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P.„..„, „„„.„.,, c„^.. 1o\ i i> 1^1 National Library Bibllothdque natlonale of Canada du Canada *4 ^ TO HER LADYSHIP THE COUNTESS OF DUFFERIN, HY HER GRACIOUS PERMISSION, THE AUTHOR RESPECTFULLY DEDICATES ■ THIS CANADIAxN EDITIOx\ OF HIS ^n^ERIc^lT ayCETHOE" 0» HARMONY. ^ /< /■ ^ Author's Preface. • * L\ presenting this work, the details of a method which I have more concisely taught for years past (with what degree of success thousands of pupils may testify), I offer no apologies for intrusion ; but solicit from the profession and the public their sympathy with an effort to develop that ability in pupils, en masse, which shall elevate the taste, and render the study of music, not only more pleasing, but also more thorough. It has been my aim, and experience has proved it not a failure, to simpUfy, even to the capac- ities of juveniles, that wliich enables them to comprehend at sight those intricacies of Harmony continually encountered in practice. Yet I do not encourage students in the idea of composi- tion, but rather of reading. If God has endowed my pupil with genius, the plain truths herein elucidated will insure it safe conduct to a path it alone can tread. To read Shakspeare well, requires an elocutionist ; to write like Shakspeare, his genius. By instruction and practice, one may become a singer, a pianist, an artiste; but only by the inesti- mable gifts of genius and inspiration are those origmal thoughts .and forms brought forth which mankind accept as models. The brevity of the " American Method " renders it unnecessary to pouit out its pecuUar fear tares. The illuatrations are soon reviewed, and require no indorsement other than the improju- diced opinion of all who are not antagonistic to clearness and rapidity, when combined with thoroughness and high intellectual culture. With the controversies of theorists over Thorough Bass, composing by intervals, what chord- successions are allowed, &c.,-&c., I have nothing to do, but will refer those who are not posted, to Weber's "Theory of Composition" (242), page 429, (575), page 794, Vol. IL, anS remarks, pages 222 to 220, inclusive. Vol. I.; Richter's "Manual of Harmony," page 81, first paragraph; Marx's "Musical Composition," pages 38, 39, 220, and 221, — works both valuable and pleasuig to the advanced student in Harmony ; though I am constrained to claim, without desire to criti- cise, that all the standard works enter quite too much, for the understanduig of the mass of pupils, into scientific details tending to discourage and confuse. They give liberally of the sub- stance, yet sparingly of the spirit. That is good in some things ; but in this we must have plainly, so far as possible, the great laws which govern tLl3 kaleidoscopic science. It Is, howQver, so much easier to find fault with others than to do better ourselves, that I shall here acknowledge my indebtedness to the errors as well as the truths of various authors, for hints which have kept mo aUve to the necessity for brief but practical principles, so sharply illustrated and impressed upon the mind as to be on unfailing Ught to guide the student in aU the wondrous and enchanting changes so ricldy and elaborately wrought by our masters. Mwm MMfi flp Mim. MAJOR AND MINOR SCALES. ^ by no means, sufficient for students who stud v.h '' "'^'^^^^^^'^ding of them, more especially those of the modem schtl tU ^""^' ^^ ""^^ ^^^^* masters, J their musical ideas with a freedom an^« ;, '' ^^^arkably fond of iUustratMK confusing to pupils generalir JSl prelt™? *' ' T''''''' ^^^^h ter^S^^ purpose. ^ ■'"® prevaihng surface-culture wiU not answer our DEVELOPMENT OF SCALES. an^^S^^rr---^^-^ (or.:epsand haLsteps,) I 2 2 34 4 5 5 7 The Scale i, «„„,. „i,„ ,„„ , ^ 3 ,^ °^^ ^' _^ J^^ ^ 6 9 10 I 2 3 2 3 6 5 6 7 8 7 8 U 12 78 a 12 C #.!• CX DX EJI FX GX A f.> AX B c Q •■■ilAfAandB?BaadCf '' ""'"^ W «"<" D ' D andEf E andPf Fand 0, AMERICAN METHOD OF HARMONY. Degrees of all Major, and their Relative Minor Scales. c A n u K C F ]) i; n ^:w-^' :g: ^:g=g: 'z^E^z g # :s ^ -(S? c A n B c F A F I! G C A Name the foUowiug letters iu exaMPLEI. F C G D, A E AKD B The above letters are the Sharps, single and double, as they occur in the Major Scales. NAME THE FIRST SHARP. The first two; three; four; five; six; seven. The first double sharp ; the first two ; three ; f&ur ; five. THE KEY NOTE OF THE MAJOR SCALE is nest above, and its relative minor next below the last sharp named. WHAT ARE THE MAJOR AND MINOR KEYS when F is Sharp ? F and C ? F, C and G? F, C, G and D ? F, C, G, D and A ? F, C, G, D, A and E ? F, C, G, D , A, E audB? Fx is the last Sharp : what are the Blajor and Minor Keys ? Cx is the last ? Gx ? PX? Ax? THE ACCIDENTAL OF THE MINOR SCALE occurs upon the Seventh, and is the same as in ths Major Scale of like name. Thus, G :^ is the Accidental to A Minor, and the last sharp in the signature of A major. NAME THE ACCIDENTAL to E minor ; B minor ; Fjf minor ; Cft ; G|f ; D|| ; A}| j Eif; Bjt; Fx; Cx; Gx. The Treble Sliarp (^x) will be necessary in Gx, minor. NAME THE LETTERS OF THE SCALES of C major and A minor ; G major and E minor ; D major and B minor ; A major and l^ minor ; E major and Cftminor ; B m£\jor and Gti minor ; Ffl ma^jor and D|f minor ; Cf, major and Aft minor ; Gft niajor and E j minor ; Dj| major and Bft minor ; Aft major and F x minor ; Eft major and C x minor ; Bft major and Gx minoi-^ Name the letters representing the flats in EXAMPLE 2. B E A D, G A^n, F These flats occur upon the fourth of the Major Scales. The Minor Key note, being the sixth, is a third above; and the Major Key note, the eighth, would be a fifth above the last flat. Thus, Bl?, D, F : Biz is the last flat named, D is the minor, and F the major key note. _ ^ . l • i.u i 4. ? rkU» Eb is the last flat : what are the Major and Minor Keys ? Alz is the last t DtzT Glz? clz? Fb? BI2I2? Eizlz? kVV'i DI2I2? GI2I2? NAME THE ACCIDENTAL to D minor ; G minor ; C minor; F minor: BI2 mi- nor; EI2 minor; Alz minor; Dlz minor; Glz minor; Clz minor; Fizmmor; Bjzjz minor. NAME THE LETTERS OF THE SCALES of F major and D minor; Bl? mjyor and G minor ; E|z major and C minor ; Ajz major and F minor ; Dlz major and Bjz mv nor; Glz mtuor and e"^ minor; Clz mjyor and Alz mmor ; Flz major and Dlz minor; Biziz major and Gtz minor ; Elzjz major and Clz minor; Alzlz major and F|z minor; Dtztz ma- jor and Bl?!z minor. AMERICAN METHOD OF UARMONY. 9 Name the Signatures to the Minor Keys of C, G, D, A, E, B, F: Cb, DKE>,FKG>,AKBb; Bb>; C%D%^^Y%G^ A^^^, C^,Fk,G^. For quick reference, we sum up the foregoing, in two simple illustrations : — ORDER OF THE TONICS AND SHARPS IN THE MAJOn AND MINOR SCALES. O G D A E B Fif C# Gi^ DJI At E|^ B|f Ma.. Tox. B F| C^ G# Dt M E# Bif F>« C^ G^ D^- A^ suabps. A E B F# C# G| D# AS E^ B# F^, 0^ G». min. Ton. ORDER OF THE TONICS AND FLATS IN THE MAJOR AND MINOR SCALES. F Bb E> Ab D> G^ Cb F!' B^> E^> Ab> Dt^ maj. tok. D G F Bb Eb Ab Db Gb Ob Fb B>b min. tos. Bb Eb A> D> Gl' Ob F> Bbb Ebb Abb Dbb Gi^ flats. INTERVALS. An Interval, in m-isic, is the distance from one note, or degree, of the Scale to another, and may be Chromatic, Diminished, Minor, Major, or Superfluous. The Major Scale, Example I., gives the best illustration. The figures above the letters are the numbers of the Scale. Those below indicate the number of half-tones in each and every interval in music. EXAMPLE 1. 12 3 4 5 6 7 8 9 . D . E F . G . A . B . D . .12 3 4 5 6 7 8 9 10 11 12 13 U 15 From the Ist to the 2d, 3d, 4th, 5th, 6th, 7th, 8th, 9th, countmg upward, the in- tervals are all Major, representing natural degrees of the Scale. Elevate the upper note of any Major interval, half a tone, and it is Supei-fluous. Depress the upper note, a haif-tone, and it is Minor. A whole tone, and it is Diminished. EleTate or depress the sound of any note, half a tone, and the mterval is Chromatic. Change the degree, and not the sound, and the change is Enharmonic. 10 AMERICAN METHOD OF ELARMONY. Illustration of all Intervals, Beckoned from 0, EXAMPLE II. i Chro. Ml. MaJ. Sup. Int. 2(1b. Dim. MJ. MaJ. Sup. -^jrft^^^^^-K Dim. Mi. MaJ. Sup. DliD. Ml. Mai. Sap. I M». ithB. BthB. I -,^l^^^^r-^ii2^^^^^-^m'± 0^JL:^t:^. Dim. Mi. Maj. Snp. eths. Dim. Mi. MnJ. gup. Ttlifl. ^^E^E^3l$^^^^^^^^^^: Dim. Ml. M.iJ. Sup. 8tlis. Dim. Mi. Maj. Sup. I 9th». I Name the Major Interval.^ of the Scale and number of half-tonos in each. ITow are the Major intervsils changed to Snpei-tluous ? To Minor? To Di- minished ? IIow many half-tones in a Superfluous 2d, 3d, 4th, 5th, 6th, 7th, 8th, 9tli ? How many half-tones in a Minor 2d, 3d, 4th, 5th, Gth, 7th, 8th, 9th? How many half-tones in a .Diminished 3d, 4th, 5th, 6th, 7th, 8th, 9th? Name the following Intervals ! — EXAMPLE II L ^^^^^^^^^^^^ No. 1. 2. 3. 4. -a>^ 5. 6. 7. 8. 9. 10. 11. 12. 13. w^Mw—^'» F**~i^ ' ¥■ ^'^^ 14. 16. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. m. 28. 29. 30. 31. 3i. 33. 34. 8S, 36. 87. 38. 3». 40. 41. AMERICAN METHOD OF HARMONT. 11 Sap. Sup. I DEVELOPMUNT OF CHORDS. By writing alternate notes of tbo Scale, they all stand in thirds, one above the other, thereby illustrating every fundamental chord in music, so far as the degrees are concerned. Any three notes thus taken, fonii a triad ; any four, a chord of the seventh ; any live, a chord of the ninth, as per Example I. A 1st, 3d, and 5th, is a triad. 1, 3, 5, 7, is a chord of the seventh. 1, 3, 5, 7, 9, is a chord of the ninth. In chords of the ninth, either 3, 5, or 7, are omitted. 3 or 5 may, if necessary, be omitted in chords of the seventh. These omissions occur when only three parts or voices are required. Less than three different notes could hardly be called a chord. Examples I. and II. give the chords in the fundamental or natural [jositions. EXAMPLE I. C.E.G.B.D.F.A.C.E.GB.D.F.A.C. Name the above Letters, in their order, from C to C ; D to D ; E to E ; F to F; G to G; A to A; B to B; C to C. In groups of four, thus: C e g i>, D f a c, &c. 13. w EXAMPLE II. Name the Letters of the above triads, 7ths and 9tli-<. Example : C e g, C e g b, C e g b d, &c. Every triad may be used in three Positions.* Example : C e g, e g C, g C e ; and these three close positions may be extended or dispersed, by placing every alternate note an 8th higher. CLOSE AND DISPERSED POSITIONS OF THE TRIAD OF C, with the 7th and 9th indicated by the small notes (-•-). The fundamental note will be written ( &) that the student may observe its situa tion in all the succeeding chords. -^ -± i -%-*- 1-*- 1st Position. zicyL^^ztL. z^z :--z^22:! -:iizr: I 2d Position. 3d Position. 4tli Position. (•) The 1st of any ciioril is tlie ftinilamental, tlie 3ra is tlie 1st inversion, tl»3 6tli is tlie 2nd inversion, the 7th is the 3rd inversion, and the 9th is the 4th inversion of the bass AMERICAN METUOD OF HARMONY. Name the Letters of tlic close and dispersed positions of each triad, — C, I>, K) F, G, A, B, first without, afterwards witli, the octave. Chord of the Seventh, in Four Positions. EXAMPLE IV. IbtPos. 2(1 Po8. aiPoB. 4th PoB. l8t. 2d. 3il. 4th. ij Ka^ne the Letters of the close and dispersed positions of the chords of the Bovenlli, iqion C, D, E, F, G, A, B, as per Example IV. Chord of the Seventh. EXAMPLE V. - yg &\ -iS) With 6th omlttod. ^ 5 ■37- sr ri'^zzz'^jii^ m with 3<1 omitted. Name the Letters of the above chords, upon C, D, E, F, G, A, B. SIXTY-SIX WRITINGS OF THE CHORD OF THE NINTH UPON G. These chords, all arising from Ghdfa, ftre instantly recognised by one who has memorized the fundamental cliords of the ninth upon C, D, E, F, G, A, B. Although not given by theorists, there is uo conceivable writing of tho chord but is of use to modern composers, who use the material as does the artist his colors, for effect of light and shade. All notes other than 1, 3 and 5, aro considered as added notes (to the triad) ; the 7th tod the 9th being of such frequent occurrence, we dignify them with the names of Seventh and Ninth ; but all otiiers wo treat as passing notes having only a momentary effect. In the old so-called chord of the Uih, Ex. C e ff 6, f, F, is a pednf note, the tonic, to which the chord must resolve. In some writings of chords of the 7th and 9th, with pedal note (11th), it has been difficult to determine (except by thei.- resolution), tohich tvas the fundamental note of the chord, yet we mav safely aecid(> upon Ike one which has a 3rd, or, if two notes have 3rds, th" one that has a 3rd and a 5th. Ex. Q e ^ b f. ¥ c e b. Q g b f. Q, s; a bf. ! 3 1 3 N.imo tlio t'lu'iil.j Hiul thc> riilnl Notes, to cnoli of the iibovo. AMERICAN- METHOD OF HARMONY. \n i CHOEDS OF THE 9th. 1st Position. "With all five i^otes. Omit 7tli Omit 3d. i 11 12 13 1st Position. 2nd Position. All 5 notes. Omit 7th. Omit r)th. Omit 3d. All Tj notes. Omit 7th. Omit 5th -0-, ^ .. "*" /2 ■*• ■•■ I^*-* 1^1; - •_•_£!> _ 0~B -•»- 5 :?tfzzi^i^zz^«:zi^zH 54 55 56 57 58 59 60 61 62 03 64 ii5 iJ« TRIADS. A Trind is Dimimshcd when each thii.i has Llireo half-tones; Minor, when the lower has three, and the upper thinl lour luilf-tones; M;\j()r, when the lowei' has four ana the upper thu'd thi-ee hah'-tones ; Superlluous, when each third has lour half-tones. 14 AMERICAN METHOD OF TARMONY. EXAMPLE X. E,fe W^^^~^^^^^^^ Hi \t 1 Vi I ll -i9- _ ^ ^ame the Letters of the Diminished, Mnor, Major, an.l Superfluous Triads m three positions, 1st, i>d, and 3d, close, upon C, Ci, C^ D DiJ E eTf Fti fI The Interval of a Major seventh is one, the xMinor seventh two, the Diminished seventh three ha f-tones lower than the eighth. The Interval of a Mbor ninlh one the Major ninth two, and the Superfluous ninth three half-tones above the eightV. nf fw'n'''-^'''^ 'f ^'T^^' ^""^ Ni^tlis Written below and above the letters of the following scales of major and A minor. EXAMPLE XI. \^^r i^^sr-^ 'i:sr*zz9i^_ EXAMPLE XII. y_^-^^*#tf fUS Name the kinds of Triads, Seventh and Ninth, in Example XHI. EXAMPLE XIII. :J: ^JF i Ei ;j Name the Trifwis, Sevenths and Ninths, in Example XIV. EXAMPLE XIV. M — -g- — ^ r 1= iE 1 The same kind and order in which the chords stand in the above Major and Mine. Scales, are also inherent in all others. *^ Aa*i.T:xCAN METHOD OF UARMONF. l& m ^ ^ CHORDS OF THE MAJOR AND MINOR KEYS. Wo will now add those technical names* known to all mvi9icians,.as representing the de^ees of the scale, and give (as shown by Examples XIII. and XIV.) the following Bummixry of chords, illustrated by figures, applicable to all keys, major and minor. We place the names of chords for the Major Scale above, and for the Minor Scale below. EXAMPLE 1. Major. Minor. Slino''. Miijor. Miijor. Minor. DiminiBhed. Major 1 2 3 4 5 6 7 8 Minor. Diminished. Superfluous. Minor. Major. Major. Diminished. Blinor Tonic. Snp.-Tonic. Med. Sub-Dom. Dominant. Sub-Med. Sub-Tonic. Tonic. To illustrate the working of Example I., we will use the scales of C major and A minor. Thus: the Tonic Chord is C ra.ajor; Super-Tonic, D minor; Mediant, E minor; Sub-Dominant, F ma,jor; Dominant; G major; Sub-Mediant, A minor ; Sub-Tonic, B diminished. The Relative Minor is A ; Tonic, A minor ; Super- Tonic, B diminished ; Mediant, C superfluous ; Sub-Dominant, D minor ; Dominant, E major; Sub-Mediant, F major; Sub-Tonic, G|| diminished; Tonic, A minor. In like manner, we apply Example I. to all scales, associating the major and minor together. CHORDS IN THE SHARP KEYS. minor Name the Chords in G major, E minor, D major, B minor, A major, Fj| I inor, E major, C# minor, B major, G|| minor, F|j major, D|f minor, C^l major, A^ | minor, G# major, E|| minor, D^ major, B|| minor, A^ major, FjS minor, E^ major, C i* minor, B || major, G VA minor. CHORDS IN THE FLAT KEYS. Name the Chords in F major, D minor, B V major, G minor, E [? major, C inor, A V major, F minor, D b mnjor, B b minor, G \^ m.ajor, D b minor, C > major, A V minor rumor, F V major, D > minor, B W major, G V minor, E W major, C V minor, A W? major, F 2 minor, D W m.ajor, B W- minor. CONCORDS AND DISCORDS. Chords may be divided into two classes. Those upon which the ear tpr^^ Chordi' Vbr'"^^ *"^' '^^i^}^^ further are called SL3, or LnLnan noli ^ tS- ^^^f"" "^?!^ ^"'^^''^ *^« ««^'* could not rest with entire satisfaction are called Discords or Dissonant Chords. All chords of the seventh and ninth I! nZl}^ 'i'T"'^'S ^H S"Pe/Huous Triads, belong to this class wt"r "i the Major and Minor Triads, ranking as Tonics and representat ve clTords S So ^&_^//,?^««-F«Conc^ the proper restinir-places fhr .nd i^!. wiiich all Discoras must hnally pass or resolve. ~ ' i l:J: ! I ' ! lip 16 AMERICAN METHOD OE UABMONT. The Natural Resolution Ex' B ;': ZViV^7::i '--^ ^-l^;'"^^ "'^ f -r^"^'^ ''"• -' "^S- ^'•S'^". to the Ton... /•«nc;L.{ra;^oth 1v(ytoVhichth'e^7sovVaVd tl eVfort ^""7^ "1 '"} ^"?^'^^' ^'^^ ^'^ is the the effect is the sa>ne, to roZl^ZyZZ'd^^^^^ V't' '""'■ J''"'*'^ '" whichever Toia , o.,e..e the manner in'wh.h iCXlTi^^-lJ^^, cSe" Sh h^sVof L'ptds'''^ ''"'*'*' ""'" re.^fvVt'n'reTnV5fac*e'' 'sK''^^^" ^° ^'"^ ^"^ "P°" ^'^^ Sub-To^fic^U^f £g . Oi^ord. must ,.J''M^'™n?u'^*;'''?li"°''' '*n'l,M''Jor 7ths naturally resolve downward one degree, as do also ih. M.nor and Major 9ths but the suije^rfluous 9th (See 6th degree of the Minor Scab '^resolves up one degre & 1" '°.''"'"8' '' 1'™J""-B a new disonant chord, which must in turn resolve to a'^finalS.'g £e".ab^^rit"Lwn^:rZ:l'XU"''"'' ' "'"^"°" "''^"^'^ ""'^''^ "^""'' '"'' ^ '""''^'^"^^ :r.iSi;f«:t"' ''^°"«^' ^"^'^ ^^^-'^' - •«-rant«:ftS;arwirwhiK;^;;^1:;;;!^^^^^^ Chords in the Major Key. .^•>j :z:iffizLzzz^^^^' 3d. 4th. 7th ^Si^ 5th. 6th. 7th. Chords in the Minor Key. ._tf?i-/-_4«i5f 1st degree. 2d. 3d. 4th. 7th. oth. Cth. 7th. G# omitted except in the Dominant and Diminished 7ths. pfjipgiiiiS ill 1st dcijTeo. 2d. 3d. 4th. 6tb. 6th. 2d. 7tl». AMERICAN METHOD OF IIAUMONY. 17 Various resolutions of discords, other than tliosc aU-cady giveu, are not uncorumon. Passages frcquemly dcnir, in which the notas of a dissonant chord move in qnitc different directions, tVj connect with those of the Tonic. Otherwise tlie freedom of Art would he too limited. A DISSONANT CUOED MAY CONNECT, not only with its own proper tonic triad, hut with any other consonant, or dissonant chord. WAGXER. , pal. % 2?: ped. * ©- ISM '=pfizz:j The dominant and diminished Sevenths Are those in most ordinary use; the Dominant most positively deciding the key, and the Diminished seventh having the greatest freedom in transitions irom one to another. All Dominant chords of the 7th are Major triads with Minor 7ths, and formed upon the 5th degree of the Scale. Hero are tlio degrees of all Dominant Chords of the 7th, and their resolution to tonics. Tiiey may he considered as \. '?. or %. accordmg to the key. F. 1) (}. E A. F B. *^ *■ ♦ ^ G C. A I). B E. ZiS: -0- 1 Here are the degrees of the dimhiished chords of the 7th with their reso- lution to the tonic. All Diminished chords of the 7th are Dim', triads, with Dim' 7ths, and formed upon the 7th degree of the Scale. m ^ms^m^m C I>, n E. E F. p a. a A. A B. 18 AMERICAX METHOD OP HARMONY. of gTa EP vTr?ol 'l\"iPTr'f ^'r^ '' '''' S^^^'^th, i„ the kev of C- o^%>:n^^^^^^^^ ^«' ^^ ^#' ^^' ^^' ^-' ^^ ^^' ^K A>, d'; . Sjl^l^^""''''^^^^ io M'hat key? G to what key? D, A E B ? Fi Cti r ti n« THE SUB -TONIC CHORDS OF THE SEVENTH, III the Majov Keys, are a Diminished Triad with Minor 7th; in the Minor Kevs a Dnmn-shed Triad with Diminished 7th. The resohuion to the Tonic if the same 'in me mminished Chord of the Seventh is composed of three Minor thn-ds; and, as there are four notes in tlie chord, there can be, in reality, but three to oomplote the Chromatic Scale. But these three are each written in iive'^lifferent ways Imuii^r " "''''''^'''~*'''"'^'"''=*^ "' ""' ^"' ^'^'^ ^^^ scales, Majo; Xil:Xkw^^&w^^ '*' ^^' ""' "^ ^^^ ^' ^^' ^^' ^^' ^^' ^^' The different writings of three diminished chords of the 7th. RTo. 1. 1 2 ^%% 3 4 5 6 7 8 ;fe ^^^^^^if=i^^^i!^%s^^^. No. 9. i ^^^^^=3^ei.i^%4^feJ No. 3. Thestudent -nay reaolve (with pencil) oloRely to the rlirht, each of the nnwiortiii- i.v,,i. nv. ., . ., there are, so fa. as the soun.l ,„,1 keyboard are cnoenfed oTy three diZt^,'^,,'';7:"„;°^^^^^^ that in No,. 1,2, wrain, each of them ■„ nine ditteren, way, were It not that'eaoh^ -^^l^^^r^^i^iX^^':^:::^ and .3, reaion for key. AMERICAN METHOD OF HAR?.ION-\. Other Dissonant Chords 19 r,nT«^^ those already given, are frequently used as passing chords or oon ?r.^h! ^4"''' V^'^^l ^^^"' T'l i^PO'-t'^nt harmonieVSse mJst Cue: t are the buperlluous triad which, found upon the 3rd degree of the Eor Irora the Dominant chord of the ninth, of the old eighth form, Minor Scale, _ Db E P G A^ B arise the following liinh-titlcd and PECULIAR DISSONANT CHORDS. J ^ Harsh Dim. Triad. 1st Pos. 2ud Pos. 3rd Pos. 6 HAR.SII Dim. Triad with 7tii & 9th. 1st Pos. 2nd ro3. 3rd Pos. 4th Pos. 7 * t 2 Double Dim. Triad. 1st Pos. 2nd Pes. 3rd Pos. 1st Pos. 3. Superlluous J j 6tb P^^P^^^ Double Dim. Chord of the 7th, 2nd Pos. 3rd Pos. 4th Pos.' Superfluous ^ 2 1-^ '~= — :k=::s— »— ^L.-^ pi=&l==^F=fe^%^i^pEp^i^l^^^ i=^?g= In the chonl of the Supei-fluous sixth, the 3d only can be doubled. SUPERFLUOUS TltlAD. WITH 711. WITH MIVOR 3d. olel'hl'^"^'''^"'"' '^"''^^!' ^^^^ ^*'' --^"^^ 9^1'. ^^■'^ ft'om Ihe Harmon!.. Minor ^cal. The one with minor 3d is u Chromatic .alteration from the former. 1.1! i i-i: ' 20 AMERICAN METHOD OF HARMONS'. Consecutive fifths and Octaves. ••pde a major fifth witlmut fauiu ''"'"^''""^« «"'"■ "^^ refer to maior flfihs, as a mimr fifth may either succeed or pre- %o;„V^ur,;tC;^h':X'l1r:,:;r;;,^^^^^^^^^^^^ <" rr.a,.ent occurrence, much more so than in four par, Covered fifths and Octaves Ocl've'"" '" """'■ "'"° ''"' '"''°'' '"°^'' '" ^"""" """'"" f™"- 'l'" i-t'Tval of a third, sixth &c., to a flfti, or an EXAM PLE I. Observe carefully the effect cf these five illustrations. 1 2 8 4 5 M=*%i^|i^-4^*ipi=iip^=f hI^H EXAMPLE 2. Play the following with and without tlie 6ths in the Bass. CtoFfi eft toFft GtoAl? DtoB!? ^^^i^^ii Consecutive Triads in three positions. S3E1 No. 1. No. 2. :E? «-_t» No. 3. or a wi^hont'^'onsec'uti'vl Oet.wesVna Fifth';'?'" ""'"'**' ' ^""''^ " "^ ^'"""'' '" '^"'« ^-n-'o-ontal Basse, to No.. 1, 8, MOTIONS OF THE VOICES. The Pour motiom to which the Voices are sabject in their rarions connections, wo present in the following :— m%^9 — • l-€ Parallel Motion. Oblique. Similar. Conlrary. m. ± AMERICAN METHOD OF HARMONY. How Consecutive Fifths are used. n USUI 'i^-^d^^mi^^ Op- 53. illustrates the possibility of .l£=iti2£z:<-:i are f-fyTa'lr^ter4S^.IS';»^^^ "hioh Ufth. and octaves Forbidden Parallels are impossible mentess^^ot ^« *^^'- ^^ a different position, with funda- binod'bfalt"\^^th.i'fffi^^^^^^^ -^y be faultlessly com- with anolher. tiufiua oass with the inversions, or one inversion ~i/-»7-;:-i.iSiir: Et^-ti:: XaiMo the faults in No. C. How could they have been avoided ? ' I f I ' I I 22 AMERICAN METHOD OF HARMONY. FORMATION OF CADENCES. A Cadence is a combination of any number or kind of chords (not less than two), and may embrace those within the key, or those of any other. A Perfect Cadence ends by the resolution of the Dominant chord of the seventh into the Tonic. An Imperfect Cadence closes without defining the key. A Cadence is Deceptive, when, at the close, the Dominant seventh leads to an unexpected cliord. The Principal Chords, in all keys, are the Tonic and Sub-Dominant Tri- ads, and the Dominant chord of the seventh ; combined with which, the Su])er- Tonic, Mediant, and Sub-Mediant Triads, form a perfect family group, which may be, in end- less ways, associated together for cadences. Here follow all that are necessary for illustrations. We shall, of course, use those chords which have connecting notes, in preference to others. Name the chords 'n each, and the kind of cadence which they form. EXAMPLE I. 1- 2. 3. 4. ■*■ -4- t- -,- -«- -«. -«- * -t- -t- Z- — * -^ J. ProgresBlon by 3ds.' EXAMPLE II. ProgreBBion by Btha. Progression by 4tli8. EXAMPLE III. Progression by 5ths. VM\ EXAMPLE IV. Progression by 4thB, witb Tths resolved without preparation. :J==I^==.^^=:|H=i5^gI=::^==J^=i=::^-z: ■J m n :|EJ AMERICAN METHOD OF HAUMONY Cadence from the Prayer in Lohengrin. 23 Proving the noble effects produced by the simple chords in the ham's of a master. EXAMPLES- WAGNER, t:l:^3:r[:^-?^- Cadence in C Major and A Minor. Combining all the triads in each key. EXAMPLE 6. Fine. ^^^^m^m^^M MODULATION, In a musical sense, is the transition from any one key to another by whatever means will cause the mind to forget the former and accept the latter. The intro- duction of flats, sharps, or naturals (as illustrated by transposition of the Scales,) give modulation to all keys, and is the most frequent mode. (See Ext. from " Elijah.") Sometimes the change in a single chord seems to swing us into a different key; and before the effect has passed away, wo are hurried on to another, and yet another, and still ou we go in our wanderings and pursuit of an object which the student must try to discover and feel. This is called progressive modulation. A change ou^ of a key and immediately back again, is caUGd transient inodulat'on. Changing to a, new key, in which we have a prolonged series of chords or movements, is called i^er- manent modulation. Jlodulation may be effected through the use of any chord of the 1th, insomuch as that they all resolve to toijic chords, for a resting-place. There fore, Example 4, (Cadences,) is modulation within the key. The Dominant 7th, from Its importance, is called Primary, whereas, all others are Secondary. A 7th is said to he prepared, when appearing in a previous chord. The old theo- rists gave as a rule, the preparation of the 7th in uU Secondary chords; but it has not been very much respected by the great composers. 24 A^^HRICAK METliOD Of HAllMONY. It must be understood that the Tonic Chords of the NEAELf'T RELATED KEYS, key of C^l . h!" ''"!* '"'^ *^ ™'"^'' "'^" ^* • ^^•■'J«^ ""-^ Minor Triads in the Eftch of the following Chords may be taken u a Tonic Byconsideriug the signatures, and omitting the chord which stands u fluh-Tonir to the k^v \JvlT^" ^uccesHion, the Tonic and Relative, Sub-Dom and Kelative, JJom and R jitive ti Have Major Keys. D D E C we to all fTFff^f^^F^ -» — -j» — -m r — f. — r — ii^P^^^^^E=f: ■■^—--m- -p- Modulation from C Major to its nearest relatives by Dominant Tths. CtoA F D G E OC :=r-P: m Modulation from E? Major to its nearest relatives by Diminished 7ths. If there are any fault* in the two following Examples, point them out. =1: ::<•=* k I Modulation by Dim. 7lhs, to the Minor keys, and by Dom. 7th ■•! '; the Major keys. A rft D B E Git A A i^s^j^:^pi4^=:^w^^^ ?si •4- 2^^3^gi^^r^^i t— r- i 1. lid A minor, iads in the odulate for ) the key, we eluUve to all :5e=eI 7ths. C F :=!==: 7ths. 3^ A r£ ■1 m A.MEIUCAX METllOi> OF HAKMOXY. E X A M P '- E V. FromC to E, iiiui iM-a -fEiElE^^ i9- :<2::;3 8 -z?- n: g I . 3 t*- MODULATION TO ALL KEYS, FROM 0.* :^.--g;zi!?-.zsiF2: The foiH^going examples in Moduhuion, should oil be written dispersed, ur.on !,ass and treble staves, by lowering the first and third voices (counting up) an octave Ob- serve, that those cadences which close with key note as the upper voice, are somewhat more complete and satisfltctory to the ear, than those ending upon the 3<1, or 5th of the romc Chord. The reason is, that 1, 3, 5, 8, of the Tonic, represent the bass, alto, tenor and soprano voices; and it sotmds odd that the lower voices should close with the highest note. This peculiarity only holds good in compositions for the voice The bass and tenor are an octave lower than where generally written. Were the four hlrmLr"" ""' ^' ""' ""' '"'" """' "'"' "'"' ''' ^' ^' '^' "'^'^^ ^^ "^^ EXAMPLE. VII. . CLOSE AJfD DISPEB8ED CADENCE IN THREE POSITIONS. • Each of th^do six examples are to be considered as Nitiir-ii wiot „, ci,» i the Notes only are written. The student must sup^ J ^^^^^^^^^^ l^T] " '""'"• ^'"'°^^' incnb;,- :..) cxiimj.les. i < J ""' r.ijcesgarv tjorlss r,f c.^vation aii.l .lepressioii; and we have 26 AMEUrCAN METHOD OF HARMONY. MODULATION TO WEAKEST BELATED KETS, J^r l^n? AS-'K *^ ^IS^^g^-- ^"O Mino. key. EXAMPLE. 8. L--J-4--t_j_j_^_^ D tErtizs: iHzrzzdirliijzi^nrfziq-i-a-^ _ — — '-#-5 — «- B ::d=jddid-:-h-i-4-J-4 9-h-3-^p^;=^^^^i?ci=i^ .=|:=£:ti[:=fzid G E ipzEzt: Jitzizzuli*: C tc; 3^ i Sequence of Diminished Sevenths and Triads Cousidei- the Signatures uud wc have mpdulatioa to all ktyt ■#.^** EXAMPLE 9. OBAGFEDCDEFGABC 3 11 ^^ ■^♦-ii^-^—H-^--^ • ♦ •ji: Modulation from C to F without a foreign tone EXAMPLE 10. ° ==^ ;:v.zfzitzzif:-ig: :^: -K5>- f (51 inor keys Egg; m -^-r- s E 9. B C a. r«-» IS PB AMERICAN METHOD OF HARMONT. 27 Modulation within the Key, and Sequence of Triads & 7ths. 'EXAMPLE II. 4 — I- -1 1. ^•^ — F ta h: la .1 »- ^F The small notes may be omitted or used, to augment the harmony. * By adding the sharps in regular order, or throwing off the flats in tht dame order, the above gives us Modulation with prepared 7ths, from C to CJ{, or from Cfe to C. Modulation from Tannhauser Overture. EXAMPLE 12. A V V V ^1 ^^1 "^ V V ff I A A V I I V V V [j- ~1 SI -h TROMBONES, TRUMPETS & TUBA, A A :::i^: -+- A :±i^ A EXAMPLE 13. In nearly all compositions by go^d writers, there are constant changes of key, out and back, like the ebb and flow of the sea. :i ay " Ho watching over Igrael." — "Elijah." i9- pips Il-P 1 — -J 1 — -F :t: ^ r-0-0 2?! =li n iii^ -(2.. IT' -I h ;^ffl -i« AMERICAN METHOD OF HARMONY. , The preceding extract is a foir sample of a large proportion of the music writter Uv our great masters, -as regards freedom of movement, in passing by a! identat wherever then, fancy call.; and illustrates to us how litt!. depemlenfe L" ito b placed in the signature, by whicJi to tell the key of the music Name the Chords and Transitions of Key. We now hint at, tut delay the Modulation, through a succession, or SEQUENCE OF DIMINISHED SEVENTHS. 8va _ Name the Chords in the above. Very chamiing effects in combinations and modulations are produced by SUSPENSIONS, In which one note is delayed; thereby keeping back, or suspending, for a time the one next below or above, to which it must, being the same voice, ultimately pas c^-' etlve ward aEeT '" ""'" ''"" ' '^^"^' ""^ *^°«^ ^-™ *'^- -ol up.' '<5>- t:3L Iff r-^ Double suspensions frequently occur, Exs. 3, 6, 7, 8. J-^ I r- ^ ■ r I I 10. ■Oh aiiai^fii r Name the notes Suspended in each example. Further than this, it is unnece to .llusjrate, uisonmeh as that abundant examples will be constantly met with in n VV^e will tlieretore proceed to another subject. unnecessary music. AMERICAN METHOD OF HARMONY. 2^ Cuopm. i i HARMONIZING OF THE SCALE. «o^J'pi'''''i'^r 1 ^"'P'^^t^,^* ^^^'•As in any scale, are the Tonic Triad and Domi- nant Chord oi the seventh and nmth. Very many passages of melody (single notes) seem to chn- exclusively to these two chords, and demand of them an accompaniment whereas others reqnire the three principals, Tonic Sub Dominant lind Dominant, and often the melody progresses over the notes of ^Hr/^if^r. ^- *' •"*? "u ""/"'' '^^"* ^^^y ^^''^ P««« by accidental note, or chord, the three principal chords are our main reliance. NUMBEES OF THE SCALE AND CHORDS WHICH SDPPORT THEM. EXAMPLE 1. 1st. 2a. 3<1. 4th. 5th. Cth. 7th. 8th. Ton. Dom. Ton. Dom. Ton. Dom. Dom. Ton. The thi'ce principals are more frequently used. EXAMPLE II. i*t- 2(1. 3d. 4th. 5th. Cth. 7th. 8th. Ton. Dom. Ton. Sub-Dom. Tea. Sub-Dom. Dom. Ton. The Glh may be supported by its ovm chord, and the other notes as in Example 11. EXAMPLE III. let. 2il. 3d. 4th. Bth. 6th. Tth. 8th. Ton. Dom. Ton. Sub-Dom. Ton. Sub-Med. Dom. Ton. Name the support of each number in Examples I., 11., and III. Every note of the scale is found as 1st in its own chord, 3d in its Sub-Mediant, 5th in its Sub-Dominant, and 7th in its Sup.-Tonic chord of the seventh, as also 9th in the Sub-Tonic chord. Thus, each note may be supported by either of the following triads, 7ths and 9ths, in which it is found, within the key. TWELVE SUPPORTS WITHIN THE KEY, FOR A SDjGLE NOTE. EXAMPLE IV. The student may know how many chords C will be found in, by chromatically clo- Tating or depressing each of the other notes in Example IV. 30 AlIERICAN METHOD OP HARMONY. Example IV. gives the chords m which C is to be found. The same holds good with every note of the sea e. and serves to show the great variety of™ m which scale may be harmonized, by the chords within the kev All melodies are confined to the two progressions, Scale, and Clwrd In Scale progressions, the melody changes from a note of one chord to a note oi some other chord. See Ex. 7, 8 and 9 ^""lu w d same chord. ^Sef Ex ' 5""'' *^^ """^'"'^^ ""^"^^^^ ^'"""^ ''''' *° ^"^^'^'^ "^^^ <>^ ^e EXAMPLE V. ■*• ^1 1). 4. fi tl r .1 .1 4. B. 8. !). U. 12. Name each of the twelve chords which support C, and omissions, if any. Exam- ple IV. should be written out upon every letter. TREBLE HAEMONIZINa OF THE SCALE, AND SEQUENCE OF TRIADS. EXAM PLE VI. 1 . '>. ;^ -1 -. fi -7 u n in 14 . .^ ^ 8. 9. 10. 11. 12. la. 14. 15. IC. 17. 18. 19. 20. 21. 22. Name each of the abo^e Chords, the Position, and Fundamental Bass. Example VI., iu C major, may represent C minor, C|| major, C^f minor, C 2 major, and should be so written, by accidentals; as also the same example upon D, E P G A, B. I r > > > , EXAMPLE VIL 1 ^.=^=^^r. le: ZST- i EXAMPLE VIM. —(5? :k: -SL ^_^^^^p^==|^ifjiS EXAMPLE IX. ^ w "^ ♦ * AMERICAN METHOD OF HARMONY. 31 ime holds y of ways I liord to a ote of the wm V. Exam- Name in regular order, the Chords and Position which support the scales, m Ex- amples VII., VIII., and IX, ; and wMch of them represent Examples I., II., and III. EXAMPLE X. This Example changes key, first by accidental, second by accented notes which indicate a new key, and lastly, by accidental, leadmg back to the original key. r4: :? WM^- Until well skilled in harmonizing a melody, the student should always write the three upper voices first, and then add the bass. Keeping the voices as close to the Soprano as possible, will cause each part to be good if the Soprano is and avoid the sense of thinness often felt when the voices are dispersed. m 1. 22. Ct2 major, ', E, F, G, r 9 i 1 DEVELOPMENT OF A MELODY. The student will, in the following Examples, realize the great work to be acWeved by the Cadences, Modulations and Harmonizings of the Scale. Every composition, gi'e.it or small, for one or more voices, has its real foundation in the Cadences. The chords, or single notes, upon the accented parts of the measure are the basis ; all others are called passing notes or chords. Let us review Example X. Ping only the accented notes, how differently it sounds ! Now, we will proceed with fvcthei illustrations for the development of a melody, and write one which will not only pass through different voices, but submit to a support from all the Major and Minor chords of the key. A Simple Melody. EXAMPLE I. -^^r-i ^r-Sr Development of the Melody ly Passing Notes. EXAMPLE II. 32 AMERICAN METHOD OF lIAllMOXr. EXAMPLE III. li'^Tiii-ri. ^J.^^^--^ The Melody is given to the Bass Voice, while the upon the first accent. upper voices accompany i^^P us*-' EXAMPLE IV, r-l- ■4" ^■T- rf i^Si^aSii^^feigs Hannonizing of both Accented Notes, with Melody passing from Voice to Voice, as in Example III, EXAMPLE V. The same Harmony as Example V, with Melody in the Bass Voice. It mav be given to the Soprano, two octaves higher, and the accompanimenrbroken uj EXAM PLE VI. tr-tH -5-3 ~ T^==^=f =l==-^=;=l=1=5:j-=: iig^^iiSi^i wn chord, ii ccompany i to Voice, It may 3ken up AMERICAN METHOD OF HARMONY. 33 ifl HAEMONIZING A MELODY, And developing a melody from chords, is, by no means, a difficult matter ; and the student will be quite safe in applying the knowledge gained in forming cadences, close and dispersed, to developing simple melodies from the cadences, and in arranging them in a variety of ways. COMPOSITION. Is the art of combining the various cadences in rythmical fomis, either as chords, or developed into single note-passaaes of melody, by adding to the harmonic notes of the chords^ others as passing notes. RYTHMICAL FORMS. Every melody, or musical composition, is divided into Sections of two measures. Phrases of four measures, and Periods of two phrases, the first of which is called the Thesis or question, and the second, the Antithesis or answer. OBSERVE THESE POINTS. I. Over what chord the melody progresses from each accented note. II. Whether accidentals which occur are merely passing notes, or those leading to a new key or chord. III. In developing a melody from a cadence, we are to use no progressions con- flicting with the chords which form the cadence, keeping in mind what are accented and what are passing notes. IV. The melody is confined to no one voice, although it is most naturally in the soprano. It must, however, close upon the key note to be satisfactory. V. In arranging, the three principles are to form the basis. All other chords used are secondary, or accessories. VI. Notwithstanding a note may be supported by any one of the great number of chords in ^hich it may be found, there must be a good reason for using those which are unusual, or out of the key. VII. It is more useful tc 'r.r!.i stand clearly the works of a master than to write poorly ourselves. VIII. It is better to arrange well, though plainly, than to exhibit difficulties without elegant design. IX. Ask yourself, daily, these questions : — 1, What arc the chords in this key? 2. How may they be combined for cadences? .3. What are the nearest related keys ? and how can I modulate to them ? ^ 4. IIow can I harmonize these scales ? 34 AMERICAN METHOD OF HAKMONY X. The Four Fundamental Principles in hamiony, which control all the infinitely-varied effects, are — 1. Development of chords from all scales. 2. Combination of chords for cadences. 3. Modulation to and from all keys. 4. Harmonizing of the scales. \^-^ THOEOUGH BASS. I would say to the student who may be questioned as to Thorough Bass, that it is an art designed only for practical musicians, as an aid by which to read orchestral scores. Figures are placed under a bass note, to indicate the chord whose principal notes are as many degi-ees above as the figures represent. As to its utility for other purposes, I will quote the opinion of Godfrey Weber, page 51 : — " A senseless old practice, — a practice long since known to be worthy of rejection, and for that reason long ago abandoned, though now again sought to be revived, — a practice which every intelUgent friend of the musical art must desire to see extenni- nated." COUNTERPOINT Is point for point, note for note, composition in two or more voices, a further carrying out of what the pupil has thus far done in forming cadences, harmonizing the scale, &c. For example, your exercises in four .voices, are Compound Countei-point. Omit the tenor voice, and they will represent Double Counterpoint; retain only the alto and soprano, and we have Simple Counterpoint. , The great oratorios and masses to which students have now such easy and cheap access, furnish the long-coveted facilities for study and improvement in this branch of the art, and put dry theories at a discount. In conclusion, the almost innumerable technicalities, and illustrations of what this or that may or may not be allowed to do, the figuring of the chords, &c., &c., preva- lent in the various works on Harmony, I have purposely avoided, choosing only to Hse such illustrations and language as will give the clearest understanding of those princi- pies which our masters have given utterance to, through their compositions.