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Lorsque le document est trop grand pour dtre reproduit en un seul cliche, il est film6 d partir de Tangle sup6rieur gauche, de gauche d droite, et de haut en bas, en prenant le nombre d'images ndcessaire. Les diagrammes suivants illustrent la mdthode. by errata led to ent une pelure, fapon d 1 ^ 2 3 32X t 2 3 i . 14 5 6 HARMONY ON TB8 Inductive Method. BY HUGH A» CLARKE, Professor of Music, University of Pennsylvania. •--■;' ■'%' PHUiADSU'HIA : L E I-: c*(; W A T . Iv E R, No. 1113 Chestnut Street. Coprrighl, 1880. bj Lu * WilKlm. It : ^•r.^'ffv--- jc^--- (A ^^ «A ^ t INTRODUCTION. This book makes no claim to be a new theory of Imrmviny; but merely a new eystcm of teaeliiii-j; harmony, by what in universally recognized as the best method of teaching, viz., the inductive. The theory of harmony is the province of the acoustician, not of the musician. It is often asserted that music has gained largely by the labors of the acousticians; but this is not so evident, when we remember that all the best music was written before the science of acoustics was born. The instinct of genius discovered, afcer many trials and mistakes, what combinations and successions of sound were agreeable and expressive, without asking or caring why. And the science of sound has made but little advance in explaining this "why;" and has not added one chord or progression that was not known to Bach. Science can analyze sounds, but not music. It can say to what the various qualities of sound are to be attributed; but can give no explanation of their effect on the emotions. Indeed, the best authorities on acoustics, viz., Ilelmholtz, Pole, Parry, are agreed that it is useless for tlie musician to theorize as to the origin of chords. It is enough for him to know what combinations and progressions if iMHIKi'-' r-^ 4 INTIlOlit CTION. praclit't' iiiul t'X]K .it'iiCf li:ivi' proved fr'xxl. >'o lictlcr proof is icciuirctl of tlin nscU'ssiicss of this tlicorizing iibout Iho orifriii of cliords, tluiu tlic divprsily of views witli n'giird to tlio origin of the minor clionl ; o\ving,to the fiiot,th!it its thinl rannot bo an ovi'rt(«io of its fiindamental. Tho object of the writer on harmony and compo- Hition ought to be, to reduce, to some Hystem, the mass of facts (for want of a better name) of v.liioii our modern miisie is tlie outgrowtii. These facts are: Ist. A te?npered scale. 2(1 (and resulting from tlie llrst). A number of keys related in many ways. 3d. The possilile combinations of sounds, called chords. 4th. The seeming rules tliat govern the successions of these combined sounds. Rules, be it remembered, that are not the i-xpression of some natural fact ; but are merely the residt of a consensus of tlie best taste in the art. Tliese foui' facts make up tlie substance of har- mon;/, and form tho groundwork of composition, which deals chiefly with melody and form. Many departures will be found in this work from the usual methods of teaciiing, notably the following : .. 1st. With regard to the formation of the minor scale. }.'00(|. >'o ■iiH'ss of tliiw lIs, tlinii tilt' origin of tlio ( tliir> pu|)il various examples, wliich were to be transposed to all (he keys, until they were II xed — parrot fashion — in his memory. When ho wisiied to make a modulation, he m\ist remember one of his " patterns." Hy mastering the rules her« given, the pupil can make his own modulations in endless variet}-, iind make them understandingly. It is well to bear in mind that music is an art, not a science ; although the 8tud.v of harmony is often wrongly called the science of music. The rules of musical construction are not the result of scientilic investigation; l)ut are deductions from the practice of those distinguished by their artistic eminence. Many musicians think these rules are the expressions of some natural law. Many, not musicians, think they are tlie arbitrary and often unreasonable dicta of musicians. IJnt botii are wrong. Good taste is the only arbiter in matters of art. And since the standards of tnste vary with every period of the world's history, it is not possible p way. It is great poet, ling liitn his ! from usual ble |iri^lt! in four Himplu, OS. Hitherto on, lias i)cen liieii were to ly wore fixed 3n he wished er one of his r« given, the i in endlcHS nc i8 nn art, harmony is music. The till' result of ictions from their artistic se rules are Many, not y and often ut ixitii are in matters of to vary witli not possible } INTBOIU'CTION. T to give to any of itH decisions the nt^imp of perma- nency, and say : ThlH is ft rule that can never be broken. In conclusion, the author would express h.s tlmnks to his numerous pupils, both present and p.st, for the warm interest they huve iMken in the progress of this work, and for their kind wislu's and iu CHAPTER I. 1. An Inters-al is the difTerenee in pitch between two sounds. 2. The name of an interval depends upon the number of letters it includes ; the kind of interval upon the number of semitones it includes. 3. There are five HHr7s of intervals, viz.: Major, minor, augmented, diminislied and perfect. The following table contains all the kinds of seconds, thirds and fourths. Thirdt. Fourlhi. Seconds. ^^^^^^^E^l^-I^^^ Semitones \ 2 MIn. Moj. 3 Aujt. a 3 4 5 4 6 6 Dim. MIn. Mnj. Aug. Dim. Per. Aug. 4. By inverting these intervals we get all the kinds of sevenths, sixtlis and fiftlis. Sevenlhi. -^ — -o — o- Sixths. -fil — s- :=g^liE|B^^^^^^^ Fifth: -O — r« — r»- Semil<>B<-i 11 10 U MaJ. MIn. Dim. 10 9 8 7 Aug. Maj. MIn. Dim. 8 7 Aug. Per. Dim. f. On examination it will be found that the inver- sion of a second produces a seventh; of a third, a sixth; of a fourth, a fifth. Also, tiiat an interval and its inversion together make an octave— and, as (9) n ! ii.^^ 10 ci.abke's harmony. the octave contains twelve semitones, an inttTval and its inversion must make twelve semitones. Thus the major second contains two semitones, conse- quently its inversion must contain ten, etc. We also find tliat the inversion of a major interval pro- duces a minor, and the reverse ; of an augmented, a diminished ; of a perfect, a perfect. Removing one of the sounds of an interval an octave does not chiingo its name, except in the cases to be pointed out hereafter, thus : Third. Third. I W^^ i Both these intervals are thirds, or the second example is a third plus an octave. 6. Intervals are also divided into consonant and dissonant. The consonant intervals are : The major and minor thirds, and their inversions, the minor and major sixths. The perfect fourth and its inver- sion, the perfect fifth ; and the octave. A conso- nant interval is One that gives repose to the ear ; a dissonant interval does not ; but it must be resolved, a term that will be explained in its proper place. Before going any further the student must become thor- oughly familiar with all these intervals. This is best done by writing them out, •ommencing with every ti, # *nd t> in the scale. *l. A tetrachord is a series of four sounds, ar- ranged as follows : From first to second, and second I an inttTval tones. Thus ones, conse- n, etc. We interval pro- lUgmonted, a emovlng one ,ve does not o be pointed d example ia a msonnnt and : The major ;, the minor nd its inver- !. A conso- ;o the ear ; a be resolved, )er place. become thor- B is best done fl, # and \> in sounds, ar- , and second CliARlCE'S HARMONY. 11 to third, are major seconds ; from third to fourth, a minor second, thus : G, A, Bi^C. 8. A major scale consists of two ti-trachords sepa- rated by a major second, tiius •. Tetrachord. Tetrachord. ^ I ==.l^^=:±E~?r:: :A: -«- m Separating whole tone. 9. Every tetrachord' may be found in two scales, viz. : The scales of its first and of its last note. Thus C, 1), E^F belongs to the scales of C and F; F, G, A, Bj^ to the scales of F ami B.^. 10. Scales having tetrachords in common are called related scales. Thus the scales of F and G are related to C, because they eacli h ive a tetracliord that also belongs to C ; therefore every major scale has two major relations, because C is the model for all major scales. Scale of G. { Scale of D. Scale of C. i|^ i Scale of Bh. Write tetrachords, commencing with every J. t and b, and mark the scales to which they belong. No letter must be repeated or omUted in any scale. I Kfr CHAPTER II. 1. A common (^horrt (or perfect chord) consists of three sounds. The lowest is the root; tlie re- maining sounds are the third and fifth over that root. The tiiird may he major or minor ; the fifth muKt be perfect. A chord with a major third is called a major chord ; with a minor third, a minor chord. Since there are only seven letters used in music, it follows that seven groups will make all the common chords tliat are possible, thus : Fifths. — E, F, G, A, H, C, T). Thirds.— C, D, E, F, 0, A. B. Roots. — A, ?>, C, D, E, F, G. These groups may be modified by ift, 1», elc. For example, the first group, A, C, E, may be etc. ; but the lettert never change. 2. Six common chords may lie written in every scale. Three will be major; three, minor. The seventh note of the scale, called the Icaxliini note, cannot be used as the root of a chord, because the fifth over it is diminished. (12) W !' " " I' B hord) consists root; the re- Ifth over that liiior ; the fifth major third i-; third, a minor letters used in ill make all the s : C, D. A. B. F, G. ic. For example, ^ ritten in every I, minor. The ? leadincf note, rd, because the Cr-AUKK'S IIAIIMONY. 13 Example : 1 i=l-E 3 15 8 Dim, fifth. H Tonh. Subdom. Dom. I.cacling note. The major chords are on the first, fourth and fifth notes of the scale. Those notes are called the tonic, siibdo.ni.iant and dominnnt, and the chorda written on them are called by the same names. The minor chords are on the second, third and Mxih notes of the scale. These notes are called the super! onic, n.ediant and submcdiant, and the chords written on them are called by the same names. 3. It is easier to -write Buccessioirs of chorda in four parts (or for four voices) ; but as tlie chord consists of only tlirc., sounds, it is necessary to double one of tlie members of the chord to make a fourtli part. We will commence by doubling the root, thus: 1 i C is the root; it is at the base and doubled by the highest voice or part. 4. A chord with its root at the base and doubled in one of the upper parts may be written in t'.iree positions, called : Octave, tierce and quint. I mm sJ m I 14 ni.AUKR'S HARMONY. Octave {He). Tierce (3). Quin/ (5t). ::ff± m -«- zs^ SJS^ i 8e. ZJSr. 5t. is: m Cloit Harmony. Diiperied Uarmomj. In all its posilions apd doubling this chord is etill tlie chord C, E, O. This doubling might be carried to any extent; but it can- not niter the name of the chord. 5. In writing a succession of common chords with their roots at the base, the following rule must be observed : Never write two chords in succession in the same position. If it be desired to malie the succession as smooth as possible, retain all notes common to two or more chords in the same part (voice), thus: St. se. The following examples are to be written according to these -nles, Tiz. : Ist. The base note is the root. 2d. The root only is to be doubled. 3d. Two i-hordg in the same position must never be written in succession. 4th. Make the chords as oonneoted as possible. ■' m I'OiinMiirnrairmi - At. lil m Harmony. ■d is gtill the t; but it can- mon chords ig rule must 11 succession to make the in all notes e same pail 3. 5t. 8e. 1 ording to these iver be written CI.ARKE'rt HARMONY. 15 I fi. The knowledge gained must now be applied to the harmonizing of a melody. The following re- marks will point out the way to accomplish this : (1 ) Every note in the melody may be the root, tiiird or fiftli, of some one of the chords in the scale. If it be treated as a root, tlic chord will be in the octave position; if as a third, the chord will be in the tierce position ; if as a fifth, the chord will be in the quint position. Example: 6 8 8 ^^^^^ -9' N. B. — Two' chords may be written in the 8 position in suc- cession when the extreme parts move opposite ways. In this example, C is treated as the root of the chord of C, consequently it is in the octave position ; D as the fifth in the chord of G, consequently it is in the quint position ; C as the I utitr" 10 (!IiARKE'8 HARMONY. third in tlio oliortl of A, conaetjuently it ia in the lierc.^ pubi- lion, etc. (2) Begin and end with tlic tonie ciiord. (3) After deciding on the chord any givon note is to liave, write first of all the root in the bass. Ilarmonizo llio folla^^ing plirase of melody in as many ways as possible : -e) — g- ^ -1 — ®- i Three chords aro possible for the first note, two for the B«c-ind, three for the fourth. 1 \e following melodies must be harmonized according to fhcao rules ; they should oil bo transposed to all the keys and harmonized over and over. Note. — The bass must never proceed by long skips, it is best not to exceed u sixtli. i ^SM5i-|- V ^« T f g, l /a » f. "°^ m E ^;^n^^^m ^^ The bass should never ascend or descend two fourths or fifths in succession. the tieroj pubi- )ld. givi'U iioto is le bass. in ts many ways m jlo, two for the ed according to all tho keys and long skips, it is two fourths or ^mt claeke'h harmony. IT It cannot bo too often repeated that common chnrdu onli/, with tho rootM at the base and not doubled, are to be used ill those exerciscH Examine each chord as you write it, to see if it conforms to these rules This is the only way to suooooc a the absence of a leiichcr. 1 Tho progression of common cliords is perfectly free, tliat is, any two common cliords may bo written in Hiicecssion, but some successions tlo not sound us well as others. They arc not to be understood as forbidden, because the effect of a progression dc- peiids altogether on the design of the composer and tho context The following rules might be given for such successions : Two /nnjor chords whose roots are a whole tone apart do not sound well, except in the following positions : At No. 1 — two and three are sometimes used; four is hardly tolerable; five is intolerable. •i 3 4 6 Two minor chords whose roots are a whole or half tone apart are bad in any position, except in the passage ot No. 2. M^:^^^^ J:: I, 18 CLARKR H HARMONY. A minor chord followed by a mnjor whuno root in u minor third higher, is bad unless in the following positions: (1^ ::*: P m jBt m Oood. Better. A mi^or chord, followed by a minor or the revorHc, wlioso roots are a half tone apart, except in the following pogitions : :t i^^fEiE^^ (^ m ^ ^ zgiz m Nos. 1 and 2 are best. 8. It is not always necessary to use the root of a /jhonl for a base note. Tlie third or fifth may be so nsed. When the third is used for a base note the , chord is said to l)e in Its Jirst inversion i when tlie fifth is used for a base note the chord is said to l)e in its second inversion. It is important to remem- ber that tlie name of the chord is unchanged, iio matter what the inversion of the letters composing it m&y be, thus : s root in II minor isiliona: fa 1 reverHc, wlioso wing positiuuB : -Ol- m the root of a fth may be bo base note the , oiii when tlie is said to be nt to rcmem- nchanged, iio rs composing CI.ARKR'et HAKMONV. 19 i EE^: -•- i In thift oiample the Ittliri »re C, E, ; it la therefore the chord of (.', To And Iho mot of a chord it is only neoensary to arrange the lelturs composing it, ao aa to read: 1, A, 6. The loweat will be the root. Example : 1 i 3 5 « EE^lEllEl^iEi^: 1 a 6 No. 1 is the chord of A, Ist inversion, the letters read A, C, E, 41 2 " " Q, 2d " with root doubled, 0, D, D, •■ 8 " •' C, Ist " with fifth doubled, C, E, G, i fi A, >f C " " K, Ist " with fifth doubled, E, 0, B. The pupil should write all the common chords in all the keys; in nil their positions and inversions. Remember that position applies to the hightst note of a chord with its root at the base ; and invenion applies t a chord with any member but the root at the base, and has no regard to whiit may be at the lop of the chord. 9, Hitherto we have doubled the root of the chord only ; but it in not the only member of the chord that can be doubled, but is the 6e.s< when the root is at the b.ase. But when the first inversion of the chord is used, the fifth is just as good a monibei to double as the root. (For the present the third must not be doubled). I II > J 20 clahkk'h iiaumuny. In llie fnllnwinn OKtimplc, tlio first inversion of iomo of tli« ehonU w.ll lio foiinil— Honiu with root, nome with flftli doubled. N. D.— The doubliiiK of a membor of a chonl nt uniaon in exprrsHcd )iy*writing llio nolo ns above. It is hm (hough two of the gingers in a qiinrtetto hud the game note to sing. 1, Chord of (', Ho position, lloot doubled. Tonlo chord. " 0, IbI invcTHion, " Doiii. C, Ho position, " Tonic " " (", iHlinvcrtdon, " " " " F, 8e position, " Subdoin. " " D, 1st invoTHion, •' Sup. tonlo " " G, 8o position, " Dom. " << (;_ Ho " " Tonic " " F, 1st inversion, " Subdoin. " " 0, 1st " " Dom. " " r, 3c position, " Tonic " " 0, 1st invcrHion, Fifth doubled, '• " '< 1), Ist " Root doubled Sup. Icmic " " l», 3« position, " " " C, 6t " " Dom. " •< C, 3e " " Tonic " In writing the following exercises, it is optional to molto the notes cither roots or thirds of chords. Try both and let (he ear decide. The f .Unvini; example will point out llio way : No. 1. (1 2. II n, 11 4, 11 r., (1 c>. 11 ">, 11 8. 11 0. *i 10, 11 11, 11 12, 11 lil, 11 14, 11 15, 11 16, 1 it ■i --o — i ;i of iomo of tli« til flflli (loubUd. 'tot ^< \ — ^ I IS 14 1A in oril at uniHon in U an tliough two e lo Hing. Bil, Tonic chord. Doni. " Tonic " Siibdoni. " Sup. tonic " Uom. Tonic " Subdoin. " Dom. " Tonic \ed, •• led Sup. Ionic " Uoni. " Tonlo " ional to malco the botli iind let the t out tlio way : ci.aukk'h iiahmonv. 81 Thin i^ I'videnlly in ilie key "f «' ; it """"t Hicreloro liogin nnd •nd witli ilie loniu cliord Tlio neti.nd notn miiy 1>« root of the chord of K. or the third of the cliord of V. (Try liolh). No. ;i cniiiiot l.o a root, heing llio leading nolo; II must therefore ho iv third in chord of tl. No 4 may be root of C, or third of .V (Again try both) No. 5 root of A. or thirl of F. (Again try both). No. root of F, or third of U. (Again try both). No. 7 root of 0, or iliiid of E (Sou dinngreoable progren. kloni, piige 17). 10. The following rtiUi muHt bi- Htrictl.v observdJ : Never let two \mrU or voices proceed in octavt-s or imiis with each other. (Any two parts mny bo an octavo or llftii iipart ; but not twice in succession;. P^ ^ ^1^^ P=^--'3F^3= i^^^^^ In the first bar, the bans and tenor are a fifth apart in the fl-st chord, f}' and also in the second, ^ \ making two fifths In succession between the same two yoices. Abo the bass and alto are on octavo apart in both chords. Consecutive fifths and octayes, lilto this example, only occur when two chords are written in succession in the same posi- tion ; hence the rule forbidding it. In the second bar, fifths occur twice in succession between the alto and soprano. In the third bar. fifths occur twice in succession between the tenor and alto. (Consecutive or parallel fifths will be treated farther on). I Clarke's harmony. 15 i=^ ^ t=f::rt f- t=r«=t -«--p £s i S ra #, ^ - x^ ^ STK = :g=»p:>-c p tS>5^ i w^^ ^m =^^ B 3^^i^ ^y ^ :^ i.^ r- 1 igE p iSM ep f= Transpose these exercises into all the keys. 11. The next step is to use this first inversion when harmonizing a melody. The following re- marks will make it easy : Every note in the melody may be the root, third or fifth of some chord ; but if it be treated as the third of a chord, the first inversion cannot be used, because it is forbidden as yet to double the third. If the note in the melody be treated as a root or a fifth, either the root or the third may be used for a base note. 1 23 4& 87 8 ± W: No9. 1 and 8 must have the tonic chord, which will be in the octave position. No. 2 may be treated as root in the chord ot' D, and mw^- have the root or third at the base ; or it may be treated ns the ^ m :^^ m iipSi first inversion B following re- ! the root, third I treated as the jannot be used, ouble the third, d as a root or a ly be used for a hich will be in the )rd ot" D, and ma.*-- y be treated os the clabkk's harmony. 23 fifth in the chord of O, and may have the root or third at the base. No. 3 may bo root of E, third of C, or fifth of A ; if treated as third of C, the root must be at the base ; with the other two chords, either root or third may be at the base. No. 4 may be root of F, or third of D. No. 5 may bo root of D, or fifth of Q. No. same as No. 3. No. 7 sara ' as Nos. 2 and 6. (Try all these varieties itiid observe which sounds best j if several sound equally well, observe the different effects they give). The pupil should now be able to harmonize the following examples. It will be well to bear in mind the following remark : It generally gives a better effect to make the extreme parts, bass and soprano, move in opposite directions ; ». «., when the bass descends, let the soprano ascend, and t'ic« vena. This is not a rule, but only a remark. ^ ^^ -^^ L^^lr r r r 1 ^ Note. These examples, even if well harmonized, sound un- satisfactory ; owing to the wan* of the perfect cadence, treated in the following chapter. I !T fc^ IT 24 CliABKK'S HARMONY. 12. We proceed now to the use of the secciid in- version of the common cl ord, i. p., with the lifth for a base note. A chord with its fifth at the l«vse, is nhcaijs (witli two exceptions whicli we will ignore for the present) a tonic chord. Therefore, in tlie key of C, with ths chords so far at our disposal, the only chord that can be used in its second inversion, is the chord C, E, G. The following rules must be observed when it is thus used : Ist. It (the second inversion of the tonic) must be preceded by some chord belonging to the scale. (This seems superfluous at present, Init its impor- tance will soon be seen.) 2d. It must be followed by its dominant (excep- tions will be pointed out in time. -&■ ^^ in In this example at X ^'^ second inyersions of the tonio chord, (ho first example is preceded by th^ gubdominant chord, the second by the supertonic. (These are the most agreeable to use before this second inyersion, but any other can be used ; as was remarked before, it depends on the de- sign of tlie composer and the context.) The close of this example is wbat is termed a full or perfect cadence It is the way the great majority of compositions end, viz.: with second inversion of tonic, followed by domi- nant with root at the bass, followed by tonio in octave position. , 11 the aecc iid in- ;h the fifth for it the base, is ve will ignore jrefore, in the r disposal, the ond inversion, rules must be le tonic) must g to the scale. l)ut its impor- ninant (excep- X f^ m ions of the tonic th^ Bubdominant ese are the most on, but any other epends on the de- 1 a full or perfect r of compositions ollowed by domi- Q octave position. , CLARKE'S HARMONY. 25 We found that the best note to double, when the root was at the base, is the root; when the third is at the base, either root or fifth ; but wlien the fifth is at the base, the best note to double is the fifih ; next, the root. Every change in the position or inversion of a chord gives a new effect to the chord. The octave position is grave, massive and full of repose ; the tierce is graceful and inclined to melancholy, p-.ir- ticularly when used as a final ; the quint is bright and eager, always indicating something to como. With regard to the use of the different members as base note : A chord with root at the base, is like a cone in a state of stable equilibrium ; witii its third in the base, in a state of neutral equilibrium ; with its fifth in the base, in a state of unstable equi- librium. A careful study of the following example will enable tl e pupil to write the exercises that are appended. =^ ■»^ * 1 •-©- zst ■-^^ s^ 4:: i * * Where these marks if: are, the second inversion of the tonic chord may be used ; because No. 1 , the F preceding, may be harmonized by the chord of F, or by the first inversion, chord of D ; No. 2, the A preceding, by the chord of A, or first in- version of F ; No. 3, by the same as No. 2. And in each case the note following may be harmonized by the dominant chord. After 1 and 3 the root of the dominant is at the base ; No. 2 the third of the dominant at the base. The remaining notes are to be treated according to the rules already given. 2 r-ji' d6 Clarke's harmony. : The marks X >■> ^^^ ^'^^ exercise indicate the places where the second inyersion of the tonic may be used. m ^e ?^ :fc^ -4— L. -9- X X ^^^^^^^W ^^^^iTF -1 — 1- «-•-■ :p^ 1:::?:=^ 1 jgg^P^^JF^lpg^Pllif 13. We now give an example to illustiatc how this second inversion may be used wlien harmonizing a melody. After writing the exercises that follow, tho pupil should carefully go over again from the beginning, and should trans, pose all the basses and melodies given into all the major keys and harmonize them. This is absolutely essential to tbo cou)> plete mastery of the subject. I --»=is: m p gg ff -» 1 * 3 8 At No. 1 w» have a note belonging to the tonic chord, pre- ceded by a note that may belong to chord of D or G ; it is fol- lowed by a note belonging to the dominant chord. No. 2 belongs to the tonic chord, etc. No. 3 belongs to tho tonic, etc. ) the places where id. tp:: 1^ X '^m EfJE^ £EF illustiatc how en harmonizing tho pupil should and should trans- all the major keys lential to tbo com- m * 3 Jonic chord, pre- D or G ; it is fol- iDt chord. No. 2 [8 to tho tonic, etc. clabke's harmony. ST In short, whenever we find C, E or followed by 0, B or D, the C, E or O moy have the second inversion of the tonic, and tho Q, D or D the dominant chord. The use of this second inversion of tho tonic is tlio only thing met with so far that is at all difficult, and a, little study and perseverance will soon overcome it. I W ^? l f ff CLn[ I?^'5^^S5 k T^f^' l ^ricJir^- g^ 14. The third of a chord may be doubled under the following circumstances : 1st. When the parts or voices doubling it are moving in opposite directions. 2d. When two chords are written in succession in the tierce position. 3. The doubling that results from slriking full chords on the piano, organ or orchc-stra. I! 'JL-' . S8 CLARKB'8 iiahmony. No. 1. The E is doubled by the bass and soprano, the bnsi ascending, the soprano deBcendiDg; in the second bar the motion is reversed. No 2. In the first bar the C is dpublcd by the soprano and tenor ; in the second bar tlie A is doubled by the same voices ; but in this cose they proceed in the some direction. This is the only woy an exception to the rule about writing two chords in the tierce position in succession can occur. The third is doubled to avoid tho oonseotftivo fifths and eighths that would result from doubling the root. No. 8. The harmony reduced to its simplest form is only the chord of C, tierce; G, quint; D, tiercj; A, quint. The doublings in this case are merely for the s ke of fuller effeot, and the harmony is to be judged as to its correctness by re- ducing it to its simplest form, viz. : :g= E i m m The same remark applies to Ibo pvrolKl Cflhs and octaves in this last example. Two chords in succession in tho octave ^nd quint position sometimes occur, when the extreme parts move in opposite directions. I goprano, tlie bnsi ) second bar tho f the Boprano and ' tho same voices ; lircotion. This is 30ut writing two , can occur. The fiftlis and eiglitlis jlest form is only i; A, quint. The ke of fuller effect, correctness by ro- l fifths and octaves ctavciind quint extreunc parts , clabke's harmony. 99 ^^^^ $^ i No. 1 is common in terminations. No. 2 is an example of consecutive fifths, from the slow movement of Beetho'cn's "First Symphooy." The second inversion of the dominant chord may be used M follows: i^^^H^^ X X SI ^ m^ It must be preceded and followed by the tonic chord.' It must never occur on the accented part of the bar. If the tonic before it have the root at the base, it must after it have the third at the base, and vice versa. This example has two notes in tho bar, therefore only one accent; if there were four notes in the bar, the third would be an accented note. A subdominant chord maj' be used in its second inversion, provided it is preceded and followed bj' the toaic, with tlie root at the base. 80 CLARKE'S HARMONY * ^mm^m * ^ ■.T- 1 At H: the Beoond inversion of the subilominant occurs; in each case it is preceded and fgllowed by the tonio, with its root at the base. inant occurs ; in te tonio, with its CHAPTER III. 1, The minor scale is formed from the major, by reananginy the notes, commencing witli tlie sixth. It is called the relative minor of the major scale, from which it is formed, and has the same signatnro. 2. The most important chords in the scale are the tonic, siibdominant and dominant. In the major scale these are all major chords. It was found (p^ge 12) that six chords might be written in every scale, three major and three minor. By rearranging the scale in this way, the three minor chords will occupy the position formerly occupied by the three major chords ; i. e., the first, fourth and fifth notes of the scale, or tonic, subdominant and dominant. C maior. I m Sr-^S- :«= k O major. m HBMft s A minor. E miner. ^ - ^f « " " '■tl , ^^a^^ A is the sixth note in C major. The chord, A, C, E, is the tonic of A minor and the sixth or submediant chord in C. D, P, A, is the subdominant of A or supertonio of C. £, G, B, is the dominant of A or mediant of C. (81) I JJ' J9 OliABKE'rt IIARMONV. Thin in Jho oldest foi'm of tlie minor ncnlc, nnJ ooncRpondii to tlio Qrecli llypo-Dorian (or, according to Qlarvanua, iColinn) ; the major loalu being tlie Lydian (or Ionian, accord- ing to UlareanuH). This form of tlic minor scale in very Hide used now, because it does not admit of any liarmony but com- mon ohordc. 3. Two forms of minor scales are used at present, called the melodic and the harmonic. In the melodic the sixth and seventh are raised in ascending. In the harmonic the seventh only is raised, both ascend- ing and descending. This is the only form with which we have to do at present ; hence whenc^ver a minor scale is mentioned, until further notice, it is always understood to have the seventh raised. No. 1 is the melodic scale of A minor. No. 2 io the harmonio scale of A minor. 4. We have found (page 11) that every major scale had two major relations. It follows, since the minor is formed from the major, that the relative minors of these major scales must also be related to the given scale, thus : C major has for major relatives, F and G. The relative minor of C is A. The relative minor of F is D. The relative minor of O is E. Consequently we have in every scale a group of six U , nnd oorreitpoiidH ig to Qlar«anu8, or Ionian, acoord- Huulo in very 111 lie liarmony but ooui- ised at present, In the melodic aacending. In id, both ascend- jnly form with nee whenever n, ler notice, It is raised. it every major Hows, isincc tlio lat tlie relative also be related F and G. a group of six ("I.arkk'h harmony. m keys, Ko clowly interwoven tliat llioy cannot be iUh- nnitfd, and we can paHH from any one to any ollu-r, without niakinj? a permanent change of key ; or, in other words, any chord belonging to A minor, F and I) niinor, (1 and K minor, can be nsed in the key of C. In all of these minor keys the seventh must bo raised to make a leading note. Therefore in A minor we will find O^; in D mim)r, C^f; in K minor, D^. Tliereforc every raised note in any given scale Avill be a leading note to some related scale. And no note in tlie scale (with one exception, to be men- tioned later) can be raised unless it leads to a re- lated scale. i ^pr-^^ dfp-^-'^ Zo=a^ 4(0 T 8 W 10 11 13 1. Tonic. 2. Leading note to D minor. 8. Supertonio. 4. Leading note to E minor. 6. Lending note to F mnjor. 7. Leading note to mnjor. 0. Leading note to A minor. We SCO from this example that a cbromntic scale may be written in any key without using a sound foreign to its rela- tions, except in one place, viz., the Clh. 5. Four common chords may bo written in the minor scale. 8* . tlio 1 10 re iH only i-\ <5> rr '^=9- m •i IS 14 1ft ci.arke'h harmony. 86 No. 1. Tonic. No. .'. Uoininanl of D minor. No. n. Tonlo of D minor. No. 4. Dominant of ('. No. Ti, Tonio of C, flmt inveriion. No. (1. Dniiiiimnt of A minor No. 7. Tonio of A minor. No. 8. Dominant of major. No. 0. Tonio of mnjor. No. 10. Tonio of major, first inrergion. No. 11. Dominant of B minor. The F mimt be »harp, be- oange E minor is the relative of 0, ond Q has an F Minor relations. ••••G (leading note Fi(). D (leading note C#). Major relations. F (leading note Et]). C (leading note Bt)). Et> (leading npl^t D). 1 3C OLAItKE'S HARMONY. An eaE>y wny to remember the notes that may be raised, is : They are the first, second, fourth and fifth of the scale. In the exercises that follow, will be found both basses and melodies, to be harmonized. There are no neir rules as yet to be observed ; but we have made a gain of four chords, viz. : The chords that contain the accidentals, which chords are the dominants of the related scales. These exercises mutt be transposed to all the keys. iS^^ ^^ ^^^^I^ S^^g^ ^gE^^^^ ^ iL flZpg ^•-^k=W=^z ^^^ 1 gff| --= 77=q^ '^=^"=fe=|^^ Sp^ pz^^— m 9!Ee 3fc==:^ a ys T --» :pz t=T=± :p=±=^ -®- "ZZ — — ^ i ^^^^irf i ^^ ^^m X may bn raised, is ; of the scale. nd both basses and new rule? as yet to r four chords, viz. : hich chords are the exercises mutt be ^^1^8 i^ *^ • — *- ^^ r 'ZZ — — ^ i ^^S ■^V;- clauke's harmony. 37 PlS^^^l^^felpi 1. In addition to the related scales there is another scale from which we cin borrow some chords, viz., the parallel minor. By parallel minor is meant the minor scale beginning with the same ke5-note. Thus the parallel minor of C major is C minor; it has three flats for signature, being the relative minor of El,. Rule. In any given major scale the chords be- longing to its parallel minor may be used. These chords are three in number (one being the same, whether the key is major or mi.i0r, viz., the dominant). C Major,' w^- m 4 6 6 5 6 *^ i|E(6|):4ae^l minor, parallel minor of C major, and relative minor of Ey I , 1j# I II 38 CLARKE'S HARMONY. We now have a means to hnrmoniie E'c or Al> in a malody in the key of C, viz. : By C, E^ ; F, A>, C; or A', C, E^ ; which laal chord includes botii these notes. C, Eb, 0.— Is generally used as follows, t. «., preceded by the major tonic or dominant, and followed by the dominant or chord on the sixth of parallel minor. ^ ( ^=± t fc^Ofa : ^ ^=Tfi= F, Al>, C. — Preceded by the tonic, or major subdominant, or submediant, and followed by the tonic. Al» C, E'?. Preceded by the tonic or dominant, and followed by the tonic or dominant. ^Sg^^^ n yi it E Bl n b ' Al> in a malody 1; or A', C, E^! preceded by the lie dominant or subdominant, or ifeft ant, and followed fe M m CLARKE'S IIAEMON'-'. 39 All these chords are frequently used in succession, as follows: '^P- -»- ffi in W- 1 8. The last common chord is the chord of the lowered supertonic, which is formed as follows : Rule The supertonic of any scale, major or minor, may be lowered, and a major chord may be written on it. Thus the supertonic of C is D ; lowered, it becomes D^. The major chord written on it is Dj,, F, A^. This chord should be preceded by the tonic or subdominant, or by one of the chords of the parallel minor, and should be followed by the dominant, or by the second inversion of the tonic. This chord is more frequently used in its first inversion than in any other way ; and in this form is called the Neapolitan sixth — for some unknown reason ; and has a strange account gifcn of its derivation. (See Grovt't Diet., Neapolitan tixth). I 40 CLARKE'S HARMON',. ^ ->- 7(S> f -W ^^^^^ -»■ a g— :t=a: i 1, 2 and 8. First inrerBion of lowered aupertonic : preceded by tonic, major and minor; followed by dominant, or tonio second inversion. 4. The chord is preceded by the chord on sixth of parallel minor, and has the root in the base. 6. Preceded by subdominant of parallel minor. In the following example from Weber (Der Freiscliulz), the second inveri-ion of this chord is used, followed by the dominant. ^HM L t-rrt ^;^ ^ m ^-f^ 7±Z± ^. '?^ '^. m ^^ag^^^ss liiiii f :f=l m apei'tonic : preceded dominant, or tonio on 8islh of parallel minor, Der FreiNcliuIz), the Ted by the dominant. ^ ^M irtSi^ig P ^SS CtARKE's HARMONY. 41 ^^{^^j^I^}^ 9. We return now to the rule (on page 24) that the second inversion of the tonic must be preceded by 8om,i chord belonging to its own scale. This must be now understood to include all the chords thus far mentioned, viz., the chords from the parallel minor, the lowered supertonic chord, and even some of the dominant chords of the related keys ; but the rule still holds good that this second inversion must be followed by the dominant chord. I X -1- r ^ -o — ^ X 1^ i a ^^^pr^^ I X ^^^^ No8 4, 5 and 6 are not commonly msS. with, but can be rery effective. These three examples (4, 6 and C) areacon-radiction I 42 clabke'h harmont. or exception to the rule (page 86), that the dominant must be followed by (he tonic. (The progresgions of the dominant will be more fully treated in the next chivplor). Another rule must now be given, viz. : When a note is altered by an accidental it mast remsin in the same part or voice that it had before alteration, thus : Bad. Oood. ^mm^ O' B n d No. 1 is bad, because the C is natural at the one extreme of the firt chord, and sharp at the other extreme of the following cliord. No. 2 is good, because the CIK occurs in the same part or voice, vi7., the bass, that has the Ct]. A passage like example 1 is called a cross or false relation. It cnn occur sometimes without a bad effect, as will be pointed out in the proper place. Inminant must be Ihe dominant will n a note is altered part or voice that ine extreme of the of the following the same part or or false relation. w will be pointed CHAPTER IV. • 1. The dominant cliord may have the seventh over the root added to it. This seventh is minor. Being a dissonant interval, it must resolve ; i. c, move always in one direction, viz., downwards one degree. ^- -^^<:^=S''-^ i :^g^^^ In this example we haTe the dominant chord of C with the seventh, F, added. The voice or part that has the F, mutt afterward have E. J'he note to which the seventh descends, is the third of the tonic chord ; hence the rule, that the domi- nant must be followed by the tonic. But there are other chords in the scale that contain this resolution note, that may be struck after the dominant. This gives us three progres- sions for the dominant with seventh : 1st. To the tonic chord. 2d. To the chord on the sixth of the scale. 3d. To the dominant of the relative minor. The first progression can take place no matter what the poii- lion or invTiion of the two chords may be. In this progres- sion the third of the chord must ascend one degree. (43) If .44 CLARKE'S IIARMONT. The second progreesion can only take place when the roof of both ohordB are at «he base. In this progression the tliird may descend when (he fifth of the chord is at the top. The third progression may talie place no matter what the position or inversion of the *wo chords. In this progression the third does not moTC, because it is the fifth of the following cl ord. The root mast be raised chromatically to the third of the following chord. It is of the greatest Importance that the pupil should fix in his memory these three progressions of the dominant chord with sevenths. The following examples mutt be worked out in every key. ^gjj g4— ^ "^^ i^^^^^^ aoe when tha root* 'ogresBion the third at the top. 10 matter what the n this progrcsBion flh of the following sally to the third of pupil should fli in lie dominant chord tit be worked out in »^3?L 1 clabke'h harmony. 45 '^E^M^^^^^- In the above examples we h»Te CTery rariety of the first progression of the dominant with seTcnths. No. 1. AVith roots of both chords at the base, and seTenth, fifth and third of the dominant chord at Iho top. It will bo seen from this example that when the roots of both chords are nt the base, the fifth of the tonic must be omitted, owing to f-e progression of the sercnth and third of the dominant. (It is common in terminations to let the third of the dominant descend to the fifth of the tonic, but it is in questionable taste.) No. 2. We have the first inversion of the dominant with setenth in all positions. No. 3. We have the second inversion of the dominant with seventh in all posiiions. This second inversion of the domi- nant is under no restrictions as to its use ot any time, owing to the presence of the seventh. The small notes in the bars indicate that the D ntiy go to C or E ; if it takes the E, the third is doubled ; but it occurs in contrary motion, and is very effective, particularly when it occurs as at X- No. 4 is the third inversion of this chord, viz , with the seventh for ft base note. The small note in the first bnr of this example shows how Iho third of the tonio may bo doubled in contrary motion. From these examples we get the following rules for iho first progression of the dcaiinant with seventh : Ist. When the root of the dominant is at the base, the tonic must hove its root or fifth at the base ; never the third. 2d. When the third of the dominant is at the base, the tonio mutt hove the root at the base. IT 46 CLAHKRH IIAUMUNY. 8d. When (be flfib of the dominknt is at tb« baio, tho tonic muat have ib« root or third (somctimei tbo flftb, but it ia not good). 4(b. When the BeTcnlh of the dominant is at Ike base, the tonio mutt hare the third. Second progrciaion of dominant with seventh ; No. 1. TbeeeTcnth iaat the top. The third of tlie dominant muat ascend. The third of the chord on the sixth niu.H bo doubled, to avoid the conaeoutive fifths, which would occur if the D were to take the E. No, 2. The dominant has the i. ih at the top. , The third in this case can either ascend or descend. No. 8. The dominant has the third at the top, oonspquently the third of the following chord must be du ibled. (See rule for writing two chcrud in tieroe position). The sniall notes at the end of each bar signify that the chord on tho sixth of the parallel minor is included in this second progression. Example 3 ia sometimes followed by the chord on the sixth in tho octave position, but rarely :i^ in ':g^ -9- i t tb« baio, tho tonic no flftb, but it ia not ', is at Ibo base, the Tentli ; ^ bird of tlio dominant 1 the sixth niu.U bo rhich would occur if e top. , The third in he top, oonspquently do ibled. (See rule i). Tlie sniall notes liord on the sixth of ad progression. le chord on (be sixth OLARKE'H HARMONY. Third progression of dominant with sevcntht (^tei^^^J (^^^^^^^ ( :=li5^5|j> 'n --sQ> 2! — u — 9- — \--~^ — 9-^ —6 ( -» 9- -9 !»- J 1 ^- ^m (P^i^#^#. m^^^m n Iq thoM esftmples are %\\ tho vurielios of which Ihij. pro- groosion ia oapkbte. I l^;i%. 48 ChARKBH IIAH>U»NY. n will bo »ccn llmt ilie root of the first chord alwnyH ho- conici the third of the .ccond (by the ohromatio alicratlon, effected by the #). Thli !• In Moordftnce with the rule on page 42, Ihnt wheneter a note Ir altered chromaUcnlly It niu»t remain in the Bame part or Toice that it hiid previous lo alter- alinn. It will also be accn that the aetenth alwaya descends one degree. It is evident that this third jirogression of the dominant (I. c, lo the dominant of the relative minor) con only liiko place in a mnjor key. This leuvea but two progressions for Iho dominant wilh seventh in a minor key, tIi., lo (he tonlo and to the chord on the siilh. (The author cannot insist too strongly on the neocusity of becoming thoroughly f iniilin.r with these three i-.ogrcssions in every form and in every key, before proceeding any further. Their Importance will become more -ad more manifest as we proceed). The exercises that follow should be writtoT repeatedly and transposed to all the keys. A careful study of this example will indicate how this new chord may be used vthen harmon- ising A boss or melody. It must first bo remarked that all the dominants of the re- lated keys may also have the seventh added, and henceforth must not be used without the seventh. We have already found that every nolo in the soaie may be either a root, third or fifih (except the loading note, which cannot bo a root; the supcrlonic, which cannot be a third ; the subdominant, which cannot be a fifth). We now find thr.t they may nearly all be sevenths. b* :* -f^ — m No. 1 is the seventh iu the dominant of the related key, obord nlwayH ho- romatlo allcrntion, ) with tba riilo on omallcnlly it muMt I proviouH lo alter- h always d«*oends n of the dominant lor) cnn only liiUo vo progrcinions for ', Til., lo (he tonio on the neocusHy of reo )>i'ogroi8ion8 in leding ony further. Dore nianifeijt as we ito-1 repeatedly and idy of this eiample used i^hen harmon« ominants of the re- Icd, and henceforth We have already I either a root, third nnot bo a root ; (ho 8ubdominan(, which ey may nearly all be 1 f (ho related key, (;i..vHKi': H ii.vu.Mu.xr. 40 No. 2 is the Hcventh in (he dominant of the relative minor, A. No, 4 in the sevonlh in the dominant of the key. No. 5 is (he seTenth in (he dominant of D minor, (ho rela- tive minor of F. No. is (he seventh in the dominant of K minor, the rela- tive minor of 0, No, 7 lins (o be lowered to Ui', because C is the dominant of P, and ll.> is (he minor sevenlh over C; .ilso, 11 \n tliit in (lie key of F. (This gives us a means to harmonize D^ if it should occur in a melody in (ho key of C). Since (he sevondi always descends, it is necessary before (readng a note oh n sovenlh, to observe that it must be followed by a note one degree lower than itself. Bar 1. Tonic, domionnt of key, with seventh, followed by Bar 2. Chord on sixth, followed by dominant of F, seventh added, second inversion. Bar S. Tonic of F, followed by dominant of 0, seventh added, first inversion. Bar 4. Tonio of 0, followed by dominant of A minor, sevonth added, first inversion. I CliARKE'S IIABMONY. Bar 6. Tonio of A minor, followed by dominant of D minor, Beventh added, third inversion. Bar 6. Tonio of D minor, first inversion, followed by same, tierce position. Bar 7. Second inversion, tonio, followed by dominant, with seventh added. Bar 8. Tonio of C, with fifth omitted. The same melody, with another harmony : (I Z=^^- '^ ^s^:e m W^^^ -9 9- -9 — ^ m The pupil should analyze this without difficulty. Try to find opportunities for all the resolutions of the domi- nant. 5iES^^ ^ ._f__>_^b^ r ;^^*i g L,|, linant of D minor, followed by Bame, by dominant, with ^ m BBculty. lutions of the domi- .-T-^-J-W- 4- m Clarke's harmony. 51 ^^9 »-q*=g ?=^:8F=^ -i—r-^r S pi ^ ^jgfiigEg j ^ ^^pg ii p^^gi XT ' * ' ^ ^^ ^z=pig=f=ii?ririff _{ > _H*->- ^fe r^^ ±-T-f^ m^^^ ^mm^ m: f>~0 ■tE^EIE^tS F^ It: m -#-i- 1^ ^^^H^^il^ I 52 clyhke's harmony. Note.— It is not necesaary to write a separate chord to JTery note. If two or more notes in ruooession are members of the eame chord, the chord need not be written with all of them. Thus : Not ; mm I ! 2. When the root of a dominant chord with seventh 's omitted, the remaining notes form what is called the chord of diminished fifth on the leading note. It must follow the rules for the progression of the dominant, as though the root were present, except when it is used in its first inversion (which is the best way to use it), when the seventh may ascend or descend. ^=txa^-^«;^^=:«^ 1 a 8 4 No. 1. Dominant of D, with serenth. No. 2. Same, with root omitted. Nos. 3 and 4 are the inversions. No. 5 is llie first inversion, with the Herenth ascending. There are two exceptions to the rule that ibe seventh must descend : BT—J: m^ chord to dvery lembers of the all of them. with seventh rhat is called eading note, ession of the ;sent, except (which is the may ascend ^ m ascending. be seventh must m ^ CLARKE'S HARMONY. 68 No. 1. The dominant, second inversion, with the scTenth at the top, is preceded by the tonic, tierce position, and followed by the tonic, first inversion. This is the only way this pro- gression can take place. Nos. 2 and B. The seventh is doubled, and one resolves and tb<> other ascends. 3. Any number of dominant chords with sevenths may be written in succession, whose roots are a fourth apart, ascending, or (what is the same thing) a fifth apart, descending. The easiest rule to remember this progression by, is : Lower the third of each chord chromaticall}-, and it will be the seventh in the following chord. Jtoo/(.— B E A D Q C In this example the six dominant chords that may be used in the Icey of C are written in succession. Other progressions of the dominant chord with seventh may be met with that cannot be brought under any rule. They are not common, and can Imj better learned by studying the works of good writers than bj' attempting to give rules for them. 5lE ^^^^^s 5i:-^^^^Sfe^ 64 CLAEKE'S HARMONY. ig^^^}^^^^^^ 55^^^ 5S :f=3t s ^^^ jg^^ p g^=?= =*=F ^ f^^^f=r=g ^1 I m %^^ =^^2£ i ^ j ^ "'"S^ ^ ^ -f^Vr f^ ^^ je|F S ^^,.ai-i;i ? ^ i ^^ ^^ ^m CHAPTER V. 1. The ninth over the root may be added to the dominant chord. The ninth is minor (t. e., an octave and a semitone) in minor keys. In major keys it may be major or minor, but is naturally major. 2. The ninth resolves like the seventh, by descend- ing one degree. The first progression of the domi- nant only is possible when the ninth is added, viz., to the tonic chord. 3. The ninth cannot be used for a base note ; nor can it be written close to or below the root. 4. There are therefore only three inversions of this chord. 56 CLARKE'S HARMONY. In (his example are all the dominant chorda Ihnt can occur in C, with the ninth added. No. 1. Dominant of C, with m^or and minor ninth. No. 2. Dominant of its relaiite minor, A. No. 8. Dominant of F, with major and minor ninth. No. 4. Dominant of its relative minor, D. No. f. Dominant of 0, with major and minor ninth. No. C. Dominant of its relative minor, E. The small notes indicate Ibe resolution of the seventh, ninth and third. When writing in four parts, it is necessary to omit one of the notes of this chord. The best one to omit is tlie fifth, or the third or sevcntii may be omitted. The following example oonUlns all the inversions and posi- tions of the dominant of C, with seventh and ninth. The pupil should write all the dominant chords in the same way, with mnjor and minor ninth. 2 3 4 5 ^IJBZ. 7~g^'f =s TB^'^ 6 ^^^^ -®^- -«x'- Ep^ i '^^^^ ^ 9 10 m ^-!.»i»:t;i Is Ihnt ci»n o«cur or ninth, lor ninth, lor ninth. Ihe geventb, ninth cessary to omit le best one to eventh may be rersions and posi- 1 ninth. ihords in the same -jPv.- i i i CLARKE'H UARMONY. 6t Nor. 1, 2, 3 and 4 are the yarioua inversions of the cliord, with all the members present. Nob. 5, 0, 7 and 8 .ire ezamplea with the fifth or third omitted. Nos. and 10. Same, with minor ninth. The pupil should try to find more than are here giren. 5. Although the seventh may be added to the dominant at any time, the ninth cannot. Observa- tion of the way it is used by good composers is the only way to learn. One rule might be given, viz. : The ninth should not be added when making a per- fect cadence, unless it is done as follows : i 3- ^ — ^ I^IE ^m^ m^ The ninth is resolved before the seventh, by deseendinK to the root of the chord. J,ij=i J i 1 — T—^- r :4i4 8» 68 claukk'h harmony. ! p ^:^ :a. SSTl II m^^^m TT An analysis of this example will guide to the best manner of using the ninth with the dominant. 6. This chord of dominant with ninth is mere nscd without tl.un with the root. When the root is omitted, the cliofd may have the three progressions of the dominant. Example: It^ii «■ '^- \il prog. 'id. ad. Sd, bol!t ciordt vUh ninth, root omitted. :.m When the root is omitted, the remaining notes may be inverted in any way ; but the major ninth is rarely used as a base note. 1. 1 he succession of dominant chords, mentioned in the last chapter (page 47), c n talte place, with the ninth added. It is celdom written with the voois r)rcscnt ; but if* common without the root. m 1 le best manner inth is mere n the root is progressions I, bol!) ciordt viUh root omilled. lainin^ notes major ninth is ds, mentioned te place, with with the '\ioi3 Dot. clabke'b harmony. {)» Slii^El^ES^Tft Rooln—B K f^^mi ■szrz: mt I No. 1 is a succession of dominants with minor ninllis, root omitted. This is known as the diminished seventh cliord. No. 2 is tlie same siicceBsion ; but the alternate chords have only the seventh. The chord of B!> major is the lowered super- tonio of A, hence it can be followed by the dominant of A, na above. « The pupil should write all these chords in aV the keys and in all their inversions. When harmonixing the following exeTciscs, it U po8i>ible, whenever a dominant chord is used, to omit the root and add the niRlh. It will be seen that the lowered notes in the Bcale may all be treated ns minor ninths. We find so far that it ia poss'ble to have four raised notes in ft scale; that they are leading notes to related scales ; also, we may have four lowered notes in a Fcale which will be ninths in the dominant chords of the scale and ita relations (although there are other ways to harmonize the lowered notes). So the accidentals, that can be harmonixed in a scale, tlways occur in dominant ohords, or the parallel minor, or lowtred surertonic. \n\ 1 60 CI.AHKR'ri HARMONY. Tho dominant wltli minor ninth mny have tlie root nnd third omitted. Tho result is ivdiminiHlied tliord on tho Bccond de|?rce of b minor scale, Tho same remarks, as to invcrrtion and progresHion, apply to this chord as to tho diminished chord on tho leading note in tho minor key. It takes the place of a super- tonic chord, and is generally followed by tho second Inversion of the tonic. ^^^f^^P^ A minor. C major. •• i pr^^rrr m W^ ^ -I — h f=bp f TV i f^ r ^ ^^ ^^^^^^^ 'i-a; have the root tiniHliod thonl lu. Tho same iHion, apply to on tlio luading Inco of ft Bupcr- I'V tho second ^^ ^^ ^^ i^^ ] ms IXABKK'm IIAIIMONV. 61 i "PT ite n^-:^ ^^ mtmm^ m^m m^mm^^^^^i n ' ' 1 I ! aJ^ CHAPTER VI. 1 The eleventh may be added to the dominant. It is perfect; being the perfect fourth, removed hu octave. The third mi.Ht l)e omitted when the eh'venth is added. It resolves, by descending to tlie third of tiie chord. If the ninth be present, it generally descends to the root at the same time that the eleventh descends to the third. This chord may be inverted in any way (except the ninth, whicli eam.ot he a base note or close to tlio root). In four-part writin{,s the fifth, seventh or ninth may bo omitted. ^^^m^^^^ \ s^m^s^^m The above con.ainH examples of the way this chord i» gen- erally used when (he root !• present. 2. Tliis chord is more often used without the root. The root being omitted, tlie • lord has tlie three progressions of the dominant, and it may be in- verted in any way. The following rules must be observed : ^^^^ II > tho (lomiimnt. rth, ri'inovi'd an hon tlie t'U'Voiith g to the third of nt, it gi'iicriiUy 3 time tliat the \n clionl nmy ho th, whicli I'tiiniot t). In four-part may bo omitted. ^^m f this chord in gen- without the root. rd has tlie three id it may be in- ig rules must be n.ARKK's HARMONY «8 iHt. IftluM'h'veiith dfK that the only cliords it may follow the domi- lis group ia considered n over again, and try le dominant : Wi \th. 6lh. perfect fifth and minor enth added. CliARKE'S HARMONY. 65 The 2d group consists of minor third, diminished fifth and minor seventh, and is a dominant with major ninth rdded ; root omitted. The 3d group consists of minor third, diminished fifth nnd diminished seventh, and is a dominant with minor ninth added ; root omitted. The 4th group consists of minor third, perfect fifth and minor seventh, nnd is a dominant with major ninth and eleventh nddcil ; root nnd third omitted. The 61 h group is the same as the 2d ; consequently it may be eitlier dominant with major ninth added, root omitted, or dominant with minor nintL and eleventh added, root and tliird omitted. Consequently the 2d group in the above example may come from either G, the dominant of C, or E, the dominant of its relative minor. The 5th group may come from Bb, dominant of E!>, or G, the dominantof C, its relative minor. Therefore there are four notes In common between the dominant harmony of a major key and the dominant harmony of its relative minor. By the enharmonic change of the minor ninth there arc five notes in common, thus : 1. Dominant of C, with major ninth. 2. Dominant of A, with minor ninth and eleventh. 1^ 1. Dominant of C, with minor ninth. 2. Dominant of A, with minor ninth ; the A!* becoming 0». '■■■ 't it 66 OIr a diminished fifth. I would Bgaiu say that i*, is only for llio sake of simplicity and system thnt the domimmt is treated ..s the root of the«e chords ; not from a belief that it ia so.) i 4. The succession of dominant chords (see page 53) is also p:)ssil>le wliou the eleventh i^ added, al- though the third is not present. ere being so many 3 chords, that any ! followed by any , those marked X> ^** if C or of A minor i»ay of treating these roups as the following ominant, vii. : D, F, A, inth; or F, A, 0, which enth. This objection is dissonant interval in a armony. In all the e tninished •seventh, or a that i', is only for tlu ) dominint is treated iis elii'f that ills so.) lit chords (see page [eventh i^ added, al- olarkk'b harmony. 6t ^^^^ 2. Dominant of C. 8. Dominant of F. Bb is the lowered third of the preceding chord. 5. Dominant of G. 6. Dominant of C, with elerenth. 7. Dominant of F, with eleventh. 8. Same, with minor uinth. CHAPTER VII. 1. The supertonic of any key, major or minor, may be treated ae the root of a harmony similar to the dominant harmony. The four groups that may be derived from this harmony are always followed by the tonic chord, which sounds bjst in its second inversion. The dissonant notes in a supertonic har- mony do not require resolution, as in the dominant harmonies by descending: they generall}'^ remain stationary (because the seventh, ninth and eleventh over the supertonic make this tonic chord). If the second inversion of the tonic is to follow the supertonic harmony, the latter should have the root, third or fifth for a base note. If the first in- version of the tonic is to follow, the supertonic har- mony should have the ninth (minor is best) for a base note. If the tonic, with root for a base, is to follow, the seventh of the supertonic harmony should be in the base and the root omitted. V a w 8 4 I the 1 ad( 1 (he ] ad( ] adi ba ad ad fo lo is a< P' II. major or minor, irraony similar to groups that may always followed i)jst in its second a supertonic bar- in the dominant generall}'^ remain nth and eleventh ! chord). onic is to follow should have the . If the first in- le supertonic liar- or is best) for a for a base, is to ; harmony should ^^ \r clabkk's harmony. 60 No. 1. Supertonic harmony of C, seventh added, root at the base. No. 2. Supertonio harmony of C, seventh and major ninth added, root at the base. No. 3. Supertonio harmony of C, seventh added, third at the base. No. 4. Supertonio harmony of C, seventh and major ninth added, third at the base. No. 5. Supertonio harmony of C, seventh and minor ninth added, third at the base. No. 6. Supertonio harmony of C, seventh added, fitlh at the base. No. 7. Supertonio harmony of C, seventh and major ninth added, fifth at the base. No. 8. Supertonio harmony of C, seventh and minor ninth added, fitth at the base. ^^m ,r No. 1. Supertonio harmony of C, minor ninth at the base, followed by first inversion, tonic. No. 2. Supertonic harmony of C, seventh at the base, fol- lowed by toni> . root at the base. (In this progression the E'? is almost universally wriiten Djf.) No. 3. This is the only way this harmony, with the eleventh added, can be used, viz., with the minor ninth and in this position. No. 4. This sometimes ooouis, the third falling to the root of tbe tonic. S :! i ' TO CLARKK's IIABMONY. The Bupertonio harmony may bo written after tho lowered supertonio chord, as follows: 15 s=^ -9 9- i liil NY. (ten after tho lowered i CHAPTER VIII. 1. The chord of augmented sixth is a dominant or supertonic harmony from root to seventh, or from third to minor ninth, with the fifth lowered chro- matically. The easiest way to remember it, is : the so-called root is the minor sixth or minor second of the scale. This so-called root is the fifth of the original chord lowered, and is, strictly speaking, only a passing note between the fifth of the chord and the note below, to which it descends. This chord must be followed by the tonic or dominant. ^fej^^^ Ist example. First chord in the dominant of G, or super- tonic harmony of C. Second chord is the augmented sixth on lowered sixth of C, or lowered second of G. The third chord is tonic of G, or dominant of C. Fourth chord is tonic of C. In this example the root is present. 2d exaipple. The root is absent, the minor ninth present; D being the root. A is the fifth, which is lowered to Al», and is called the root of the augmented sixth. The augmented sixth lies between the Ab and F#. This chord may be in- Terted in three ways. It is not often used in inTcrsions how- cTer. (71) ! S ii CI^ARKE H UAKMUNY. ^f Z^SCZ ifsr -5? t^i;^ -Ml \n N:.i 1 the lowered flTth, Ai>, skips to the root. iu )S" ; bo lowered fifth aaccndg to the natural fifth. The Hixtli degree in a minor scale does not require to be lowered when writing an augmented sixth over it ; or, in other words, the dominant chord in which this note is the fifth, requires an accidental. Root: B. F^ is the fifth ; but F is natural in A minor. 2. The angirentcd sixth on the sixth degree of a minor scale may be followed by the tonic of the relative major. This progression is best with the roots of both chords in the base. Augmente)} sixth oa sixth of A minor, followed by tonic of C, the relative major. This progre^ion can be explained by our theory of the three progressions of « dominant chord. The root of the first chord is D, therefore it is only the dominant chord of £, followed by the chord on the sixth of itc scale. (The flntiot, illustration I know of Ih-.s progression is in the introduction to " Faust" — Gouucd.) Y. m the root, le natural fifth. edocs not require mentod sixth over n.t chord in which ccidental. .lural in A minor. ! sixth degree of a the tonic of the 1 is best with tlie followed by tonic of C, tar theory of the three root of the first chord lord of £, followed by 9 progreaaion is in the CLABKK's IIAHMONY. n i^m^ 1 1 ; — -<- ^__ P"^^ ¥ 1 1 i H--^ ^^M^M •«» ^^ri^^s \nr\ :d~T No. 1. Augmented sixth on sixtbdegreeofD minor, followed by dominant. * ^ 2. Augmented sixth on sixth degree of F, or supertonio of C. No. o Augmented sixth on sixth degree of C. No. 4. Augmented sixth on sixth degree of G. No. '^■. Augmented sixth on sixth degree of A minor. No. o. Augmented sixth on sixth degree of C. This is the only way this inversion can be used smoothly. No 7. Augmented sixth, lowered supertonic of C, followed by dominant ; or dominant of C, with lowered fifth, followed by dominant. 4 \) / 74 oi.arke'u iiahmony. The Augmented lizth oompletei the liit of chorda; what fbllow »re either (uepenaiona or retardation!. Introduce the •uginented sixth as often ae poieible in the fullowing example; also the supertonio harmony. ^^^^^^^ :rt?Bc:t}ff=j ^^ggtg-£^^35g -^^^^^^^ I . lilt of chords; what tioni. Introduo« the i« fallowing eiample; s^^ai it£^^F=f^ CHAPTER IX. 1. When paHsing from one chord to nnotlicr, one or more of the meml)crs of the first chord may Iw prok)ngcd into the second chord; provided, they afterward ascend or descend one degree to a member of the stoomi chord. This is jailed retardation. 111 ' II ' In the lit example the U is prolonged from the first chord (with or without a tie), in which it is a member, into the second, in which it is not a member. It then resolves, by descending onp degree, to C, the root of the second chord. The prolonged D is the retardation. The note C, on which it resolves, is the retarded note. This is therefore a retardation of the root from above. The 2J example is a retardation of the root from below. f 7 ftrr: Ill ■-V. w CLARKE 8 IIAkMONY. No. 1. Retardation of root from Bb)Te anU b«low. No. 2. notardaliun of third rrom above. No. B. Rolardation of third from bslow. No. 4. Retardation of third from above and below. No. 0. Retardation of third from above and root from below. Nu. 0. Retardation of root and third from above. No. 7. Retardation of third from above and root from abov« and below. No. 8. Retardation of (Ifth from above. No. 0. Retardation of fifth from below. No. 10. Rclardtlion of third from above, root from above •nd below and fifth from above. Tho following rules must be observccl : Ist. A retardation that renolvos upward, must ascend a semitone, except when the noto on which it resolves is tho third of a chord ; in which case it may ascend a whole tone ; or, !n other words, tho root, third and fifth ra. be retarded from ?ibove by a whole or half tone. Th'i third may bo retarded from below by a whole or half tono. Tho root and fifth by a half tono only. 2d. The noto on which the retardation resolves, must never Iw sounded dose to or above the retarda- tion (the root >nay be sounded above). V. lU and b«low. ». B and below, I and root from b«low. rom tboT*. • and root from nbovo ovo, root from above served : V09 upward, must the noto on which 1 ; in which case it 1 other words, the d?d from iftbovo by I raa}' bo retarded )no. The root anc^. tardation resolves, r above the retarda- ove). 1 r CLAWtB'H HARMONV. 77 'dM^k ♦ ' -"~"-|© 4|» No. 1. The C and D are Bounded together. No. '1 li pouible. No !) it bad. 3d. The note of resolution may be sounded at the octave below. I I ' — i J ^i^^ 4th. All t^ese retardations may occur in any of the parts but the base. The only one that can occur in this is the retardation of the third from above. ^^&=f^ I.I fTF n I 1 r^ 78 CLARKE'S HARMONY. The following example can be easily aaalyied : ^S0?^-t W- J;^! P -:jsr\ W^- z& ■I-- 9 --»-- «-- ■ i ^ J~6 -&- t==!!^!_t.-; ssr 1 =g=Tf;^ :=:- ;pil!i§ig g^S?s3!^SiE5 g^pp^^^gj?^^ 4* 1 ;Pi 15* t « " 7.j; I li CHAPTER X. li 1. An appoggiatura or changing note is a note struck with a chord ; one degree above or below one of the members of the chord. Its only difference from the retardation is, that it need not.be a member of the chord preceding the one !in which it is struck. All the remarks applying to the retardation, apply to the appoggiatura, viz. : If above the root, third or fifth, they may be a whole tone ; if below, a half tone, except below the third, when it may be a whole tone. They may skip in the same way that the retardation does. They maj' occur before two members of a chord, provided they are a third or sixth apart. ■)f I ^ ii M. I n ^ -9- r *f s B iii («2) note is a note 'e or below one only difference ot.be a member ich it is struck, ardatiou, apply they may be a :cept below the Thej may skip )n does. They chord, provided U ■f^dL-:^ -«- -1 — HS- s =*^ *^ is: H — -«s>- olarke'b iia»,:.ionv, 83 -o- f^^i^tep Ai the * we have 'ngle appoggiaturns, from A to B ; at B are double appoggiaturas ; at C tbey skip to '.be note above or to the note below their resolution. 2. Appoggiaturas always occur ou the accented beat of the measure or on the first member of a beat. 3. When these dissonant notes occur on tlie un- accented beats or on the second member of a beat, they are called passing notes. There aro five varie- ties of passing notes. 1st. Those that enter by degrees, either diatonic or chromatic. -^-J- :iU: ^-=f ^^^ f M 84 CLABKK'8 habmqny. I^^^^^l No. 1. The pabjing notes are on the unaccented beats. No. 2. The passing notes are on the unaccented members of the beats. , -^ No. 8. The passing notes are chromatic. The diatonic passing notes generally occur between two harmonized notes, as in the above examples; bv't sometimes two diatonic notes in succession are passing notes. This can only occur as follows, viz., the first note is the root of a chord, the last its fifth, or the reverse. K^^* Sometimes a passing note and changing note occur in succession, as follows : -Tt— '^ — ^ - < ^1 scented beats, icented members of ly occur between ibovc exainples; in succession are p as follows, viz., the last it& Afth, ■m Clarke's harmony. 85 The remarks with regard to retardations and changing notes apply equally to passing notes, viz, : An ascending passing note may skip to the note above its resolution ; a descending passing note to tlie note below its resolution. Also, the note of resolution and the passing note should not be sounded together; but the note of resolution may be sounded at the octave above or octave below. Also, passing notes may be doubled in thirds or sixths. They may also l)c doubled at the octave by parts moving in opposite directions. Lastly, both ascending and descending passing notes may skip to another member of the chord before resolving. nging note occur m r ««»! 8e CLARKB'H HABMONY. ^^Jri#|l a- ;^ ^^^^^^mM No. 1. PaSBiBg note, skipping to note above. No. 2. Passiog note, sklppiog to note below. No 3. Passing note, dounlcd in thir.ls an'l sixths. No. 4. Passing note, doubled in thirds and octaves, three ^"no! 6. Passing note, doubled in thirds and octaves, three ^'no. C. Passing note, douDled in thirds and octaves, fo ir parts. Appoggiaturas : ±: 1 r-f=^-^q ^t^=f= jd=dr-i-f-: |^^fe=:3 .- K \ 9^^—0 : ■# — ^ ::p^=sr: :?=*: ^ 1 Same, skipping: ^gi^^^^^ #-#- e; ^^^^^^^ y *=F*^ 1 w. 1 sixths. ind octaves, three aud ooloves, three and octaves, fo ir -M m >=* ^e ^^a ^ I clarkb'h harmony. Pnssing nfites. first specie' ; 87 bS?^^^^J^ ^^m^m^^^M >Samo ; EE^ ji^i^fe^^gi^ The second variety of passing, notes consii-ts, in striking after a harmonized note, the degree above or below, and returning to the harmonized note. i k^ E^^A^ * gg clabkb's harmony. All the remarkB concerning the pvovioJiH variety, apply to this one. N. B. m No. 1. Both the note. »bow .nd b«low the harmoni«ed note are struck. No. 2 Both the notes below »nd abore. No. 3- Doubled in thirds. No 4, Doubled in sixths. No. 5. Doubled in thirds, not«i abote and below.the Sarmon- ized note. The third variety of lABsing notes enter by skips ; but are subject to the same rules. nh 4- 1 a » * V.B. (viojiB variety, (_^ — i m t barmonized note below.the Sarmon- enter by skips ; 1,1:1 olakkg'h harmony. 89 No. 1. B ia a ptiaiag note, onterinK by ikip. It ih one dcgrcu below the note to which it puHses. It is a Henillone; because all notea of this lorl, whether pawing, chanKing or retardations, niu.'t be, if below the root or fifth of the chord, a Hcniilonc. No. 2. Same, skipping to note aboTe. No. .S. Same, skipping downwards. No. 4. Notes below and above. No. C. Notes above and below. No. 0. Notes below, doubled in thirds. No. 7. Notes below, doubled in sixths. No. K. Delow and above, in thirds. No. 0. Same, in sixths. ' Although, when these notes are above a harmonized note, (hey may be a whole or half tone. Yet if naturally a hiilf tone, they cannot be changed to a whole tone: although, if a wliule tone, they may be changed to a half tone. It is fur this reason that, at the places marked N. D., the first F is made sharp and the second natural. This first F# is a passing note to 0; the Ft] is a passing note above E. If this passage occurred in the key of Q, then both the F's would be sharp. Before treating of the two remaining rarieties of passing notes, we will give the following general rule for all the preceding varieties (including retar- dations) : The notes that lie one degree on either side of a harmonized note, may be struck Jwfore it, either by prolongation from a preceding chord, or by entering diatonically, chromatically or by skip; provided, always, that the dissonant note, be it a retarding, changing or passing note, is followed by a liarmon- ized note ; which harmonized note may either follow 90 clarkk'm harmony. immi'dlately or may bo delayed by the dissonant note if below, skipping to the note above, and vire versa, or skipping first to some otlicr menber of tl»e c'liord, TIjo fourtli variety ia a variation or ornamentation of tlie first. Tlio following example! will explain their uie: . fe:=fc--r=:z.— _::f^= I=:=i:r-=^^±U^ 'P^ ']m to w= ( RmiD :^ m t±*. i i * i i ;^.^i^^ "=$-- m 5^^ '=$■ m ,-fiL. i ■ 11' ^^^^^^ y the disHonnnt above, and vice r iiiei ibcr of the r oritamiMitatioii r use: -4^^=J^ 'mjm m ttjb ^-O- i H i -^ * IMAGE EVALUATION TEST TARGET (MT-3) 1.0 I.I |50 l™^* 2.5 112.2 12.0 1.8 1.25 1.4 Ii4 ■« 6" — ► w^^r '/ w. Photographic Sciences Corporation 4 •s? \ ;\ \ %■ 4fp ^ fi 1e/ CIHM/ICMH Microfiche Series. CIHM/ICMH Collection de microfiches. Canadian Institute for Historical Microreproductions / Institut Canadian de microreproductions historiques - ' l| ! B r --.' ' !VJ.i ' JJi.^"Jt l«' M ' >S ' J' ' -^ ? iftft.tf '!'. ' --' ? --'; 'Mi^:^f^irt?'^ i^-jp*Jtwr*r«^;* ■^ 9e ci.arkk's harmony. 8. The fifth of a major chord may be cimngcd to an augmented fifth, provided the augmented fifth ascends one degree. (This applies also to a domi- nant with seventh.) ^^^^^^^m ^t= M.j:T^^ ^^ II 7^ £ ^ 1^^ No. 1. The pecond chord is a combination of .pasBlag note E and augmented fifth, C^. 1 A'- This example is a combination of a doub'e retardation and a changing note. Such combinations are only possible when the dissonant notes, taken collectively, form part of the dominant harmony of the key of which the chord on which they resoWe ia the tonic. In this example, C#, E, Q, are part of the domi- nant harmony of D. D, F, A, is the chord in which these notes resolve. lY. nay be cimnged to 10 augmented fifth ics also to a domi- ition of .passiag note E i DuVe retardation and a only possible when the n part of the dominant 1 on which they resolve , are part of the domi- chord in which these CLARKE'S IIAKMONY. 00 S. CImnpinf,' and pnHsinjr notoH may hv donhlcd when they are ai» aiigmcutt'd fourth or diminiHiicd fifth apart ; provided, the two sounds nlwnys move in opposite directions to tlicir resolution. 11^ Passages like this may be explained on the theory of a " harmony within a harmony ; " boonuso they always boar the relation of either dominant or supertunio harmony to the chord with which they occur. 6. Passages like the following can be used, con- sisting of passing notes of various kinds. The design of such pnssages seems to take possession of the listener and cover the harshness of the numerous dissonances. 100 CI.ABKE'a UABMONY. i^^^idiBlfe Tlu'y in^^*- «i'wayH begin and oml with ii cliord. Vr.rlouH pnwageH of tliis kind can bo found ; but enough has been taid to guide lo their underglanding. 7. False Relation.— Wlien a note, occurring ui two Buccessivo chords, is chromatically changed, without remaining in the Hamc voice, it is termed a false or cross relation. ^^PU^ i ^^ hi m^^mm^ No. 1 is always b«d. No». 2, .S, 4 and "> are common. Ii IB I. ir. iU^ tl with a chord. 10 found ; but enough iding. note, occurring 141 natically changed, oice, it is termed a :^™ii ■*•. r^ «f CLARKE H HARMONY. 101 Tli« fullnwin^ niiglit l>e firiven ana rule fur tlioio progmidonit: A fitUo relntion iiiunI iipvvr bo niailo with llio third of the chonl (Exaiu|ilo 1) ; but it iiiuy ocnur with nny ollinr inoinbor. Kx- tniple 2, It Ik the seventh ; thi' iinigrcNHion iit r^re. Einmplo R and 4, It '\n the rooi thiit ir 'ored ; 8 ii Itetler than -1. Kx- an.ple T), the fifth Ih altered : tKix is very coiiiinon and Ih alwayH good. 8. Wlien liny two parts ascend or descend togetlier to an octave, from some other interval, it is called a concealed octave : ^ m Iwcause, if tlie intervening notes are pnt in as in this example, two ootavcH will rosnlt. The unpleasant effect is supposed to be obliterated when the npper part moves a semitone, as in this example. A fifth, which enters in this way, is also called a concealed fifth. I ES^ :±3= t^ 9. When the different notes forming a harmony are struck successively, instead of simultaneously, the chord is said to be broken or disj^ersed. t\ r5»T !|! 102 CliABKE's HARMONY. The following are the commonest forms of d'spersion : i"-> r f r > r r -^ No. 1 is called an arpeggio. Nu 2 bus no distinctiTO name. No. 3 is called an " Alberti bass," from lis reputed inTentor, Dominico Albert!. Of conrse, this dispersion may be varied 'n many ways. It may also have passing notes interspersed with the members of the chord. I X X XXX ^^ ^ ■¥^ ^ m XX X X X ^1^ -^ f f f\ tU ^ ^ These and many other forms ore frequently met with, par- ticularly in modern piano music. Consecutive fifths and octaves may occur between a part or voice and tlie dispor.5ed notes of the accom- panying chord ; also, consecutive dissonances. IS of d'spersion : n"TT — y^^^^ P n Its reputed inventor, persion may be varied ing notes interspersed X X ^^ ^ m quently met with, par- may occur between notes of the accora- dissonances. m A CLARKE S HARMONY. B O lOS -• — I- ISIJ -'^ i At A there are two fifths; at B, two octaves; at C, two sevenths. But the ear does not recognize them, because it is at once satisfied that the harmony is as follo'vs : dispersed or broken, for the salce of variety. 10. Concerning Consecutive Fifths. — There is an unfortun.ate prejudice against consecutive fifths in the minds of the majority of musicians, in spite of the fact that they are often used by the greatest writers. The excuse given for this is, tb^t these writers knew how to use them. If this is true, it would seem to be the duty of any who attempts to teach harmony- or composition, to find out and formu- late the riilcb by wiiich these composers worked. The following remarks are an attempt to supplj- some sucu rules : 1st. Two perfect fifths, occurring between extreme parts, arc alwajs disagreeable when the roots are within one degree of each other. The disagreeable 104 oi.arke's harmony. effect is ii little less when the root>( nre a third apart; still loss, if a fourth apai-t; and least of all, when a fifth apart. In the last two eases the softening of tlie effect is owi-ig, probably, to tlic fnct that there is a connecting sound, \'\/.. : ©- -»-• m It will be seen that the connection in tlie second example is still closer than in the first. These two cases are to be foond in tlie works of many good writers. Of course, the effect is still more softened by contrary motion between the extreme parts. (Seo example on page 29.) It is possible to have two perfect fifths, in succession, between the extreme parts, when one of them occurs between any two members of the chord but the root and fifth. The first fifth is between the root and fifth of the chord ; the second, between the fifth and seventh of the chord. (The absence of unpleasant effect here may be owing to the fact that it is the dominant of a minor key, followed by the dominant of its relative major, and these two chords having so many sounds in common.) 2d. Two perfect fifths, in succession, may occur between the middle parts (tenor and alto), as follows: nro !i third apart; sast of all, when a s the softening of lie fiict that there 1 ,he second esnmple in CAses are to be found r course, the effect is between the extreme in succession, between curs between any two ftli. Rfth of the chord ; the ic chord. (The absence ; to the fact that it is iy the dominant of its nvin;; so many sounds session, may occur 1(1 alto), as follows: clarke'8 harmony. 105 ■without any unpleasant effect. Of course, if they can occur at the distance of fourth or fifth between the extremes, they can between the minor parts do likewise. They may even occur a third apart, with- out any serious unpleasantness. T==^ 1 3d. Perfect fifths, one degree apart, may occur between the base and the tenor or alto, when they result from the resolution of nn augmented sixth chord, as follows : (This can be found in Moiart and Beethoven.) 4th. Perfect fifths, a third apart,may occur between the base and tenor or alto, as follows : m -»- ^ — S^ — If 5» •rrr^ 111 lOf) OLARKErt HARMONY. 5th. Of course, they may be a fourth and fifth apart. Otij. A diminished can always follow a perfect fifth, in a descending passage, as follows : -»- The perfect may follow the diminished, as follows : S :f: iT i I do not put forth any of these remarks ns rules (except the last, which is old) ; but merely to point out the way that con- secutive fifths are often need by good writers. No satisfactory reason has ever been given, why they should be unpleasant. Indeed, thern is good ground for suspicion that it is merely the result of education ; the learner being from the beginning cautioned against tliem as the unpardonable sin' in writing. (See Helmholz and Pole on this subject.) If the deciphering of old manuscripts is ^o be trusted, there was a time when the only intervals used were the perfect fourth and fifth as follows : P^^ This was known at diaphony. It may be that the forbidding of consecutive fifths, altogether, was merely a reaction from this unquestionably barbarous style of oompoaition. ill|i « J rourth and fifth bllow a perfect lows : shed, as follows : 118 rules (except the t the way that con- 's. No satisfactory uld be unpleasant, n that it is merely from the beginning ible sin' in writing. ^0 be trusted, there I were the perfect that the forbidding ly a reaction from position. CHAPTER XII. Suspended Dissonances and Sequences. — Before it was discovered that the seventh could at any time be struck with the dominant chord, il; was used only as a suspension and coutd be added to any chord ; but it was and is necessary to prepare it ; i. e., it must be heard as a member of the preceding chord. The modern or harmonic system has retained this rule from the old or contrapuntal system ; therefore the seventh and the ninth may be added to any chord, major or minor, by suspension. It must always resolve like the seventh and ninth in the dominant chord ; and a chord with seventh or ninth added by suspension, has three progressions, just as the dominant chord has, viz. : It can be followed by a chord whose root is a fourth above (tonic) ; a second above (chord on sixth), and a third below (dominant of relative minor). Preparation. Su$peniton. SeioluHon. i s ? i Si ^ X 1 (107) ,1 ■ 108 oi.abkk'8 harmony. Chord of £, with auspendeil seTentli ; tlio seTenih resoWes on C ; and The chord marked 1, in Rimilar to first progression of domi- nant with Hcvcnth. The chord marked 2, is Kimilar to second progression of dominant with seventh. The chord marked 3, is similar to third progression of domi- nant with seventh. Tlie seventh and the ninth are the onl}' suspensions possihlc. Tliey can be inverted like the dominant with Bcventii and ninth, in short fliords with a sus- pended seventh or ninth, arc in every respect to be treated just the mnie as dominant chords with seventh or nintii. It will be seen that a suspension differs materiallj' from a retardation, because it always resolves down- wanly and never w the same chord in which it occurs. Suspensions may skip to the note below their resolution, or to some other member of the chord. They are also frequently ornamented by passing notes. •^M^ tlio seTenih resolves progression of domi- iieooni) progression of i progression of domi- ic onl}' suspensions like the dominant fhords with a sns- v^ery respect to be nant chords with f 1 differs material!}' ays resolves doicn- ■hord in which it o the note below er member of the y ornamented by - |»-^^^. =J ci.arke's uarmony. 109 -.-=&=^-Jt^. -'z^Er=is-. »- P=i::p=ft z^ ! I I 5^^^^ — -_:rfi: m This example is founded on the following suocossion of bus- pended sevenths : (i 3tf!^at; 5=^ -t — '— f \^m\^^i^^m (^^^^i^e^^ Sequences. — A molodic sequence consists of the same phrase repeated at equidistant degrees, thus : i^'^^Ee^ m=f^^^^=^f&?^^^ A harmonic sequence consists of a series of domi- nant and tonic harmonies (general!}), or augment od sixtli and tonic or dominant liarmonies ; tlio roots of wliich proceed by similar step?!. [iJI 110 CLAR»'B'8 HARMONY. :i^¥3^:£f^ ^1 |^^t^_^^3^^ ,is=?= EE^ -®- ^ i (1^^ 1 s^ ^^^ No. 1 is a sequence of dominant and tonic chords ; the tooU fall a fifth and rise a sixth alternately. No. 2 is a sequence of augmented sixths and dominant chords. the roots falling » semitone. ..-»»,», Ti,« No. 3 contains both these examples in the first bar ine second bar is a repetition of the whole phrase, one degree higher. It would be impossible to giye examples of all the harmonic sequences that might be^made. The above examples are enough to explain the manner of their construction. 11(1 ; m ^ m i^^^3E m tonic chords ; the toots lis and dominant chords, 1 in the first bar. The lole phrase, one degree pies of all the hannonio le above examples are ■ construction. CLARK E'h HAHMONY. Ill Tlic contrapuntal Heqncncc consists of ii sucws- sion of common chords, with roots moving in some regular i)lan. Tho diminished chords cm be used, with tlic h)we.st note of tiie group for a base note, nltliouffli tliore is a rule the eontrary (see page 52). Tliis permission is for the sake of preserving the form of the sequence. fpf^fp^m ^^ ^^^^^r^^=Ffl£^^' _UJ'-iJt No. 1 is one of the commonest. The roots rise a fourth and fell a third. No. 2. Roots rise a fifth and fall a fourth. No. 8. Roots fall a fifth and rise a fourth. 112 OLARKR'H HARMONY. No. 4 oon.i.t» of a phmHO of four chord., toreated a third lower. No.. 1, a and 4 can l.o changed into harmonic sequence. easily 1 a* follows: m^'ff (^^^^^^^^^ n Of course, it is not necessary in any sequence that the roots of the chorda must always be at the base. The following example, are contrapuntal sequences, with seventh and ninth added. :=tiUi^itT5Nfefe I 1 E^S i;M wm. 4 ONV. uhord*, rcjflaleil a third nio liarmonio sequenco* '^m^ ^^^ ^ •- ^^ y in any sequence t^iat always be at the base. Urapuntal sequences, with « -J-4 =F^ I 1 » lI.AaKK's IIAR.MONV. 113 -i=^^rE^ e^^m^^ ^E^^^^m No. 1. Sequence of suspended seTentha ; roots fall a, fifth and rise a fourth. No. 2. Scijuenoe of suspended sevenths ; roots rise a senond and fall a third. No. 8..Sequenrc of suspended ninths; roots rise a fourth and fall a fifth. No. 4. Sequence of suspended ninths ; roots fall a third and rise a second No. 1 may be changed into tho harmonic sequence (described on page 68), as a suooession of dominant chords. il^i^^^^ TO If 114 CLARKK'H IIAHMO.NV. No. 2 may b« changed into » harmonic ••<|ueiioo in two wayi. (^"^^^^I^ No. 1 is » Mquano* of dominant obordi raiolTing on tlie iiitii (if ibeir toalo. No. 2 ii a iiequenMof dominant aliorda with roots omitted, reMolving on their tonio*. ! I u NV, iiequeiioo in twowayi. — — t m ordi rtsoWing on the rdi with roots omitted, CHAPTER XIII. ModuIjATIon. — Moiliiliition \n tlio net of pnnRing tVoin one koy to nnotlwr. Tliero in, imfortuimHtly, no wiiy of ilistinguiHliinjj hetweon niodiiliitionH to related nn»l nioduIntiouH to non-rolntcd kvya. The term tranHition Ih sonietimea used to uignifv a sud- den change to a remote key. It would, i)jrhat)H, bo a good method to use the term modulation to signify the change to a related key, and transition to signify the ciiange to a non-related key. It is verj' unfor- tunate, but true, nevertlielcss, that the musical nomenclature of the English language is in a very confused state. I shall use the word modulation in its generally accepted sense — to cover all possible changes of key. All modulations may be reduced to four rules : Ist. By taking advantage of the fact thnt the dominant chord is the same, whether the key is major or minor. This will give six modulations from any given key, because there are six dominant chords in every key. The following exiimples contain all the modulations that may be made by this rule, from the key of C. (116) - - ■^.m^'^.^i^ li^T^ 116 CI-AB1\.E S HABMONY. *i#- i^^f^p In 1, 2 and 3 the msyor tonics of the key are changed to minor. No. 1 becomes C minor, relative minor of Eb. No. 2 becomes O minor, relative minor of Bt>. No. 3 becomes F minor, relative minor of Ab. In 4, 5 and 6 ttie minor tonics of the scale are changed to major. These examples are, of course, mere skeletonb, being too abrupt to have any musical effect as they stand ; in fact, it might almost be laid down as a rule that no modulntion has any intrinsic beauty; it depends altogether on the wny it is usi'd. Some of the most beautiful examples in the works of the grent masters are as simple as possible ; but the manner of their use gives them all their exquisite effect. ONY. a tP ^'r--''" y"r - t the key are changed to linor of Eb. linor of Bt>. inor of A\>. ' the Boale are changed to mere skeletonb, being too ia they stand ; in fact, it lie that no modulntion has [together on the wny it is examples in tlio works of possible ; but the manner [uisile effect. Clarke's harmony. 117 It will be seen that by extending this rulo to each new key that is reached, that it is possible to pass through all the keys. For example, the first modu- lation changes the key to E^ ; then by applj'ing the rule to tlie chords in E^, six new changes would be obtained. The following examples will show how effective a modula- tion of this kind may be made. C minor. ^ i-ld- W^ ^ J. ^ -^- EE^ (i s^gi^i m=^ES^-=f-- *=«=«^ I I ±^i=^^ ^ ^^^iirl r==J:J^ fcx=t=t=^ ■X ' ' ' ■ ' : — ;■ '^ I'i III 11 Hi 118 CliARKB'a HARMONY. C major. I i W-- g ?^=Ftf m^^^ ?=i=p= i The second means by which modulations may be made, is hy taking advantage of the different places in which a major or a minor chord may be found. . A major chord may be found in six places, viz. : As a tonic, subdominant, dominant, sixth of a minor scale and lowered supertonic of a major or minor scale. gJ Z^ g Z^Z^^ .a « 0-. 1 ONY. E3^ H modulations may be f the diiTerent places )rd may be found. I in six places, viz. : ant, sixth of a minor >f a major or minor _« ffl- 1 CI*^i^B**ii^'@*a-SSirt*^SSl«i^»-^ m t i 120 CLARKE'S llABMONY. Each common chord bears the relation of tonio to the ilomi- nant that precedes it, and lowered supertonic to the dominant that follows it. The following examples gite the modulations that may be obtained from the two remaining major chords in the key of C. ^ m ■j^tzf^zzz. 5tZ«= i n F us dominant. F an isizth of A minor. ) I •' I 'or m. z^— ^ ^ -9- m F IS lowered supertonic of K (} ii>< ^ulidominant. O iM si-xtli of n minor. NY. an of tonio to the (Jonii- ertonio to iho dominant >dulation8 that may he r chords in the key of C. J— H fcs ^m X fcz«= ^ m I Blxtli of A minor. m s^i X 1 a iix Hlxth of R minor. CLAUKE S HARMONY 191 '■o-p- ■■^~ X l§::^ 1r ^m^ a as loworod xuportonic of F$. A minor chord niaj' be found in six pliicoH, viz. : Tonic and snlHlominant in a minor koy, and t^nper- tonic, mediant and subniediant in a major key. l^^^lSif X ai; p^ll^E^la «t H A minor aa subdomiuant of E. i=#i-^f=^4^i^ X jE^p^^ A minor aa mediant of K (third degree). ^i^l=3-^!^gl i A minor as supcrtonic of G, m I 122 clabke'b uakmony. (It would be superfluous to gire any more exMnplea. The pupil ougbt to bo able to construct them himself.) A major chord may have an augmented sixth added to it. No. 1. C major, changed to augmented Rizth on sixth degree of E. No. 2. C major, changed to augmented sixth on lowered supertonio of B. No. 3, G major, changed to augmented sixth on sixth of B. No. 4. Q major, changed to augmented sikth on lowered supertonio of F#. A major and minor chord may bo treated as the seventh, ninth and eleventh of a dominant harmon3-, provided the fifth from the root is added. Thuf> C, E, O may be the seventh, ninth and eleventh from D, by adding A, the fifth from the root, D. No. 1. F, changed to dominant of C. No. 2. C, changed to dominant of 0. >NY. 17 more exhmples. The m liimself.) n augmented sixth ed Bizth on sixth degree >nted Hizth on lowered ted sixth on sixth of D. ented eikth on lowered ly bo treated as the I. dominant liarmon3-, >ot is added. Thus h and eleventh from he root, D. clarke'8 iiakmony. 123 No. 3. E minor, changed to dominant of U. No. 4. B minor, changed to dominant of F#. The third of the major chord may bo changed, thus : p=i i^^=ffi because it becomes the ninth when treated as above. Tiie minor chord may also become tiie fifth, seventh and ninth of a dominant or supertoniu har- mony, b}' adding the root or third to it. ^^^^^m •«■ W W T5. ^te^ X No. 1. A minor, changed to dominant of 0. No. 2. D minor, changed to eupertonio harmony of F. No. 8. E minor, changed to dominant of D. The third means of modulation is by the chromatic alteration of chords. Common chords may be chro- matically altered, as follows : (; major. C minor. to or i'i~ to or or" ; i. €., the third alone or the third and fifth of a major chord may be lowered, or the root may be raised. 124 CLARKE'8 Il.VftMONT. The tliird alone of a minor chord or the third and fifth may be raised, or the fifth may be lowered. In the above example, C, E, Q is major; C, E>, 0, minor; r, E\>, 0!», part of the dominant of D> or D!», or Biipertonio harmony of G> or Eb ; CJ^, E, O is pm f dominant harmony of D or B, or supertonio harmony ol' ,ir E. i 1 m No. 1. C, E!», 0, as coming from Ab, dominant of Db. No. 2. C, Eb, O, as coming from F, dominant of Bb. No. 3. C, Eb, G, as coming firom F, i.ipcrlonic of Eb. No. 4. C, Eb, O, as coming from Db, supertonio of G^. The most important modnlationa of this kind are obtained from the chromatic alteration of groups of four notes (see page 64). 1^ * m^mm l?t group. Koot: a. 4tli. C. 2.1i)r4lli. EiorC. 3.1. r. Commencing with the first group, the third may be lowered alone, or the third and fifth together, or third, fifth and seventh together, or third alone, fol- lowed by fif h and seventh together. This process iaiMHa* NT. d or the third and lay bo lowered. lojor; C, E>, 0, minor; •> or H\>, or Btipertonio '{ dominant harmony ,.r E. '-^&=S^- 1 4 dominant of D!>. lominant of B':>. jporlonic of E!>. Bupertonic of 0?. ons of this kind are oration of groups of 1. 3. 1S6 Ct.ARKR H HARMONY. All jincrmpntpd sixth chord rany bo changed to a duinitmnt, and tho rcvcrMc. ^^P:^ .^m^- l^l^^l^^pi to to Nob. 1 and ;!. Augmented bixth, changed to dominant by enharraonio alteration of the sixth. Nos. 8 and 4. Augmented sixth, changed to dominant by cnhnrraonio alteration of the first, third and fi(Mi. Nos. 5 ond 0. Dominant, changed to augmented sixth by enharmonic alteration of tlie seventh. Nos. 7 and 8. Dominant, changed to augmented sixth by enharmonic oltcration of the flrst, third and fifth. The most pioliflc source of enharmonic modula- tion is to be found in the diminished seventli chord ;. This chord, it will be remembered, results from adding the minor ninth to a dominant or superton!c harmony, and omitting tho root. Three groups of sound} form all tho diminished snvonth eliords. Since there are twelve m.ijor ehorla to which the ninth may be added, it follows that each group must bo obtained from f )ur rootn ; al-.o, ' ' it^ijwwiwuliiii NV. ny bo changed to a 8 e to tnged to dominant by inged to dominant by [ and fiftli. > augmented Hixth by augmented siztli by 1 and fifth. nharmonic inodiil".- led seventli chord ;. ercd, results fro-.u Inant or supcrtoivc all the diminished wclvo major ehor la ed, it follows that hi fr)ur rootn; nl o, t'l.ABKE'rt KAKMUNY. 127 since there tiro six dominanta In every scale, it fol- lows that each group must occur Iwio;' in every 8L-ale as a dominant harmony ; alio, there boing six Hupcrtonio chords in every scale, each group mur.t occur twice as a supertonic harmony in every scale. P'or convcnicnca we will number the groui):^ as fol- lows : Tiiat from dominant of C, first; from domi- nant of F, second ; from dominant of O, third. Hooti: a, Unmtnant of C, Suporton. harm'y of l", E, A, (Db). (O.-). B, AS (Ob). r, D, D, A\ n;., o, E, iy,j. Roots: I), II, Ats (o«). Domluantof O, E, »> B>. (c;) Suportonio harmony of C, A, Oi;, Ey (F|). No. 1 occurs in C, as dominant of C and dominant of its relatiye minor. No. 2 occurs in C, a') dominant of F and dominant of its relative minor. No. 3 occurs in C ns dominant of and dominant of lis relative minor. In the following examples are all tho roaolution? possib'o to the first group. Tho pupil can easily wi-ito Ihouo of the re- maining groups. IJX <'t,AKKK'"< IIAKMilNV. f^fllYsrlT^-ffe^il Hoot: (> RtNit: r^i It, No 1. Written as coming fVotii O ; renoWoil, flrnt, an iloml- imnl or ('; Hooonil, iim Bupertuiiio Iinrmnny of F. No. 'J. Written as coining from E; roKolvcil, first, uh domi- nant of A ; RocontI, an luperloiiio harmony of I). No. H. Written uh voniinK from C# ; renolveil, flrsi, nn domi- nant of F# ; Hccond, iis Nupcrtoniu hnrmoiiy of U. No. 4. Written a8«oin!ng from !)• ; ro^olvcd, flml, an domi- nant of K'j; Hi'cond, nt Kiiportonic linnnony of A '. Olio incinlM'r of a \\. -jiar renoWod, flMt, an ilomU rioiiy of K. rexolvpil, first, us doml- noiiy of 1>. renolveil, flrHi, i\« domU ■moiiy of U. ro.iolvcil, flrHl, nx domU inony of A >. 1)0 lulfl Mild lllO IP 'initoiii'. 'I'ho ri'Miilt 111 of whioli tlio lieltl •r:!?5f— r«- il clarkkV iiakmunv. 1S9 No. 1. V held ; I lie chord li.'oomei, ftr»t, dominant of Hl», or ■econd, utiperlonio hi»riiioiiy of Ki'. No '-'. A 'held; llu- «liord hocomeB, flrtl, dominftnl of Vf, or necoiid, miixTl 'iiio hnrmoiiy of fl:*. ;>',). ;t. B hfld ; the chord hcooiiieM, flml, dominant of E, or ■econd, iuporfonio harmony of A. No » l> hold ; Ihu chord hcoomen, flfit, dominant of 0, or ieoon i>r= " «'^ 11 134 CLARKE'S HARMONY. Or in which it is a passing note on the chord of P. All the dissonantcs and the perfect fourth may be used as appoggiaturas or as passing notes. The following rules must be observed for the pro- gression of the parts : Ist. Contrast them as much as possible. 2d. Use contrary motion in preference to any other. 3d. Never use a cross or false relation. 4th. Never proceed by parallel motion to a perfect fifth, except as follows : i ^ ^=^=t: 1 (called a horn passage). Of course, this does not apply in a passage like the following, in which the same chord is repeated in another position. 1^ ■*4ll|i»«| >NY. the chord of F. perfect fourth may tassing notes. •bserved for the pro- s possible, preference to any relation. 1 motion to a perfect ourse, this does not Lowing, in which the er position. I clarke'8 harmony. 185 .5th. Never proceed to an octave in parsilU'l motion, unless the upper part rises a semitone. Gth. Never write two major thirds in succession, whose roots are less than a perfect fourth apart. Bad. ""O*'- Last of all and most important. The composition must be so constructed as to express the harmonic succession as definitely as if it were in four parts. In three parts.— Ml the preceding remarks and rules hold good ; but the following are relaxed, viz., the dominant with seventh, or any of the dominant harmonies can be struck without any preparation ; also, the supertonic harmonies. The following table gives the best way of representing all the harmonies in three parts. i j» -gt^ -g 186 olarkk's harmony. Nc. 1. Common chord. (Of course, all may he inverted.) No. 2. Dominant or supertonic harmonies. No. 3. Aunmented sixth. First, when followed by dominant; second, when followed by the tonic. The perfect cadence may be made as follows in three parts, viz., the tonic, with the root omitted and tlie fifth doubled. (It is only the position tliat en- ables us to recognize this as the chord of F.) i :f: J*.^. i Px o w ■» -^ The rules, with regard to proceeding by parallel motion to perfect conconls, are relaxed, with rosranl to the lower and middle or middle and upper parts ; but are still binding on the lower and ujiper parts. Also, two major thirds may ocr-ur (see above) between the lower and middle or middle and upper parts. MONY. 3l le, alt may he inverted.) Tmonies. hen followed by dominant ; )o made as follows in h the root omitted and y the position that en- he chord of F.) proceeding by parallel re relaxed, with roirard iddle and upper parts ; iwer and ujiper parts. lay ocpiir (see above) le or middle and upper CLABKE's IIARMOW. ^^^m ite. W=f ^^zL^ ^ 3^ f^ 137 No. 1. Fifth in parallel motion between lower and middle parts. Mo. 2. Fifth in parallel motion between middle and upper parts. No. 3. Major third between lower and middle parts. No. 4. Major third between middle and upper parts. No. 3 is much better than No. 4. With regard to fonr-part writing, nothing new need be said. It is subject to the same rules a.s three-part, and differs only in its greater variety and copiousness. 138 Clarke's iiARMONr. The following examples are intended principally to show the manner of using passing notes and 'ipPoggittt'Tas. One of the best ways to study free composition in two parts, is by examining the violin (Inots of Spohr, Pleyel or Viotti. For three-part writing, the string trios of Beethoven and Mozart. Of course, in all these compositions there are fre- quently four and even more parts produced by play- in^^ double notes. Also, many parts are merely f 1;>3 and accompaniments. Still there are plenty cf I'xamples of pure two and three-part writings to be found in them. Perhaps the finest specimen of t-.vo-part writing in the world, is the concerto for two violins, by Bach. IM lONir. intended principnlly J passing notes and 3t waj-s to study free examining the violin otti. For tlirce-part tiioven and Mozart. ositions tliere are fre- rts produced by play- ly parts are merely Still there are plenty ;hree-part writings to le finest specimen of is the concerto for CLARKE'S IIABMONY. 1S» Tlio threi- following examples are founded on this harmony. 5^-E^ .rSS^JSS^ TO ^ jT^ T^ i In two parts : ^^^ MONA*. ?^-i^Lib 9 ^m T TT ^^^^ f =^-#' :.-.r=f=3C ^^^ ^^^ S=i: 8 r -T- (*-- CI.ARKKS IIAIIMONY. 141 ,i^^_^^[^P zqir. ,p?:=^^ JTi=£. ;:^- ^ mi ■tr .^ i^m ^5=25= ®- iT=P;:^',J^ ^^P^P ■^ ■•■ I H^ M # ^ |,g?pE='=»3g4-^^ ^^slp. CLARKK'H IIAllMONV. i_J_,4_itiJj-^,-^ '^^fE^'^ =.:ip|tf=to:sl: r i ■^^' I *. i J ! x^i.*J lONV. -J. Uii: 1^^ L_J^_ , CLAKKEli IIARMUNY. 148 J i . ^ — #■ ( 1^^^^ S i-4i ; _b^ , iA..^_^i s a §1^?^ \^^L_ y — m^. i CONCLUSION. The 8tudei.t, who has thoroughly mastered tliis course, should be i)repared for the study of couuter- point, fugue, canon, and the various forms of com- position. It is difficult to study harmony without a teacher, and almost impossible to study these higher branches without a guide at first. I have omitted any explanation of the figuring of chords (thorough bass). Tliere are hundreds of works Avherein all tlie information wished for may be obtained on tliis subject. For tlie study of strict counterpoint. Cherubim's is perhaps the best work. For the study of form, no work will suffice. Some good ideas on this -ib- ject may be obtained from the works of Dr. Marx. Finally, constant writing is the only way to learn to write well. No amount of genius will make up for the lack of hard.work. (U4) ^-^iOnwi, M :oN. ughl}' mastered tliis the study of coiiuter- rious forms of com- y harmony without a to study these higher 3t. iion of the figuring of ere are hundreds of ition wished for may nterpoint, Cherubini's or the study of form, ood ideas on this "'ib- e works of Dr. Marx, e only waj' to learn to luius will make up for