KEYBO DAR

T IH

NING

HARM NY

Exercises Graded Designed to Lead the Easiest

First YearKey -Board Harmony Up to the Difficult Sight

Playing Tests Set forAdvanced Students.

THUR E. H COXP rofessor ofTheory ,

Oberlin Conservatory ofMusic .

Author of “Lessons in Harmony , ” Ear Training,

"“Choral Studies .

PART 1. PART 11.

P r ice. each. 3 1 . 2 5 ne t

P r e fa ce

The ob j ec t o f thi s book i s to furn i sh a graded ser ies of exerc i ses for p r ac t i ce in

h a rmon i z ing me l od ies and f igured basses at the key - boa rd , . so a r ranged t hat the pup i li s led gradua l ly f rom the eas i es t f i rs t - yea r work up to the d i ff i cul t .s i ght playing tes t sset for ad vanced student s .

The mater i a l was p repared and a r ranged in the course of Severa l years of ’ h armonyt each ing, where pup i l s are requ i red to “ rea l i ze” each p rob lem at thekey- board , and passannua l s igh t - pl ay ing exami nat ions befo re a comm i t tee -of Theory teachers . Th rought h i s t ra ining a l one , many students have -

been enab led to pass the harmo ny s igh t - play.

lng tes t s requi red for membersh ip in the Amer ican Gu i ld of Organi sts a

The a r rangement of the ma ter ia l i s tha t of a h andy manua l for sy s t ema t i c d a i lypract ice a t the key

- board (preferab ly i n shor t . per i od s) . The subj ect s are t aken up in

the usua l orde r , and the key board werk may pa ra l l e l any standa rd wor k in. h a rmony .

The f igur ing, i h the f igured bass, i s t ha t fam i l ia r to most Amer ican and Europeanmu

si clans . In o rder to inc lude some representat i ve French examinat ions , aa short ch apt e ri s d evot ed to the pecul iar i t i es of . the French Sys tem .

The sources of the e xe rc i ses are va r ious . The great er par t of the f i rst 63 0 Werewri tten express ly for t h i s book . Th ose from examina t ion papers are so ind icated . Nea r lyone hundred (from642 on) are typ ica l e xam inat ion quest ions from the s ight playingt ests .

and Paper work of many of the f inest mus i c schoo ls and uni vers i t ies in both Amer ica andEurope , t oget her w i th an impor tant l i st of the p rob lems Set by the Amer i can Gu i ld of

Organ i s t s , cover ing the yea rs ’07 to ’16 . The Au t hor’s request for t hese ma ter ial s , w i t h

perm i s'

s ion to pr int t hem , was .met wi t h a -most ‘

generous'

response, and hewi shes here toexpre ss the keenest apprec iat i on of the beaut i fu l examples and. the c ou r t esy wh i ch ao ;

cor.ds t h e i r use Ph i l c red i t is'

i nd i cated'

wi th"

e'

ach exerc ise . Espec i a l ment ion should be .

made of the coope ra t ion of Mr. W a r ren R. Hedden of the Amer ican Gui ld of O rgan i st s ,of Mr. Frank E .W a rd s cont r ibut ion to the subjec t of “S evenths”, and ofM.VincentDi lndy s

beaut i ful MS gi ven in facs im i l e at theend of the book .Ober l in, Oh io , 1 9 17.

Tab le o f Contents(NB . The numbers refe r in every instance to the paragraphs)

PART IChap. 1 . Tr iads P age 4

The P r imary t r i ad s ih W ndameutai Pos i t ion, to harmoni ze a bas s , 1 To ha rmoni ze a soprano , 2 The sopranoleaps , 8 Change of chord , 4 , Bass repea t s , 5 Ru l e for no common tone , u Cadences , 7 Ru l e for common

tone , 8 H a rmoni z ing f i rs t s ix tones of sca le , 9 Tendency of sca le s teps , 1 0 Rev iew primary triads, 1l F i r s ti nve rs ion, 12 Success i ve Cho rds of the S i x t h , 1 3 Second invers ion , M Seconda ry t r iad s in ma j or, i s. Th i rd sof sec . t r iads, d oub l ing, 1 8 Rule for 11 -V, 17. Ru le for n - i fl , 1 8 Seconda ry t r iads in m inor , 1 9 Augment ed interval, Spec ia l ru l es for m inor key , 20 i nvers i ons of seconda ry t r iad s , 2 1 Tri ad on Lead ing Tone , 22 P e rmi tted Consecut i ve Fi ft hs , 23 Three success i ve chord s of the s i xt h , 24 Doub led t h i rd in success i ve c hords o f the

s i x t h , 25 S im i larmo t ion of a ll the vo ices , 26 The Sequence , 27. Sequence des ign, 28 , 29 , S e quence i n m lor, 80 P h rygian c ad ence

,3 t The f igur ing (5 32 G enera l rev iew, 3 3

Chap. 11 . Cho rds of the Seventh P age 3 6

C ho rd s of s event h formed , 3 4 Dominant Sevent h , 3 5 Tr i ad (vu) not ind ependent , 3 8 i nt rod uc t i on of Dom.

7th , 37 Re so lu t ion of Dom . 7th , 3 8 i nvers ion o f Dom. 7th , 3 9 L icenses in reso lut ion , 40 The Dom . 9 th , 4 1

Tab ie of all the pr imary d i ssonant chord s, 42 Use o f Dom . sth, 43 Lead ing- Tone sevent h , M Dim inished seventh , 45. S econdary sevenths , !le Cad enc ing progress ion , 47. Doub l e funct ion o f Lead ing- T one s event h , 48Cad enc ing sevent h s in fundamental pos i t ion, 49 S igni f icance of the Cad . res . , 60 Tendency of w, 61 . O t h e rre so lut i ons , 62 int roduct ion of sevent h s , 63 Re so lut ion , 644. Super toni c sevent h , 66 Supe r t on i c n i nt h , 56Va r i ous re so lut ions , of the second ary s event h s , 57 Free r use Of the sevent h s , 58 Mas t e ry o f conse rva t i veusage , 5 9

PART IIChap. 111 . Alterat ions P age 3

A l t era t i on p resented , 80 Ru les for, 61 App l ica t ion and except ions , c ro ss - re lat ion , 62 Spec i a l a l t e ra t ionsin maj o r, 83 Dim . 7ths by a l tera t ion , 64 Augmented S i xt h , 6 5. Aug. s i xt h chord s in ha rmoni z ing a me lody,66P rogress ions compared , 67 Augmented s i x th chords “

no t of the key”, 88 No l imi t to re so lut ion, 89

Chap . IV. Modula t ion P age 12

Modul at i on by means of t r i ad s , 70 Ha lf and decept i ve cadence , 71 Suggest ions for harmoni z ing a c h o ra l , 72The tendency chord s of a key , Mod ul a t ion t h rough the Dom . 7th," Removes in the key- c i rCle , 7b Mod .

by the Dom . 7th to next - re l a ted keys , 76 _ M odu l atory inf lec t i on , 77 Reach ing a new t oni c , 78 P a s s i ngfrom key t o key , d ecept i ve reso lu t ions of the Dom 7th , Mod u l a t ion by the Dim . 7th , 8 1 Modu lat ion by

the Aug. s ix- f i ve cho rd , 82 Sequences , and use of any fo rm of the Aug. s i xt h chord s , 83 Modu l at i on by theDim. 7th on the ra ised four t h degree , 84 Sequences by way of the d im. 7th on r a i sed fourt h , 85 Modu la t ion bythe Neapo l i tan cho rd , 86 Spec i a l inte rva l s , enharmonlc no tat ion, p i vo t ch o rd s ,

Chap. V. Non - harmonic Tones P age 28

The Suspens i on, 87 The P repa rat ion, 88 The Suspens ion i t se l f , 8 9 The Resolution, 9b P ass ing- t one and

embe l l ishment s , 9 1 AppOggiatura , 92 Ant i c i pa t i on, 9 3 Compar ing the uno rnamented ha rmony , 94

Chap.V l . The French Sys temof Figured mass Page 41

Exam ina t ions by eminent Frenchmen, 96 S ign i f icance of spec ia l f igures and s igns , 96

ARTHUR E. HEAC’

OX'

C h a p . I . T r i a d s

Primary Triads'

in Fundamental Position1 .

-To h a rmoni ze t hese basses (at the key the f o l low ing rules(a) The bass must be the root of I , IV, or V.

(b) The common tone is a lways kept , the o the'

r. voices . progressing to the nea rest chord- tones .

(c) The seprano w ill begin on the root , t h i rd , or _f i fth , a ccord ing to the f igure over the f i rst bass note .

(d) The alto and teno r, w i t h -the soprano , w i l l fo rm -

a complete t r iad in c lose posi t ion. ( In rev i ew,

so lut i ons in'

open pos i t i on are recommended .)

C I IV I V I F I V I IV I e 1'

V 1 1v

2 . To h a rmoni ze t hese sopranos obser ve the fol low ing ru les(a) The bass must be the root of I , IV,or V, but the soprano may b e the root , t h i rd , or f i ft h .(b) The l as t cho rd w i l l be '

I , the tonic .

(c) If thesoprano repea ts a no te“

, do not repeat the cho rd but change to anot her . (Chord repet i t ionhas a legi t imate placebut the purpose of thesis f i rst exerc ises i s bet ter ser ved w i t hout(d) The bass shou ld not leap tWO f i ft hs in success i on in the same d i rect i on .

(e) The chords _

shou ld be so chosen as to prov id e a common t on'

e wh ich must be kept , hence forthe p resent the success ion, IV- V, or V

— IV, i s not ava i l ab l e.

(f) I f the seprano does not end on -the key- not e , i t may requi re some testing_

to d ec ide whether

the mode i s maj o r or m ino r . For examp le Nos. 12 and 1 8 must be so l ved in m inor or the ru l e can not

be kep t . L et the pupi l show .why .

2 1 V

3 . I f the soprano l eaps from one note to anot he r o f the same chord , the i nner par t s may fol lowi t above a st a t ionary bass as in He re the upper ’

three pa r t s mus t a lways present the completet r iad . Th is k ind of movement add s much to the ve ry l im i ted resources .

4 . The change f rom one cho rd to anot her i s most frequent at the bar. In chord repet i t ion abovethe same bass note , the f i rst appea rance of the chord shou ld b e on an accent i f poss i b l e , except atthe f i rs t accent of a ph rase wh i ch begins on a wcak beat

Transpose the model to other keys . and then h armoni ze the fol low ingsopranos

Model of a chord - skip melody wi th chord repet i t ion

C I V _ I IV I

5 . W hen . a gi ven bass repeats. a no te the chord w i l l rema in the same but change i ts pos i t ionTh i s i s the converse of and i s i l lust rated in Ex. 2 , i f the bass be cons idered the gi venpar t .The l eap of an octave i s equ iva lent to a repeated note ,

H armonize the followi ng ba sses tak i ng advantage of repeated bass notes

to make the soprano more i nterest ing

6 . all the prev ious exerc ises a common tone has been kept , but the progress ion IV - V or

V ! IV has been avo ided. Tr iads whose roots are on ad jacent degrees have no common tone.

RULE : I f two success ive chord s h ave no tone in common the upper t h ree vo ices must progress in cont ra ry mot ion to the bass to thenearest chord- tene

_

s,t e av’o id Consecut i ve Fi fths and

Octaves .

The progress ion IV- V i s bet ter t han V - IV. In the lat ter , avo id p lac ing the t h i rd of V in thesoprano . The_ _bass should not leap the interva l of a seventh , as at (a) . P lay all the fo l l ow ingand compare them by ear.

Ex. 4

7. A c los ing Fo rmula , or Cad ence , is formed by a r ranging the pr imary t r i ad s a s in Ex A.

Cadences are P e r fect or Imperfect accord ing to the last no t e in the soprano ; Aut hent icwhen thel ast two cho rd s are V- i , and P laga l when iV- i .

The progress ion V- I is the typ ica l se - ca l led C adenc ing Reso lut ion or P rogress ion.

P lay the fo llowing C adences in every key , then harmoni ze the basses

ppm.“ imperfect imperfect

Perfect .

Before play ing the follow ing read aga in pars . 3 - 4 .

8 . Thus far st r ict adherence t o the rule of keeping a c ommon tonedh) has been just i f ied be»cause of the impo r tance of est ab l i sh ing, in bo t h m ind and fi nge r s , the hab i t of obse rv ing th is pr inciple . i t w i l l , however , conduce to greater f l ex i b i l i ty in t he movement of t he vo ices i f the ru le isnow expanded to read as fo l l ows

RULE FOR THE COMM ON T ONEA tone common to two succes

s

i ve cho rd s is usua l ly kept in the same vo ice , but i f not kept , theuppe r t h ree vo ices progress in cont rary mo t ion to the bass , to the nea res t chord - tones .

9 . The f i rst s ix tones of the d iatonic sca le may now b e h armoni zed wi th 1 , iv, and ‘V, in fundamental pos i t ion a s be fo re , i n bo t h maj o r and mino r , ascend ing or descend ing The unmel

od ic cha racter o f the bass , occas ioned by l eap ing from roo t t o ro o t , may be excused unt i l invers ionis int roduced .

T ranspose to o ther keys

1 0 . Not all pos i t ions of the chord s are e qua l ly good for t he cont rary mot ion a l lowed under therule in ! 8 . For example , the s t rong t endency o f the Lead ing- tone in the soprano to progress to thekey

- no te , in the progress ion V - l , proh i b i t s 8 1 6 (a) . i n l i ke manne r , but to a l ess degree, the downward tendency of the Subdom inant ( four in the s ca le) in the sop rano , makes i t bes t to reach i t f rombe low i f i t is to a scend. P lay and compare (b), (c) , (d) .

Subdom . reached from Tendency o f subdom .( d) co r rected.

be l ow may a scend . cont rad ic ted .

General Primary Triads Fundamental( f) ( c) (b) (a)

1 1 . E xample 7 contains essent iai ly all the po ints invo lved .

(a) Cpmmon- t one kept in the same v o ice .

( b) No common- tone , cont rary mot ion‘

to the bass .

(c) Repeated soprano , change to a d i fferent chord '

.

(d) Repeat ed bass , chord changes pos i t i on; or, soprano leaps from.

one chord - tone to anot he r , the chord not changed .

(e) Common - tone not kept but cont rary mot ion to the bass .

( f) Repet i t ion of a ha rmony , f rom a weak beat to a st rong, at theopening of a ph rase.

P rimary Triads in theirFirst Inversion Chords of the Sixth

1 2:The vocabu lary i s now I , 1 6 , IV, IVS , V, add V6 . The fol low ing examples conta in

essent i al ly a ll the typica l progress ions :( a ) ( e )

(a ) The root d oub led in the Chord of the S i x th(b) The f i f th d oub l ed in the Chord of the Si xth .

(Avo id d oubl ing the third'

unti i p resented in ii 1 3)( c) The common t one kept in an inner vo ice rather than in the

soprano , for the sake of a bet ter me lody .

(d) Repeated note in the soprano, same chord used, but inver tedunder one of the two note s .

(e) Open pos i t i on for a few cho rds perm i ts a f iner so lut ion. Somet imes thewho le exerc i semay be done in open

'

pos ition (at the Opt ion of the pup i l) .

( f) Rule for cont rary mo t i on ( ii-

6) does not app ly to successive c hords wheree i ther one i s inver ted . The progress ion here ( IVs - V) is ca l led Mixed M ot ion .

Transpose Exs‘

. 8 and 9 to other keys , then harmonize the fOlloWing

1 3 . Insuccess i ve chord s of the s ixt h 1n close pos it ion,w i th a stepwi se bass, i t i s c or r ec t tod oub l e the th i rd in one of the ch ord s to avo id consecut i ve f i f ths and octaves . Ce r t a inpos i t i onsperm i t doub l ing the roo t and f i fth a l terna tely , but for th i s some exper ience i s necessary. In gen

earai , have the roots progress in para l le l s i x thsWi th the bass , and i f in doubt doub le the thi rd in oneof the chords , but never the t h i rd of V“, wh ich is the Lead ing- tone . For except ions , it it 27, 28.

(a) The t h i rd doub led in IVS , the ro ot in V“.

(b) The f i f t h d oubled in we , the roo t in vs .

( 0) Consecut i ve fi fths and oc taves. cor rec ted at (a) .

(d) The f i f t h d oubled in IV“, Lead ing- tone d oub l ed in V6 (poor) .

(0) I f the Lead ing—tone in the soprano fol l owed i ts t endency to the Toni c , consecutive octavesw i th the bass would resul t ; fur t hermore , the l eap downward in the soprano , when i ts s t rong tendeney upwa rd is so ev ident , produces a d i sappo int ing e f fec t . Test at the P i ano .

( f) Success i ve chord s of the s i x t h w i thout a s tepw ise bass , no need of a d oubled th i rd .

(g) All the vo i ces progress ing in sim i l ar mo t ion wh i le the chord rema ins the same , permiss iblei f consecut i ves are avo id ed .

.Transpose Ex . 10 (A) to other maj

or keys, then h armoni ze the fol lowingf igured basses and sopranos a long the same l ines

mus t b e on an accented par t of the measure , or the accented f ract i on of a beat , and the V wh ichfol lows i t must be re l a t i ve ly unaccented . The bass- no t e of the s ix- four must be doub led , i . e . the

f i f t h of the chord . So st rong is t h i s formul a t ha t any s ix- four cho rd on an ac cent tends to dec la rei t se l f a t onic cho rd and prom i se a c l os ing cad ence wh ich , i f admi t ted at an unsui table p l ace inthe ph rase , gi ves i t a weak and ha l t i ng cha rac ter.Since t h i s accent ed t oni c s ix- four chord re so l ves so emph a t i ca l ly to the V ( and in fact is a

V w i t h i ts t h i rd and f i ft h d e layed ), i t shou ld be preced ed by some fo rm of the subdom inant o rtonic harmony , fo r i f preceded by V, v i r t ua l ch o rd repe t i t ion f rom weak to st rong be ats resul tsa poor progress ion , pa r. 4 .

From the above,i t is ev id ent that the int roduc t i on of a s ix- four ch ord d emands mo re t h an

o rd inary care , o r i t may spo i l the phrase wh i ch cont a ins i t . i n Ex . 12 , the s ix- four cho rd i s

shov’

vn o n unaccent ed bea t s , i nt roduced in spec i a l ways . Und e r the se r est r ic t i ons the s i x - fourch o rd is l a rge ly shorn of i ts power to p romi se a ful l close, and in t h is subord inate r e l a t i o n b ecomes a med i um t h rough wh i ch the vo ices pass, ra th e r t h an an ind ependent h a rmony.

C los ing Formulas , The Authent i c Cadence wi th on an accent .

(a) By far the most impo r t ant s ix- four cho rd i s the 12 on an accent , in the authent iccadence , a ful l o r compl ete c lo se .

(b) The c lose is pa r t ia l '

when the ph rase end s w i t h a V preceded by an accented i f.

Tes t t hese phrases a t the p i ano .

https://www.forgottenbooks.com/join

1 6 . The t h i rds. of the secondary t r i ads are the pr inc ipa l tones of the key and may b e doub ledra ther freely for the Sake of a bet ter me lodic out l ine. The upwa rd tendency of the l ead ing tone and

“

the'

downward tendency of the four t h and s i xth degrees of the sca le , espec ial ly whenin the soprano ,mus t more or less determ inethe chord to b eiused and the tone to be d oub led .

W ith the int roduct ion of the secondary t r iads and the resulting increase in the number of poss ible progress ions r anging in va lue from good , to fai r, er poor ; the student must d epend l a rge ly on

the study of inodels compared and tes t ed by ear a t the keyboard . Here dependence on rules , or eyememory, w i l l net at a ll suff ice .

Ex. 1 4

1 7: In Ex . 1 4 , s tudy the v ar ious p rogressi ons from n to V.

- The u an exce llent subs t i tu te for IV, a nd w i t h the same t reatment , i . e . , cont ra rymot ion

'

to an ascend ing b’ass .

GENERAL RUL E FUR I I —V '

M'

V N

G i ve up the common tone and lead the uppe r t h ree vo ices cont rary to an ascend ing bass . (Does not

app ly in invers ions)(c) The common tone kept . P oss i ble h e re for t he sake of the me lody . Not recommended .

Improved at, (d) .

( e) Bad on account of the obj ect ionable Covered Octaves . These in the outer vo ices are

espec i a l lybad because the soprano tone (F) has a d ownwa rd tendenev (4 1 6) and i s , never t he less ,compelled

'

to a scend .

( f) G ood . The invers ion o f V and the u l t ima t e d ownwa rd reso lut i on of the (F) in thesoprano are exce l lent . Here the common tone i s best kept .

(g) (h) Freer 'tfeatment o f the voices , but good .

( i) ( j) The 11 a fter V. Use se ldom . I f used t hese are among the few fa i r progress ions .

1 8 . In Elm s, study the var ious p rogress ions from n to 1 2.

(a) (b) An exce l lent subst i tute for IV- Ig in the c los ing cadence . ( Compa re w ith Ex . i t)(c) Imposs ib le on account of the consecut ive f i fths.

GENERAL RUL E“

FOR 1 1 - 1 2

H armonize the following exerci ses(The n , m , and V! i n maj or keys)

Make sui table use of occasiona l secondary tri ads

Inth e next few exerci ses some of the less common progressions.

153 ,

Study aga i n Ex . 14 (g) to (J) and 1 5 (e ) ;

SecondaryTriads in Fundamental Position in Minor keys1 9 . The subord inate t r i ads in minor III ', VI) are used in the

“

same t hree ways as t hosein major , but w i t h far less f reedom. The no and III

’

are bo t h d i ssonant chord s , somet imes ap

proached , or l e f t , w i t h d i ff i cul ty on account of the augmented interva l (6 - 7) in the Ha rmonic minor sca l e . The mo st used progress ions are shown in the fo l low ing example wh ich should b e stu

d ied and t ransposed to o t he r keys .

!r V V VISpec ia l rules v io la ted .

(a) The VI as a connec t ing cho rd .

( b) The 1 1° a s a subs t i tute for the subd om inant . (Far oftene r used in i ts f i rs t inve rs ion ,(c) The lll

'

as a s imple t r iad , bes t reso l ved to the VI (the cadenc ing reso lut i on) .20 . In s t r i ct wr i t ing no vo ice may progress an augmented int e rva l , and wh i le th i s rest r ict i on

i s qu i t e prope r ly d is rega rd ed unde r ce r ta in c i rcumstance s , as fo r exampl e , in cho rd repe t i t ion, the

s tudent sh ould r igid ly ad h e re to the fo l l ow ingTWO S P EC IAL RULES FORTHE M INOR KEY.

Rule 1 : In the p rogress ion ll"

- V , gi ve up the common tone and l ead the upper thrce vo i ce s incont ra ry mo t i on to an a scend ing b as s , Ex . 16 (b)

Ru le 2 : In the progress ion ,V.

-VI oe -V, d oub le the t h i rd inV I and d o not om i t the f i fth . Two

vo ices move cont ra ry to the bass (d) .

The III’

and VI i n m inor keys

Inversions of the Secondary Triads .

2 1 . The Secondary t r i ads are all used in the f i rs t invers ion, f requent ly w i t h d oub l ed t h i rd ,and preferably in the octave pos i t ion, t. e . ,

w i th the roo t in the h ighes t pa r t , but cond i t ions may.

j 'ust i fy any pos i t ion and any doubl ing.

The bes t of a ll t hese -chord s is the 1 16 wh ich in bo t h majo r and m inor -i s much super ior tothe fundamenta l pos i t ion , and i s the best subst i tute for the subdom inant . I ts b ass , the t h i rd of

the chord , i s the subdominant .a‘

nd the best t one to d oub l e . The pos i t ion of the f i f t h (f i ft hh ighest) i s the poorest .

The t reatment of the -ot he r f i rst inver s i ons i s best l earned from the examples , and th roughpract ice in harmdniz '

rng f igured basses .

The second inve rs ion of the seconda ry t r i ad s of l i t t l e va lue . I f used at all i t must conform s t r i c t ly to the requ i rements of par. 14 .

(a) Same rule as for n -V and 11 - 12 ( it 1}

22 . The Tr i ad on the Lead ing- Tone i s a d i,ssonant ,

i

e r tendency, chord and l i ke the Dominant Seventh Chord f rom wh ich i t i s '

d erived (ii 3 e)'

i t r eso lves regu l ar ly to the Ton i c‘, rare lyt o the VI .

GENERAL RUL E FOR THE‘LEADING TONE TR IAD

Use the Lead ing Tone Tr iad in the f i rst invers ion only , double the thi rd , or f i f t h , and reso l veall par t s st epwise to a comp l e te I or I 6 The f i f t h progresses up or d own. The consecu t i v e f i f t hswh ich resul t f rom the proper t reatment of t h is chord are unobject ionable , one of t hem b e ing d i sm in i shed and no t appear ingw i t h the bass (outer par t) Somet imes the th i rd , and more ra re ly thef i fth , may be le ft by a l eap .

A l l the progress i ons in Ex . 1 8 a re e qua l ly good in b ot h ma jor and minor , except t hat the deceptive resolut ion

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i s bes t - rest r ic t ed to ma j or only .

Ex. 1 8

(a) to (f ) Typ ica l regular reso lut ions of v1 1 °6.

(g) Doubled t h i rd , one t h i rd be ing left '

by a leap .

( h) Doub led f i f t h , one f i ft h be ing left by a l eap , perm iss ib lebut not usua l .

Decept i ve reso lut ions to VI , not f requent , avo id in m inor(k) By us ing v

'

no6 the major sca le may now be harmon i zed .

Transpose ( k) to every maj o r key

2 3 . As a rule consecut ive f i f ths in the o rder d imini shed to per fect in an upward d i rect ion, andpe rfect to d im ini shed d ownward , are pe rm i t ted , prov ide d the bass i s not one of the v o i ces wh ichp roduce the f i f t hs . .In the case of t r i ad-

s , invert ing one or bot h per fect ly ‘meets t hese cond i t ions,Ex. i s (d) (e) (f) .

2 4 . In t h ree success i-ve chords of the s i x t h w i t h the bass ascend ing s tepw i se gene ral ly use

c l ose pos i t i on , and d ouble the f i f t h , t h i rd and root i n success ion; w i t h a d escend i ng bass ,doub le roo t , t h i rd and f i f t h

, Ex. 1 9 (a) , but see a l so (Hi 25 , 26 .

I

2 5 . I f the upper t h ree vo i ces a ll move in cont ra ry mot ion to the bass the t h i r d may b e

d oub l ed in successi ve ch o rd s of the s i x th as at 1 9 (b) . Th i s i s f requent ly preferable to a mere lymechan i ca l observance of i1 24 , . espec i a l ly in approach ing a cadenc ing s ix-

‘four ch o rd . He re , asin 1} 18, the f i f t hs o f the chord s may not appea r above the r oot s .

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The S equence

Sequence a success i on of sim i l a r h armoni es resul t ing from a symmet r i ca l progress ion of the gi ven pa r t . The

“ ini t i a l . -des ign,or pat tern , i s usua l ly repeated tw ice, or more , inan ascend ing or descend ing ser ies , and usua l ru les for chord progress ions , d oub l ing, etc . , a re

f requent ly d i s regarded in o rder to ob ta in the requi red symmet ry . P ract i ce in bo t h w r i t ingand pl ay ing sequences i s . strongly ur'ged a s one o f t he pract ica l ways of ga ining f reedom at the

keyboard , and f am i l i a r i ty w i t h the vo cabu la ry of chord s , and chord p rogres s ions , in a ll the

keys .

Ex.2 0

Ex.2 i

Transpose to every majo r kev

2 9 . I n Ex. 2 1 ( a) the d e s ign aga i n f i l l s one measure but t h i s t ime embraces four chords insteado f two . Th i s d es ign i s t hen repeated , each t ime a t h i rd lowe r , but is a l tered in the fourth measure to make a cad ence . The same des ign cou ld be s l igh t ly a l t e red and d escend stepw i se in t he success ive measure s a s at 2 1 (b) . L et the s tudent e xtend t h i s sequence t h rough severa l b a rs and add

a cad ence .

3 0 . A sequence in m ino r usua l ly empl oys the Or igina l Form of the m inorscale,

.thus‘

avo idf,r1

__g the augmented second , but whe re the ch a ract-er '

of the des ign pe rmi ts , the ra ised sevent h i sgener a l lyused , ‘

Ex. 22 (a) (b) .

Sequence in mi nor, using or iginal form

Ex.22

P h rygian Cadences. Transpose

Ex. 2 3

Some lines from old choralslch w i ll d ich l ieben me ine Starke . Me ine Hoffnung stehct

3 2 A t ri ad in fund amenta l pos i t i 'on mzay p recede or: fo l low a chord of the s i x thon the same

bass no te.,The f

'

iguri‘

ng'

i s 5 6 or 6 5 ac'

cord i'ng to the-. or-d

'

er of the two. chords . The int e rva l s ,6 and 15 , must_not b e doubl ed and should appear in success ion in one voi ce, usually , but not mecessari ly, thesopr ano . I n most cases one of t he two int e rval s (the 6 or 6) is . a pass ing t one and

as . such i s usually bo t h taken and left stepw ise

(me) IVS 11 VII

Transpose to o t he r maj or'k

Ex. 2 5

General Review in the use of Tr iads3 3 . Mr.W alter R .

, Spald ing in h is t reati se on Counterpo int says , “So let the student be per.suaded to acqu i re a sound and fac i le techni que i n the t rea tment of trlads.Nothingwi ll g i ve himsuch a good founda t ion for future deve lopment when he comes to f ree ch romat i c w r i t ing.

” In the

fo l l ow ing rev iew exe rc i ses the prob lems are grouped under four general head ings , accord ing to

t he i r cha racter , and the grade of advancement expec ted . Thus the f i rst se t o f sop ranos can be

used as rev iew befo re any invers ions are reached , -wh i le the l ast l i s t , s e l ected from exam inat ionpapers , demands a comprehens i ve grasp of all t hat has been presented in the fo rego ing pages .

B asses easy to moderately d i fficult

Sopranosg vocabulary, the t ri ads (ei cept fundamenta l posi t i on only52.

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Old’

French Noe l .

O Ewigke i t du Donnerwort . 1 642

Examinat ion ! uest ionsA l l the fol lowi ng (272 to 289) are from examinat ion papers that have

b een used inOber l i n Conservatory of Music fore lementary c l asses .

The student i s advised to wri te a s .we l l a s play them .

273“

8 1 3

282.

283 Unfigured

At the use ?“ cho rd s , o t herw i se t h i s i s an unfigured p roblem .

These 6’s mean f i rs t inve rs ion , roo t i n soprano . (No t usua l ma rk ing)

Suppiy a l t o and t eno r

C h a p . I I . C h o r d s?Of th e S ev en th3- 4 . A Chord of the Sevent h . i s formed . t h i rd to any t r i ad . Th i s

added t h i rd is a seventh above the roo t a nd , s ince the interva l of the'

seventh . i s a d i s s onance,all chords of the sevent h are d i ssonant Or t endency chord s , requ i r ing r e so lut ion ; t ha t i s '

t hey must progress (so’

oner or l ater) to consonant chords , chords of repose . The chord of mos tcomp l ete repose i s the f ina l toni c t r iad and toward t h i s , as an u l t imate goa l , all the d i ssonan te l ement s of a musica l ph rase tend to progress . The ch a rm of many a passage d epend s ch ief lyupon

“

an a r t i s t i c trea tment of t hese d i ssonant e l ement s as t hey emerge fromand d i sappea r inthe s t ream of the musi c . The d issonant chord wh i ch most conclus ively r esolves to the t on i c , i sthe Dom inant Seventh .

The Chord of the Dominant Seventh(P rimary Di ssonant Chords)

3 5 . The Chord of the Dom inant Sevent h cons i sts of the .Dominant t r i ad to wh ich i s added thenex t

, (upper) t h i rd , a m inor .seventh from the roo t . Ex. 26 (a) (b) . Thi s chord is the same in both major and m inor yet d i f ferent from all o ther

'

seventh chord s . I ts t h i rd is a lways the l ead ing tone ,a ma j o r t h i rd , i ts f i f t h i s per fect , and i t s sevent h

,m inor. Conta ining as i t does the most import

ant tones of the sca l e excep t the tonic i t may b e sa id to h o ld a s t rat egic pos i t i on in the key as

P rimary .Chord Of the Seventh . I t i s f l anked by the d om inant as roo t , hy t he subdominanta s sevent h , wh i l e i ts t h i rd , the ‘

lead ing t one , unm i s takab ly d e f ines the key by i ts t endencyt owa rd the keynote , Ex.26 (c)

3 6 . The t r i ad VII° i s not an independent chord but an in incomp lete dom inant sevent h chord.as may. be seen at Ex . 26 (d) . See a lso par. 22 .

Tonic ( d) Vll°

Ex . 2 6

CV vgor 7 or 7 or 7 cv V s

hor 7

hor 7

5 3

Introduct i on of the Dominant S eventh3 7. In genera l di ssonances requi re ca refu l i ntroduct ion as we l l as resolut ion . The seventh of

the V7 howeve r ent ers w i t h a lmost the freed om of a consonance . W hen the seventh 1s in the preceding chord i t i s usua l ly kept as a common tone and t hen sa id to be int roduced by preparat ion .

Resolut ion of the Domi nant Seventh

3 8 The regular. re solut ion of the V7 i s to I , the seventh d escend ing a degree ; the t h i rd as

cend ing to the tonic , .or leap ing downwa rd a t h i rd If in an inne r vo ice w i t h the bass ascend ing;the roo t leaping upward or downward to the root of t he tonic , and the f i f t h usua l ly d escend ing a

d egree , but some t imes ascend ing for spec ia l me l od i c reasons . If the V7 is comple te i t may re

so lve to v i (decept i ve) . Among the many i r regula r , or l 'e ss usua l reso lut i ons , shown l at er (Ex. 3 2)

the sevent h may b e found s t at iona ry (de layed r eso lut ion or none at all) or.

i t may even ascend .

The fo l lowing exampl es are representat ive and , except ( h) , equa l ly good in m inor. I n fundament a l po s i t i on a s a t ( b) , f i f t h om i t ted and roo t d oubl ed , the uppe r root become s a common toneve ry good s ince t h i s prov i des a complete t r i ad on the I .

zit Dist ingu ish interpre ta t ions of?fl and 87.

Transpose to o the r keys .

Exerci ses conta ini ng the Dom i nant Seventh Chord in fundamenta l posi t ion

291 . a

Inversi ons of the Dom inant Seventh3 9 . The re are t h ree invers ions o f the V7, a l l of wh ich are usefu l . Regul a r reso lut ion to the

tonic t r i ad i s by far the mos t usual . In t h i s reso lut ion the vo ices usua l ly p rogress as when inthe fundamenta l pos i t i on except the ro o t i t se l f wh i ch i s genera l ly ret a ined as a common t one .

Comp le te f igur ing i s se l dom used unl es s need ed to ind ica te certa in interva ls altered , as the ra isedseven in the m ino r sca l e . Unl ess the seventh i s in the bass two f igures are ind i spensab le, those ind icat ing the roo t and sevent h .

(a) Usua l re so lut i ons .

(d) P a ss ing sevent h in the bass .

(e ) The 3 2 ove r the s ame b ass no t e requi res f i rst a t r i ad in the fund amenta l pos i t ion and

then a sevent h chord in the t h i rd i nve rs ion( f) Cho rd repe t i t ion- the vo ice h av ing the seventh l ast must re so l ve i t .(2) The f i f t h o f V7 re so l ves upwa rd st epw i se , the re su l t i ng d o ubled t h i rd in the I i s no t

b ad when passed t h rough in such a way as no t to emphas ize i t .Two so lut i ons for the f igure s equa l ly good .

( 1) An apparent s ix- four chord formed by the f low ing uppe r pa r t s ( read last l ines o f ! M) .(m) The t h i rd d escend s by a leap of a t h i rd w i t h good e ffec t .

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Exerci ses contai ning some“

i rregular resoluti ons of the Domi nant Seventh Chord

Ex. 34

40 . For the sak e of obta in ing a mo re ad vantageous po s i t ion o f the par t s , a be t te r me l ody ,Or to avo id monotony of trea t ine nt , the d om inant seve nt h ch o rd re so l ve s i r regular ly in s t ill o t h e rways t h an t h ose shown in example 3 2 , but the progress i ons shown in the fo l lowing examples shouldbe regard ed as l icenses adm iss i b le to the student only a fte r he has t ho roughl y es tabl i shed h is t e chnic and matured h is judgment

Good Be e thoven Andante . op.u ,N3 2

The Chord of theDominant Ninth4 1 . A dominant sevent h chord enla rged or ex tended by the add i t ion o f a t h i rd above the

seventh becomes a f i ve t one chord named f rom i ts l a rgest i nt e rva l the Cho rd of. the Dom inantNint h . In maj or keys t h i s added

- t one i s a ma j or n int h above the ro o t ( some t ime s m i nor bych roma t ic inf lec t ion, ! 63) and in minor keys i t i s a lways a m ino r n int h .

In minor

42 . I n the dom inant. n int h and i ts r eso lut i on to the t onic t r iad i s found the -bas i s o f,

con

s t ruc t ion and reso lu t i on of all the P r imary Di ssonant“Chords. “

In o t he r wo rds the primary d i ssonant chord s, in. bo t h cont ent and t endency, show t hemse l ves to be more or l ess com

plete forms of the V9 (or V 7) . Th a t an incomple t e fo rmwhose apparent root is the lead ing tene ,as _ tor examplet he vng, does not take a cadencing reso lut i on - ( ii 440

7is - add i t iona l proof that the .

rea l roo t , Wh i ch i s a lways the d om inant , i s om i t t ed . B efore. go ing further'

i t w i l l b ewe l l to exam i ne a tab l e

,o f the pr imary d i ssonant ch ord s .

Table of the Family of Pr imary D issonant Chords ;The roo t of a ll these chord s , whe t her -present .or not , i s the dom inant . and t hey all re

so l ve regu l ar ly to the ir'

toni‘

c tr iad .

I n maj or I n mi nor

Lead ing tone tr ia d Lead ing tone t r i ad

Lead ing t one Dim . sevent h chorc‘seventh ch o rd (Frequent ly bo rrower

for use i n major)

Dom. major nint h(Never used in m inor) C h ord of

Reso l u t i on

‘

Dom . sevent h Dom . sevent h

Introduct i on Resolut ion of the Domi nant N inth

“

Ex . 3 6

On the use of the Dominant Ninth Chord4 3 . In Ex. 3 6 (a) (b) (c) the nint h , l i ke the sevent h , be ing a pr imary d i ssonance , requi res no pre

parat ion, but preparat ion of e i t he r nint h o r roo t conduces to smoot hness of ent ry, espec i a l ly inminor .( d) W hen ne i t her nint h nor roo t is p repared t hey should be approach ed in cont rary mot i on.

(e) Keep the nint h a fu l l nint h above the root . Th i s excludes cont ract ion t o a s econd and a l somakes the nint h be l ow the roo t imposs i b le . (The n int h be low the roo t can be found in mod e rn wo rks) .

( f) (g) In four - pa r t wr i t ing , on ly two i nvers ions are pos s i b le . Exact ly as w i t h V7 the root in yan invers ion i s bes t kept a s a common t one , the o ther vo i ces fo l lowing t he i r tendency.

L (h) Conse rva t i ve t reatment places the n int h in the h ighes t vo i ce . At D?) the n int h in the teno ri s c l ea r ly a pa ss ing tone .

( i ) He re the nint h in the a l t o i s a suspens ion . I t i s impo r tant to s tudy t hese f igur ings ( h) ( i)fo r in h ighe r examinat ions the s tud ent i s l i ke ly to b e confronted w i t h s im i lar problems . W hen

the f igure s a re gi ven in fu l l a s h ere , i t is a sugges t i on o f the requi red int e r v a l fo r e ach v o i cerespect i ve ly . No t a go od pract i ce but some t imes unavo i dabl e .

( j ) Inte rch ange o f chord membe rs .

(it ) P as s i ve re so lut ion as w i t h V7. There i s usua l ly u l t imate reso lut ion but t h is is not necessa ry.

( 1) G i ven to i l lust rate a necessary procedure w i t h t h i s f igur ing. The 7 6 must be in the octaveabove the o t h erw i se a second w i l l appear be tween the roo t and n inth . C ompa re w i t h (e) .

N o te in add i t i on to t h ese po int s the appa rent reso lut ion to 12 and to the I II“ in (d) . These a re

sca rce ly mo re t han acc id ent a l cho rd fo rmat ions occas ioned by the f low ing pa rt s . Th ey l ie passive ly be tween two fo rms o f the dom inant ha rmony.

fig

{u LI 1

’

9

0

Mode ls to be t ransposed to other keys( It is impo r tant to s tudy c l ose ly eve ry fu l l f igur ing)

The d escend ing sca le us i ng V9

Exerci ses containingthe Dominant N inth’

Chord

The Chord of the Seventh on the L eading-Tone in Major(Al so cal led the Lead ing Tone Sevent h).

44 . The Cho rd of the Sevent h on the Leading Tone in Maj o r is a d om inant majo r n int hchord w i t h roo t om i t t ed . The om i ss ion of the generato r. ( the dom inant) does no t affect the characte r of the rema ining chord members wh i ch are int roduced and reso l ved e ssent ia l ly as in V9

L i ke the comp le t e maj o r n int h , t h is cho rd can no t reso l ve to a m ino r tonic .

For s imp l ic i ty t h is cho rd i s f igu red as a ch o rd of the seventh , and as such shou l d b e comple te.

The bes t pos i t ions keep the sevent h (or ig ina l nint h) in the soprano , o r at l eas t above the lead! ing tone . The t h i rd inve rs ion is ra re ly used s ince the o r ig ina l nint h i s too h arsh in the ba ss ,

e xcep t wh e re sk i l l ful ly h and l ed . A rensky'

ln h is “ 1 000 Exe rc ises"and Tscha i k ovsky in h i s“Ha rmony

”us e t h i s t h i rd inve rs ion

,always reso l v ing i t to a If cho rd . Fo r a typ i ca l examp l e

‘

see Ex . 3 8 ( e) b e l ow .

The typ i ca l reso lut ion of the roo t pos i t ion i s to a tonic t r i ad w i t h d ouble t h i rd . The con

secut ive f i ft hs wh i ch r e su l t in t h is reso lut ion wh en the th i rd of the t o nic is no t d oub l ed are oh

j cc t ionab le and must b e av o i d ed , e x c ept as a t (391) wh e re the fi ft h s in t he- inner vo ices comeund e r ! 23 .

In 3 8 the v i i“; i s such to the eye on ly . I t may b e exp l a i ned t h at the b and (l a re

pass i ng tones and t h e r efo re the bass (ro o t o f IV) is free to l eap, o r i f prefe rred t hat the bass invn

°

g leaps a four t h downward to the roo t of the t onic .

The reso lut i on to some inve rs ion of the V 1 and the pass i ve resolut i on are natura l d e r i vat i vesof the regu l ar Vo p rogress ions .

Study the progress ions in Ex. as by ear as we l l as eye . L earn tbe best ones and t ransposet hem to o t he r k eys .

The seventh (o r ig ina l ninth) in soprano : these po s i t ions are best .

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Exerci ses conta ining the D imini shed Seventh Chord

6 4 ! {3- 6

(Secondary Dissonant Chords)

4 6 . All chords of the seventh o t he r t han t hose on the degrees V and v i i : are ca ll ed Secondary Seventh Ch ord s . Be ing for the mo s t pa r t more d i ssonant t han pr imary sevenths t hesecho rd s are gene ra l ly int roduced wi th grea te r care , the seventh , e spec ial ly when maj o r, requi r

ing preparat ion or ent ry s t epw ise from above . W h i le the mode rn t end ency is t owa rd an ln

c reas ing freedom in the us e of all d issonances the s tud ent shou ld p repa re and re so lve ev e ryd issonance t hat need s i t .

When the s tud ent ’s technic in the hand l ing of d i ssonant sevent h s is es t ab l ished a l ong con

servat ive l ines i t w i l l be we l l fo r h im to s tudy the poss i b i l i t i e s und er a b road gene ra l ru lel i ke the one l a id d own by Frank E. W a rd (Co lumb ia Un ive rs i ty) as fo ll ows “The sevent h orthe roo t mus t b e prepa red in eve ry instance ,although many of the prepara t ions a re by sub s t i

tut i on . In advanced wo rk I am gu id ed mo re by my own mus i ca l expe r i ence and a d ec i d edt as t e for the r ich d issonances of mode rn mus ic t h an by wha t i s s e t down in tex t book s.

"

Th is is e x ce l l e nt d oct r i ne fo r eve ry ea rne s t s tud ent . L e t h im p repa re all second a ry d i ssonance s a t f i rs t d i rec t l y i f poss i b le , l at e r by sub s t i tut i on where the e ffec t is not too harsh andthe passage ga ins by i t , and s t i l l l ate r judge eve ry d i ssonance on i ts own mer i t s and use i t a si t b es t se r ves a mus ica l purpose .

The Cadencing Progression of all Chords of the Seventh47. The f i rst s t ep towa rd an und e rs tand ing of all the sevent h cho rds is to cons t ruc t se

quences of the se v ent h s based on the cadenc ing reso lut i on of the dom inant sevent h chord to itst on ic . In such s eque nc es eve ry sevent h cho rd w i l l b e led to the t r i ad ( o r seventh cho rd ) s i tuat ed a f i ft h l owe r ( four t h h ighe r) jus t as V7 re so l ve s to I . The sev ent h of e v e ry seconda rys ev ent h ch o rd w i l l be pre pa red and re so l ve s t epw i s e d ownwa rd .

P lay Ex . 4 1 (a ) , (b) , (c) , etc . , i n many other keys

NB m ino r

The cadencing resoluti on of a ll Chords of “

theSeventh

t o ta l impress ion i s t hat of pushing.on to the c l ose in t ha t f i na l t on ic h a rmony wh ich round s out the

who le .

"Now the roots of t hese chord s are the success ive f i ft hs reckoned upwa rd f rom the k eyno t e ,and the cho rd fa r thest .removed t ona lly f rom i ts u l t imat e ton i c i s the one bu i l t on the most d is tantf i ft h in the ser ies , name ly the um) . The cadenc i ng re so lut ion i s t he refo re a progress ion downwa rdtoward the ton i c by stages o f f i f t hs . Thus the r e so lut i on of V“) i s d i rec t . B e tween i t“) and I i s theBe tween wit) and I are bot h the ul7l and W7) ; wh i le fart hest removed and l e a s t used , mu s t

touch th ree inte rveni ng cho rd s on i t s way (cad enc ing) to the u l t imat e tonic . Th i s w i l l b e mad e

c l eare r , perhaps , by the fo l l owi ng t abl e .

Tab le of Secondary Seventh Chordsin their Relation to the UltimateTonicTr iad

d ill remove .

3E! remove .Chart2@ remove . i “! remove Ul t ima te Ton ic .

5 1 . The t endency of IV to progress to v and of 17 to progress to u inc l ines one s t rongly to thev i ew, so we l l se t fort h by P ercy Goe tch ius , t ha t t he se two cho rd s are i ncomple te no and we respectively j ust a s the v i i ; progress ing to l i s an i ncompl e t e V 9 ( 15 2 . The c adenc i ng reso lut ion, t h ough the mo s t impo r tant , i s but one o f s evera l p rogress ions

poss i ble to seconda ry sevent h chord s ; for, prov ided the genera l ru les of good vo ice l ead ing are oh

se rved , any of t hese chord s may progress to any t r i ad or sevent h cho rd whose roo t . t h i r d o r f i f t hi s a prope r reso lut i on of the sevent h (f

Conservat ive Genera l Rules for the Seventh ofAll Secondary

'

Seventh Chords

The SupertonicSeventh Chord55 . The most impor tant t ha t on the. supertonic .

' I t i s a lmos t as '

valuableas

the d om inant seventh and i s int-

reduced w i t h near ly the sa

'

me'

freedom . The fundamental pos i t ionmayom i t the f i fth , the invers ions Should be complete . The finest form of t h ischord i s the f i rst invers ion(Rameau

’s"Chord of the Added S 1xth”) All invers ions are poss i b le, but the second invers ion i s rather

weak in the maj or key. The chord i s trea t ed the same in bot h maj o r and m inor .

(a) Complete 117, seventh here a l so exp la inab le as a suspens i on) .(0) P ass ing seventh .

(d) (e) (f) P repa rat i on by subst i tut i on .

(h) ( i) Fi ne use o f the f i rst invers ion i n cadences .

(j ) (k) (1) Some of the commonest er rors .

(m) The pass i ve reso lut ion , except to a 12, i s usua l ly fo l l owed by anot her form of the same

chord , the vo ices mov ing s tepwi se .

Supertonic Ninth56 The Super t on ic N int h i s recognized by some t heor i s ts and composers . F or examples

see be l ow, Ex . 44 (a) (b) O the rs w i l l ca l l th i s ninth a suspens ion reso lved when the V7 i s r each edBut s t i l l o t hers wi l l d eny the ex i s tence of a d ominant ninth , c l a iming i t i s a lways a suspens i on .

The s tudent must in any case prepare and reso l ve the n int h in 1 1 9 s ince i t i s d i ssonant . A few fig

ured basses conta ining t h i s supe r t onic n int h w i l l be found , the f irst .ones , Nds . 406- 7.

Unf igured . Cadence

‘ 3 93 .

l i ne wi th 11g- V - l o r ng400 .

Various Resolutions -

of the Secondary Sevenths

57. The‘

general pr inci ples fregard ing resolut i on of the sevent h (! 52) may now be conc isely“

s t a t ed as fo l lows (under t h ree head s)A . The seventh . reso lves d ownward one d egree to the roo t , t h i rd , f i ft h , or (rarely) sev

enth , of the succeed ing chord . Th i s i s the t rue (act i ve) reso lut ion of a'

genuine seventh ,whether

prepa red , pass ing, or t aken by a l eap .

B The sevent h rema lns st at i onary (pass i ve reso lut ion) becoming the root , t h i rd , orf i f t h o f the succeed ing chord . Th i s i s frequent ly a mere de l ay of the d ownwa rd reso lut ion, butwhen the seventh has become pass ive , by b ecoming a roo t , t h i rd , or f i f t h , i t ceases t o d emandreso lut i on .

C The sevent h'

i s led"

upward one degree i f the bass d rops a t h i rd to the no te of re

so lut ion (reso lut i on by subs t i tut i on) , ot herw i se bad covered octaves would resu l t , se'

e Ex.32 (g) .

.The maj or sevent h may a scend Whenever i t'

funct i ons as a retard at ion . I t i s not t h ena t rue s event h , nor ean i ts p rogress ion b e c a l led “reso lu t i on of a sevent h”, but l i st s of second

a ry s ev enth s usual ly inc lud e i t .

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Freer use of the Seventh58 . C red i t is due to Mr.

-Frank E .ward for the fo l l ow ing interest ing exampl e of a f ree ruse of the sevent h . I t w i l l repay carefu l analys is . W h i le it may be contended that some of thes evenths are mere ly pass ing tones, and cer ta in appa rent s eventh chords"the resu l t of pass ing tones,i t may be answered that pass ing seventh s “

are pass ing tones, and that morethan one ana lys i s . i s

poss ib le for many comb inat ions of tones . The d ist inct ion between p repared sevenths - and sus

pensions'

i'

s also d i ff i cu l t to def ine s ince the same progress ions -may seem d i fferent in d i fferentsur round ings . It should b e no ted that the - ent ry of a maj or seventh . i s softened -if the s eventh

and fifth are in Outer partS , . or at least fa i r ly p rom inent . The free ent ry of the majo r seventh b y. an.upward l eap is smoo thest when i t i s rea lly a pass ing seventh “by “

Subst i tut ion” as in

the sevent h measure of t he illust rat ion . In all cases much depends u_po'

n .the d i spos i t ion of the pa rts.

59 . S ince f igured bass in s ight p lay ing e xam ina t ions is usua l ly set for the purpose o f t es ting the cand idate‘s mas te ry of conservat i ve usage, the student is adv i sed to “l ook we l l to his d issonances,

"but at the same t ime i t shou ld be unde rs tood t hat th i s is no t a p l ea for the ru les ofthe

“o ld schoo l” as an end in t hemse l ves . in c los ing th is s tudy of d issonances used as pa rt s of

cho rds,attent ion is ca lled to the fo l l ow ing exce rpt s . In t hese exampl es consecut i ve fou r t h s ,

f i ft hs , sevenths and nint hs , and d issonances ne i t her prepared nor reso l ved come sw a rm ing in

from some mus ica l e l fl and to p lay t he i r p ranks upon the conse rvat i ve pedagog and cha l lenge hisd isapprova l . Even in Hucbaldus we have a prophecy of some ul t ra mode rn methods .

lessons to rea lly advanced workKey to 501 Exerci ses in

“Modern Harmony”HEACOX, ARTHUR E. Book IKeyboa rd Traini ng in Harmony . Book I IThi s method of t each ing harmony makes the subjectmore interest ing and enjoyable to many pup i ls than theusual wr itten exerc ises.

( S chm id t’

s Educa t ional Ser ies No. 1 81 0 - 5)H ILL, ALFREDHarmony and Me lody .

“ Inst ead of every composer having to rediscover a ll the ways of wr i t ing , it is proposedto systemat i ze the m a teria l so that anyone wi th averageta lent can use i t . The idea i s to teach student s to loveand understand mus ic by making music ; just as onelearns drawi ng by drawing and h ot

‘

t'

y read ing about itin a book .

"

STANDARD BOOKS ON H ISTORY AJOHNS , CLAYTON Nd TAP PE!Do you Know That Va luable h ints, observa t ions . Firs tthou hts and facts about mus ic . and cc

Cri t ical and H istorica l Essays. America's great composer naturehas furnished one of the outstanding books on the history and development of the art of mus ic. It conta instwent y -one chapters in wh ich Mr. MacDowell out l inessomewha t the technica l s ide of mus ic, and gives a gen

era l idea of the h is tory and aesthet ics of the art “SPALDING, WALTER R.Music : An Art and a Language. P resents a workingknowledge of the structure and m odes of presentat ion ofstandard works in music, and i s wr itten pr imar i ly witha view to tra in ing listeners .

S IGHT READ ING AND EARFAELTEN , REINHOLD N“ MAKWIOne Hundred Ear Tra ining Exercises in P rogressive S ightOrder . Deals wi th rhy thm, p itch, intervals , chords, et c. 3 .50HARRIS CUTHBERTFirst Steps in Ear Trai ning. An easy and pract ica lmethod of ear t ra ining up to a stage sufficient ly advancedto meet the needs of the average mus ic student . Aknowledge of the rud iments of mus ic up to key s ignatures and time signatures is all that is needed to precede

(Schm id t’s Educa tional Ser ies No. 859)

SOME PRACTICAL TH INGS IN P IANO PMA practical handbook ving mus ica l precepts and pr inc iples of arti st ic p

touch , peda l ling, vo ice 1 ng , etc., and conta ins numerous illustrations as we

THE ARTHUR P . SCHBOSTON 120 Boy lston St reet

725

Exercises Graded and Designed the

First Year Key-Board Harm ony Up to the Difficult Sight

Playing Tests Set forAdvanced Students.

Professor of Theory , Oberlin Conservatory ofMusic.

Author of Lessons in Harmony ,”

Ear Training ,

” “Choral Studies .

PART I. PART II.

P r ice, each , 3 i . 25 net

The ARTHUR P . SCHMIDT Co.

BOSTON NEW YORKM Boylston St . 8West 40th St.

w i gm by m am a w a

Tab le o f Contents

(N.B . The numbers refer in every instance to the pa ragraphs)PART I

P age 4

The P r imary t r iads inFundamental Posit ion, to . harmonize a bass , 1 To ha rmoni zea soprano , z The soprano

leaps, 3 Change of chord , 4 , Bass repeats,5 Rule for no common tone , 6 Cadences , 7_

Rule for commOn

tone , 8 Harmoni z ing f i rs t six t ones of scale , 9 Tendency of sca le s teps, 10 Rev iew primary triarhm Fi rst

invers ion, 12 Success i ve Chords of the S i xth, 1 3 Second invers ion, 14 Seconda ry t ri ads in major, i s. Th i rd s

of sec . t r iads, d oub l ing, 1 6 Rule for n -V, 17'

Rule for n- I i , 1 8 Secondary t r iads in m inor, 1 9 Augmented interval, Spec i a l rules forminor key , 20 Inversi ons of secondary t r iads , 21 Tri ad 0 11 Lead ing Tone , zz P ermi t

ted Consecut i ve Fi fths, 23 Three success i ve chords of the s i xth , 24 Doub led t h i rd in success ive chords of the

s i x th , 25 S im i l ar mot ion of all the vo i ces, 26 The Sequence , 27 Sequence de81gn, 28 , 29, Sequence i n mlor, 3 0 P h rygian cadence

,3 1 The f iguring (5 32 G enera l review. 83

Chap. 11 . Chords of the Seventh - P age 3 6

C hord s of sevent h formed , 34 Dominant Sevent h , 3 5 Tr iad (vii) not ind ependent , 3 6 Int roduction of Dom.

7th , 37 Reso lut ion of Dom 7ih, 38 Invers ion of Dom. 7th , 39 L icenses ln resolut ion , 40 The Dom . 9th , “Tab le of all the p r imary d i ssonant chords, 42, Use of Dom. 9th, 43 Lead ing- Tone seventh , 44 Diminished sev

enth , 45 Seconda ry sevenths , 46 Cadencirig progress ion , 47_

Doub le funct ion of Lead ing- Tone seventh , 48

Cad enc ing sevent h s in fundamenta l posi t ion, S ign i f icance of the Cad . m s , 50 Tendency of IV, 5 1 Other

resolut ions , 62 Int roduct ion of sevenths , 5 3 Resolut ion , 64 Super tonic sevent h , 65 Supertoni c n inth , “

Vari ous reso lu t ions , of the second ary sevent hs , 57 Freer use of the sevent hs , 58 Mastery of conservative

usage , 69

P ART IIChap. III . Alterat ions - P ag0 3

A l terat ion presented , 60 Ru les for, 61 Appl ica t ion and except ions , c ross- re lat ion, 62 Spec i al alterationsin maj o r, 63 '

Dim . 71119 by a l tera t ion, 84 Augmented S i xth , 65 Aug s i xt h chords in harmoniz ing a melody,66.P rogress ions compared , 67 Augmented si xth chords “not of the key”, 68 No l imi t to reso lut ion, 69

Chap. IV. Modula t ionModu la t ion by means of t r iads , 70 Ha l f and d ecept i ve cadence, 71 Suggest ions for harmoni z ing a choral , 72

The t endency chord s of a key , 73 Modul a t ion through the Dom. 7th,” Removes ia - the key-c i rcle , 75 Mod .

by the Dom. 7ih to next - re l ated keys, 76 Modu l atory inflec t ion, 77 Reach ing a new toni c, 78 P a s s i ng

from key t o' key , decept i ve reso lut ions of the Dom. 7ih , 79 , 80 Modu lat ion by the Dim . 7th , 81 Modulati on by

the Aug. six- f i ve chord , 82 Sequences, and use of any form of the Aug. s i xt h chords , 83 Modulat ion by the

Dim 7ih on the ra ised four th d egree , 84 Sequences‘ by way of the dim. 7th on ra i sed fourth , 85 Modulati onbyt he Neapo l i tan chord , 86 S pec ia l inte rva l s , enharmonic no tat ion, pi vot chord s , (Ex.

Chap. V. Non- harmonic Tones P age 28

The Suspension , 87 The P repa rat ion , 88'

The Suspens ion i t se l f, 89 The Resoluti on, 90 P assing- tone and

embe l l i shments , 9 1 Appoggia tura , 92 Ant i cipati on ,‘9 3 Compar ing the unornamented harmony , “

Chap; VI . The French System of Figured Bass Page 41

Exam inat ions by eminent Frenchmen, 95 S ign i f icance of spec ia l f igures and s igns , 96

C h a p . I I I . A lte r a ti on s60 . One or more tones of a cho rd may b e chromat ica lly al tered w i thout produc ing a modulat ion

or essent ially affect ing i ts or iginal relat ion to the key. The a l terat ion may be int roduced chromat ica l lyor d iatonica ily, t hat is the unal tered fo rm of the chord may or may not precede the a l terat ion . Fur

thermore all such al terat ions are essent ial ly melod ic and the tone combi nat ions resul t ing t herefromshould be cons idered ornamenta l va r iant s of the or igina l chord . In t h is sense only i s i t wel l to use

the term “a l tered chord .

” Cer ta in comb inat ions conta ining the inter va l of the augmented s i x t h areusua l ly termed Cho rds of the Augmented S i xth , anot her is popular ly known as Neapo l i tan S i x t h ,ano t her the Diminished Sevent h on the Ra ised Four t h degree , and so on. These terms are convenient and are used in pract ical ly all the o lder t reat ises on harmony, but w i t h the development ofmodern harmony a long chromat ic and hor i zonta l l ines and the resul t ing broader concept ion of the ch a racter of a l terat ion in general these cho rds se em to have less c la im to independence thanwas formerly acco rded t hem . Wh i le th is change of v iew po int does not essent ial ly change the t reatment ofthe a l tered notes i t does s impl i fy the subjec t of al terat ion in genera l .

61 . In p lay ing a l terat ions from a figured b ass i t i s bes t to ob serve the fol low inggeneral rulesa l t hough there are except ions to t hem all.

Rules for Alterationst . The alterat ion i s never doub led .

2 . The no te wh ich is to b e a l tered i s not doub led unless one of t hese progresses s tepw i s ein the oppos i te d i rec t ion.

3 . Ra ised no tes cont inue to ascend , lowered no tes,to descend .

A. The a l tera t ion i s made in one and the same vo ice .

f” ,

5 . Chroma t ic a l terat ions usual ly fo l low the ch romat ic sca le ! wh ich always lowers the seventhall others are ra ised in ascend ing and lowered in descend

Exerci ses in Alterat ions (Genera l)

if

Some Special Alteration in the Maj or keys63 . In the major, 1 1 , 1 1 1 , and v1 , may appear by a l terat ion as major t r i ad s , or as apparent

dom inant seventh chords , tak ing most f requent ly but not necessar i ly, the cad enc ing reso lut ion (1? (See a l so The usua l ind ica t ion i s u s , etc. , w i t h invers ions the 3 -beingp laced in b racket s to d i s t ingu i sh i t f rom o t her figures (u

tiJ) .

O ther a l te rat i ons f requent enough to just i fy spec ia l ment ion , are V9 inmajor wi th m inorninth (V910; the 11 7 w i t h l owered f i f t h and the I7 w i th l owe red seventh wh ich funct i ons as a

'

d ominant sevent h , (apparently in the subdominant key) .

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The Diminished Seventh Chord (byAl terat ion) onVa riOus Degrees

Invers ions as des i red

Alterat ionswidenproduce the Chords of the.

6 5 . For purposes of compar ison th e Augmented S i xth in all the fo l low ing examp les is . f - d i and ai

ways between the bass and soprano . The poss ib le ar rangements are

'

numerous .

In the following exerc ises the augmented s ixt h somet imes becomes , by invers ion, a d im in

66 . To use the augmented s ixth chord s in harmoni zing a melody (or in.modulation, f 89) iti s necessary to be able to think their spelling and .resolut ion accurately and readily. B are t he

suppor t of f igured bass i s lacking and ;the problem demands mental concent rat ion and more

than ord inary care in lead ing the vo ices .

L ea rn f i rst to construct the augmented si xth chord whose bass 1 s a major third below the keynote . Thi s i s the legi t imate

“chord of the key

”hav ing subdominant funct ion

(der i ved from IV or II) and resolving to tonic , or dom inant harmony . To bui ld the chord at the

p iano proceed as follows .

i . S t r ike the keyno te , add the major third below i t for the bass , to these two add the aug

mented s i x t h above the bass in any upper part . (These three no tes are the same in all

four forms) . Then for the fourth voice d ouble the t h i rd (above the bass) in a use an aug

mented four t h -i a a d oub ly augmented fourth in ii i» , and a perfect f i f th in Th i sp rocess i s i l lust ra ted in Ex. 52 . Resolve as ind icated in the example.

In Gmaj . or c min. Their regu lar resolutionin the key

Ex. 5 2

The means augmented

Some except ional progressions permitted

67. Ex.“ C , ( a ) The bass in a weak s ix - four is be t ter led s tepwi se ; ( b) Consecut ivefi f t hs in reach ing the chord , bad in outer vo ices ; ( c) Unnecessary cross - re lat ion , approachft and at ch roma t ica l ly; ( d ) Bad f i ft hs in outer pa r ts in resolving to V (now free ly wr i t tenwi than inner par t ; (c) B ee t hoven, op . 57 ( t ransposed ) , the t rue reso lut ion to It is e l ided , the sus

pens ion improves the progress ion; ( f ) Fi fths now'

wr itten free ly ; (g) Regu la r resolut ion , but

by subs t i tut ion , unvoca l but poss ib le , ( h ) For ins t ruments any al tered tone may be taken by a

leap of an augmented inter va l , smoo t her in an inner vo ice .

The fo l lowing simple sopranos invi te regu lar use of the AugmentedSixth chords

“of the key

”. There i s no need of any but the smoothest

progressi ons

Use four augmented - ti t!l cho rd s , any forms .

68 . I t has been shown (! 65) t ha t the augmented s i xt h chords are , so to speak , a by

product of ce r ta in chromat ic a l tera t ions . Once t ho rough ly fami l iar w i t h the so - ca l led augmented s i xth chord of the key and its regula r resolution . to I i or V, the s tudent i s ready to en

la rge his view of the use of the augmented s i xt h chords by const ruc t ing t hem w i t h the bassnote on ot her than the major t h i rd below the keyno te . The a l tered tones , fo l low ing their tendeney, tend to reso lve t hese chord s as before “

to a s ix - four chord or a t r iad (major or minor) ,t hough not necessar i ly to a 12or V. B ut when the chord of resolut ion is an accented s ix- fouri t tends s t rongly to as se r t i tse l f a s the ton ic of some other key ( as) .In a pass age not intend ing modulat ion but serv ingas a med ium for vo ices progress ingmore or

l ess ch roma t ica l ly, the use of the Augmented s i x t h on va r ious degrees in the key i s somet imes

effect i ve as perhaps in bu i ld ing up a c l imax . Th i s use of the chords i s i l lust rated in'

the follow

ing examp le where resolut ions are found to vi2, mx, 1 12, e tc . However, such a passage has l i tt leto recommend i t . I t serves as an i l lust ra t ion of poss ib i l i t ies but i s too over loaded wi th one d ev i ce to be of much va lue.

6 6 6+

69 . Fina l ly, t h e re i s no l im i t to theways t hese augmented s i x t h chord s may be r es o l ved ex

cept tha t set by the t as te of the composer . The interva l of the augmented s i x t h i tse l f, in add i t ionto fo l l owing i ts convent iona l tendency ou tward to the octave , may a l so be found in the werks ofthe great compose rs progress ing in a ll the ways shown at 66 (a) . Here cont ra ry , ob l i que and s im ilar mot ion may be found , and e i ther par t may l eap . I n 65 (b) note excerpt s from the mastersi l lust ra t ing t h i s var i e ty of t rea tment .

Mozart

The al to and tenor may beadd ed . to the following

C h a p . IV . M o d u la ti on

Modulation by means of Tri ads70 . Th is means of mod u lat ion i s best i l lustrated in the Chora l where the melody leads s imply

and natura l ly to cadences in near ly re l ated keys , t hus providing an interest ing va r iety in the bar.

moni c set t ing. Keys so reached are usua l ly po ints of but momentary repose. The succeed ingl ine of the chora l may resume the or igina l key d i rect ly i f des i red . That is, such modulat ions asweare cons ider ing aremore in the na ture of mere inf lect ions to one s ideor another of thepr inc ipa l key.

In the fol lowing model s from B ach’s Chora ls note the b rackets wh ich ind icate how one may considerthe two keys as in a sense over lapp ing. The t r iad wh i ch seems to be long to e i t her key and t husfa l ls w i th in both b rackets is somet imes termed a pivot

- chord . In Ex. 56 (e) a p i vo t - chord i slack ing, but the modulat ion is qu i te sat isfactory. L et t he pup i l solve th is us ing a p i vot - chord .

In 66'

(g) note the accented s ix- four and how s t rongly i t declares i t sel f a ton ic chord ( it

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72 . The fol low ing suggest ions w i l l be found in l ine wi th the best genera l usage .

1 . The t r iad at each h o ld i s usua l ly in fundamenta l pos i t ion and ha s ton ic function“

, i . s. , itcan he figured as a tonic chord in the key of the chora l , or as tonic in the related k ey to wh ich thel ine may have led .

2 . Since the hold marks a po int of repose more or less compl ete, s cho rd of the seventh i sobv ious ly inappropriate at th is point and i s ve ry rare .

3 . I f not tonic in funct ion , the t r iad at the ho ld may appear as the V in a halt cadence,Ex.57

(a) (b) ; as the v1 (rea l ly a tonic) in the d ecept i ve cadence (c) ; or as the final maj o r t r i ad in the.

P hr'ygian cadence ( it The V in the ha l f cadence may b e reached t hrough the 11 or IV aswe l l ast h rough the I , but i s l ess usua l . The . last two _ chords of a l ine may be I - IV, but th is aga in i s a

cadenc ing formu l a exp la inable as V - I in the subdom. key.

4 . In genera l d o not int roducea chord on a weak beat '

and car ry i t ove r to the succeed ings t rong bea t , unless beginning a l ine . Compare 57(d) i and 2 , and (e) 1 and 2 . There may b e

occass iona i va l id except ions , b '

ut let the student f ind how many in one hund red l ines of the

Bach chora ls .

5 . I t i s genera l ly in bet ter taste to harmoni ze a repeated l ine in a d i fferent manner thesecond t ime, 57 ( f) .

6 . The pa r ts may cross occas iona lly , but do not cross the Soprano .

7. Avo id many six- four cadences . Avo id many of any one form of cadence .

In the fo l low ing l i st the more d i ff icu l t chora l s are most ly p laced towa rd the end .

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Chri stus der i st me in Leben

All“ ist an Gotten Segen

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Ich dank dir schon dut ch de ineu Sohn

Froh l ich so l l me in Ilen e sp r ingen

1 5 4 6

Modulat ion to a key through one of its Tendency chords

73 .The tendency - chords of a key whi ch reso l ve most emphat ically to its toni c t ri ad are

(a) i ts Dom. 7111, (b) i ts Dim . 7th , (c) . ita Aug. S ix- fi ve , and (11) the Dim. 7th on i ts rai sed fourthdegree. By means

-of any o ne of these chord s one may modulate from any key major or m inor toany o t her key, ma jor orminor ; but some modulat ions are much smoot her than others and some

are too ab rupt to be sat isfactory, especially when made through the Dom. 7ih.

(8) Modulation through theDom .7th of the.newkey74 Th i s modulat ion wi ll be used first to next - related keys, i .e.,

to thosewhose s ignaturesdo not d i ffer by more than one sharp or flat . The next- related keys to any given major key are

i t s Dom inant , Subdominant , and their three relat i ve minors ; and for any given minor i ts Domi nant , Subdominant , and the ir three relat ive majors. The tonic t r iads o f these keys can beformed f rom the scale of the given key , using the ascend ing ma j or , and descend ing originalm inor, Ex. 58 .

Next- rela ted keys to C major e lated keys to a minorEx. 58

C d r e 1 P I G I a r a t G I Fl e r dr C I

75 . Keys whose signatures d i ffer by but one sharp or‘f lat ' are sai d to be one remove

apa r t , the d i fference in the signatures exp ress ing exactly the number of removes fromone keyto anot her . From C to D i s therefore two removes , C to Fit s ix removes, _

C to f (minor) four i smoves . The relat ion of all the keys may be seen in the fo l lowi ng char t . The arms wi ll alwaysinc l ose the next - related keys o f any to whi ch the ar row po ints. B racke ts i nclose enharmonic

keys .

76. Mod ulat ion from any key to i ts f ive next- re l a ted keys may be made by progress ing fromthe old tonic to the new Dom. 7ih. Common tones are best kept , the other voices go ing to the nearestchord - t ones . On reaching the new tonic i t shou ld be establ i shed by add ing a cl os ing cadence .

Modu l a t ion from C maj or to i ts f i ve next—re la ted keys

or GV' 1° IV 1: v7 1 cr FV’ 1° Cadence 0 1 t v; m om .

(a) (b) Mod u l a t ion t h rough V'. i n genera l modulat ion t h rough aninvers ion of the Dom . 7th conduces to grea ter pl ast ic i ty , and re

serves theW7) for the clos ing cad ence.

(0) Mod ulat ion by V} , chromat i c sop rano.

61) Begin w i t h a l', a f ine road for thi s par t icu la r modul at ion.

(e) No common tone , the t h i rd of the old tonic must be d oubled to a

I .V 7 “a d Cad.

v o id an augmented second . (A rat her abrupt modulation,made smoo ther by us ing a pi vot chord , e. g. , C l

arvi}

Modulate by the Dom.

'7th from every major key to i ts five next - related keys

Modul a t i on from a m inor to i ts f i ve next re lated keys

a ! 0V' leand cm. arc dv: l and Cad . a i land Cad .al GVS land Cad . al FV :

Modulate by the Dom.

’7th from every minor key to i ts f ive next - related keys

Exercises wh ich Modulate by the Dominant Seventh Chord7

Modulatory Infl ect ionsThrough Apparent Dominant Sevenths

77. In the fo l lowing exe rc ises the appa rent Dom. 7th reso lv ing to i ts apparent tonic, cannot b e sa id to produce o t he r than a flee t ing imp ress ion of modulat ion. Such p rogress ionsmay be te rmed modulatory inflections . See 1} 63 under wh ich the fo l lowing exerc i ses cou lda lso be placed .

Exerci sesW hich Cont ai n Modula tory . I nf lect ions

537. 3 6

78 . Through some invers ion of the V7 (or fundamental pos i t ion if necessary) reach a new

tonic at each -t as in the-fo l lowing model . As has already been shown, i t may b e quest ioned

whether t hese are modulations at all . In any case the imp ress ion of the s uccess ive (apparent) to

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Exerci seswhich modulateby t -hé Dimini shed Seventh Chord

(0) Modulat ion through theAug. Six- five chord of the new key82 The new tonic is reached as an accented s ix- four, to which is added V7 1 . Ot he r

pos iti ons are some t imes used .

GP G

o r Ft i’

C l s‘C I Bbi

’It C I G:

‘

(a) (6 69m) Some of the smoothes t ways of reach ing the Aug. S ix f i ve : at (b) from a l‘

(0) th rough an Aug. S i x - four - th ree to avo id con. 5ths , (d ) the Aug. S ix- fi ve fi rst in o t her thanconvent iona l fo rm to escape con. ti the , or a cross - relati on.

(9 Free yet qu i te pe rm iss i b le approaches to the Aug. S ix- fi ve . One shou ld avo idcon. l ths , but may d is rega rd augment ed inte rvals and cross - relati on in any modu lat ion by a l te r.ed Chords .

Extend through the octave, ascendi ng by half steps .

This and s im i la r sequences from EJ. L ehmannlby permission)

Ascend ing by whole s teps .

or I2 v7 1 E

83 . A lso invent and play sequences s imilar to 570 - 1 . Fina lly modulate from any ,

key to

eve ry o t her in the c i rc le , 1 75 . (The othe r Aug. S i x t h cho rd s are also available for these modulat ions , but the Doub ly Aug. Four th lead s to majo r only).

(d) Modulat ion through the Dim.7th on the

raised fourth degree of the new key84 . Use t h is cho rd prefe rab ly in i ts fundamenta l pos i t ion (permiss ible in f i rs t inversion)

and reach i t . through the neares t cho rd - tones . Reso lve it to the new toni c s ix- four chord , on anyaccent , and add V7 I . The cho rd is often ind icated by

(a) (b),

Typ ical mode ls .

(0) The old tonic taken in f i rst invers ion avo ids an augmented second .

(d) The modulat ing cho rd tak en in its f irst invers ion.

(e) Cross - re lat ion is un'

object ionab le as in pract ically all p rogress i on to modulatory (al tered)cho rds, see under Ex. 62 .

(f) The augmen ted second , good . Compare th is modulati on wi th (b, , wh ich is ident ical in sound .

(g) Th is cho rd i s some t imes spelled as a Dim. 7ih on the ra ised second of major keys (5ea) .

85 . Pass from key to key in exerc i ses 550 to 655 by way of the Dim . 7th on the ra i sedfourth degree of the new key, Add to each new i i a V I o i cadence .

In the same manne r modu late from any key i n the c i rc le (f 1 6) to eve ry o ther key .

Sequence of modulat ions by the use of the Dim .7th on the ra i sed fourthExtend t h rough the octave ,ascend ing by half s teps .

Ex tend th rough the octave,ascend ing by major seconds .

C I DW w I! V" I EW r I i etc .

Also i nvent and play sequences s imi lar to 678 - 9 a scending or descendi ng

by other i nterva ls .

Modulation through the Neapol itan Chord of the new key86. The Neapo l i tan Chord is not, proper ly speaki ng, a tendency cho rd a l though p roduced

by alterat ion: but its charact eri st ic reso lut ions to the tonic s ix- four or to the dom inant of its own

key ent i tle i t to a place among the mus ic ian‘s modulat ing mate r ia ls .

Exerci seswh ich modulate by the Neapoli tan chord of the new key

Analyze ful ly and“ t ranspose

S equence of modulat ions by the use of the N“ot . ine

'

-

newkey

Extend t hrough the octave ascending byh a l f s teps through

,

major keys .

Ex.65

Modulation tSpecial Intervals

Deceptive Resolution, Pivot Chords

07 a per All! Down a ha l f s tep

Ex. 65 . Add a clos ing cadence to each of these except (e) wh ich needs a V7 - l only, and modulate all these d is tances in the same way from every major key .

(a) The o ld t oni c is a p ivo t - chord qu i tted as V in the new key .

(b) The new Dom. 7th is the Aug. S ix - fiveenharmoni cally notated) of the old key (a p ivot -c hord).(c) The old tonic is NO in the new key (a pivo t - cho rd) .(d ) The N“ of the old key is the V in the new, to wh ich is add ed the seventh . A pivot - chord,

bes t in the th i rd invers ion. Note that (k) is the enha rmonic equ i va lent of (d) ; avo id fi fths as at ( l) .

(e) The old Dom . 7ih is the Aug. S ix- f i ve (enharmonicaliy no tat ed ) of the new, a p i vo tcho rd and mus t a lways be comp lete.

(f) (g) Decept ive reso lut ions . The vn°r° of the old key is enharmonicaily mm of the new,

a pivot - cho rd usab le in both minor and maj o r keys , par. 45 . By th is means one reaches those keysone, two, or th ree minor th irds d istant (or enharmonio equivalent) .

(h) ( l) l odulations by the Dom. 7th to rathe r d istant keys . Good because the th i rd of the

Ex. 66

1 . The Suspension87. The Suspens ion is a prepared d iscord a degree h igher (or lower) thanthe chord- tonewh ichi t temporar i ly d isp laces, and to wh ich i t logical ly resolves : Three factors are i nvolved ; the Preparat ion,

The Suspens ion i tse l f , and the Reso lut ion .

In' the fo l lowing suspens ions, locate the par t to wh ich each figure refers .

Th e P reparat i on

88 . The P reparat ion may be any cho rd - tone , but preferab ly not a pass ing sevent h, unlessnot t i ed to the suspens ion . Those sevenths and n int hs w h ich may ente r th rough a leap frombelow are suffic i ent prepara t ion (a) (l) (c) (d) .

The preparat ion is usua l ly as long or l onger t han the suspens ion. Th is ru l e is frequent ly relaxed when the preparat i on i s not t ied ove r to the suspens ion (d) . Occas iona l ly the ru le is frankly d i sregarded .

P reparat ion by subst i tut ion is not perm i tted , s ince a t rue suspens ion i s a prolongati on of

what was fi rs t a cho rd - tone . (Except ions do not need p lace here) .

The Suspensi on89 . The Suspens ion should b e fore ign to the cho rd w i th wh ich i t appea rs,the more c lea r ly

so the bet te r . Bes t when i t is a sevent h above, or second be low, some legi t ima te cho rd - membe r .The suspension shou ld enter upon an accent , or an accented par t of a beat . I t i s f requent

ly mo re effect i ve when not t ied .

The suspens ion may de lay the ent ry of a root , thi rd , fi f th , or d im in i shed sevent h , (a) to (f)Ex . 66 . The de lay of root or th i rd i s the more frequent , d e lay of the f i fth best when res t r i c tedto a cho rd of the sevent h , or in a sequence , (b) and later. (Ex. 69 a , b) .

The term, Retardat ion, i s usual ly used to des ignate the suspens ion wh ich resolves '

upward (g) .

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The Suspensi on 6 5 ; Redupl icat ion of theResolut ion

(a) Suspens ion of the f i ft h in a t r i ad , An 8 is unders tood . Never double the 6 northe

5 , See a lso par.3 2 . A l though in i tse l f a consonance, thes i xth here de l ays an expected f i fth inthe dom inant t r iad and is t he re fo re accepted by the e

'

ar as a t rue suspens ion.

(b) The 4 3 suspens ion gi ves the in the succeed ing measures the character of a suSpen

s ion a lso . P l ay (a) (b) as a sequence, cont inue i t ‘

and add a c adence .

(c) The.

n inth demand ing reso lut ion, fa i ls to es tab l i sh a as a ch o rd tone . He re aga in the

ear accepts the 39 ‘

as a suspension. G enera l ly speak ing, as ide from“

such favo r ing cond i t i onsas have been quoted , _ the suspens ion of the f i fth in a t r iad is weak .(d) _ P ermiss ib le appearance of the reso lut ion in the tenor s imul taneous ly w i t h the suspen

s i on, see aga in if90 . The tenor app roaches the c stepw ise in cont rary mot i on . Th i s i s con

si dered a compensat ing feature. in th i s par t icu la r progress ion.

(e) Re tardat ion in the bass w i t h redup l icat ion of the reso lut ionin an upper'

vo ice, b ad .

“

At (f) a fa i r cor rect ion . (g) A doub led majo r t h i rd or doub l ed Lead ing- t one i s worse w i t h“a suspens ion than w i thout i t .

The Suspension saves cert a in .Consecut ive F i fths ,

l

but never Consecuti veOctaves.B ad Covered Octaves . Suspensions in two ormore part s

(a) Consecut ive f i fths w i th a fi rs t inversi on are saved by the suspens ion. W i t h the bassthese

_ _fifths are ques t ionab le (b) .

6 m . t ‘“ 4 4 £1 4 9

in open pos it ion

Suspensions in the soprano only

Suspensions in any voi ce except the bass

s s 4 8 9 8 7 ° 9 °4 3 9 8

Suspensions in the bass only

No te . The suspens ion in the bass i s somet imes ind icated by a d iagona l s t roke followed by the regular figureswh ich wou ld express the chord were t here no suspens ion . This is s imp ler and c learer than the most ususl figuring.

Compa re Nos . 601 and 602 the so lut ions of wh ich should b e ident ica l .

Suspensions in any voice6 s

9 8 8 6 5

Note . in many papers the , i s p laced before the figure a s in these from the Gu i ld exam ina t ions .

2 . Passing Tones and Embellishments91 . W hen P ass ing- tones and embe l l ishments are to be used

_in a figured bass, d ashes are

used -after the usual figur ing as in the fo l low ing e xample .

4 3 4 3

(a) The chords are ind ica ted as usua l and the d ash cont inues the cho rd wh i le the bass moves .

S igns : pass ing - tone , (O) Accented p ass ing tone, (E) Embe l l ishment .These ornaments , toge ther w i t h the pass ing sevenths , afford a v ery f l e x ib le b ass, as w i ll beseen in the fo l low ing cho ra ls from j . S . B ach .

(b) (c) (d) (e) Some common fau l ts and t he i r cor rect i on.

(f) Good . No fau l t can be found w i t h consecut i ve per fect f i ft hs i f e i ther membe r of the secfi f t h is not a cho rd - tone .

In Ex. 72 the fragments are from Bach‘s so lut ion of the chora ls wh ich fo l low. (616— 619)

B ach Chora ls. conta ining suspensions,

pa ssing tones and embelli shments.

Supply the al to and tenor.

Tug, der ist freudenre ich

617° Allein zu d ir, Her r j esu Chr is t

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Ex. 1 4

3 . Appoggiatura , Ant icipat ion92 . The AppOggiatura is br iefly def ined as an unprepared suspens ion. I t isfmost express

ive when on the accent , but unl i ke the suspens ion i t may appear on the unaccented beat . I t istaken by a leap of an augmented second or more . I t is commonest in the h ighes t v o ice .

9 3 . The Ant i c ipation is the Oppos i te of a suspens ion in t hat i t becomes a d isco rd by taking a tone of the following Chord before t hat chord enters . The ant icipat ion is unaccented .

I t usua lly enters s tepw ise but need not do so .

(b) Ap .

(a) (b) Appogg iaturas on the accent , and on the second ha l f of the beat respect i ve ly . S ign,Ap.

(c) Ant ic ipat ion in the soprano . S ign, A .

S imu l taneous appoggiaturas . (e) , S imul taneous ant ic ipat ions .

Exerci ses conta ini ng the Appoggiatura and the Ant icipat i on

Mozart

appoggia tura , ant i c ipa t ion or pas s ing t one a t the

Ornamental Resolutions of the suspens ion,

appoggiatura , passing tone and embell ishment

The suspension ornamenta lly resolved . Sign : S . orna .

S.om a S. om a

(a) The suspens ion takes any su i tab le chord - tone be fo re reso l v ing. The res o lut ion ma intai nsits relat i ve p lace in the measure .

(b ) The sus e i n l e a s to the other nei bhor of the resolut ion to which it t hen p roceed s

The suspension ornamenta lly resolved

The Appoggi atura , P ass i ng- tone and Embell i shment orna.

menta l ly resolved . The Free Ant i cipat ion and Free ToneE.orna F. A .

(a) The other neighbor of the reso lut i on or any su i tab le cho rd - tone'

may preced e the reso lution.

(b) (c) The pass ing - tone and the embe l l ishment are d i s t ingu ished from the appogg i atu'ramere ly by the way in wh i ch t hey are approached . The o rnaments d o not d i ffe r essent i a l lyfrom“ t hose of the appoggiatu ra .

(d) The Free “ Ant ic ipa t ion is left by a leap and is a member (a c tua l or und e r s t ood) of thecho rd w h ich fo l lows . S ign: F. A .

(e) The Free Tone isnei ther a membe r of the chord w ith wh ich i t appea rs nor to wh ich itp roceeds . S ign: F. T .

+orna o rna

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Examples of French f i guri ng

The“i '

Ex .

’77

Suggested arr. The “a i? The Lead ing Tone 7i h .

Dim . 7i h .

Al tera t i ons i f necessary :

TheV7andV9

over - ton ic .

S imp l ici ty in'

denot ing p r imary d i ssonant chords .

Exerci ses i n French figuring

C h a p .V II . E x am i n a i 1 0 1 1FrOm the A .G.O., Noted Conservatories, and Other Sources

From .

“Rules and Inst ruct ions for P lay ing"Thorough - bass or Accompaniment ia _

Four Parts ,made for his Scho la rs in mus ic by j ohann Sebastian Bach

Eight d ifferent basses under one choral1 . Ch. Ki tt elfiast pup i l

He r r Go t t , d ich loben a lle w i t .of j . S . Bach

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Th rough the courtesey of Mr.W a r ren R. Hedden , Cha i rman of the Examinat ion Commi t teeof the Amer i can G u i ld of Organists,permission i s gi ven to present the fol low ing s ight - play ingtes t s from the yea rs 1 907 to 19 1 6 inc lus i ve , t h i r ty- four examp les . The papers forand

’09 , conta ined no s ight - p laying from f igu red bass .

G iven Melod ies A .G. O. Assoc.

A. Fe l lowsh ip

A . Assoc . t u t

A. Asso c . n u

A .G .O. Assoc. i s“

A.G.O. rei im sim oi’

s

A .G.O. Fe l lowsh ip,was

F igured BassesAG O. Assoc .

, sei o

A.O. O. Fehowship, mm

A GO. Assoc nsu

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KNOX CONSERVATORY OF MUSI CExaminat ions in Harmony

'

ohnW. Thompson , by per.

8at

s

3 sin s s

CORNEL L '

CONSERVATORY OF MUSICExam inations inAdvanced Harmony

(See it 58 freer t reatment of the seventh ; s im i la r t end ency in these f rom Co rne l l .)Ho race A. M i ll er , by per.

lvadeli A-

. Swi nd ler'

(Co rnell)

OBERL IN CONSERVATORY OF MUSICh 3Dim 7t chordsGeo . S. D ick inson

P arenthem ind icat e unconvent iona l pos i t ions .

HARVARD UNIVERS ITYFinal Examinations

W a l t er R. Spa ld ing , b'

y per.

687 (W r i t ten W0“ ) Ha rva rd Univer m o

At a use one of the augmented s ix t h chord s ; at b a Neapo l i tan s i xt h .

COLUMB IA UNIVERS ITYExaminat ion papers (writtenwork)Secondary sevent h cho rds Frank E.W a rd ,

(The s i gn i s here used to ind i ca te any non- ha rmonic tone , M t . a .)

Co lumb ia Univer.

B». 3(These a l tera t ions are nonha rmonic (embel l ishments etc.) or may be pa r t of an a l tered -

cho rd . ma n.)

NEW ENGL AND CONSERVATORY OF MUS IC

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TRINITY COL LEGE OF -MUSIC , L ONDONH igher Examinat ions , Jan. 191 3 .

Five pa r t s. P ass ing tones (8th no tes) , and cross ingof inner pa r ts perm i t t ed . (W r i t ten) ( Licent ia t e in Mus ic.)

9 8 6

By per.

its

Four pa r t s . (W r i t ten ) (AS SOOi fl e in M0 S“)

Tr ini ty C ol.Mus . by per.

(As soc ia te in Mus ic)

m inty hy‘

pe r.

"

FromExaminations in“

the Art - ofTeaching. (L .Mus. and mai ns.)

Eleven f igured basses by perm iss ion of the

ROYAL COL L EGE OF MUSI C , L ONDON“Figured bas s t est s wh ich have been used in the o rgan d i v i s ion of the R.C. l . examinat ions forAssoc iatesh ip ll .) in the prac t ica l wo rk at the o rgan.

"

R.C. M . London

R. C.M.

,Lond on

R. C. N .

,L ondon

R. C . N . , L ond on

R.C.M.,London

2 s6

OXFORD UN IVERS ITYFrom Examinat ions for the

degree of Bachelor of Mus ic, 19 14 . (Wr i t ten)Unf igured bass by per.

Ha rmoni ze , us ing in su i tab le p l aces the following cho rds : d im in i shed seventh, Neapo l i tan S i x th ,ma j or t h i r teent h , t h i rd invers ion cf the French S i xt h .No te . I f unfam i l i ar wi th Engl ish Theory i t w i l l suff ice to subst itute

‘

for‘fmaj or t h irteenth” 11 16 re

so lv ing to V7 o r I,and t

'

or “th ird invers ion of the French S i x th”, 2: w i t h a d im inished 8t d (or 1 0th) be.

tween the bass and one of the upper pa r ts .3

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FRENCH M INISTER OF PUBL IC INSTRUCTIONFrom the Examinat ions for specia l professors

of vocal musxc inNormal , Lycee and H igh school s Chapu- i s , by p“Durand a C ie . P a rt s.

be +4

+4

NAT I ONAL CONSERVATORY OF MUS I C , P AR I SFrom the compet it ive -Examinations , men

’

s c lass , 1 900721 0 G iven Soprano.

Durand l C i r . Pa ri s .

Exam inat ion in accompaniment From “ Lo-cons d’Ha rmenie” byAlbe rt Lav ignac (of the Na t ional Cons . , Pari s ) .

0 +4s

From L econs d’ Ha rmon ie”, Lav ignac .

Modere' G ab r i e l Faure

P er. of Henry L emo ine a Go.

17 Rue P igalle , P a rts .

From “Lecons d

’ Ha rmonie’,Lav ignac.

Alex .Gu i imant

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Thes- following b eaut iful manuscript from the hand of the composer.

M. Vincent D’ Indy, is his own solut ion of N9. 72 5 . By permi ssion.

o.F. ( 503

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