ex . 122.- ~B~ -O.- -Q.- II The regular or most natural resolution of a note chromatically lowered is to the note a semitone below: Ex. 123 \ -P- 9 T-^- -I <5> II In place of this so-called "regular resolution" the altered note may remain stationary, or it may change enharmonically : Ex. 124. /-" Remaining stationary. Changing enharmonicallv. 92=^F^= ± ?g I=t ^= = g= t ^ =^=F -e>- -Q-- ^=fe: te^pM^g^g r> : F- F THE DIFFERENT ORDERS OF MODULATION. Modulations are divided into two Classes or Orders. Modulations of the first order are those that differ only in oi>e accidental, either in signature or scale construction. A modulation from C to G would be of the first order, because there is but one differing note in the construction of the two scales — F#. From C to e would not be a modulation of the first order, because, although there is but one accidental more in the signature of <" than C ( \'% ) the construction of the minor scale calls tor the seventh note (- I PRACTICAL HARMONY. 6* Note. The student is sooner or later puzzled to explain why it is that the successions from the fifth degree to the fourth degree, and the fourth degree to the third degree, are disagreeable : Ex. 12S M~ (k~%~ %- - 5th 4th 4th — &- -&- -S>- -O.- II 3d while the same successions reversed, i.e., from the fourth degree to the fifth degree, and from the third degree to the fourth degree, are agreeable Ex. 129 1 T— - -&>- -&- 4th 5th 3d 4th In art there are many things which cannot be explained. Any attempt to explain the tritone is useless and illogical ; it is suffi- cient to realize that one progression sounds good, another, bad. To modulate from C to F, the modulation can be effected by introducing any chord — except the chord on the leading-tone — which contains bv, the characteristic note of the key of F, and following this by another chord or other chords defining the key. Note. In the following exercises the modulations are to be made in the fewest possible number of chords. The modulating chords are to be considered as parts of a phrase. GENERAL RULE. The old key may be quitted from a chord formed on any degree of the scale — except the seventh — and the new key entered on any degree of the scale — except the seventh — containing the charac- teristic note. To the rules for melodic progression given in Chap- ter II. should be added the progressions in example I 16. 68 PRACTICAL HARMONY. EXERCISES. I. T<\ modulate from any major key to its dominant. Leave the key of C from a chord formed on the first degree in root posi- tion and inversions, entering the key of G on its dominant. The following example shows the general order to be observed : Ex. 130 -<5> From root position. From first inversion. From second inversion ^ -&- jGL- -s>- ~w- -a.. s 5E F 1 - t=f _ a — — ~~ H XT — &~ 1 — ^ L '^— — i& — -- hg — — & — i TO " Bt- GS ~&S>— H ^r f? 1 1 1 II Leaving C from root position, entering G on inversions of the dominant. II. Leave the key of C from chords built on each degree of the scale — except the seventh — i.e., the second, third, fourth, fifth, and sixth degrees, entering the key of G on its dominant. Inversions of chords may be used, and as many examples as possible of each progression should be made. The rules given for the six-four chord in Chapter VII. should be observed. III. To modulate from any major key to its subdominant. Leave the key of C from each degree of the scale- — -except the sev- enth — entering the key of F on the fourth degree. The new key is entered on the fourth degree, because, in modulating to the key a perfect fourth above the characteristic note of the new scale occurs on the fourth degree. The modulation from the third degree of C to the sub-dominant of F will be found very difficult on account of the tritone. One should remember that all faulty progressions are softened by the ust- of the first inversion. IV. To modulate from any major key to its relative minor. In this modulation the new key cannot be clearly defined except by the use of its dominant. PR A C TIC A L HA RMONY. 6 9 JVbte. The diminished triad on the second degree of the minor scale, although not containing the characteristic note — leading- tone — of the scale, is most useful in determining a modulation. In the following examples, the diminished triad should be considered as on the second degree of the scale of a, and not as on the seventh degree of the scale of C. Ex. 131. This will be more fully explained in " Harmonic Sequence. " Leave the key of C from chords built on each degree of the scale — except the seventh — entering a on the dominant. V. To modulate from any minor key to its relative major. Leave a and return to C on the fifth, the third, and the first degrees. The entrance to the new key on the dominant will be found the most decisive. For convenience, the relatives are condensed here : Each major kev has five closely related kevs, three of which are of the first order and two of the second order. For example, C has for relatives of the first order a minor, G major, and F major, and for relatives of the second order d minor and e minor. Each minor key has five closely related keys, only one of which is of the first order. A minor has for relative of first order, C major, and for relatives of second order G major, F major, e minor, and d minor. If the teacher think best, he should now arrange modulations of the second order. OBSERVATIONS. CONCERNING MODULATIONS TO REMOTE KEYS. It is of great importance that the chord or chords forming a remote modulation be of sufficient duration to prepare the new key ; and as a rule, it is best for the more important chords to be placed on the strongl) -accented part of a measure. A succession of chords containing material for an effective modu- lation may be made thoroughly ineffective, either by introducing 7 o PR A C TIC A L HA RMON Y. the chords on the weak part of the measure, or by giving them so little time and emphasis that the modulation is indecisive. In general, a modulation is as much more satisfactory as there are notes common to the modulating chords. Among other ways, satisfactory modulations to remote keys may be effected by the following means : I. Major chords may succeed each other with good effect, provided they have one note in common : S N S ~> ■N S~ :x. \32.l :fe "S>- -(52- — \ ter~ — r II II. By the use of chords which alone do not produce a definite modulation but are common to several keys. In the following succession : . 133. ^ -- -&- 9i- — & ^5?^ [I The second chord may be considered as if in the key of F, and thus leading to that kev : Ex. 134 ! -v %- C/ - ' -<52_ g -«- -G>- -(52- 6 4 -&- 9^F -&- & C -f5>- -G>- I 1 or as if in the key of a, and leading to that kev : Ex. 135 -&- sr ~>2~ sr -&- -&- - -72- t& G> — J2Z .a. -a. -<5>- sr i PRACTICAL HARMONY. 7* or as if in the key of B 9 or 69, and leading to either one of these keys : Ex. 136, B? or lb -fe= II -<2- 2iZ- — ^- 3^ -9«s>- II III. By enharmonic change Ex. 137 -&S>- :^ 55= 3«: -<52- IV. By several modulations into closely related keys, leading gradually to a remote key : Ex. 13S 1 =ff^=^=F=d-^F^- ~^M .1 (_ ~^- II Note. The early masters rarely used modulations to keys other than the five which are called the nearest related. . If keys were used not closely related to each other — as F and G — it was only in cases where these two would be closely related to the principal key of the piece. For example, F and G would be closely related to C. One must not suppose that the preceding examples exhaust the les uirces of modulation. The possibilities are too numerous to catalogue. PASSING MODULATIONS. It was stated at the beginning of this chapter, that a modulation cannot be determined by one chord, even though this chord contain a note or notes foreign to the principal key. A phrase may contain chords having notes foreign to the key and yet not destroy the unity of the principal key. Such are termed "passing modula- 72 PRACTICAL HARMONY. tions," "transitive modulations," or "borrowed chords." Anew key is, in general, rarely determined except by the aid of a cadence. In the following : Ex. 139, i & -& 5% -s>- -J- -- <5>- - I , 1—4- 2? fiT- ^ -p-^,:^-^ _0Z__ -i5>- — f2- .^-i^- - gr ■iS>— ST - " i o -«-hg =4=4: -iS- :J^=t -<9- S o "s? _ -5<- L >5h -sf- -- -9- -S>- ^i=zp= EEE$d e E 5E pr^ r ^=5 "S^ -19- -7? I] Although here are notes foreign to the key of C, there is no mod- ulation. It is best to look upon those chords containing the foreign notes as borrowed from other keys. Note. When the prevailing mode of a piece is major, chords are often borrowed from minor keys. When the prevailing mode is minor, chords are rarely borrowed from major keys, because the major chords imply too strongly, a modulation. From this point the student should unite in one note all those notes which may be repeated in a measure. The few exceptions should be explained by the teacher, as they occur. Ex. 140. ~s>- ?— -0- T^ instead of I -4—4—4—4- :*=*=3|=*:=H & Jl EXERCISES. MODULATIONS OF FIRST ORDER, AND BORROWED CHORDS. Allegretto. !.[« -P= t I * *=£ * 6 6 # PRACTICAL HARMONY. I 6 6 6 % 3JJ | 73 6 a 6 4 J ^ iz=t • — &- ^EElflS? -g» &~ ^-- m -m — »- t E V 6 4 6 gES^&^E^ Egjggg e 4 5 3 6 3 8 3 3 5 4 5 3 5 8 - § ,4 8 3 P6 - 5 ^fcs W C' ■Ts ■5- ~^y Adagio. s « 6 4 6J a 4* 2. z^tfi =^4:=^: -^ ^ -*2-# EzEEi^S 6 6 j, 6 6. 4 4 $ r4d: -z*- 25 ^5 q 586 6 6 6, 3 5 4 6 .43 34345, (Hi "??- ^5T^- 6 6 . 4 fr- it ^•^fjgZg-(g {EE^EEEEEt * s^i - £=£ F. Vd.SeeEx.1 31.jK Allegretto. 4. §i|=^ a 95 t) : rr— <^- (S SECOND ORDER. 6 6 4 ?2= =F 6 £ ^ 9* 1 si ^^iii 6 5$ _(g • - -|SLi_ F— («- 6 5 J -- -(S2. L - «*— -^^ sb m zte^^Ez^fea^L^zz ^i±= 6 . u6 . 4 3 22 -<&- ^ • ■^— g>- sj 6 5 * 5* sjf sb be S J ** S* t ± b © 9** be sb sb b4 s ,b 5$ 3$ 5> 5$ 3 It -(«- S* se -22- _(2- Si 3ZZ£ -(5»- -»- s>~ -G>- — <&- -- 6 I -Ol- ^r -&- j2- 1 HARMONIC SEQUENCE. In sequences, the ear being gratified by a regularly recurring responsive figure, certain harmonic or melodic successions may be introduced which would otherwise be disagreeable. The most pronounced of these are the use of the triad built on the leading-tone, which we have not used before, and the freer use of the six-four chord. The triad built on the leading-tone when heard alone : Ex. 141 is weak and disagreeable, but when heard in sequence : x Ex. 142. it becomes more agreeable. PRACTICAL HARMONY. /5 The six-four chord may be used on any degree of the scale ; provided the fourth is prepared and resolved according to the rule in Chapter VII. : Ex. 143. *=£± The chord of the sixth is much used in sequence 4- Ex. 144. ^ -£?- J G>- &- T=f ■»-hs: ■&- &- — i- I I w The melodic intervals prohibited in Chapter II. under "Melodic Progression" are permissible in sequence. It is best not to use these intervals in the first measures, which form the model, as they would there be difficult of intonation. After the figure has been announced, any of these intervals may be used. The model should contain as many of the principal triads as possi- ble, and must conclude with one of them. The perfect symmetry of the sequence may be broken at, or near the close, in order to gain a more melodious or more tuneful pro- gression of the parts, or to gain a more satisfactory close in any way. See seventh measure in example 143. Sequences are said to be tonal or diatonic, when intervals are re- peated in the same key without regard to differences in the quality of the intervals : -h — r* 2 ^- Ex. 145. a 1 \/a % o *> 1 *> '-«? ko & J U- g : &-&*■&■ III! 6^6 6 gi^ . h^ I-: •! j 11 7 6 PRACTICAL HARMONY. Sequences are said to be real or modulatory, when the quality of the intervals represented by the model is exactly repeated : Ex. 146. tistt aa d -*=- -s>- -B>- 6 <2- 9J=t dzte -S>- 6 m ±=g 1.^ ±B: -<&- $ -!> :^g =t=F -te>— -s>- fe ^ :te: It is recommended that the pupil play the following exercises from the figured bass, instead of writing out the other voices as he has done heretofore. The position of these voices in the first chord has been omitted purposely. As the greater number of these basses may be harmonized in two or more positions, the pupil should choose that position which seems to him the most desirable. EXERCISES. TONAL SEQUENCE. '•PP§@|SeIe3? ->& 1- : Eees z± -a. II If5> ,1— £2— ° 2 - \$^1rF3^F=i=f=£ -3—^2- 2t ! 6 — 3 6 6 4 3. m^^-^^Mimi^^ R PRACTICAL HARMONY. 77 6 4 6 >-^gg t=± "—& — —&— M 1_ -— <2- 6 4 6 6 -<9- ~P-- .a.- 1 ■ gfes b£=4 £*=* rfEp :rf ■#-*- F 75^ I 6 .m —s)-&- f-* - &—&- =^_f2_-P_ P— ^. -f=2-£ 2s *= ^H 6 6 4 7. 33 i^: 3= 6 6 6 « 4 ^^P -P—&- ^=? E3fet^ 6 6 6 6 4 _~ 4 --S-- _ 6 6 -£2- -f 2 — r <5» ?5 — i (S*- ^= gpEEg t=p 6 6 43 E^i^=i 8. 3sa$ -(2- -(2- :t: -=1 5-?- £ =t== - g»- -f2- -I (S-- gllH -- £==r -*+^-# H9-T- e 10. Hg^ 666666 66 i=3 *> t= o P £2 1=*= =B n. gi3 343 6 6 6 6 „ 6 „ -O-. 3 43 34 3 343 343 343 6- -&-i—C — -> • ;— :} o ^- I 6 6 6 -~ 6 4 6 ,, 6 4 6 6. 46, 6 4 3 i2 .i mmm^m w^\ i * 1 1 - 1 1 g n 13. t)- (• I F^^TTTHr (- ~r~ "^ — g* ,->— l ■i * li 7 8 PRACTICAL HARMONY. EXERCISES. REAL OR MODULATORY SEQUENCE. 1. ;§±e ° i :p= «b el) sbebsbsb 5b6bobsbs!> b sb sb, b b b , b b 4bb b j f== r^rp^ = » = b< I 2. »JS=t -(2- :t 5Q 5D 5j 5B 5fl 5fl 5Q * £=E 5$ 5$ 3. ;§3t -25f- -- -<© 1 1=F^ : 5$ 5$ « * 6$ Srf 4$$ 5$ s ^EE :J^: -^ II 4. 333 sb 5b s jt b b 3bbS B x: b sb y^^s ^^±=^?=gt±=fe =o<- ttS 5b 5j t3: ' 6 S« + *$ 5$ **=£ ' ^ :§^ I 5. mtt 60 6 , ^ 6 , B 6fl 5fl 5fl B B 5B6B4B5B 5B 4H?— jg-i— I J I t h> — xzpq=±|4: - g<— - ^ S ^ -^ II 5 f lb 5 ° 6. gig 5 4fl =&*" :t^ 6 B sb 4b 6b 6b sb sb 5fl 4b 4b B b -=fc I The student should now compose several short sequences, both tonal and modulatory, following the suggestions given on pages 74 and 75. CHAPTER X. RESUME. Note. In this concluding chapter of Part I., subjects which were purposely treated as briefly as possible in the preceding chapters, will PR A C TIC A L HA RMONY. 79 be discussed more fully. Matter which would have there been cum- brous and confusing, will here be useful and more readily under- stood. CHAPTER I. At example 14 it was stated that it is correct, as a general rule, to use sharps in ascending passages and flats in descending passages. Modern writers usually choose accidentals which are nearest in tonal relationship to the key in which the phrase occurs. A descending passage like the following: -s Ex. 147. -<& h. J=t -fS>- would be much better notated thus : Ex. 148. — \ =3=t -*— S *=ttfc -&>- because the FJJ is nearer the tonality of C than is the Gi?. The same would be relatively true of the following: Better notation. Ex. 149. re=^g^ gE|:| jJ E^g it*- "III In our musical notation we recognize no interval smaller than a semitone. For reasons which have to do with the matter of temper' amcnt, the whole step is theoretically divided into nine equal parts called the Pytliagorcan Commas. The comma is supposed to be the smallest appreciable interval between two sounds. Note. The terms half-step, and semitone, are purposely used as synonyms. Of the nine commas dividing any whole step, that portion of them representing the diatonic semitone is the smaller, and receives but four commas, or four-ninths of the whole step. The chromatic semitone is the larger and receives live ninths of the whole step. A comma, then, or one-ninth <>t" a whole step, is the interval that separates the diatonic semitone from the chromatic semitone; i.e., it is the difference between the Hat and the sharp which may separate a whole step. So PRACTICAL HARMONY. ILLUSTRATION. COMMAS OfJE Y/pOLE STEP FIVE COMMAS, CHROMATIC (lar S e) HflLFSTEP COMMA I COMMA 2 COMMA? C0M " A 4 COMMA |5 COMMA f FOUR COMMAS, (i§ DlflTOfllC (Small) flflLFSTEP. 6C0MMA,7 COMMA r 8C0MMA9 FIVE COMMAS, I u FIVE COMMAS, FOUR COMMAS, [) V CHROMATIC (Lar S e)fiflLFS7E^, DIH TO Hie (Small) HflLF-STEPJ \^^ WHOLE STEP. On instruments of a fixed sound, like the piano or the organ, the whole step has been divided into two equal parts by a system known as the tempered scale. With this system the QJ and the Di? are identical. On instruments where the sound is formed by the executant, like the violin or the violincello, the musician is governed by melodic in- stinct and submits involuntarily to the fine difference existing between the flat and the sharp, making use, ordinarily, of the large half-step in ascending passages and the small half-step in descending passages. If this is understood, the student will realize that an instrument like the piano or the organ is never perfectly in tune when played with stringed instruments. The difference is slight, but sufficiently marked for the piano to sound colorless and unsympathetic, when entering alone after a full passage by the strings. CHAPTER II. SCALES. The chromatic scale is composed entirely of chromatic and dia- tonic semitones. Anv major or minor scale may be transformed into a chromatic scale by the use of the intermediate semitones which separate the whole steps. These intermediate sounds in noway imply a change of key, and the supreme characteristic of the chromatic scale may be said to lie in the fact that sharps, flats, or naturals, foreign to the key, may be freely introduced, and cause no sense of modulation. PRACTICAL HARMONY. CHROMATIC SCALE OF C. :x. 1 50. J r73_^**=^ MS **+ m w 8i or: { 55^3*3=*** K 1 g II Musicians differ as to the best notation of the chromatic scale. Composers are often inconsistent, at one time writing the ascending series with sharps, at another time with flats. As a note sharped is nearer the semi-tone above than the note quitted, it would seem to be the better notation to use sharps in the ascending major scale and flats in the descending scale. An important exception is made in the flatted seventh in ascending, and the raised fourth in descending. The chromatic scale in minor is usually written as follows: Ex. 1 52.'^2tM^_gEp^EibzE -P^MH^ l rlzpzp^iffi bL} The question of the notation of the chromatic scale is one on which there is great diversity of opinion. Conditions have so much to do in determining which shall be written, sharps or flats, that it would seem wiser to attempt no inflexible ride. No further proof of the inconsistency of musicians ;is regards the 8s PRACTICAL HARMONY. notation of the chromatic scale, need be given, than the follow« ing example by Beethoven : Ex. 153. ssgggggjilil i About the only thing on which composers seem to agree, is in writing the fourth note sharped in the ascending major scale, and the seventh note flatted in the descending scale. ( For an expla- nation of this, see examples 147 and 149.) This done, they evidently think of the convenience of the performer. It should be understood that we are now discussing chromatic melody. Chromatic harmony will be considered later. THE ECCLESIASTICAL SCALES. The " Gregorian Tones," " Church Modes" or '•''Ecclesias- tical Scales" as they are variously named, are of Greek origin. If the student will play a scale from each note of the scale of C, using white keys only, he will obtain the seven different forms of these Church Modes, or scales, as they would now be called. Each mode has a different order for its steps and half-steps. As many pupils have a desire to know something about these scales, we add the following typical list : The Dorian, or First Mode F. D. -J The Hypo-Dorian, or Second Mode. F. D. The Phrygian, or Third Mode. F. D. The Hypo-Phrygian, or Fourth Mode. F. D. 2^| The Lydian, or Fifth Mode. F. I). -&~ ^JESE^g-l E The Iiypo-Lydian, or Sixth Mode. F. D. h=+=l=± r> ^m The Mixo-Lydian, or Seventh Mode. The Hypo-Mixo-Lydian, or Eighth Mode. F. 1). F. 1). • *> HiEliipli ^ 3 d: ^ •J] PRACTICAL HARMONY. S3 It will be seen that the Ecclesiastical Modes are formed of the notes of our scale of C, each starting from a different degree. These scales are grouped in pairs, so to speak. The first, third, fifth, and seventh modes are termed Authentic. Each of these has a collateral mode at the interval of a fourth below ; they are distin- guished by the prefix Hypo ( under ) . The Hypo modes are termed Plagal. It would seem, at first glance, that if harmonies were formed on these different modes, without the use of accidentals, the general tonal effect would be the same as our key of C major. These modes are characterized, however, not only by the different order of intervals in each, but by the constant recurrence of two chords, called the Final and Dominant, corresponding to our Tonic and Dominant. It is the insistence of these two chords which makes each mode distinct. These chords are designated by a whole note in the preceding list of scales. The Final, or Tonic, is marked with an F, the Dominant is marked with a D. It will be noticed, that although the order of intervals in the Hypo-Lydian corresponds to our major scale, the points of repose coming on F and A remove it farther from our idea of key, or tonality, than either the Lydian or the Mixo-Lvdian. In order to avoid the relation of the tritone, the B is sometimes flatted. If B were flatted in harmonies in the Lydian Mode, the tonal effect would be much like our major mode. This svstem was later extended to fourteen modes. Modern composere have at times employed these scales with good effect. Handel has made frequent use of them in his ora- torios. Saint-Saens and Brahms have employed them with charm- ing results. CHORDS. The terms chord and triad have been intentionally used as synony im in the preceding chapters. A triad is always a chord, but, as will be seen in Part II., a chord may be larger than a triad. TRIADS. Tiic triad, or chord of three sounds, forms the essentia] and indispensable element of harmony. Until the close of the sixteenth century, this chord, united to certain effects known as S4 PRACTICAL HARMONY. "artifices of composition, " to be explained later, was the only one used. The triad on the leading-tone, although classed by some theorists as an independent triad, is classed by the greater number, and by all the modern French theorists, as an incomplete dominant 7th chord. This will be fully explained In Part II. A triad formed on any note of the major scale, except the leading-tone, is consonant, and may be used as a tonic. For example, any triad in the key of C when standing alone will be accepted by the ear as a tonic, either major or minor, according to the degree on which it is formed. In other words, they all are consonant chords ; they give a sense of tepose, requiring nothing to follow them. The triad on the leading-tone, on the contrary, is, with its Uminished fifth, distinctly dissonant :— -73- 1 '•id in no sense gives the feeling of repose or finality : something '~ust follow it. This triad in its first inversion, was classed among the concords I the so-called ancient strict style : Ex. 154.< -73- 6 -G>- ;H This inverted chord was often written by early composers in preference to the dominant chord. This will be understood when Ihtj true generator of the chord has been discussed. This leading-tone triad in its first inversion seems to be the con- necting link between the strict style and the free; the bridge over which one passes from the old to the new. It contains no diminished nor augmented interval from the bass, nor the interval of a fourth from the bass, yet it possesses all the distin- guishing characteristics of a dissonance as explained in Chapter VII. J'RA C TIC A L HA RAW NY. OMISSION OF VOICES. *> The third of the dominant chord is often omitted. As the third of this chord is always major in cither mode, its suppression causes no ambiguity. Passages like die following are of frequent occur- rence and entirely satisfy the ear : ^=F(k)g Ex. 155. The omission of the third of any chord other than the dominant, by very reason of its ambiguity and strangeness, has a particularly pungent effect. This is especially true of a tonic : String Quartette Ex. 1 56. MELODIC PROGRESSION. Students often ask why the apparently easy interval of the major sixth is forbidden. Experience proves that this interval is difficult of correct intonation unless another voice has anticipated it in the preceding chord : Ex. 157 1 II -