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TRANSCRIPT
MUS lC LIBRARY
UNIVERS ITY
OF CALIFORN lA
BERKELEY
PRE FACE TO THE SECOND E D ITION.
There a re ma ny rea sons for m e to feel gratified at the successof my Ha rmony method . W
' i thout a prefa ce I sent the first edi tionof the book in to th e world , because the work wa s to speak for i tself .
Only in the last para gra ph 84) did I add concluding remarks inorder to indica te my standpoin t . Composers , teachers a nd studen tshave used a nd praised th e book .
As the thorough bass figuring is practically obsolete,and can
contribute nothing towards expla in ing the chord forma tions a nd
chord relationships in modern ha rmony , i t is not employed here .
M y signs indica te the tonal functions o f chords on ly .
‘
Th e tonalfunctions reveal the fact that a l l chords a re related to each otherin groups, a nd tha t these again have subordina te groups . Th e severa l subordina te groups o f chords cannot be ranked in a single a lphabe tica l fi le , a s the thorough bass methods vainly attempt to do
,but
must be looked upon a s clustered a round higher chord -groups , and
these aga in around o ther points , a nd so on un t i l the ton ic is rea ched .
Th e system o f modern harmony is founded solely upon the re l a tionship by the Fi fth a nd the Third . Th e modern key extends fa r beyond the ori ginal boundaries , and is not l imited to a scale , which isin i tsel f nothing L
‘
i t a chord w i th passing tones .
Th e p rincip l e or“ va ria tion ” that I brought forward is founded
upon the m a ster works ,a nd adheres to the la ws of logic a nd sci ence .
W i th this Harmony system , every chord o f W a gner’s ,from Rienz i
to Parsi fa l , can be so logically explained ,that he does not appear a s
revolution ist , but a s a wonderful exp l orer in the realm of tones .
M y essay on th e Ke y- extension o f M odern Ha rmony forms an
addition to the text - book , because i t conta ins i llustrations of theextreme limits of chord relationship .
To the presen t edi tion also a re a dded E xamination and ReviewQuestions ,
which,no doubt
,will be welcomed by ma ny teachers .
Th e well - nigh inevitable typographica l errors in the text have beencorrected ; there being no reason to cha nge a ny thing else in thebook .
I hope that this new edition will make many new friends a nd
tha t the book wil l be productive o f much good in the field of h a r
mony stud y a nd tea ching .
CARL W . GRI M M .
C I N CI N N ATI,July 1 6
,1 90 6 .
Copyr igh t 190 0
P A R T I .
CHAPTER ].
I N T R O D U C T I O N .
1 . RHYTHM ,M E L ODY AN D HARM ONY a re the three
essen tial fac tors of music . Rhythm is the change , but systematicgrouping , of tones of var ious duration . I f tones of differen t pitcha re heard one after another in logical order
,we get what is called
M elody ; if tones of diff eren t pitch a re heard together,we get Ha r
mony (a chord) . In its widest sense Harmony means the science of
chords , their relationship and connection . I t is the laws of harmonythat we shall explain in this book
,but i t wi ll be seen a s we proceed
that the question of rhythm or melody is often so c losely connectedwith that of harmony that i t is impossible to treat of one withoutalso paying some atten t ion to the other .
§ 2 . I NTE RVAL S .
—An in terval is the distance and difference between two tones , heard one after the other or at the samemomen t . In tervals have numerical names . These names dependon the number of l etters which a re included from one key of thekey -board to another , or from one degree of the staff to another . In
te rva l s a re measured by means of hal f-steps (hal f tones or semitones) and whole steps . A half-step is the term of measuremen tfor the smallest:distance . I t is the distance between any one note ,and the nearest note to it , above or below . F or example , on thepiano , the neares t note to C is B on the one side (below) , and C1} onthe other side (above) . F roni B to C
,a nd from C to Ct; a re , there
fore , both half steps . S imilarly from P1; to Ffl , a nd from F fl to Gwill be hal f—steps ; but from G to Awill not be a half-step , for A isnot the nearest tone to G ; Gil (or A2) comes between them . I t is
evident that two half-steps together will make a whole step . Th enomenclature of in tervals
,especially the modified ones , is , unfor
tuna te ly ,in a somewhat confused state and not uniform in al l text
books . Th e c lassification adopted here wil l recommend i tself forits simplicity , because the in tervals a re arranged into on ly threec lasses:normal , en larged and narrowed . First of all we will learnthe accurate s ize of the normal intervals , and then the modifications(augmen tation and contraction) of them . I f a tone be sounded and
the same tone be repeated , or sounded simultaneously by some other
instrumen t (or vo ice) , a p rime is formed, for example
Th e word prime means an interval of one degree ; i t also meansthe starting note , the one from which the other notes a re counted .
A prime makes use of on ly one letter for two sounds which havethe same pitch ,
or very n ear ly the same,a s the paragraph on
(3)
modified intervals wil l show . This prime is also cal led perfect . ” Instead of a lways wri ting down the name of a n interval
,we
will use figures . F or the word prime the figure 1, seconds a re ih
dica ted by 2 ,thirds by 3 , e tc .
A second (2) is an interval between two conj unct degrees ;i t inc ludes two letters . A “
normal ” second contains one whole
step , for example :E This second is also called a major
second .
A third ”
(3 ) is an interval of three degrees i t includes threeletters . A “
normal ” third contains two whole steps , for example:
This is also named a major third .
A “fourth ”
(4) is an in terval of four degrees ; i t includes fourletters. A normal ” fourth con tains two whole steps a nd one half
This is also cal led a perfect fourth .
A fifth ”
(5) is an interval of five degrees ; i t includes five letters . A “
normal ” fi fth contains three whole steps a nd one half
This is also called a perfect fifth .
A sixth ”
(6 ) is an in terval of six degrees ; i t includes six
letters A normal sixth contains four whole steps a nd one half
This is also called a major s ixth .
A seventh (7) is an interval of seven degrees ; i t includesseven letters . A “
normal seven th conta ins five who le steps :I t is a whole step smaller than the octave . This is alsocalled a minor ”
seventh . I t is to be borne in mindthat our term “
normal ” and our figures do not indicatemerely a d egre e ,
but an exact s ize of the interval . Our figure 7
always indicates the minor (dominant ) seventin E $0 2 1therefore
,we indica te the major seventh
seven th . Th e mark : (short crescendo sign ) means raised ,
a s will be further exp la ined in the paragraph on“ modified ”
in
terva l s .
An octave (8) is a n interval of eight degrees ; i t includeseight letters . I t is always the distance from one tone to the next
(above or below) of the s ame name . A norma l octave contains
six whole steps: This is also called a perfect octave .
A n inth ”
(9) is an interval of n ine degrees ; i t includes n ineletters . I t is composed of an octave and a second . A normal ”
n inth con tains seven whole steps This is also cal led a
major n inth .
A “ tenth ”
(1 0 ) is an interval of ten degrees ; i t includes ten
lette rs . I t is composed of an octave and a third . A “
normal ”
tenth contains eight whole steps This is also called a
major ten th . I ntervals larger than tenths a nd even tenths a recommon ly reduced to the nearest octave , and so to their lowest
terms . Thus the t is usually spoken of a s a third,
a s if i t were counted from the c o n the third space . I t will befound useful to impress upon the memory that:the normal or “ major ”
second (2) is midway between the primeand third ; i t is at a n equa l distance of a whole step from each ;
the normal or “ perfect ” fourth (4) is between the third a nd fifth ;there is an interven ing space of a half step from the third anda whole step from the fifth ;
the normal or ma jor s ixth (6) is next to the fifth ; a whole stepfa rther away from the pr ime than is the fifth .
E XE RC I SE .
—Wri te out the normal intervals up to the tenthsof the fol lowing notes:g
,d,a,e , b , ffi , cfi , gfi , dfi, afi , efl , bij, f, blZ,
e l2 , a lz, diz, g lz, c ,l .
3. N ORMAL U N D E R-INTE RVAL S .
— Intervals a re us
ua l ly reckoned upwards , but occasionally also from the upper tonedownward ; then i t must be expressly stated . I n either case the inte rva l is , of course , the same , but when reckoned downward i t is
called an under- interval . Thus the interval is a fifth,
but f is th e under-fi fth from c .
E XE RC IS E — Wri te out the under- in tervals down to thetenths of the fol lowing notes g , d , a , e , b , ft), cfi, gt), d#, f , biz, eh, a lz,dll , n, c , m, a s follows :
1 u2 u3 u4 115 u? 118
u unde r.
4 . MOD I FI E D I NTE RVAL S .
— Intervals may be modifiedeither by raising or lower ing one of their tones . Care must betaken not to change the name of the in terval . Thus , if we wish to‘
en large the normal fourth C— F by a half- step we must wri te C— F fi ,not C— G lZ, otherwise the interval will not be represented a s a mod
ifi ed fourth , but as a modified fifth .
is the sign for raising the pitch of a note a ha lf step .
(short decrescendo mark) is the sign for lower ing the pitchof a note a hal f step .
TABL E .
S /zowz'
ng t/ze mea ning of til e /fig ur es wit/z a nd
F or c
l—J ra ised (augmen ted) prime ,
raised (augmented ) second ,lowered (minor) second ,raised (augmen ted) third ,lowered (minor) third ,
raised (augmen ted) fourth ,
lowered (dimin ished) fourth ,raised (augmented) fifth
,
lowered (dimin ished) fifth,
raised (augmented) s ixthlowered (minor) s ixth ,
raised (major) seven th ,
lowered (dimin ished ) seventhraised (augmen ted) octave ,lowered (dimin ished ) octave)
9
1 0 <
CO
QO
IO
IO
A
A
A
A
A
A
co
oo
oo
x'r
sl
ow
cu
u
oi
ua
sk
F or e .
S 1 lowered under-prime,
2 lowered under-second ,2 raised under- second ,3 lowered under- th ird
,
3 raised under -t hird,
4 lowered under - fourth,
4 raised under - fourth,
5 lowered under - fi fth,
5 raised under- fi fth,
6 lowered under - six th,
6 raised under -sixth,G
5:
5
Ci
r:
S
25
C
C3
G
F or e
u 7 lowered under-seventh ,
u 7 ra ised under- seven th ,
u 8 lowered under-octave,
u 8 ra ised under -octa ve,
u 9 z u 2 u 9
u l 0 > _ u l O
E XE RCI SE .
—Wr i te out tables similar to the a bove,us in
each of the fol lowing notes a s a starting po int :g,d,a,e,b
,ffi , cfi
g,
gfi , (if), at} , f , blZ, e lZ, a il , dbl , n,ch
,fll .
I f the half- step is expressed upon the same staff -degree,i t is
ca lled a small or chromatic hal f-step ; if i t is expressed upon con
tiguous degrees , i t is called a great or diatonic half- step .
Ch roma tic D ia tonich a l f-step . h a l f-ste p .
Th is cl a ssifica tion , wh ich m igh t be ca l led a“
h armonic c la ssifica tion,of
in terva l s is en tire ly suffi cien t,b eca use we figure e ve ry in te rva l from th e funda
menta l tone of a ma jor or minor ch ord,and conside r it in its re la tion to th e one
or th e o th e r . Th e re fore, we wi l l ne ver h a ve to figu re doub ly con tra cted or e x
te nded inte rva l s l ike a“diminish ed ” th ird
,for e xampl e e —
giz found in th e
ch ord:c— e —
g W e cou l d indica te th is and a l l such “ me lodic ” inte rva lsa s doubl y con tra cted or e xtended by using th e se signs 2 and 5, for e xamp lee —
g 3 i but,a s th e course wil l sh ow ,
our me th od ne ve r requires th e doub l e l owering or ra ising signs .
CHAPTER II.
T H E P U R E P R I N C I P A L H A R M O N I E S .
(TO N I C AN D D O M I N AN TS .)
§ 5 . MAJOR AN D M INOR CHORD S . (TRIAD S ) . Therea re only two kinds of consonan t chords
,maj or chords and minor
chords ; all dissonant chords a re to be conceived , explained and in
dica ted a s modifications of major or minor chords. M ajor chord andminor chord are th e two foundation stones of harmonic structure ; dissonant chords a re only modifications of them . Th e major chord con
sists of a fundamen ta l (pr ime) ,major third and perfect fi fth:ETh e minor chord consists o f a fundamen tal (prime) , minor third and
Th e minor chord is the very opposite
of the major chord , in sound a s well a s in construction . Th e majorchord sounds clear , strong and cheerful , whereas the minor chord
sounds dark , weak a nd sorrowful . I f we look c losely at the in tervals of these chords , we fi nd in the major chord a minor third abovethe major third g
e , minor th ird .
cmajor third .
I n the minor chord we fi nd i t reversed , namely a ma j or thirdabove the minor third :g
e ll ) major third .
cm inor th ird .
Th e major chord consists of a major third a nd a perfec t fi fth,
the minor chord shows the same intervals i f measured downward !ma j or third (
x/l perfect fifth ,
gA
major third (iper fec t fifth
c v
Th e minor chord then ,in its construction ,
is the exact oppositeand counterpart of the major chord . These two kinds of chordsa re co-equal in value and impor tance ; they express contrastingmoods . Th e tones forming these chords coalesce (blend) into aperfect unity
, a nd around these two chords all mus ic revolves .
6 . CHAIN OF FI FTHS ,MAJOR AN D M I N ORTHIRDS .
I n order to lea rn with certain ty all major a nd minor chords , pupi lswill do well to impress firmly on their minds the chain of fi fthsproduced by the natura l notes . Perfect fifths a re formed by thetones of the natural scale in the fol lowing order:
e memorized perfectly)al l of which a re composed of three whole steps and a hal f- step .
Th e connecting fi l th,B F
,of this ser ies is no perfect fi fth ; i t is too
sma l l by a half-step . I t is called a dimin ished ” fi fth . I f theperfect fi fth above B be gained
,then F must be raised a half-step ,
that is,F becomes F t) ; i f the perfect fifth below F be taken , then B
a ) 5 )
must be lowered a half-s tep ; that is , B becomes Bk:ETh e fifths derived from B F distinguish themselves from all othersin this:that the two notes have diff erent S ignatures (a s at a ) thelower one is natural note
,the upper on e h a s a a s at b ) the upper
one is na tural note,the lower one h as a l? ) whereas al l other fifths
have l ike signatu res , th a t is to say ,either both notes a re na tura l
notes ,or both have a or both have a D. F or the fifth of Ffi is Cf},
because both notes of the F C a re raised a ha lf—step , so that the proportion remains the same ; the fi fth of Cl} is Gfi , e tc . I n like man
ne r E D is the under- fi fth of E D, because both notes of the E B a re
lowered a half-step , so tha t here also the proportion rema ins thesame ; the under - fi fth of E ? is Ail , e tc . I n other words , when wesupply with sharps and flats al l notes o f the above rows of na turalnotes in the order o f fifths
,we will produce new series of fifths:
_ 9 _
(ascending with F fi— Cfl— Gfi- D fi- Afi— E fi— Bfi l
0 be memorized(descending wi th b) BQ— E h—Ab— Db— Gb— CQ- F Q perfectly)At Bi? and F lZ we have reached the end again ; for if F ifi is the fifthof B i t cannot be the fifth o f B and if Bl? is the under- fi fth of F i tcannot be the under-fi fth of the fifths Bfi Pt; and BlZ F lZ, againa half-step too small , require
,therefore , in the former a further
raising of the upper note,in the latter a further lowering of the '
lower note . To the above enumerated irregular-looking perfectfifths , Bil F and B F E belong likewise those derived from B F
,
viz .:Bfi F x and Bil l? F lZ E As for the
rema inder , on ly such fifths possess th e proper s ize again a s haveboth x or b? prefixed:
Triple sharpings and fi a tt ings surpass the l imit of the imaginativefaculty . Th e double-sharps and double - fl a ts already test i t greatly ,since they presuppose the single sharpings and fi a ttings , and losesight of the natural notes en tirely . I f the pupi l is perfectly familiar with the ser ies of fi fths:
F x . Cx . C x . D x . Ax .
NF5. cit. G3. nit. Ali. E li. Bit\
x
F . c. o . D . A. E . B .
NF lZ. clz. ob. Db. Ab. E a. it .
G lzlz. D lztz, Abb. E ll . Bib.
then he wil l be acquain ted with the main pillars of all major andminor chords , the fundamentals and fifths . I t is the aim now to
make him thoroughly familiar also with the major and minorthirds . Th e three major thirds without chromatic signs a re F A,
C E and G B . They “
ca n be easi ly remembered , because they a re
the thirds of the first three notes in the chain of fifths :F C G]D AE B . I t is clear that those thirds which a re derived from F A, C Ea nd G B by sharping or fl a tting both notes must be major thirds
The remain ing thirds without chromatic signs ,D F
,AC
, E G a nd
— 1 0
B D,a re minor thirds. To make major thirds out of them the
upper note must be sharped or the lower note fl a tted
I t is c lear that those thirds which a re der ived from D F, E G ,
ACa nd B D by sharping or fl a t ting both notes must be minor thirds:
I n order to make major thirds out of the preceding minor a x mustbe used for the upper note of the sharped ones , or a il l? for the lowernote of the fl a tted ones
Further poss ible major thirds we gain by double-sha rps a nd doublefl ats before both notes of the th re e ‘
ma jor thirds without chromaticS igns : F x Ax
,Cx E x , G x Bx
, Phil AlZlZ, ClZlZ E D? a nd GD? E QiZ. To
turn the ma j or thirds FA,C E , G B ,
and all those der ived fromthem
,into minor thirds the upper note h a s to be lowered or the
lower note h a s to be raised .
E XE RC ISE — Wr ite in notes al l major chords from F bll,a s
cending in fifths , up to G x ; a nd l ikewise all minor chords from D lZiZascending in fifths , up to E x .
F major chord ( indicated simply by f) .
D minor chord (indica ted simply by dm) .
in 2 minor .
§ 7 . Any [one ca n be l /ze meméer of three maj or and threeminor chords , for example the note A:
f 3 f finfi d l n 5
A is the 1 , 3 or 5 *
of a major chord , and the 1 , 3 or a of a minorchord .
E XE RC IS E — Write the six chords to which every note be
longs . S top where threefold chromatic signs would become nec
essary .
§ 8 . I NVE RS ION OF CHORD S — A chord is in its fundamen tal posi tion when the pr ime is in the bass . 1 1] close posit ionthe notes will always form the in tervals of prime , third a nd fifth .
1 1
W hen any note not th e fundamenta l is in the bass ,the chord is
said to be inver ted.
A chord is in its fi rsi inversion, when the third is in the bass .
I n close posi tion the notes form the interva ls of prime,third a nd
sixth , a nd for this reason this chord is often ca lled the e l iam’of th e
M in i a nd six th , or common ly enora’of fi l e six i/z.
Achord is in its second inver sion,when the fi fth is in the bass .
I n c lose posi tion the notes form the intervals of pr ime,fourth a nd
sixth , a nd for this reason this chord is commonly called the six -f ouro/zor a
’.
When a chord is in open position and the close posi tion is
wanted , then bring every note a s nea r to the bass a s poss ible ; tha tis
,an octave lower .
CHORD S AN D THE IR INVE RS ION S .
F U N DAM E N TAL PO S ITI ONClose posi tion . Open posi tion .
(Prime in th e bar s) .
5
8
1
F IRST I N V E RS I ON Close pos i t ion . Open posi tion .
(Th i rd in th e ba ss) .Ch or d of th e six t/z.
6
3
1
S E CON D I N V E RS I ON Close posi tion . Ope n pos1t ion .
(Fi fth in th e ba ss) .S ix -f our M ord.
I n compa ring a chord and its inversions , on e will fi nd the tonesforming the chords a lways the same , but making differen t impressions .
,
Th e chord in its fundamen tal position is the fron t V iew , so to
speak , a nd the inversions a re the s ide views of th e same chord .
Th e chord in its fundamental posi tion sounds restful , the inversionsrestless a nd full o f motion ,
therefore , the inversions a re found on lywithin a composition
,but never form its end .
E XE RC I S E — W rite the inve rs ions of al l maj or and minorchords .
3°
9 . KE Y — Tones combine to make a chord , a nd chords combine to make a key . Akey is a fami ly of chords . In it the principa l chord , the one that gives the key ~ its name , is ca lled Tonz
’
e (indica ted briefly by T) . From it the key branches out to the right(upwards) and to the left (downwa rds) . Th e nea rest rela ted chord
upwa rds is the one s i tuated a fifth above the Ton ic,and i t is ca l led
the Upp er -D omina n t or Over —D omina nt,or simply D omz
’
na ni (indica ted briefly by D ) . Th e nea rest rela ted chord downwards is theone s ituated a fi fth below the Ton ic
, a nd i t is ca l led the U nder -D om
ina nt or S noa’omina ni (indica ted briefly by S ) . Th e D ominant rep
resen ts the higher s ide of the key a nd the Subdomina n t the lowerside . There a re on ly three kinds of functions (oflice s) within akey
,namely ,
Ton ic ,D ominan t a nd Subdominan t . Al l the other
chords wil l have to be considered a s relatives (modifica t ions) of
them .
Akey is ca l led a maj or key when its ton ic , the pr incipa l chord ,
ma j or . Akey is a m inor key when its ton ic is a minor chord .
C-M AJOR KE Y .
g
Th e three chords,T
,D
, S , give the s ignature of the ma jor key .
A-M I N OR KE Y . (Pure M inor Key) .
mT
O‘
O
Th e three chords,niT
,m S ,
mD, give the s igna ture of
‘ theminor key .
E XE RCI S E — Write the schemes of all major and minor keys .
§ 1 0 . S CAL E S .
— A scale , generally speaking , is a series of
tones arranged according to their pitch , into half a nd whole tonesteps . M odern harmony considers scales a s broken chords , whosegaps a re filled up with tones (pa ssing tones) of the key .
Th e principal chords consti tuting C-ma j or key a re :
S T
g
Th e C-major scale is a broken C-ma j or chord (Arpeggio) withthe gaps fi lled up with the other notes of the key , for example
S 3 D 3
Th e principal chords o f Aminor key a re :
h is
A-minor scale is merely an A-minor arpeggio ,whose gaps a re
fi l led up with the other notes of the key , for example :
mS 3 mD 3
E XE RC I SE — Write all the major and minor scales , indicatingthe Ton ic tones with white notes and the passing tones with blacknotes .
g 1 1 . HARM ON I C M IN OR S CAL E . . MAJOR DOM INAN TIN M I N OR KE Y — M odern taste is n ot satisfied with the old pureminor scale , but demands a leading tone (half- step) to the octave inascending the scale . I n A-minor
,therefore , a G is wanted :
m a D 3
This is known a s the Harmon ic M inor S cale . I t introduces anote not in the signature of the key . Th e signature of a minor keyis produced by the mT, m8 and mD . Instead of a minor D ominantwe get a major D ominan t (ma D ) , which brightens up the higher (D )s ide of the minor key . So bes ides the inD we can use also a maD
in the minor key . Th e major D ominant br ings a major chord , thatis a foreign chord , into the minor key , sufficiently indicated by thefact that the g is not in the signature of A-minor . Th e mixedmodes (keys) a re a product of modern t imes , they we re unknown to
an tiquity a nd the middle ages .
maD
f a g b
E XE RC IS E — Write the schemes of al l minor keys,including
in them the ma D,a nd write also all the Harmon ic M inor S cales .
12 . M E L OD I C M I N OR SCAL E S — Because in theHa rmonie
M inor S ca l e the progression from the sixth to the seventh degree isnnmel oa
’io (diflicul t to sing on accoun t of the augmen ted second , 1%
steps) the s ixth degree is raised , and in this manner the M e lodic
M inor S ca l e is produced
Ascending . D e scending .
Th e descending M elodic M inor scale is the pure minor sca legiven in § 1 0 ,
i t is therefore sti ll in use .
E XE RC I S E — W rite a l l M elodic M inor scales .
g 13 . M I N OR S U BDOM INANT IN MAJOR KE Y — Th em ajor key is br ight a nd cheerful . Th e minor key is dark a nd
sorrowful . Th e minor key is brightened by intensi fy ing (brightening ) its D ominan t side by us ing a major D ominan t chord instead of
a minor . Just so the ma j or key is darkened (made sombre) by intensifying (darke n ing) its S ubdominan t side by using a minor S ubdominan t chord instead of
'
a major . Remember that major a nd
minor a re oppos ites , not on ly in the construction of chords but alsoin the construction o f keys , consequen tly if we want to fi nd thecorresponding chord in the major key , we must look for it on thereverse side of that of the minor key ,
and vice versa .
S
f ah c
E XE RCI S E — Wr ite the schemes of a l l ma jor keys,inc luding
in them the mS .
14 . FOU R - PART WRITIN G — Having become fami liarwith a l l the maj or and minor keys and with t h e maj or and minorchords belonging to them , the next step is to learn h ow to connectthese chords with one another . F or this purpose writing for fourparts (voices) is considered the best form of practice .
Th e voices a re called S opra no ,A/z‘o
,Tenor a nd B a ss . Th e
S opr a no is the upper part , i t is the princ ipal melody . Th e B a ss is
next to i t in importance , i t is the lowest of the four parts . Th evo ice next below the soprano is the Al to ,
a nd the one next abovethe bass is called the Tenor .
Th e soprano should not go higher thanE
and the bass
should not go bel
S ince the chords have on ly three di fferent tones , one of themmust be doubl ed when there a re four parts .
Th e lowest note (the fundamenta l , of a chord is the best fordoubling . I t may even be trebled . Th e next be s t note to double isthe highest note (the fi fth
,of a chord . Th e third should , gen
e ra l ly ,not be doubled . This “
doubling may occur either in thesame tone region or in another octave .
Th e highest note (5 ) of a chord may be omitted , the third isnever omitted .
may be omitted,but also doubled .
must not be omitted,a nd generally not be doubled .
good ba ss tone (fundamental) , best for doubling .
When these notes a re read in the Bass clef,we get a major
chord ,when read in the Treble clef we get a minor chord .
Remember the fol lowing scheme in regard to the distances ofthe voices from each other
SOPRAN O
not more than an octave .
AL TO
less than an octave .
TE N OR
may sometimes be more than an octave .
Th e best note for the bass is the pr ime (fundamental) of a chord ,the next best note is the third . At the close of a period (musicalsentence) i t is str ictly the rule to have the prime in the bass. Tobegin and close with the fundamental tone (1) in the soprano givesgreat dec is ion a nd repose to that part .
Th e exercises a re to be written in the simplest way with thetwo clefs , treble a nd bass . On the. treble sta ff wr ite the Sopranopart with the note-stems turned upwards and the Alto with thestems turned downwards . On the bass staff wr ite the Tenor withstems upwards and the Bass with stems downwards .
We a re now able to distr ibute the tones of a chord among thefour voices in such a manner , that the
“
sound e fl ect will be a goodone ,
for example , the C-ma jor chord
Fundam en tal tone in th e Ba ss a nd D oubl ed .
E x . 1 .
(Al l good .
a ) Th ird in th e Ba ss . 6 ) Fifth in th e Ba ss.
(Al l good . )
I n example 2 a t a a re cases where the fifth is doubled, to which
there is no obj ection . At 6 ) a l l the fi fths a re doubled,a ccording to
the tempora ry rule— when the fi fth is in the ba s s,i t must be doubled .
Th e following positions of the chord a re faulty
E x . 3 .
I n the fo l lowing example the fifth of the chord is omitteda ) 0 )
(Good .
D oubling of the third,which is to be avoided altogether for the
presen t , sounds very bad when the fifth is omitted .
E XE RCI S E — Wr ite out‘
a number o f maj or a nd m inor chord safter the E xamples 1— 4 ,
making them “ good ”or
“ bad .
”
§ 15 . M OVE M E NT OF PARTS .
-Parts (or voices ) mayremain stationary , or move up or down . When two parts move upor down at the same time they a re said to move in simil a r motion .
When they go in the same direction , keeping the same intervala pa i t , they a re said to move in p a r a l l e l motion . When one partgoes up while the other goes down they a re said to go in con tra rymotion . .W hen one part remains stationa ry while the other goes upor down the motion is obl ique .
16 . RU L E S F ORTHE M OVE M E NT OF THE PARTS .
Th e principal law of part-writing is tha t ea c/z pa r t s/zonld g o its own
na tura l p a t/z. N o two parts must move .in paral lel octaves or fifths ,because these b l end into one tone so per fectly. M oving in oc ~
taves would mean on ly a repetit ion (strengthen ing) of another part ,and instead of four pa rts there would on ly be three . I n conse
quence of the similar sound of octave-tones , i t is even not a l lowable
— 18
obj ect ionable , because the rule prohibit ing consecutive octaves and
fifths concerns only progressions to tones of differen t names :
(Good) .
1 7 . CLASS I FICATION OF CHORD CONN E CTION S .
In order to become readily acquainted with the var ious difli cul tiesof the different chord connections , and l earn the inheren t force andmean ing of each
,i t will prove a good plan to classi fy the chord
connections by naming them according to the intervals the fundamen tal notes produce and noting the mode of the chords . Th e
pr incipal chords of the major key a re T,D
, S a nd mS . We havethen six possi ble chord connections, each having its own individualeffect a nd peculiari ties , a s the pupi l wil l learn .
F if t/z step , ma jor to major ,F oa r t/z step
,ma j or to major
,
W/zol e tone step ,major to ma jor ,
F onr t/z step ,major to minor ,
W /zol e tone step,minor to major ,
Cl ia ng e of modeQP‘
P
S‘O
N
H
Th e principal chords of the minor key mT,mS
,inD
ma D,a nd we have the same number of chord connections a s in the
maj or key .
ma D
Here we fi nd the same progress ions a s in the major key,but
we have to figure them downwards (the opposite way ) , because theminor key is always the opposi te of the major key , and vice versa .
F if t/i step , minor to minor ,F onr t/z step ,
minor to minor ,Wbol e tone step , minor to minor ,F onr tlz step ,
minor to maj or ,W/iol e tone step , major to minor ,C/za ng e of mode (of c/zords) ,Q
P‘
F‘
PO
N
E“
18 . F I F TH STE P . (M ajor to major,T— D ; minor to
minor , mT— mS ) . Th e Fifth step is , in the major key , a step to thenearest related chord on the upper side ; in minor , i t is a step to thenearest rela ted chord on the lower side . In major it means a rising(soaring upwards) , in minor a fal l ing (s inking downwards) ; thus ,in the first ca se a strengthen ing of the major character
,in the. latter
a strengthen ing of the minor character .
Th e fo llowing a re good progressions from the Ton ic to theD ominan t :
E x . 8 .
E x . 9 .
Th e fol lowing progressions have faults:
E X . 1 0 .
8 8 1 5 8
RU L E — N ever double the third of the major D or the third of
the minor 8 , because it would be equiva lent to doubling the leadingtone (half- tone progressions) a nd subsequen tly produce consecutive(paralle1)
'
octaves . Th e doubling of the third is allowed in con
tra ry motion in the T, mT, S and mD .
E XE RCI S E — Imitation of the progressions in E xamples 8and 9 ,
starting with the other forms of the C-major chord given inE xampl es 1 a nd 2 ; observe all the rules .
Th e conditions for zo/ z'
tz'
ng in minor a re the same a s in ma jor .
Th e mS h a s one note (in A-minor key , a) in common c w ith the mT,
besides the possibi lity c f making a leading tone step (e — f) .
Th e fol lowing a re good progressions from mT to mS:
E x . 1 1 .
E XE RC IS E — Imitation of the progressions in E xamples 1 11 3 , start ing with a number of other minor chords .
19 . THE W ORKI N G OU T O F E XE RCI S E S — W e willnow work out an exercise of eight measures , which gives occasionfor further remarks . Take the exercise:
1 3
n D T D T T fi T D T . .
5 5
Th e signs T,D ha ve been explained (s a jor ton ic ,
D z ove r
dominant) . Th e numbers 1 , 3 ,5
, wri tten below or above , mean thatthe particular -note (pr ime , third , fifth ) of the chord is to be in thelowest or highest part . Th e two dots mean repetition of the
same chord (the change of posi tion is always al lowable a nd generally recommended) . Th e perpendicular strokes a re the bars .
means the time signature . N o particular key is asked for , yet a l lthe exercises given in this kind of notation a re intended to beworked out in al l keys ,
or at least in a great number of them . I f
we choose for the beginn ing to have th e prime‘
of the chord doubledin the soprano ,
in the key of B? maj or ,our trial wi l l perhaps turn
out thus3 1 3 3 1
T D T D I‘
D T D T D T D g‘
g'
r
E x . 14 .
N otice that the middl e pa r ts (alto and tenor) have here the dutyof keeping the outer pa r ts (soprano and bass) together , that is , theirrole is to sustain notes as much as possible . I n the seventh mea sure we have the dominan t chord with two notes foreign to it ,namely ,
the fourth and si x th,which tend downwards to the th ird
and fifth of the chord , that is the D with two suspensions ; i t iscalled domina nt six -f our chord .
22
Suspensions shall be treated of later on,but this cho‘
rd formation is so common that we use i t even in the simplest exercises .
Th e suspensions a re dissonant tones ,which a re not allowed to be
doubled , so i t becomes necessary to double the fundamen tal .Th e student is warned against doubling the fifth in resolving
the chord of six -four (D 2) in to the plain dominant chord (D
(Good ) .
E XE RCI SE S .
M AJOR.
T0 be worked out in a l l fl /aj or Keys.
D T D T D g
(3) T D T D TD T D 2 30 5 5
3 1 5 3
T D T D T D D D 23,8
b’
r e tc .
e tc
3 1 5 3 1
g T D T T D T T T D T1
r__m'
r
23
N . B .
— The note after the last l etter of each exercise indica testhe length of the c losing chord . N otes under the letters show therhythm to be a dopted .
Th e pupil should a ccustom himsel f to t ie sustained notes and towrite them a s long notes within the same measure . I t is good p ra ctice
,and the work will l ook neater .
M I N OR.
To be worked out in a l t zl f inor Key s .
mT mS mT mS mT mS mT ( 9 )
3
' mT
mT mS mT mS n mS mT3
3
(10 )it mS mT mT mS mT
3
3 1
mT mS mT mS mT mS mT
l'
13 5 1 5 3 1
(12)72
m8 m'
T m.
S mT mS mT ‘1
u I
3 5 1
m8 mT mS0 0
I
§ 2 0 . THE W ORK IN G OU T OF A CANTU S P IRM U SBesides exercises in which the harmon ies a re indicated by theirtonal functions on ly , we will have throughout the course a secondse t of exercises consisting of given melodies for certain voices . Of
ten a given melody (voice) makes impossible the nea rest and bestconnections of chords . I n this second se t of exercises the h armo
n ies a re not'
ca l l ed for by T,D
, S , e tc ., but the fundamentals
(primes ) of the chords a re indicated by small letters (c::c-majorchord , am z a -minor chord) . Th e pupil should always add thesigns of the tonal functions when work ing out th e exercises .
Th e following example i l lustrates h ow to proceed :
(S oprano )
E x . 15 .
3(12 i? g
N . B .
— Th e note i tsel f indicates the prime of a maj or chordwhere there a re figures without the chord letter
,or where i t is
without or where every sign is wanting (m : minor) . Th e fi gures indicate the tone to be put in the bass , but if the bass voice isthe given melody , then that par t icular tone should be put in th e so
prano When a figure is over a letter i t shows that that member o f
the chord should be in the soprano part ; when a figure is under aletter it means that tha t note of the chord should be in the bass .
Th e ea ntns fi rmns is wri tten in its proper place on the staff ;soprano a nd a lto on the upper staff , with note -stems of the formerupwards , of the lat ter downwards . Tenor a nd bass on the lowerstaff , note -stems of tenor a re written upwards . of bass downwards .
Th e chord s igns are written above the upper staff when thesoprano is given ; they a re written between the two staves when thealto or tenor is given ; they a re wr i tten below the lower staff whenthe bass is given . Th e given voice should always be indicated byc . f. (ca ntusfi rmzzs) at the beginn ing of the staff . This is a very mecessary precaution in order to avoid making an error by altering thegiven part when making corrections .
Th e above example , when worked out a nd its tona l functionsindicated
,may turn out similar to th is :
3 g (12 3 8
E x . 1 6 .
T D T D T D T D T . . D T D gg T
26
(18)
ah elz ah elz a lz e ll
(19) Bass given .
M IN OR.
Soprano given .
m m em am em m em a m em m em m m
m m dm g m dm g m dm g m
(23) Alto given .
6m m 6172 em om em bm em em m em om
g m em g m a n m cm
(25) Tenor given .
f fim m f fim m
f m 512m f m . . f m 512m f m
(27) Bass given .
m gfim cfim m efim m
g ?” 1” g fl’
l 771 772
21 . F OURTH STE P . (From major to major chord ,
T— S ; from minor to minor chord , niT— mD ) .Outwardly the connection T —S is the same as the return ing
Fifth step D — T, and the chord connection mT— mD coinc ides inexterior a s regards the melodious connection with the return ing Fifthstep mS — mT. Th e mean ing is , however a very differen t one , be
cause the subdominant s ide is the oppos i te of the dominant side .
Going to S means to go below the T into the lower tone -region ;going to the mD means to go above the mT into the higher toneregion .
Th e third of the S , and the third of the mD ,can be doubled if
they a re not arrived at by s imilar motion .
E x . 1 8 .
E XE RCISE S .
M AJOR .
(29 ) T S T S T D T.
(an T S T S T S T3 5 3 1
T S T T ( 93 5
(31 )-2 T D T D
’
I‘
S T S TS T D i g T“
3
e tc
T D T D T s T D3
f
e tc
M I N OR.
mT niD9 1
mT mS mT3 1
m S mT mD mT mS1 . 5 3 1
(35 )73 mS mT m
'TmS m5
T1
mT mS mg
T mS mT (f )3 1 3
3 5 3 1 3 5 3 5 1
(36 )"2 mT mS mT mD mT mS mT
5
n'
-_i' I.
e tc
M AJOR .
(37) S oprano given .
(38) Al to given .
(89> Tenor given .
d iz g iz ch g ? dbt’
2 g tz d lz g lz
(40 ) Bass given .
M IN OR.
(41 ) Soprano given .
( 772 777 ( 777 772
,
C777 £7 777 C7”
(42) Alto given .
771 m dz); g m g m dm m a n g m.
(43) Tenor given A
777 777 6 771 777
N . B .
1. ,
1
8 777 772 6 777 am €7IZ
3
(44) Bass given .
gfi tn d #7n m cfinz
777 771
N . B .— In the fi rst measure of E xercise 43 a t ie h a s been used
to indicate that the ba ss note e is to be held out .
member of the second chord . This method of marking wil l befound very useful in indicating and e x p l a imng in a simple way themost complicated formations of the so-ca lled P eda l -point (organpo int) .
6 777 (1 777 8 777
44m gfi
Th e e is also a
3 0
§ 22 . W HOL E -TON E STE P . (M ajor tomaj or chord , s — D ;minor to minor
,mD — mS ): Because these two chords have no tone
in common ,they br ing the r isk of consecutive fifths a nd octaves .
C-m a jor . A-m inor .
E x . 1 9 .
mD mS .
Th e very simple way of avoiding consecutive fifths and octa vesis to use con trary motion ,
but then all the parts can not move byhalf or whole-tone steps . E mploy the lea ding tone (half-tone) stepwherever possible ; i t wi ll help to lea d the other parts in to theirproper pa ths .
Another difficulty to be met in this chord connection is the a ugmentedf onr t/z , or trz
'
tone (three whole tones) .This skip occurs in going from 8 1 , to ED 3
, or mS 3 to mD 5. I f wri tten a s a dz
'
mz’
n
z’
s/zedfi ftn i t is good . Augmented in tervals Bad Gooda re diffi cult to sing when the harmon ies change
,and for th is reason
a re to be avoided . When a chord possessing these notes is sus
ta ined this progression is allowed , but a s we use no such chords forthe presen t , augmented intervals a re forbidden without any excep tion .
E X AM P L E S I N M AJOR .
Too much sk i pp ing.
25 26
At N os . 6— 1 0 in the preceding example the bass part skips tothe fifth of the dominant , but l n this chord connection i t must oftenbe permitted for wan t of better ways . Besides , the D zn a ny posttzon after the S will define (indicate) the key accurately Th e s ix
four chord (D 4 ) will be found the natura l connecting link betweenthe two dominants .
E X AM P L E S I N M I N OR .
E x . 23 .
32 _
I n order to accustom the studen t to reading score the next exe rcises ought to be worked out on f our stoves ; every part is to bewritten on a separa te sta ff . Al l notes a bove the middle line shouldhave their stems turned downwards
,all lying below turned
wa rds ; for notes on the middle line either way is good .
E XE RCISE S .
M AJOR .
(45 ) T D T SD T.. D T S D T3 1 3
(l e g T D S T S D g gTS T D T S D gg T
c-
r
(A7)-2 T D T S T D
‘
T S D 53e tc
T S D T D T D S D g g };I
3 0 3 3 1
(48 ) T S D T S D T D T D T;
5 1 3
(50 )-3—
; TS p T S D T S D T S D g g T
M IN OR.
5 1 3 3 3
(5 1 ) g mD mS mT mD mS mTmD mg
S mTmg
D m53 3
5 5 5
mTmD md
S mTml
D 111
5
8 mTmD mS mTmDm8 mT1 1 3 1
— 34
M AJOR.
(57) Soprano given .
oh ell biz a ? eh arz biz
45 f f) f i?
(59) Al to given .
612 612 b 812 0 12 612 3 612 n
e b e a b e b 3 a
(61 ) Tenor giggin .
net! 612 d iz g iz dh éflz d tz
(63) Ba ss g iven .
3 a g a
M IN OR.
(65) Soprano given .
m m om m tam f fim
cfim f fim m f fim efim om f fim
m m m m cm g m m
f m g m m m
(67) Alto given .
m m cm g m dm m dm cm
(69) Tenor given .
m g m em g m dm cm g in
m cm dm m m m g m
1 13m gfim dfim gfi tn m d fim rn g‘
nm d fim gfim d fim gfi
g):
(71 ) Ba ss given .
771 (7772 (2771 771 777 777 (f77l (1 772
777 777 777
m 6 712 m m m
m em 17m em m m m m
F OURTH STE P . (M ajor to minor,T— mS ; minor
to ma jor , mT There a re no particular diffi culties to bemet in this chord connection ; instead of one leading tone (half-tone)step there a re two possible .
E x :24 .
T m 8 T mS T mS mT m aD mT maD niT maD
I n progressing from the 3 of one to the 3 of the other chordavoid th e a ugmented fifth I ts inversion a s diminished fourth
is good , when a turn ing half-step follows .
E x . 25 .
mS T mS maD mTmaD
When the turn ing half-step does not follow then the dimin ishedinterval is not good , consequently the 4 > must not be used in closing an exercise (or piece) .
(Bad .
m aD
Th e six -four chord of the ma jor dominant of the minor keymust have a “ minor ”
sixth the tone corresponding to thethird of the mT. I t is sh own in the figuring by a attached to the6
, which means that the sixth h a s to be lowered a hal f-tone , D 2?
e2> 2" e a c ,
e? e a c# . Th e D ? can a ct l ike a mT and have th e5
same changed resolutions a s the D 2 in E x . 17 on page 25 .
§ 24 . W HO L E -TON E STE P . (minor to major , mS — D L
maj or to minor , maD -mS ) . I n connecting these chords we fi ne.two half- tone steps
, otherwise the same diffi culties (consecutive oc~
taves and fifths) a s in the whole - tone step where both chords a re 0 3
the same mode
— 38
m 8 D maD mS
But besides the tr itone step we fi nd another obstacle , namely ,
an augmented second wr itten a s a dimin ished seven th it
is good .
E x . 27 .
D 18 D m aD m S
25 . CHAN G E OF M OD E (OF CHORD S ) . (S — m-S ,
mD — m aD ) . I n this connect ion the chords have two tones in com
mon ,the other tones a re a chromatic half- tone step apart . I t is ob
ligatory that the chromatically altered tones a re kept in the samepart
, otherwise the e a r is not able to perceive the change of b armony , and made to believe that the same harmony is repeated , butthe chromatic tone on ly out of tune . This disagreeable effect isknown under the name off a l se r e l a tion (cross-r e l a tion) .
Good.
Th e actual effect of bad relation is felt on ly in this change ofmode of chords , and not in other chord connections .
E XE RCISE S .
MAJOR.
3 8 5
S ms T mS D T1 5 3
5 3
D T mS D T1 1
1
T mS T 1113 T1 3
(75 ) E :T D T S mS T m3
S DT S mS Dgg T3
re tc .
M I N OR.
3 5
mT inD mT mS mT 1nD m aD m S in D m S9 o o o 9 a 6 9 3
l I
D3, 2> b mT mS mT D mT mS mT3
D ? mS D 1nT3
5 3
mT mS D inD maD mS D3 1
m5
(78 ) E mS mD m aD mT mD mT mS mT3
O
I I I em
3 3 5
maD 1n S inT
l'
1' 9
— 4 0
26 . M OD UL ATI ON is a change of key . I t occurs whenever a new chord is made the central point of the tona l system . Webreak the bounds of the key ,
when we change the functions o f h ar
mon ies , that“
is , when we treat\a ny one of them a s having a new
meaning . I n the fol low ing exercises a modulation (change of
meaning of one function to another) takes place wherever the signof equality (z ) is .
Th e au thor’s Revo lving Chart of Harmony , N o . 1 ,will be a
gre a t h e lp to the student in l earning a nd the teacher in i llustratingHarmony ,
especial ly M odulation . I t shows the different positions(funct ions) a ny chord can have in the various keys , because bymerely turn ing the disc to a ny key desired the chords belonging to
i t can be seen at a glance , a nd the changes of functions be observed .
E XE RCISE S . (M odu l a ting ) .
:T mS m aS l D T I D fi g T D T
S m S I i gITi D m S | T S mS T D mS
m a S D T S mS D E l
(fl/oda l cziz'
on {0 fil e key of fi l e D a na’ba rk) .
t 3
(sow- o ri
fi s n T D T z D S D Z S D
3 3
S D T D T S D T'
m S D i g1
o
( l l/[adu l a f ion [a fil e lz
'
f j' of {118 S a nd ba d ) .
(8 1 ) E 1nT 111 8 D mD m S 1nT mD mS
(9e tc .
1nT D 2>§ inT mS m aD mT 1nD mS mT
3
1115 D li> § 1nT
(M odu l a tion l o 1118 key of f/15 7115 a nd ba ck) .
(86)
ah ah d lz a h a ll d iz a il
(87) Tenor given .
f ilm m f ilm W f t)? 3
(89) Bass given .
a ll db a lz
m (l g hm
m a dm m m a a’m cm dg
>§ m m m g m a
§ 27 . PRACTI CAL W ORK ON THE P IAN O .— Ca
dence s a re no musical pie‘ces , nevertheless they a re the types o f
harmon ic motion , and consequen tly very important . Th e studen tought to play all maj or and minor cadences on the piano accordingto the following pattern :
1 37
3
T s ng g I T lT n g
I n the minor key play :1 1 3 3 5 5
mT mS D e g mT imT mS mT mT mS D Z> § mTiI t would be an excellent practice now , to review al l the e x e r
c ises by working out a nd playing them on the piano a i sz’
g /zt .
I t ought to be tried , because the pupil‘
s harmon ic knowledge andability should be at h is fi nge r
’
s ends .
CHAPTER III.
T H E P R I N C I P A L D I S C O R D S .
§ 28 . THE PRIN C I PAL D I SCORD S . (D 7, S
G,mS G ,
mD 7 ) .Before we will acquaint the student with other concords of the key
,
we wil l explain the almost indispensable principal discords of thekey . They a re the dominants with additional tones , which help tomark them very pointedly a s S or D . These added tones a re tonesborrowed from the other dominan t . Th e M ajor Over -dominan t addsthe prime of the subdominant (in C-major , g b d f ; in A-minor ,e g# b d ) . I t is called domina nt seven t/z e/zor a’ (D 7
)
T
f [a c e j g b d d [f a c j e g# b
S m aD
Th e M a jor S ubdominan t adds the fifth of the dominan t (in Cma jor , f a c l d) .
f a c [e ,g b ] d
S D
I t is cal led subdomina nt six t/z c/zor a’
(SS) .
Th e M inor S ubdominan t adds the fi fth of the minoroverdominan t (in A-minor d f a b ; in C-ma jor f a? c d) .
mT T
d f a [c e g ] b f ab c [e g b ] d
mD D
I t is called minor subdomina nt six t/z c/zor a’
(mSG) .
Th e M inor Over-dominan t adds the pr ime of the minor sub
dominan t (in A-minor , e g b d)
d [f a c ] e g b
mD
I t is called minor domina nt sevent/z ckor a’ (mD 7) .
Adding a tone of one dominant to the dominan t ly ing on theother side circumscribes the key in the same way a s does the suc
cession of two dominan ts — it po in ts to their ton ic .
CHORD S OF TH E D 7 AN D S 6 AN D THE I R I N V E RS I ON S .
Inversions.
Fundamental Inversions.M p0 81t10 n. M2 ) 3 ) 4 ) 5 ) 6 ) 7 ) 8 )
Th e old thorough -ba ss figur ing would coun t the intervals of allchord forma tions from the lowest tone upwards and cal l N o . 1 sev
e nth chord N o . 2 chord of fi ve -six (g) , N o . 3 chord of three- fourN o . 4 chord of the second N o . 5 chord of the fi ve -six (g) ,
N o . 6 chord of the three four N o . 7 chord of the second and
N o . 8 chord of the seventh We do not need n or use al l theseterms .
E XE RC I SE — W ri te the principal discords (D 7, S
6,mS 6 and
mD 7) of a l l major and minor keys
M 9 . THE RE SOL U TION S OF THE DOM INANT SE V
E NTE CHORD .
c ) d ) [bad] e )
E x . 8 0 .
Th e seventh always moves by step of a second . I t genera l lymoves downwards a nd makes the lea ding tone (half) step , E x . 8 0
,
a and b . Tones forming the interval of a second strive away fromeach other [b]. M erging the one tone into the other [d] is of goodeff ect on ly in case i t is produced by instrumen ts (and voices withinstruments) of strongly contrasting tone-colors . Th e pupil shouldavoid th is reso lution . Th e upward motion of the seventh [c] is a l
lowed on ly when the downward motion would cause doubling of -th e
third . Where the same harmony is repeated , the seven th maychange p l aces with some other tone ; in E x . 8 0
, e , the rule for progre ssion is merely transferred to the bass . At b a nd g the fi fth in thechord of the seventh h as been omitted . We know that the fifth of
any chord can be omitted ; here i t wa s done to have the ton ic chordafter i t complete [with fi fth
,g]. I f we h ave the D 7
complete [f]then the subsequen t ton ic will be incomplete [without fifth]. I f weth ink the g 5 given for the tenor , and the 3 called for a s ba ss notein T
, then a downward motion of the seventh would create a faulty
— 46
third -doubling , because doubling both prime and third in four-partwri ting is cons idered very ha rsh . Third -doubling is good on lywhen the chord is complete ; i t is bet ter to treble the fundamentalnote .
I t is impossible to have the seventh a s bass note for the secondlast chord ,
because the prime of the tonic is required for the bass,
whereas the seventh h a s to make the half- tone step to the third,
E x . 31, c . When the D '7 is not
'
fol lowed by the ton ic , but by the S ,
the seven th need not progress by step o f second,although this will
usually happen afterwards , E x . 31,a , b .
( U r— “
fl 5 )
E x . 31 .
(Good) . (W rong )
Th e mD 7 progresses l ike the maD 7, E x . a . But when the
seventh becomes part of the m8 ,i t
, of course , need not move , E x .
32,b .
mT mD 7 mS
Th e resolution of the mD 7 may be disguised by means of intermediate tones .
E x . 33 . A
m0 7 m8 mT M W1118 mT mD7 m8 m
'
l‘1110 7 m8 mI
'mi) 7 1118 M mD7 m8 m1
30 . THE RE SOL U TION S OF THE SU BDOM I NANTS IXTH CHORD .
— In this chord the sixth , when sounded togetherwith the fi fth
,must str ive towards th e seventh , or force the fifth to
the fourth ,because tones of a second strive away from each other
(no matter whether in the same octave position or not) .
T 8 6 D
When in the C-m a jor cadence the 6 (d ) of the S 6 chord is in thebass , and the D follows , the d can be sustained [E x . 34
, a], althoughit is not necessary . Th e d can proceed first to g of the D and thento c of the T [E x . 34 ,
b], a nd even the D 2 may be also inserted[E x . 34 , c].
E x . 34 .
I n the last two cases [b c] the S S , with the sixth in the bass ,a cts l ike a D 7
of the D , with the prime in the bass . Why thechords of th e sixth readily take j ust the dissonant tone for the basswil l be quite c lear to us later on
,when we will have to consider
domina nts of M e domina n l s and the possibi l ities of chromatic altera tions of chords . As soon a s the 1 is raised the 8 6 becomes D 7
of
t h e D , likewise the mS 6 as soon a s the 1 and 3 a re raised ; but thes ixth h as become the prime (fundamental ) .
Th e use of added (dissonan t) tones with the dominant chords‘
assens the danger of consecutive fifths and octaves cons iderably ,a s
it gives to chords which otherwise have no tone in common , two
such tones:
E x . 35 .
8 6 D 7 D 7 m8 6-
ms6 maD 7 mD 7 mS 6
— 48
As regards the figuring of the exercises . we must explain thatthe 6 or 7 beside the chord -s ign (T,
D, e tc or chord - letter c ,
g, e tc . ,
or simply asks for the chord of the s ixth or seventh . N umbersabove or be low the signs tel l what particular tone is to go in thebig /zest or lowest part .
Th e minor subdominant sixth -chord (ms G) is subj ect to thesame treatmen t a s the maj or sud minant sixth-chord (S 6 ) .
E x . 36 .
1,
l 1
“
1
m8 6 T mS 6 D m S 6 T(D2)mG
S D T S D T S D 2 g T5 6 6
g 31 . FIGU RATION .
— W e will take another step forwardin the next exerc ises by practicing the S implest forms of fi g ur a l z
’
on
or ornamentation , that is , we let one part move in shorter notes(half the value) than the others . We will make use of on ly the following three varieties:
(A) P a ssing Zones , which fi l l in the gaps between a n interval ofa third ; for example . if the unfi gured pa rt had e and g in succession ,
then f (or fit) would be the pa ssing tone .
(B) Aux il ia ry tones. Th e insertion of a neighbor- tone (a whol eor half-step) above or below where the unfi gured part uses the sametone twice in succession (c b c ,
c blZ c,c d c
,c d lz c) .
(C) C/zord tones . I n cases where neither of the above can
be applied,a second note of the chord may be inserted . F or
example,in the figuration of the C-major chord g might be used
between e and cl
. Occasional ly a leap to the octave might be ma de ,or even the same note repeated .
Figuration increases the danger of faulty parallel progressions ,
because the inserted tone may produce consecutives which were notin the unfi gured wri ting . Avoid in figuration of the ba ss pa rtskipping from the fifth of one chord to the fifth of another .
I n the following i llustration for figuration exercises we markth e inserted tones:p z p a ssing tone , au z a u x il ia ry tone , ch :
chord tone , r : repeated chord tone . Th e bass is the part fi gura ted.
32 . M OD UL ATI ON (CON TI N U E D ) . I n the following exercises a few more ways of modulation have been employed , namely ,the change of mean ing of a chord by the addi t ion of the dissonan ttone essential to its new meaning . I n N os . 91 and 92 the tonicchanges to subdominan t on accoun t of the sixth cha ra cteristic forthe subdominant being added . I n N o . 93 the T is m ade a D 7 bythe addition of the 7 . I n N o . 95 the mT is stamped a s a 111 8 , be
cause the 6 is added to it ._ Another way of modula ting is to eb rom a tica l ly al ter the th ird of the T. Th e ra ising of the th ird of aminor tonic gives the resulting ma j or chord the mean ing of a n overdominan t (N o . the lowering of the third of a major ton ic givesthe resulting minor chord the mean ing of a subdominant (N o .
W here i t happens that the part for fi gura tiOn h a s half a nd qua rter notes mixed
,and the figura tion is to be in eighth notes , more
than one intermediate note will have to be introduced where therea re ha lf notes. without , however ,
going beyond the resources men
tioned . Th e fol lowing will suffi ciently explain h ow to proceed
Pa rt for figura tion:
Fig ured pa rt:
Th e auxiliary tones on both s ides will have to be used,and
skips in to octaves will have to be made .
Work the exercises with figuration for soprano , alto , tenor andbass parts ,
and then wi th divided figuration .
E XE RCI SE S . (F or fi gu ra tion ) .
Al l in e ig /zl /z nol es
6
(9 i ) ji- T S
G
ID 3“
T mS T0
2 S6I37 T ms D 22
1 I
7 — D 7 T S6 D 7 T
D 7
{ 11186 T D T z D S T S 6
'
S6 D T D T S mS 6 D Z
3
mS T — D 7 T S D T'
mS T D
T mS6 D 2 § T
mT inD
mT D ? 2 mS6 mT
1°
i
mS6 m aD 7 mT
mT mD mS6 m aDT
mT maD i nT — mD 7 mS D ? S
mTmS D 5? {mT (f )
(96 ) E mT‘
mS m aD mT mS6 D2,> g
mT—
3< m aD mT maD mT mSG D2
>§ ImTU
— 52
E XE RCISE S . (N ot for fi gura tion ) .
(T/ze tona l f nncl ions a r e l o be a dded in working out ) .
(97) Soprano given .
g6 d g d a d a
gd
g m cm d em g m
6 6 >g m d cm d 4
(99) Alto given .
6 12 a il d bfi e lz a lz
biz}; g d lz d lZm 6 2
1 17
em am m am 6 b m 7 d in a m e‘ am 6 b ‘
em b enz a nz 51>
53
(1 0 1 ) Tenor given .
biz m‘
a lzin 3 et abm m ebma
(1 0 3) Bass given .
d 6‘
7
I l l ma m blZma m m
ma in m m m elzm a lz/n
33 . D I M IN I SHE D TRIAD . In the simple concordof three tones we might occasionally omit one note
,the fi fth . I t is
sti ll more easi ly done when a fourth (dissonan t ) tone is added to
the chord . On page 45 (E x . 30,b a nd g) we omitted the fi fth in the
dominant seventh chord in order to have the fol lowing ton ic chordcomplete .
W e can also omit the fifth in the ms 6 chord . Th e three remaining tones , d f b , of this chord , when put in this order , b d f, form
54
the so-called dimin ished tri ad , because from b to f is a diminishedfifth . Th e only tone to double is always t h e pr ime becausethe dissonant ton e (6) may not be doubled . W e indicate this c hordby striking through (cancell ing) th e fi fth b d f z dm s
‘3 (mS5) .
6
I f we omit the prime in D 7 (g b d f ) we fi nd a nother6
diminish ed triad . Th e note that is perm itted to be doubled is the fifth ;the dissonan t tone (7) may not be doubled . We express the omission of the prime by striking through the l etter ; g
' 7z b d f
E x . 39.
P A R T I I .
CHAPTER lv.
RE L ATIV E AN D CORRE L ATIV E CHORD S .
(A. R E L ATI VE S AN D CORRE L ATI VE S O F TH E T, S , D , m T, m D AN D m S .)
34 . CHORD GROU PS . Th e principal chords of a key a re
related to each other by the Fifth . There exists another relationship of chords , a nd that is the relationship by the Third . F or
example,around C-major chord group themselves A-minor a nd
E —minor chords
We call A-minor chord - the relative chord of C-major . E -minoris also a relative chord of C-major
,but to distinguish i t from the
other relative chord (A-minor ) , we will call i t the cor re l a tive ekard
of C-major . When the principal chord is major then the relativeand correlative chords a re always minor . Th e relative chord is situa ted a minor third below the prime of the principal (major ) chord ,
and con tains the prime a nd third of the latter .
Th e correlative chord is si tuated a major third above the primeof the principal (major ) chord , and a fifth above the relative chord .
Th e correlative con ta ins the third and fifth of the principal chord .
b Correlativechord .
Th e Dominan t and Subdominant chords a re a whole tone step(double fifth step f— c—
g) apart , and move around the Ton ic a s
their cen tral point . Th e relative and correlative chords imitatethis relationship within a smaller circle
,they a re on ly a fi fth step
apart move around their principal chord ,and can be used a s sub
stitutes for i t .
E XE RCISE .
- Find and wri te the relative and correlativechords of all major chords .
Around A-minor chord group themselves C-major and F -majorchords .
f
Here we fi nd another proof that major a nd minor a re opposi tesin all things . I t h a s already been stated that when the principalchord is major
,then the relative a nd correlative chords wil l be
minor , consequently when the principal chord is minor then therelative and correlative chords will always be major . With themajor chord we found the relative chord si tuated a minor thirdbelow ,
here the relative of a minor chord is S i tuated a minor thirda bove the principal (minor ) chord . C-major is the relative chordof A-minor chord . I t con tains the third and fi fth of the principalchord .
Th e correlative chord is a major third below the principal(minor) chord , and a fifth below the relative chord . F -major Is thecorrelative chord of A-minor chord . I t contains the prime and
third of the principal chord .
Principalchord .
C Correlative
f chord .
E XE RCISE . .
— Wri te the relative and correlative chords of a l l
minor chords .
35 . THE RE LATIVE S AN D CORRE LATIVE S OF THEPRI N CIPAL CHORDS (T, D , S , ) OF THE MAJOR KE Y .
Th e relative and correlative chords of the Tonic a re named Tonicrelative (abbreviated Tr , ) a nd Tonic correlative (abbreviated Tc . )Th e relative and correlative chords of the S ubdominant a re namedS ubdominant relative (S r) , and S ubdominan t correlative (So ) Whenwe omit (cance l) th e 5 of the S 6 we get the relative chord of the S ,
S r . Th e relative and correlative chords of the D ominan t a renamed D ominant relative (D r) a nd D ominant correlative (D c) .
S r S S c Tr T Tc D r D
— 58
Haydn . Andante va rie . F minor .
mS mS c
Beeth oven . Op . 27 , N o . 2 . Sona ta .
E x . 43 .
mS c m aD 7
3
Th e functions of e and mTc a re held by the same chord,and
so a re mTr a nd c .
§ 37 . CLASS I FI CATION OF CHORD CON N E CTION S(Continued ) . Th e principal chords and their relatives and correlatives make possible the following chord connections , some of theclasses have been met before
,for example
Th e Fifth step,
1 8, IN MAJOR: S r— S c , S r— Tr
, S c— Tc
,
S c - D r,Tr— Tc , D r— D c . IN M INOR : mD r— c
, . c — mTc,
mD r— mTr , mTr— mTc,c — e , e
—mSc .
Th e Fourth step,
21,I N MAJOR: D r
M I N OR: mSc— mTc, e
— mSc .
Th e Whole tone step,
22,I N MAJOR : S r — Tc
, S r— D r,
Sc— D c, Tr— D c . I N M I N OR : mD r— mTc
,mD r— e , c
mSc,mTr— mSc .
Th emew ch ord conne ctions a re:The M inor T/zird step , é40 . I N MAJOR
,de sce nding from m a jor to m inor
ch ord . I N M I N OR,a scending from m inor to ma jor ch ord .
T/ze T/zird step , Q 41 IN MAJOR ,a sce nding from ma jor to m inor ch ord .
IN M I NOR , de sce nding from m inor to ma jor ch ord .
T/ze LV/zol e tone step , b42 . IN M AJOR ,a scending from ma jor to minor
ch ord . I N M IN OR ,de scending from m inor to m a jor ch ord .
Tbe Ha lf tone step , é 43 . I N M AJOR,a scending from m inor to ma jor
h ord . IN M I N OR , de scending from ma jor to m inor ch ord .
Th e F our th step , Q44 . I N M AJOR,a sce nding from m inor to ma jor ch ord .
IN M IN OR,de scending from ma jor to m inor ch ord .
T/ze [ll znor T/zird step . 345 I N M AJOR ,from m inor to m inor ch ord .
IN ,M I NOR ,from m a jor to ma jor ch ord .
T/ze Tr itone step , Q 46 . I N M AJOR ,a sce nding from ma jor to m inor
ch ord . IN M IN OR ,de scending from m inor to m a jor ch ord .
Tr . D c — D r . IN
Because M inor is the opposi te of M ajor,we have to figure the
chord connections in i t the opposi te way we do in M ajor a nd fromand to chords of the opposi te mode in order to fi nd the equivalentchord connections . Th e conditions for wri ting these progressionsa re given farther on .
§ 38 . SPE CIAL FEATU RE S OF RE LATIVE AN D COR
RE LATIVE CHORD S . Th e relative and correlative chords a llowthe doubling of any of their tones . Being derived from the T
,the
doubling of the third of a Tr would merely mean a doubling of theprime of the T
,and point to the chord from which i t is derived .
D oubling the third of a To would be merely the doubling of thefifth of the T from which i t is derived Th e same holds good of allthe relatives and correlatives in the M ajor or M inor key . Th edoubling of the third of a relative or correlative can even occur inparallel motion .
E x . 421.
T S r Tr S r D Tr D r T S r D r mD r e rnT mD r
T S r S r D r D Tr mT mD r mD e mS mTr mT mD r .
Proceeding by skip. to the 5 of the relatives and correlativesshould be avoided , because i t produces the undesirable eff ec t of sixfour . I n the cadence the natural posi tion of the Tr is a fter the T,
the S r comes after the S ,and the D r after the D . Th e correlatives
form a natural connecting link between the principa ls a nd theirrelatives .
E XE RCI SE — P lay the pure major cadences (T S D T) of allkeys and insert the relatives and correlatives where they be long .
P lay the pure minor cadences (mT mD mS -mT) a nd insert therelatives and correlatives where they belong .
— 60
§ 39 . THE D E CE PTIVE CL OS E I N THE MAJORKE Y . Th e relative and correlative chords pa rtake somewhat of thenature of their principal chord . Th e Tr can certain ly not have theexact mean ing of the T
,but it can be used a s its substi tute . When
the Tr t akes the pla ce o f the T after a D 7,at the end of the cadence ,
we get what is known a s a deceptive ” c lose . Th e doubling of
the third of the Tr (which is the doubling of the fundamen tal toneof the T) is really cha ra cteristic in the deceptive close . Th e equallypossible ways of wri ting a s at (h ) , doubling the prime of the Tr ,
or
a s a t (i ) , doubling the fifth of the Tr a re exceptions . In this decep tive c lose the bass moves upwards one degree
,while the other
parts make their regular progressions .
C ) d ) e )’
f ) g ) 11 )
D'7 Tr
Th e 5 or 7 may be absen t in the D . Th e distance of a n octavebetween alto and tenor , a s a t (c ) , is allowed in all deceptive closes ,
when both pair of parts form thirds .
THE EQU IVAL E NT OF TH I S MAJOR D E CE PTIVECL OS E is
,in the minor key ,
from the m8 to the mTr a s fol lows(with or without the S ixth to the m8 ) :
E x . 46 .
m 8 mTr mS 6 mTr mS mTr i m’
3
1‘
r m S m’
gr mS mTr35
E XE RCISE — Write these deceptive closes in all keys .
6 40 . M IN OR‘
THIRD STE P . I N MAJOR ,de scending from ma jor
to m inor ch ord:S —S r , T— Tr or S c , D— D r or Tc .
~ IN M IN OR ,a scending from
m inor to ma jor ch ord:mD — mD r , mT— mTr or c , mS — e or mTc .
Connecting the relatives (and correlatives) with the principalchords ,
from which they a re derived , causes no difficulties a s thechords h ave two tones in .common (the in terval of the major third ) .
Th e third part progresses a whole tone step , and the bass usuallymoves from prime to prime .
— 61
E x . 47.
T Tr D D r 8 S r mT mTr mS e mD mD r
Q4] . TH I RD STE P . I N MAJOR ,a scending from m a jor to minor
ch ord S — S c or Tr , T— Te or D r,D — D c . IN M I N OR ,
de sce nding from minorto ma jor ch ord mD -c or mTr
,mT— mTc or e ,
mS — mS c .
Th e chords have two tones in common ,possess a leading tone
(half step ) and permit the doubling of the fundamental tones .
c ) d ) e ) f ) g ) 11 )
E x . 48 .
E xceptional leadings of parts a re possible without violating anyrules . This chord connection h a s a special mean ing a s c losing stepin place of the return fi fth step
,for example D r— T or e — mT
instead of D — T and mS — mT. In order to put more vigor in to theparts , they a re then usually made to proceed by skip , especially inthe major close . S chubert wa s very fond of this progression . I t is
also possible in the minor key .
E x . 49 .
Igr T I
gr T D r T m
iSr mT e mT e mT e mT m
3
8 r mT1
é 42. W HO L E -TON E STE P . IN MAJOR,a scending from
.
ma jorto minor ch ord :T— S r , D — Tr or S c . IN M I N OR ,
de scending from minor to
ma jor ch ord:mT— mD r,mS— mTr or c .
_ 62 _
Th e chords have no tones in common,therefore there is danger
Of consecutive fifths and octaves , which can be easi ly a voided,if the
possible leading tone step is given up or the third doubled in t h erelative (or correlative ) chord .
b ) C ) d ) e ) f ) g ) h ) i) k )“
1)
T S r T S r T S r S r mTmD r mD r mD r mD r3 3 3 3 3 3 3
See a l soQ39, E x . 46 .
é43. HAL F -TON E STE P . IN M AJOR,a scending from m inor to
m a jor ch ord ‘:D r or Tc S ,D c — T. I N M I N OR,
de scending from m a jor t om inor ch ord m Sc— mT,
mTc or e — mD .
This chord connection gives r ise to some diffi culties,namely
,
risks of consecutive fifths a nd octaves,tri tone (augmented fourth) .
They can,however
,be avoided .
a ) b ) c ) d ) e ) f ) g ) h ) i ) k ) 1 )
E x . 51 .
b44 . F OU RTH STE P . I N M AJOR,a scending from minor to ma jor
ch ord S r— D . I N M I NOR ,de scending from ma jor tom inor ch ord :mD r— mS .
This chord connection h a s the same meaning a s the whole-tonestep without its dangers . Two parts move by whole- tonesteps
,and the bass usually moves from prime to prime . Because
the relative is used a s a substi tute for the principal chord , i t is veryimportant for modulation .
E x . 52 .
S r‘
D
I
sr D mD r mS mD r m 83 3
é 45 . M I N OR TH IRD STE P . I N MAJOR,from m inor to minor
ch ord :S r— D c . I N M IN OR,from m a jor to ma jor ch ord :mD r— mS c .
This chord connection h a s a chromatic.
step,which observe .
E x . 53 .
S r D c mD r msc
é 46 . TR ITON E STE P . I N M AJOR, a scending from ma jor tominor ch ord :S — D c . IN M IN OR ,
de scending from m inor to ma jor ch ord
mD — mS c .
Con tains one possible augmen ted step,which ca n be avo ided if
the Chromatic or the leading tone step is observed .
E x . 54 .
D c mD mSc mD msc3 3 s
§ 47 . M OD UL ATI ON . (Continued ) Th e use of relativeand correlative chords opens up a surprisingly great number of
modulations , as the following tables will show . From each keythere a re s ixty- two modulations possible into six major a nd six
minor keys .
— 64
E XE RCI SE .
— S tudy the tables by figuring out into whatkeys the change of functions .will lead . An excellen t practice is toplay the cadences up to the chord changing its meaning’
,and then
enter the new key with the chord indicated . Compare Part 1, § 27 .
E x . 55 .
T s S rz mTmsgD g> 7
When the new key is en tered by the D side,for example
,mT
,
mS ,mD r D
,then the modula tion p lunges too rapidly to the end
,
and is not satisfactory . I t is better,therefore
,to turn to the S side
after such a change of function,and then finish in the customary
manner . Th e fol lowing exercises e nd in the same key they start .They were not devised for the sake of beauty ,
but for the practiceof modulations of
‘
the most varied k ind . Th e author’s RevolvingCha rt of Harmony N o. 2 , wi l l be found an immense help in thestudy of modulation .
E XE RCI SE S .
(D ivided fi g a ra tion in eig h t/z notes . S ee Qo
3
(1 0 5 ) 2 T Sr D ‘ T mTr mD mS 6 maD3
mT= S r T Tr z D r S r mS6 D T
3 0 0 0 9
I l l
(1 0 6 ) E mS D 7 mT mTc=mTr mS m aD 7
l'
1'
19
mT mTr mS — S e S D27 T D D c=mT
I5
— 66
(1 13) E :T D T S | Sr : D c D mS IT S T ]D z mS c f?
7 mT mTc mS .‘mS c : mD r mD 7
mS6 maD
7 mT mS6 mT mS — D c D . .
7 T S 1118 T
Tce S DZ7 T S S r D D c=S r S DZ .
7 T'
Tr3
Ss r mS maD mT mTr mD rz mS c‘rnS 6
6
mT mTc mT'
mTrz-e mS D ?
71nT e D2>§
mT mTc mTr mS mT=Tc Tr S D 2
(1 14 ) E :mT mS mT mD mD r z mSc mS maD
mT maD mT ImS c S D i7 IT Tc D
D c— Sr S mS
6D 7 IT D 7 T D = mS c ni S D .
7
mT mD m aD mT mTc — rnD r ni S6 D i
>.
7 ImT mD
mD r mS mS CZ mD r mS D2> § mT mTr s S r3
D T. mS T Tr S r c Sr D27 T Tc T
3 1
Tr z D r S D217 T Sr D23 T Tc Tr D s Tc
mTr mS6D ? D 7 mT mD m5
"1
N . B .
N . B .— Hold ou t th e tone in th e ba ss, even wh ere it does not form pa rt of th e ch ords
ca l l ed for.
67
B . RE L ATI VE S AN D CORR E L ATI VE S O F TH E m is AN D m a D .
§ 48 . Th e letter S indicates the S ubdominan t chord in a majorkey
,the D indicates the D ominan t in a major key . When the
major D ominant is used in a minor key , we indicate i t by maD ;
when the minor S ubdominant is used in a major key , we indicate i thenceforth by miS ,
because mS should indicate the minor Subdominant in a minor key . Th e relative a nd correlative chords of themiS a re called minor S ubdominan t relative and minor S ubdominan tcorrelative . I n C— major key they a re the following chords
miS c miS miS r
Th e relative and correlative chords of the maD a re called ma jorD ominan t rela tive a nd major Domina n t correla tive . I n A— minorkey they a re the following chords
maD r maD maD c
Th e miSc occurs frequently , while the maD c is rare and conse
quently less familiar .
Bee th oven . Andan te in F .
E x . 56 .
E x . 57 .
W agne r , F l ying D utchman .
Bee th oven . Anda n te in F .
E x . 58 .
E x . 59 .
L iszt . D an te — Symp h onie .
sv a b a ss a .m m
maD c maD r
I t would increase this book considerably beyond the s ize allottedto a text - book
,to bring i llustrations of all chord connections from
the m a sters but the assiduous pupi l can mark such in h is book ,a s
he finds them in h is study of Harmonic analysis .
$49 . CLASS IFI CATION OF CHORD CON N E CTION S .
(Con tinued ) Th e connecting of the rela tives a nd correlatives of
the miS ,or maD
,with the o ther chords of the key in troduces
chords of the same mode in succession,the result is a number
of new chord connections . Th e c lasses that have been met beforea re:
Th e Th ird step . I N M AJOR ,a sce nding from m a jor to m inor
ch ord :miSc— m iS . I N M IN OR ,descending from minor to ma jor ch ord :
maD c— maD .
Th e Fifth step . 5 18 . IN MAJOR ,from ma jor to m a jor ch ord :m iS c
miS r . IN M INOR,from minor to m inor ch ord maD c maD r .
Th e M inor Th ird step $40 . I N MAJOR , de scending from m a jor to
minor ch ord :miS r m iS I N M I N OR a sce nding from m inor to m a jor ch ord :m aD rf maD .
Th e Tritone step . I N MAJOR,a sce nding from m a jor to m inor
ch ord :miS r— S r . I N M IN OR,de sce nding from m inor to m a jor ch ord
maD r— mD r .
Th e M inor Th ird s tep . é 45 . From m a jor to m a jor ch ord : S — m iS r ,mD r— maD . From minor to minor ch ord:S r— miS ,
mD — m aD r .
Th e new chord connections a reT/ze C/zmma l zc step . 6 5 1 . IN M AJOR ,
a sce nding from ma jor to m inorch ord. IN M INOR, de scending from m inor to ma jor ch ord .
69
The Th ird step . Q 52 . I N MAJOR,from ma jor to ma jor ch ord
,a lso from
minor to minor ch ord . I N M I N OR ,from m inor to m inor ch ord
,a l so from
ma jor to ma jor ch ord .
The D im inished F our th step . Q53 . IN MAJOR ,de scending from ma jor
to minor ch ord . IN M IN OR,a scending from m inor to m a jor ch ord .
Th e Ha lf Tone step . é 54 . I N MAJOR ,from ma jor to ma jor ch ord ,
a l so from minor to m inor ch ord . IN M IN OR,from m inor to m inor ch ord
,
a l so from ma jor to ma jor ch ord .
Th e Augmented S econd step . é 55 . I N MAJOR ,a sce nding from m a jor
to m inor ch ord . I N M I N OR ,de scending from m inor to m a jor ch ord .
Th e Tr itone step . 56 . I N MAJOR,from ma jor to ma jor ch ord
,a l so
from m inor to minor ch ord . IN M INOR , from minor to minor ch ord,a lso
m a jor to ma jor ch ord .
Th e D iminish ed Th ird step . é57 . I N M AJOR ,de scending from m a jor
to m inor ch ord . I N M I N OR ,a scending from m inor to m a jor ch ord .
§ 5 0 . D E CE PTIVE CL OS E IN THE M I N OR KE Y .
When the mTc takes the place of the mT after a maD (with or
without the seventh) a t the end of the cadence,we get the most
frequen t form of deceptive close in the minor key .
E x . 6 0 .
m aD 7 mTc
Th e distance of an octave from alto to tenor may be approvedof in al l cases where both couples form thirds . a ) - c) a re the typica l forms of the deceptive c lose in minor . d ) a nd e ) a re rare a ndnot so good ,
because the third instead of the prime is in the bass .
§ 51 . CHROM ATI C STE P . IN MAJOR , ascending from ma jor tominor
.
ch ord miS c— S r , m iS r— Tr or S c . IN M I N OR ,de scendin g from m inor
to ma j or ch ord m a D c— mD r,maD r— mTr or c .
There is an occasion for a sustained note,and also for two
chromatic tone steps,but likewise danger of consecutive fifths and
an augmented fourth .
E x . 6 1 .
I
misr Tr maD r mTr
é 52 . TH I RD STE P . IN MAJOR, from ma jor to ma jor ch ord:miSc— S ,
T— miS r . Also from m inor to m inor ch ord :_Tr or S e — miS .
IN M IN OR,from m inor to m inor ch ord :m aD c — m D
,mT — m aD r . Al so
from m a jor to ma jor chord :mTr or c — maD .
This chord connection meets with no diffi culties, but possesses
the peculia ri ty of a chromatic step . A leading of parts a s at b) andf wi ll be employed very rarely , because there a re skips in nearlyal l parts .
C ) d ) f ) g ) h )
m1sc S T misr Tr mismaDc mD mTmaDr mTr maD
£53 . D I M I N I SHE D F OU RTH STE P . I N M AJOR , de scendingfrom m a jor to m inor ch ord :miS c — Tr or S c, m iS r Tc or D r . I N M I N OR,
a scending from m inor to ma jor ch ord :ma D c— mTr or c,maD r — mTc
or e .
Ha s two leading tone steps a nd a chromatic step,also possi
bil itie s o f an undesirable augmented second and an augmentedfifth .
E x . 63 .
miS c Tr miS r Tc maD c mTr maD r mTc
3, 54 . HAL F -TON E STE P . I N M AJOR ,from m a jor to ma jor
ch ord:T— m iS c , D— m iS r . Al so from m inor to m inor ch ord Tc or D r— m is .
IN M I N OR from m inor to m inor ch ord mT —~ m aD c,m S — m aD r . Al so from
m a jor to ma jor ch ord mTc or e — m aD .
A chord connection which h a s dangers of consecutive fi fthsand octaves
,because a l l th e notes can form
‘
l e ading tone steps ,
when the chords a re placed side by s ide . Th e augmented secondis qui te an obstacle . Th e best way to avo id these risks is to doublethe third of the relat ive or correlative chord .
71
E x . 64 .
T ~m iS c D r miS mT maDc e maD
§ 55 . AU GM E NTE D S E CON D STE P . IN MAJOR ,a scending
from m a jor to m inor ch ord misc— Te or D r, miSr— D c . I N M I N OR,
de scend
ing from minor to m a jor ch ord! ; ma D c— mTc or e , m a D r— m S c .
Possesses the possibi li ty of two augmented seconds,two aug
mented fourths , an augmented fi fth and a n augmented sixth,all of
which a re permitted only in inversion ,when they produce dimin
ish ed intervals .
E x 65 .
miSr D c miSc D r maD r msc maD c e
9 56 . TR ITO N E STE P . IN M AJOR,from ma jor to ma jor ch ord :
miS c — D . Al so from m inor to m inor ch ord :mis— D c . I N M I N OR ,from
m inor to m inor ch ord m aD c — mS . Also from ma jor to m a jor ch ord maD
mS c .
This chord connection h as three tri tone steps a nd an augmentedsixth ,
which a re to be avoided . W hen the possible dimin ished thirdstep is made
,the connection becomes simple .
E x . 66 .
miSc D m is D c m aD c mS maD m Sc3
é57 . D I M I N I SHE D TH IRD STE P . IN MAJOR,descending
from m a jor to m inor ch ord :m isc— D c . IN M I NOR,a sce nding from minor
to m aj or ch ord maD c— mSc .
Connect ion ‘
of very distantly rel ated chords . An augmentedse cond ,
a n augmented fourth a nd two augmen ted sixths a re obstacl esin the way
,but there is the possibi li ty of making two dimin ished
third steps simultaneously .
E x . 67 .
miS c D c maD c mS c
58 . M OD UL ATI ON . (Continued ) A great numberof modulations a re made possible by the use of the miS a nd its
relative and correlative chords , or the ma D and its related chords .
From a major key fi fty- four new modulations can be made into tenmajor and seven minor. keys . From a minor key the same numberof modula tions can be made in to ten minor and seven major keys .
E XE RCISE . S tudy the following tables a s advised in § 47 .
T m isr m is= 1 r Tr m is m 1S r=T m is m iS c=Tm isc S r m a D r S ma D r S
S m isr D r m a D c D m a D c D
m isc m aD r S r 111 18 m a D S c m is m a D
D = m isr Tc m a D r mTr m a D r mTrm 1sc S c m a D c m D r m aD c m D r
D c m is e D c m is e
m a D c m a D r msc m a D r m is rm a D c c ma D c msc
m isc c
mTc mTc
mT m aD r m aD mTr mTr m a D m aD r=mT mTc m aD m a D c mTm a D c e m isr m S m iS r m S
mD m a D r m is r m iS c m is m iS c m ism a D c m D r mD r m a D 1n D c =m a D m D
’
m 8 m a D r mTc m isr Tr m is r Trma D c msc m isc D r m isc D r
m isc e m a D S r msc m a D ma D r
c m isr S c m is r S r
m isc D c m isc S c
m a D c D c
c Tc
Th e obj ect of th e following exercises is to crowd therein,in the
smallest space possible , some examples of the chord progressions towhich the preceding paragraphs a re devoted .
I n working out,the tonal functions of the chords a re to be
added by the studen t .I n analysing , adhere to the ol d key a s long a s possible
, and tryto locate the pivoting points of the modulation on the heavy beatsof the measure .
A change of posi tion by way of fi guration may occasiona llybe resorted to ,
in order to make smoother progressions to the following chord possible , but the given part must never be a ltered .
A few passing tones a re used , fi nd them a nd mark them p . t .
E XE RCISE S .
(1 15 ) S oprano given .
bh eIz em d"a . .
7 bm . . g m biz bIZ f"
(120 )
g m3b d 7em e m g m
cIZ hIZm ab d g 7
3 3
(121 ) Bass given .
772 772
bIZ f I? m dm
772 (1 772 g b 772
6> 6 5772 772
4772
3
KE Y TO E XE RC IS E S N os . 115 122 .
(Th ese sol utions ca n be used a s new e x er cises,wh en worked in dzfi
’
e r en t keys .
(1 15) E T (p . t . ) D Tr m iS r= T D 7
(p . t . )a o o a o a o
I I I
T D 7 T S Sr — m iS D 7 T S (p . t . ) D7 T m iS
a 0
L’
I
m iS r z miS c T S D i (pio
t . ) D T
M
(116) 3 mT m aD C Z mD mS D2> §1; I
'
5 I'
I
mT mS mSc — “ maD7 mT mTc = miS r D 7
o p pI y I I I
.
T (p . t . ) Tr='
miS’
D 7 T m i’
S r s c mS D2> § mTv I
(1 17) i : T Tr s D D c — m iS D I T Tr
miSc -s r mS mT maD maD C Z m aD r mS D 7
o o1
oI I I
l
miS r z miS c miS D r S D 2 3o o 7 7— 1
.
maD7 mT mS mT m aD r s mS
0 O 0 D
I I
maD c mS e z maD0 O O
I
mT mTc maD z m iS r miS6 D T m iS c= mD r mS
(1 19 ) E mT maD mTc mS mTmTr : maD mS
mT maD r mTr mD r r — miS c
D7 T S
o
z m iS c D T.
m iS Sr : m aD c mS D 6>3
5 mT
(12 0 ) g:T miS m iSc S D 7
T S S r : n1 aD c mS maD r m aD 7
3 3
I
mT m aD c mD — maD c mS c mT m aD
mD r 1 miSc
(12 1 ) g T miS r miS c D T z miSc D T
S Sc m iS miSc : m aD mS mS c mT mTc
‘
I'
maD mS c mS maD maD c mTr—z miS r m iS
6D2 T
O 0 OI.
V
(122 ) E mT mD m aD r mSc mT mTr maDO O 9
m aD c mS D ? 53 mT mD r D3 27
“9 0 9
l o 3 o
T S Sr m iS m iSc= mD r D ? mS6D2 mT
9
C. TH E M I N OR SU B D O M I NAN T W ITH RAI SE D TH I RD (m S 3<) AN D TH E
MAJOR D OM I NAN T W I TH L OW E RE D TH I RD
59 . Th e miS in the major key a nd the maD in the minor keyintroduce an augmented second in to the scale
_n 77 __
Very often,especially in figura tion by mea ns of a uxilia ry or
passing tones,this augmen ted in terva l is reduced to a whole tone by
chromatically altering the 8 of the m5 or D .
E x . 68 .
But these tones may be ha rmon ized in such a manner tha t theymust be looked upon a s chromatica lly a ltered thirds of the m8 or D .
b )
E x . 69 .
mT mS 3< maD mT m iS T
Apparen tly this gives the major key a minor D and the minorkey a major S . N evertheless they must be looked upon merely a s
licenses , and not a s key-making (principa l ) chords . Th e artificial
notes a re supposed to lead to the third of the maD or mis ,when
they do not do this,then the progressions a s musical ellipses require ,
leaps in the conception . Th e raised third of the m8 (mS 3<) if usedwithout modulation and without progressing to the 3 of the maD
will produce e fl ects peculiar to the D orian mode of the fifteenthto th e
'
sevent eenth cen turies . Th e lowered third of the D if
used without modulation a nd without progressing to the 8 of the mis,
will reproduce the characteristics of the M ixolydian mode . Th emS 3< i llumines the minor key a nd the D 3>
clouds the ma jor key,
even when the natura l ly expected chords do not appear .
W agn e r. L oh engrin ,Vorspie l
E x . 70 .
F or D 3> se e a l so S ch ubert , E x . 156 , on page 124.
D . TH E D O lVI I NAN TS O F TH E D O M I NAN T (D D , m D D , m a D D ) AN D TH E
SU B D O M I NAN TS O F TH E S U B D O M I NAN T (SS , m iss, m ss) .
60 . A major key can branch (reach ) out above the D and
below the S and use the chords beyond without inducing a modulation . Th e use of the D D (D ominan t of the D omina n t ) , gives the Dside especia l stress . Th e extension of the key to the SS (S of the S )a nd espec ia l ly to the miSS (miS of the S ) brings darker shades in tothe key . Th e same holds good of the mS S . Whereas the mD D a nd
maD D bring brighter sha des in to the minor key .
E x . 71 .
T ss s T T ss mis T mTmD D mn'
mT m D D maD mT3
W'
agn e r . M e iste rsinge r , I Act , 2d scene .
E x . 73 .
W agne r . Pa rsifa l , I Act , l st scene .
8 8 D 3> S T Tr S D 7 6 5
3 6
E . THE TO N I C VAR IAN T (TV,m Tv ) AN D R E L ATI VE S (Tvr , Tvc , m Tvr , m Tvc . )
61 . Th e chroma tic alteration of the third of the T producesa “
chord of the opposi te mode,in C-major key the c-minor chord ,
in A-minor key the a -major chord . I t is indicated by Tv and mTvrespectively . M ost beautiful eff ects a re obtained by the use of the
variants of th e T. F or the major key i t is simi lar,in effect
, to acheerful landscape made dark and gloomy by a passing c loud . In
the minor key the effect is the reverse , l ike a desolate scene madeen trancing by sunshine . By using the varia n t of the ton ic
,the
darkness in major,or brightness in minor , is cast over the en tire
key,and does not spread on ly over a part of the key
,a s with other
chords (miS , SS ,maD e tc ) . Th e Tvr (Ton ic varian t rela tive ) in
C major is e lzmajor , the Tvc (Ton ic varian t correla tive ) is a tzmajorchord . Th e latter is
.
frequently used for deceptive c loses . Th e Ty rcan be used for deceptive c loses also . Th e mTvr (minor Tonicvarian t relative) in Aminor is ffim , the mTvc (minor Ton ic varian tcorrelative) is cgm chord .
E x . 74 .
D Tvc miS Ty r mS 6 mTvc maD mTvr
Ch opin . Op . 30 , N o . 3 , M azurka .
E x . 75 .
— 8 0
S ch ube rt . Op . 94,N o. 4. M oments musica ls.
f
maD 2> mTv (enh a rmonica l l y wri tten . )chma jor dbma jor .
ni aD'7 ma i
>
Sometimes composers wri te chords enharmon ically changed .
I t is done to make the reading ea sier,if i t is not done for the sake
of modulation . I n the last example,which is in C ? minor ,
S chubert has a whole (middle ) movemen t in D jz ma jor key , insteadof i
-major , a nd bringing a bi t of i t a t the -
end of the piece aga in ,
he wrote i t with the same signature i t appeared at first .
E x . 77 .
S ch ube r t . D ying S tra ins. N o . 8 . Atl a s.
p . t .
lord l y h e a r t; a nd now th ou h a st th y tor m e n t .
mTvr
82
E x . 8 0 .
S ch ube rt . Op . 1 0 3 . Fa n ta isie . (Four h ands . )
as T
These chords have their relatives too,and appear more fre
quently than some would suppose .
C-ma jor .
a S c as asr a’
l‘
c aT aTr aD c aD aD r amiS r amiS amiS c
A-m ino r .
ae amS amS c amTr amT amTc amD r amD ac amaD c amaD amaD r
This ser ies of chords gives most exquisi te tints to tonalharmony .
E x . 81 .
L isz t . Rh apsodie Hongroise V I .
1 fi - L fi L A.
W agne r .
E x 82 .
Tvc Tvr
W’agne r. L oh engrin , Act I , Scene 3.
E x . 83 .
(S r)W agne r . Flying D utchm an
,Act I I I
,N o . 13 . Rh e ingo l d ,
Fourth S cene .
b )
\Vagne r . L oh e ng rin ,Act I , S cene 3 .
E x . 85 .
L iszt . D ante -Symph onie .
— 84
W agner . L oh engrin , Act I , S ce ne 3 .
E x . 87 .
E x . 88 ,
W agne r . M e iste rsing e r , Act I I I , S e cond scene .
aTc aTr4 3 e e nh fb S
miS c
63 . CL O S E S OR CAD E N CE S , a re successions of
chords lea ding to a momen tary or complete end of a phra se , section or movemen t .
A COM PL E TE CL OSE is a close on the Ton ic at th e end of
a period or section .
A HAL F CL OSE is a c lose on the D ominan t . I n a widersense also on the S ubdominan t , and all chords derived from eitherD omina n t .
A D E CE PTIVE CL OSE is a temporary c lose on a relative orcorrela tive chord of the Ton ic ,
and leads to a new cadence . Thisclassifica tion conforms in the ma in to the terminology genera l lyaccepted
,but it is fa r more comprehensive .
COM PL E TE CL OSE S
from the D ominan t wi th or without the seven th ,and from the Sub
dominant wi th or without the sixth .
E x . 89 .
D (7) T S (6 ) T m iS (
6 ) T mS (5 ) mT mD (7) mT m a D (
7) mT
- 85
Th . D ubois . Postl ude in Afor Organ .
E x . 9 0 .
T Tr T
I 3S ch umann
’s Tocca ta , Op . 7 , cl oses S I miS 6
1 T.
Complete d oses a re also possible ‘ from the relatives of theD ominants .
E x . 91 .
T S r T miS r T e mT mD r mT m aD r mT
Complete closes a re possible from the correlatives of the D ominants .
E x . 92 .
61 )
D c T S c T misc T mS c mT c mT maD c m'
l‘
I t is also possible to close elliptically from the mS 3< or D3>
(skipping over the expected maD or miS ) to the Tonic .
8 )
E x . 93 .
mT mS 3< mT D 3> T
— 86
O ther closes would be from the aD,as , amiS ,
ams ,amD
,
amaD and their relatives to the T. A few a re given below,the
studen t can work out the remaining ones .
E x . 94 .
T a S r T mT amD r mT a S c T ac mT T aD c T mT amS c mT
HAL F CL OS E S .
Th e term h alf close h a s usually been restricted to endings on
the major D ominan t , but there is really no binding reason for this .
E x . 95 .
T D Tr D S D S r D m aD mTr maDmS maD e maD
This selection shows what is generally meant by a half c lose .
I t is certain tha t a ny domina n t or a ny rela tive or correlative chordof either dominan t may become the bearer of a ha lf close (p rincifpal subdivision ,
c lose of a part) . Th e following small selectionwill show a further number of good effects .
E x . 96 .
S T miS Tr S T S r D r S r s
— 87
mT mD mT e e mD mTr mS mD e
D E CE PTIVE CL OSE S .
We have already explained some deceptive close s in 39 and
§5 0 . They a re endings in which a Ton ic relative or correlative takesthe place of the expected Tonic .
f ) g ) h )mi )
m
Tr S Tr miS Tr S To 1118 mTr maD mTcmaD mTr mD mTr mDmTc
A series of new possible forms of deceptive c loses is gained bythe use of the relative and correlative chords of the tonic variant .
E x . 98 .
D Tvc D Tvr D r Tvc m iS Tvr miS Tvc S r Tvr
mS 6 mTvc m8 mTvr e mTvc e mTvr maD mTvr m aD mTvc
— 88
Th e last deceptive closes give rise to difficulties in retaining thekey a nd come near being modulations . In order to countera ct thisimpression
,they necessi tate the use of chords of the mS 3< or D
3> for
the return over the maD or miS a nd the ea rliest possible regainingof the mD or S or their relative chords . N umerous c loses possiblefrom
,and to
,the aS ,
amiS ,aD
,aT,
amS ,amD
,amaD a nd amT
,the
studen t wi l l know h ow to work out and analyse according to theabove comprehensive classification .\Vagner . L oh engr in ,
Act 1 , scene 3 .
de ceptive c l ose .
I n old polyphonic music i t wa s essential that every composi tionshould end with a major chord
,even though the key in which it
wa s wri tten wa s minor . Th e third thus ma de major by an accidental sharp or natural wa s called the Tierce de P icardie .
”
E venBa ch conscientiously observed the custom . I t is sti ll a favori tepractice to close a minor piece with the mTv . Schubert , wh oa great innovator in Harmony
,attempted the opposi te . His Im
promp tu , Op . 9 0 ,N o . 2
,begins in E 12 major , thus :
S ch ube rt . (Beginn ing .
E x . 1 0 0 .
and ends in E bminor thus(E nd)
E x . 1 0 1 .
Tv miS Tv m iS Tv miS D
A piece ca n a lso close with the 8 in the ba ss
Th . Ku l l ak . Op . 62 , N o . 5 , W ieg en l iedch en .
E x . 1 0 4 .
L l sz t e nds 1118 Tra urige M onch W i th th e 3 of th e C—mm or ch ord i n t h e ba ss .
E ven the c lose with the 5 in the ba ss h a s been ven tured .
S ch um a nn . Op . 7,Kre is l e ria n a .
E x . 1 0 5 .
A composer ca n begin a nd end with a ny chord he chooses .
“Then a piece closes with the T
,i t na tura lly con forms to the proverb
all’s well that ends well . ” Where a composer merely “ quits,
”
there the listener h a s to fi nd the c lose for himself .
64 . CL ASS I FI CATION OF CHORD CON N E CTION S(Conc luded ) . Th e obj ect of arra nging chord successions into classesis to po in t out the inheren t a nd la ten t force con tained in them ,
and
their va rious techn ica l diffi culties , to the studen t . Th e guiding pointsfor all chord connections a re the avoidance of doubling the thirdsof the principa l chords in pa rallel motion the a voidance of a l l augm en ted in terva ls the possibi li ty of doubling the thirds of a l l rela tiveand correla tive chords ; the use of susta ined tones
,half steps and
chroma tic steps where fea sible . Th e fol lowing review con ta insnea rly al l chord connec t ions possible , especia lly if we absta in fromconnecting extremely dista n tly rela ted chords
,a nd do not consider
their connection with the in termediate ca dences (se e I t is sur
prising to se e h ow ma ny chords can be conceived a s belonging to thekey a nd ca n be used without inducing a modula tion . In this labyrin th of chord successions the tona l functions tell wha t offi ce a ndimporta nce the chords have in the key . Th e en tire number of
chords is rea lly to be reduced to on ly three groups . They a re eitherTon ic
,D ominan t or S ubdomina nt ha rmon ies , a s the letters of the
tona l functions indica te . W e name the chord connections accordingto the in terva ls the fundamen ta l notes produce
,and mark the mode
of the chords . By inverting the in terva ls all chord connections
_ 91 _
can be included within the interval of a tri tone (augmented fourth) .
A fifth is but a fourth ,when inverted . Th e following table will
explain this . Th e inversion of an in terval is the placing of thelower tone an octave above the original upper tone , or V ice versa .
(S ee also
ugme n te d
Th l l ‘d .
Augm en tedS ixth .
D im i n i sh edTh i rd .
To i llustrate the plan of —cl a ssifi ca tion again ,we will take c and d
,
ma jor or m inor chords , for example . Their fundamenta l tones forma Whole tone step but there a re diff eren t kinds of Who le tone stepsin chord connect ions
,because the major or minor chords can succeed
each other,thus
a ) major to major chord , c— d .
5) major to minor chord , c— dm .
6 ) minor to minor chord , cm— dm .
a’
) minor to major chord,cm— d .
E very succession h a s its peculiari ties , inheren t force and meaning . Th e succession c minor to bizmajor for example
,is not classed a s
a seven th step,because its explanation will be found in its inversion
,
th e Whole tone step,major to minor chord
,a nd thus in all simi lar
cases . N ow follows the list of chord connections with variousremarks .
1 . Ch a ng e of [Mode (of Chords ) . M a jor to m inor ch ord,or vice ve rsa .
E a sil y unde rstood . Occurs in th e ma jor key be tween S — miS ,a l so Sr
DD,D — D 3>
, T— Tv ,e tc . Occurs in th e m inor key be tw e en mD — maD
,
mD r— mS S ,m S — m S 3<,
mT— mTv,e tc .
Ch roma tic step . (E nh a rmon ic with Ha l f tone step . ) a ) M a jor to ma jorch ord . miS c— D D , mSc— m aD D
,e tc . Ascending th e se succe ssions p ro
duce bea utiful e ff ects of sudden brigh tne ss , descending of suddenda rkne ss .
6 ) M a jor to m inor ch ord . S e e %51 , furth e r possibil itie s a re S S — D c ,T— aT,
.mS c — mD D,amT— mT,
e tc .
C ) M inor to m inor . Compa re 2 a ) above . miSS — D c,miS — a S ,
mSSm aD c ,
e tc .
(1 ) M inor to m a jor ch ord . amiSr— a S c or D D , misS - aD r,ac or
m S S — amaD r , ae — maD D , e tc .
3 . Ha lf Tone siep . (E nh a rmon ic with Chroma tic step . ) a ) M a jor to ma jorch ord . (Q54 and D — Tvc
,m aD D — c or mTr
,mD r— amT,
e tc .
5 ) M a jor to m inor ch ord . A ve ry difficu l t step in tona l h a rmony . TamiS r , D — a niiS c, am aD r4 mT,
amaD c— mS ,e tc .
5 ) M inor to minor ch ord . (é54 . ) mTvc— mS , S c or Tr— m iSS , D c
Tv,aT— S r , e tc .
d ) M inor to m a jor ch ord . (é43 . ) D 3>— m iS r , Tr— S S , Tv— miS c , S rTvr
,m aD r— m S 3<,
mD D — mTr,m aD c— mTv ,
mTvr— mD r , e tc .
4 . W/zol e Tone step . (E nh a rmonic with D iminish ed Th ird step . a ) M a jor tom a jor ch ord . (Q Th is ch ord succession m akes th e impression of a
S and D fo l l owing e a ch o th e r,a nd cre a tes th e de sire of h a ving th e Ton ic
a ppear . Th e wh ol e tone step is rea l l y a doub le fif th step,c — (g ) — d .
U sua l ly a ch ord fo l lows wh ich is re l a ted ‘
to one of th e two ch ords . Bu tch ords ca n a l so
“
be brough t in a se rie s of wh ol e tone progre ssions and
produce b ea utifu l e ff e cts a s th e th e e xce rpt of L iszt ’s D an te S ymph onyin Q 62 sh ows . miS r — S S , S S
— T, T— D D ,Tvc— SS ,
miSc— Tyr,Tvr— S ,
T— aS c ,m S 3< —maD
,mTr— m S 3<,
amT— msc , e tc .
6 ) M a jor to m inor ch ord . (é42 . ) S — D 3>,DD — Te or D r
, Tvr— miS ,
mS 3n , mTc or e — m S S , maD — mTvr , e tc .
C) M inor to m inor ch ord . (é22 . ) Compa re 4 a ) . mis— D ”,D 3>— Tr
,
Tv— S r , mT— mD D ,m SS - mT
,mD — mTvr , ac — mT
,e tc .
d ) M inor to ma jor ch ord . (é24 . ) M ake s th e impression of a m inor Sfo l l owed by a m a jor D ,
a nd na tural ly cre a te s th e de sire of h a ving th e
skipped ch ord (th e T of bo th ch ords ) fol l ow . miSS T, Tv— DD ,mT
maD D ,m S S — m
’
h r,e tc .
5 . Aug mented S econd step . (E nh a rmon ic with M inor Th ird step . ) a ) M a jorto ma jor ch ord . amiS - D
,amT— maD D
,e tc .
5 ) M a jor to minor ch ord . (é55 . ) S — aD,mS c— mTvc , amT— mD D , e tc .
5 ) M inor to m inor ch ord . amiS r— Te or D r,m iS S — aT
,mS— am aD
,e tc .
d ) M inor to ma jor ch ord . Certa in ly ra re . amiSc— aD r , amTr— amaD r
e tc .
D im inish ed Tlzird step . (E nh a rmonic with W h ol e tone step . ) a ) M a jorto ma jor ch ord . D D — amiS ,
amaD r— mS c , m aDD — amS ,e tc .
6 ) M a jor to m inor ch ord . a D r— amiS r , amaD r— ae .
C) M inor to minor ch ord . a D — miSS ,amaD — mS S ,
e tc.
(1 M inor to ma jor ch ord . (é aD — S S , mTvr— amT,e tc .
7 . fi l inor Tbird stefl . (E nh a rmonic with Augm en ted S econd ste p . ) a ) M a jorto m a jor ch ord . (Q D D — S , T— Tvr
,aTc or a S r— T,
aTr— D, S S
miS c , mS c ,
— amS ,e tc .
b) M a jor to m inor ch ord . Of good e ffe ct,l e ads l ik e th e W h ol e tone step
ba ck to th e in termedia te ch ord th a t wa s skipped. D — m iS S , D D — miS ,
m aD D — mS ,m aD — msS , S S — miS c , maD c— mD D ,
e tc.
6 ) M inor to m inor ch ord . (é45 . ) 1nD — miSS ,aT— Tc or D r
,Tc or D r
— D 3>, S c or Tr— Tv ,
maD c— mD D,e tc.
d M inor to ma jor ch ord . m iS S — m iS c , D c — D D ,m aD c
maD D,mS S— mS c , e tc.
8 . Th ird step . (E nh armonic with D iminish ed Fourth s tep . ) a ) M a jor to
ma jor ch ord . (Q SS — D D , Tvc— T,Tvr— D
,T— aTr or aD c
,mD r
maD D ,mTc or e — mTv , mSc— mS 3
<,e tc .
17 ) M a jor to m inor ch ord. (Q SS — S r , mD r— mD D ,e tc .
6 ) M inor to m inor ch ord . (Q52 miS S - S r , Tv— Tc or D r, D
3>— D c,
mSS — mD D,mT - mTvc ,. mS — mTvr , amTr or amS c— mT,
e tc .
d ) M inor to ma jor ch ord . miS S — D D,amiS c— T
,miS — a S r , m SS
m aD D,mT— amaD c
,amD r— maD
, e tc .
Th e se fa r re a chmg ch ord conne ctions a fe usua l l y emp loyed for modu la tions .
Th is step can occu r a l so from,a nd to
,th e tonic a s a c lose .
But g ene ra l ly th e re l a tive of th e tonicfol l ows h ere .
T amiSc T mT amaD c mT
9 . Aug mented Th ird step . (E nh armonic with Fourth step . ) a ) M a jor tom a jor ch ord . amiS — a S r , amT— amaD c
,e tc .
6 ) M a jor to m inor ch ord . amiS — S c or Tr , miS c— aS , c or mTramaD
,amD — maD c
,e tc .
6 ) M inor to minor ch ord . amiS c— aT,e tc .
d M inor to m a jor ch ord . Possib l e wi th inte rmedia te cadence s on l y.
1 0 . D iminish ed F ourth step . (E nh a rmonic v‘
Vith Th ird step . ) a ) M a jor toma jor ch ord . T— amiS ,
aTr or aD c— Tvc , maD — amT, e tc .
6 ) M a jor to minor ch ord . U ndoub ted ly ra re . aTc— amiS r, e tc .
6 ) M inor to minor ch ord. aT— miS ,amaD — mT, maD r — amTr or
amS c, e tc .
d _M inor to ma jor ch ord . (5 Tc or D r — Tvc,Tv - amiS ,
aT— S ,
mTvc— mTc or e ,amaD — mTv ,
mD — amT, e tc .
1 1 . F ourth step . (E nh a rmonic with Augmen ted Th ird step . ) a ) M a jor to
m a jor ch ord. (é2l . ) S — S S , S3Q mD r , maD D — maD ,
maD — mTv, e tc .
6 ) M a jor to minor ch ord. (Q S — miSS , D— Tv, maD D — mD ,
mTv— mS ,e tc .
e ) M inor to minor ch ord. (é2 l . ) S r— D 3>, mis— miSS , Tv— mis,
mD D — mD, e tc .
d ) M inor to ma jor ch ord . (Q Th is ch ord conne ction is usua l lyunde rstood a s h a ving th e re l a tionsh ip of S r— D (mD r— mS ) , a nd “
cir
cumscribing th e tonic th us , it is a n importan t me ans of modu l a tion .
Th e step occurs a l so a s :D 3> — T,mis— SS , Sc or Tr— D D
,miSS— Tvr ,
mT— mS 3<,mD D — maD
,mSS — c or mTr
,mTvr— m aD D
,e tc .
12. Tr itone step . a ) M a jor to ma jor ch ord . (Q Th is ch ord conne ctionstands in th e re la tionsh ip of a minor s and ma jor D (ma jor or m inorkey ) , conseque n tl y m ake s a big swe ep , a nd wil l le ad ba ck to an in te rmedia te ch ord . L ike a l l fa r re a ch ing steps it is frequentl y empl oyed inmodu l a tions. m iS r— DD
, Tvc— D D, S S — aTr or aD c
,mTc or e
maD D , e tc .
6 ) M a jor to m inor ch ord . (Q miSc— D 3>, SS— Te or D r
, Tvc— S r .
Tvr— Tr or S c , T— a S ,mS 3Q maD c , mTc or e — mD D ,
mD r— mTvc ,mTr or c — mTvr
,amD — mT,
e tc .
6 ) M inor to minor ch ord . (Q miSS— Tc or D r , mss— maD r , mss- mTvc
,amTr or amS c— mD D ,
e tc .
d M inor to ma jor ch ord . amiS r - D,miSS — aTr or aD c, mS— amaD r
,
ae — maD,e tc . Very distantl y-re l a ted ch ords . Th e e x cursion from
th e re l a tive s of th e tonic ough t not b e with out a n obje ct . Th ese ch ord
successions are used more a s a means of modu l a tion th an as m ovementsW ith in tona l h a rmony.
F ifth step . (.é 18 ) Th e most re adil y unde rstood ste p of a l l . Compa rea l so with Fourth ste p 21 . As can be se en from th e foregoing l ist , a
gre a t number of ch ords fore ign to th e sca l e may be introduced into th ekey, with out ch a nging i t . Ch ords c lose ly re la ted can
‘be re adi ly e x
ch anged a nd fo l l ow one anoth e r , but wh en ch ords distant ly re l a ted a re
brough t a fte r e ach o th e r , th en th ey a re usua l l y succe eded by a n inte rmedia te ch ord ,
one th a t is re la ted to both .
E XE RCI S E S .
Th e fol lowing exercises a re not for figuration ,but a change of
posi tion may occasional ly be employed for the sake of ga in ing asmoother progression to the next chord . M odulations have beenavoided in order to be better able to survey the extensive relationship of chords.
(123) IE T D 3> T amiS c T
5 Sr m iS D2 3 I T
(124) j ; mT mTr e mT mS mS3< mD D m aD D
mD mD r c mSS mS mD r ac
3
mT mTvc maD m aD r mSS mSc mS mT
m aD c mS maD i>
(125 ) 3 T D Tr Sr DD D 7 Tvc m iS
v 1'
5 I “
T Tvr T
(126 ) E mT mTv e mSc mD D maD D m aD9 0 0 e tc .
I I l
mT amD r | mT mTv maD
0
| mTvr m aD D
m aD mS 6 m aD7 mT 9
(127)”
g:miS D r Tr miS c m iS D D D2 3
T aD c T Tc T D D 3> miS r m iS6 D 2
9‘9 I
95
(128 ) 2:mT mD D m aD c «m aD m S c mS 3< m aD r
1 L JmT m aD D mD maD
7
r
(129 ) E : T Tr S r D D D D c D 3> m iSr
T miSS s mis6 T D TF.
(130 ) i mTmTc mS a e m aDD m aD mTmS c mSS
l I L 4
mTvc m aD mT mTvr mTO
(131 ) 3 TTV D r D DcSS miSS miS6
I; a S rI l
-T Tv miSc I Tvc Tvr m iS c miS r miS D 7 T f° '
m aD mTmaD 7 e mT .mTr m aDmaD c
f l’
B I’ e tc.
V
mSS mS D 7
l mT maD mDD I maD mT mTr
amS c I mT mS6 D52
? ” 7 mT
(133 0 1 :T D 7 Tr T D D 3> SS miSS S S r S c DD
D S r a Sc T Tvc miS miSr DD Dc D T
(9
miS c D c D ~ m iS T '
(134) 3:mT mS 3 ,
< maD 7
| mT am aD c mT
maD maD D mSc mS 6 l mT
— 96
I n the preceding paragraphs the most daring chord connectionswere explained . W e went a s fa r a s i t is at a l l possible in the connection of chords related to one and the same ton ic . A great manyof the chord successions considered in these paragraphs usuallyinduce modulation . Th e greatest power of expression in harmonydoes not consist in the frequen t change of key
,but rather in ex
tending the boundaries of the key a s modern composers have done .
Our view of tonal harmony h a s now become extensive, and the fol
lowing chapters lead to more common chord formations and willbring easier work .
CHAPTER V.
D I S C O R D S . C o n c l u d e d .
§ 65 . THE THE ORY OF D I SCORD S . “ fe have already
become acquain ted with some dissonant chords . W e will nowa rrange them in to groups , according to certain principles
,because
then o ther simi lar formations will be understood immediately .
Th e principal and character istic discords ( the D ominan ts with theirseven ths a nd the S ubdominants with their sixths) have been explained in § 28— 30 . D issonance is the in terference with the consonance of a ma jor or minor chord
,and the resul t a str iving to
regain that pur i ty again . D iscords a re full of impulse and spiri t,
and produce a restless craving in the mind . Th e consonance of amajor or minor chord is disturbed
a ) by the a ddition of tones foreign to the complete chord .
b) by the de l ay ing of chord tones by means of neighbor tonesforeign to the chord (Suspensions ) Th e foreign tones enteron the accented beat .
c) by moving a step of a second (h alf or whole tone step) f roma chord tone (passing tones and cha nging or auxi l iary tones . )Th e foreign tone en ters on the una ccen ted beat or
'
p a rt of abeat
,a nd is merely a n insertion between two chord tones .
These a re the most easi ly in telligible but weakest kind ofdiscords , so - called passing dissonances
,
” passing dis
cords ”or
“ passing harmonies .
” We have used them extensive ly in figuration exercises .
a' by c/zromqtz
'
c a l ter a l z’
on of chord tones (Altered chords. )
These four k inds of dissonan t formations can be uni ted inva rious way s in every ma jor or minor chord
,no matter wha t its
function is in the key , whether T,D or S ,
or one of the relativesor correlatives of these .
A. AD D E D TON E S . Added tones to a major chord .
Th e same formations a re possible wi th the minor chord .
98
S U S PE N S ION S in a major chord,ca n be used also without
sharps and flats:
6> ‘fi15> s
'
o> 8 2 < 3K 3 35> s
u 2< 1 u §< 1ug< i é
'
2< 3
S ch ub e rt . Am M e e re .
E x . 1 0 6 .
Th e resolution of a suspension may be deferred (disguised ) byinterpolating tones of the resolving chord between the suspensionand its resolution a) a nd b ) . This is a n ornamen tation of the dissonance . Th e ornamen tation may be varied in many ways c ) .
D 7 T9
A r esol ul ion o} p rog r ession occurs in the case of a suspensiondissonance
,when the progression of the pa rt takes place which
,
had the chord remained , would have removed the dissonance , butat the same time several parts move
, so that a newchord is produced . Th e suspension (fourth) c ce rta in l ygoes to the third b
,but the other parts move at the
same time to the chord of the seventh on e .
C . PAS S I N G TON E S . (Pa ssing ha rmon ies derived from a concord . )
f“
(33
4 1‘
u g/\
Tsch a ikowsky . Op . 37 , N o . 12 . Ch ristma s.
E x . 1 0 7 .
T aiz z c
1 0 0
Apa ssing tone may en ter freely on a heavy beat with more or
less good eff ect,for example
L eading tones (that is , tone s a ha lf step above or below a ny toneof a chord ) can be used , irrespective of what precedes
,a nd at a ny
posi tion relative to the rhythmic division of the music . I n the fo llowing example a leading tone (c ) is sustained a s a suspension toneinto the next chord . Th e auxiliary tone anis sustained a s a suspension , while efZiZ acts a s mere auxiliar y tone between th e two diz’s .
W agne r . Tristan a nd I sol de . Act I I , scene 2 .
E x . 1 0 8 .
D . CHROMATI C AL TE RATI ON O F CHORD TON E S .
Al tered ”chords a lso in four pa rts with the unchanged form of
the altered chords . )
M oza r t . D on J uan Overture .
E x . 1 0 9 .
— 1 0 2
S uspensions in t/ze D 7, 0
9a nd 0 9 >
(se e
D go> 9>
Ha
w
p.
R
u
m
mono
Al te r ed Tones in M e D 5
Al ter a tions e tc.,in fi l e D 7
, 09 >
a nd D 9.
$0 ) if? )s>
Al ter a tions e tc.,of t/ze [Maj or S ubdomina nt ,
Al ter a tions,e tc .
,of t/ze M inor S uodom ina nt .
Only a very limited number of possibi li ties h a s been pointedout . Because i t is exceedingly instructive
,the studen t is requested
to work out discordan t formations of a number of major and minorchords of differen t keys . I t will teach the studen t to unravel themost puzz ling chord forma tions
,a nd he will lea rn to refer them to
their respective tonal functions in the key . Solely from this securerock can any successful advance be ma de in to the endless se a of
possibi li ties . Th e studen t should from now on analyse the ha rmon icconstruction of composi tions . At first
,these should be simple songs
,
dances , lighter piano pieces , sonatinas , and gradually the works ofBach ,
Haydn ,M oza rt , Weber , M endelssohn ,
Beethoven, S chubert ,
S chumann ,Wagner
,e tc . should be thoroughly studied .
Th e fol lowing se t of exercises is to be worked out in such amanner that every example , a s much a s possible
,uses prepa red
dissonances on the accen ted beat . As before , work every examplewith figura tion of the SOp rano ,
alto,tenor
,ba ss a nd with figura tion
divided among the four parts . Remember the following in regardto the working out of these exercises
A) F or the prep a r a tion of tne dissona nce a chord tone en teringon the preceding unaccented beat will serve (the chord tone ca n bea prime
,third or fifth of a ny major or minor chord , also the sevenths
of ma jor or minor D ominan t chords or the sixths of major or minorS ubdominan t chords) .
B ) Th e dissona nce must move 5] step of a second. On ly the 6 ofa major or minor S may proceed like a fundamen ta l tone , when theS 6
‘
a cts l ike a D 7of a D ; se e 30 .
C ) When the pa rt to be figured offers no opportun i ty for theuse of a prepa red dissonance on the accented bea t , the syncopationis to be con tinued by ty ing a note common to bot/z cnords . In sucha case the syncopated pa rt need not necessari ly move by step of asecond ,
but i f possible may move to a chord tone which will give aprepared dissonance for the next accen ted bea t .
D ) In figuration of measures contain ing three bea ts , or wherethe figuration is to use three or more notes to each chord of theother pa rts
,on ly the note immediately preceding the accented beat
is to be tied . Th e syncopation is then on ly pa rtia l , a s ca n be seenfrom the following short i llustra tion .
— 1 0 4
(Rh ythm :o‘ la ' )
E x . 11 0 .
T Tr 8 S r D2
(Rh y thm $1J. divided fig ura tion . )
E x . 1 1 1 .
D Tr S S r D 7 T
Because the syncopa tion merely delays a tone, consecutive
octa ves a nd consecutive fifths which would occur i f the syncopationwere not employed , a re forbidden .
Octa ve s.
E x . 1 12 .
Th e fol lowing example will help to make the a pplication of
the rules c lear . We will fi gura te the tenor pa rt .
— 1 0 6
§ 66 . DOM INANT N INTH CHORDS . Th e principal discords,
have been explained in 28— 30 . I t wa s poin ted out that aseven th could be added to the D , § 28 . Other seventh chords havebeen exhibi ted in the preceding pa ragraph a s suspension or pa ssingchords
,e tc . Th e on ly time a ny other seven th chords tha n D 7 may
assume grea ter importance,will be shown in
,
the para graph on
S equences . Th e D 7 borrows its added tone from the S,the
seventh is the 1 of the S . Th e D omina n t N inth chord (D 9 ) borrowsthe 1 and 3 of the S , (in C-major i t is G b d f a ) , and since we havea miS ,
this chord h a s a sister ”
in the major key,when i t borrows
the 1 and 3 of the m iS (in C-ma jor , Gr b d f ah) , the D ” . Th eminor key h a s only one D n in th chord
,n amely the maD chord with
minor n in th These chords a re used with great freedom .
Schumann begins h is Over ture Genoveva with this chord
E x . 1 14 .
m aD 9>
Haydn,in h is Quartet in G , Op . 76 , uses the D 9 thus
E x . 1 1 5 .
Being derived from the D the D 9chord h a s the same qua li t ies
a s the D ominant,a nd resolves like i t to the T.
E x . 1 1 0
D 9 D 7
I n 3 1 the fa ct wa s men tioned that the disson a n t tone of a
principa l discord may be used a nd“ then be dropped without requiring
a subsequen t resolution ,a nd thus the 9 ca n disappea r without reso
lut ion . S e e E x . 1 15 . I n four pa rt harmony one of the notes h a s
_ 1 0 7
to be omitted . As usua l , the fifth can b e most rea dily spared,but
the third a nd seven th can be left out , very often the prime is omitted .
Th e leading of parts wil l decide which is the best for each ca se .
E x . 1 1 7
9”9 '
9D5
T D/7
Generally,the tones ha ve to be kept well apart . Th e chord is
particularly well adapted for instrumenta l music . I t sounds bestwith the prime in the ba ss , although other tones can be used . Th eomission of the prime of the D ominan t chord With lowered (minor)ninth
,produces the familia r D iminished S even th Chord
se e 79 .
O ther nin th chords than these must be expla ined a s suspensionor pa ssing chords and sometimes a s sequentia l chords
§ 67 . Very rarely wi ll i t become necessary to employ thatformidable looking chord , the DOM INANT E L E VE NTH CHORD(D I t is the D omina nt with ‘the 1
,3
,5 of the S superimposed .
This chord h a s six tones , but usua l ly one or two a re missing . Whilesome theorists deny the existence of this chord altogether
,o thers
have tried to explain the en tire key by means of the Ton ic chorda nd this D ominan t eleventh chord . There a re tone combinationswhich a re expla ined satisfactori ly on ly by referring to this chord .
I t is one of those chords which directs attention to Organ po in t formations . I t h a s the cha ra cter istic of all principa l discords tha t the1 1 can disappear without resolution .
T’
Dg'
D9 T
\V a g_ne r , Trista n a nd I sol de . Vorspie l .
E x . 118 .
68 . DOM I NANTTHIRTE E NTH CHORD . To the chordsof the D 1 1 trea ted of in the preceding paragraph
,another third
,
either major or minor , can be added . As each ma jor a nd eachminor thirteen th can have a major or minor n in th with i t , i t fol lowsthat there a re four varieties of the chord .
M a jor Key . M a jor Key. M a jor Key . M inor Key .
E x . 1 19 .
— 1 0 8
As a matter of fact these chords never appear in their completeshape , partly because some of the tones fo
‘
rm harsh dissonances withone another , a nd partly also because most music is wri tten in fourpa rt harmony ,
where at least three of their tones must be omitted .
In many cases all of the lower part of the chord is wan ting . Sometimes only three tones of the chord appear .
“ fa gn e r ,Trista n a n
'
d I sol de . Act I I . I ntroduction .
0E X . 1 - 0 .
Compa re E x . 137 .
p t . D Ib9>
LI
53
I n the ma jori ty of ca ses the chord of the thirteenth may betreated a s a suspension chord . S ti ll there a re instances in whichthe movemen t of the tones is such (skipping from tone to tone orletting one disa ppea r unresolved ) that the chord must be lookedupon a s a fundamen tal discord .
§ 69 . ANTI CI PATION . Th e an ticipa tion is to some exten tthe reverse of
’
the suspension,a lthough not so important a s the
latter . Th e suspension delays a tone of the chord already sounded,
while the an ticipa tion precedes i t . Th e suspension is placed on thea ccen ted part of the measure or beat , the an ticipation on the uniaccen ted part . Th e antic ipa ted tone may be rea ched by degrees(a ) or skips (b ) . I t genera l ly occurs on notes of short duration
,
a nd usua l ly a ppea rs in the upper pa rt , but i t may occur in a nypa rt
,or a l l .
b ) a nt . c ) ant . (1 ) ant .
E x . 121 .
'
Th e anticipation may occur in several parts (se e c ) . Atthere is an in terpolated tone of the sounding harmony between thean ticipation a nd the chord to which i t belongs . S uspension and
an ticipation can occur simultaneously in one a nd the same chord
— 1 1 0
Th e an ticipation can be used in a syncopated manner
E x . 126 .
Th e following wonderfully exquisi te melody of the great masterdisplays anticipations , suspensions and mere syncopations . Th e
studen t should fi nd them .
Be e th oven . I X Symph ony . Andan te modera to .
v e spre ssivo .
E x . 127 .
o 4
rv
o 4
V I
Sometimes even suspension or passing tones may be anticipated .
”
§ 70 . M E L OD I C E MBE L L ISHM E NTS (Concluded ) . I f two
chord tones are'
a fourth apart , a s for example,in ascending from
the fi fth to the octave of a chord there will be two passing tonesbetween them . I f the tones a re farther apart , more passing tones
can be inserted . Th e p assing tone is a toneforeign to the harmony , passing diatonical lyor chromatically between other tones belonging
to the chord .
— 1 1 1
E x . 128 .
Pa ssing tones may occur in several parts at the same t ime .
Passing tones by skip can appear thus
E x . 129
These passing tones a re merely the neighbor tones to the oneswhich follow . Another kind of pa ssing tones by skips consists inlaying hold of the neighbor tone in the opposi te direction to the tonewhich fol lows
E x . 130
E ven a suspension tone could be embellished simila rly
E x . 131
Circumscriptive pa ssing tones (double a ppoggia tura s ) consisto f the lower and upper (or vice versa ) a uxilia ry of any chord tone .
E X . 132 .W’
ebe r . Ronde a u bril l an t .
— 1 12
Th e lower auxiliary tones used a s embellishmen ts sound usuallybest when they a re a half tone step below the chord tone . Th eaugmen ted second in the Harmon ic M inor S ca le wi ll have to beconsidered a s the result of the use of passing tones by skip .
Th e Chromatic S cale is but a diatonic scale with chromaticpassing tones , lea ding- tones to the dia ton ic tones .
Ascending . D e scending .
Th e notation of the Chromatic S cale depends upon the key inwhich i t occurs a nd upon the chord with which i t is connected. Th eascending Chroma tic S cale h a s sharped (ra ised ) , the descending ,fl a tted (lowered ) tones .
§ 71 . There is a kind of syncopa tion in which two or moreparts merely drag be/i ind the rest .
Regu l a r progre ssion . D e l ayed prog re ssion .
E x . 133 .
e tc .
X -5 ‘
Compare the famous unisono passage in Beethoven s OvertureL eonora ”
(N o .
72 . D E LAYE D PROGRE SS ION S . One or more pa rts maydelay a n expected progression ,
thereby forming tones foreign to thechord . These delayed progressions a re altogether differen t fromsuspensions
,a s the parts may move by skips
,which would preven t
the use of suspensions,because these must resolve by degrees.
xHaydn . Sona ta E minor . Fina le .
I .
4
E x . 134 .
— 1 14
I n the next i llustra tion the grace note c); is a delayed p rogre ssion and acts like a suspension W t h falls to g instead of going to d(or possibly b ) .
Bize t . Ca rmen,N o . 5 .
E x . 138 .
CHAPTER Vl .
SEQUENCES, INTERMEDIATE CADENCES , PEDAL POINTETC, ETC.
73 . S E QU E N CE S a re the repetitions of a long or shortmotive (group of tones or seri es of chords ) up or down the scale .
Th e sequence is not really an harmonic,but a melodic formation ,
and so long a s the sequence lasts,the harmonic functions a re sus
pended,which explains why leading tones and dissona nces may be
doubled , e tc . I t is also here where other seventh chords than theD ominan t seventh chord
,seem to appear with equal rights
,yet they
have not the lea st tonal sign ificance or influence,they a re merely
copies (shadows ) of the chords in the motive . A sequence requiresat lea st two repetitions of a motive . Th e series of chords used a s a
pa ttern must proceed logically and be faultlessly connected . Th eviola tion of rules that do occur in the imitation ,
a re a mere natura lresult of the strong melodic curren t contained in a sequence , whichis a fter all but a mechan ica l tra nposition . Th e Spiri t of persistenceprevails in a sequence . A sequence can even exist in one pa rt .
Th e following ha rmon ic sequences (which a re so many simultane ous pa rts ) will explain what h a s been sa id .
E x . 14 0 .
— 1 15
[SK D7 D 6 Tn] inks mD c e mSjl
Because in the imitations of the sequence motive the tonalfunctions cease to operate for a time , there is no reason of trying toindicate them . Therefore we on ly mark the chords of the motivea nd mention whether the sequence ascends or descends . Bra cketsmean imita tions and the number of blank brackets indicate thenumber of imitations desired . Th e extension of a motive is almostun l imited any figuration in the motive may be accurately imitated .
Y e t the sequence h a s never been bound to strict exactness . Com
posers often produce fi ne effects by slight changes . Very in terestingexamples of this kind will be found in the first eighteen measures ofM ozart’s well known C—minor Fantasi a (e Sonata) . S equencesusually imi tate at the in terval of a second ,
but can do i t also at thein terval of a third or more . Very often they then move in to otherkeys (se e 81 on M odulating S equences) . A beautiful i llustrationof such an one is given here , i t contains an in termediate cadence(se e
Wag ne r . Ta nnh auser Ove rture . a sc . seq:a t th ein te rva l of a th ird .
E x . 141 .
D 7 Tv D 3> (D )an t . S S
— 1 16
E xcell ent eff ects a re also obtained when the length o f thesequence does not coincide with the time of the measure
,and thus
the chords (or tones ) which correspond wi th one another come ondiff eren t beats of the measure .
Be e th oven . L eonora O verture , N o . 3 .
a sc .
E x . 142 .
A fi ne example of a n a scending sequence using the in termedia tecadences (se e 74) is the following
W agne r . S ieg fried ,Act 1
, S e cond S cen e
a sc .
E x . 143 .
m8 mT1 < maD D mS 3< mS c maD mT
I n moving from one phrase to the next,consecutive fifths or
octaves resulting from the last chord of one phrase to the first chordof the following phrase a re unobj ectionable .
‘
A similar example of a sequence of augmen ted tria ds is thefollowing
W agne r . M e istersinge r, Act I I , First Scene .
E x . 147 .
W i th great freedom in the figuration,the chord tone g is used
instead of the chord tone b which is nearest to the pa ssing tone ;and simi la rly in al l the chords following . I n § 72 i t wa s shown thata suspension tone can be made to resolve by skip to another than itsproper a nd expected chord tone . I n the i llustration above
,a simi lar
liberty of p rogression occurs in that the pa ssing tone does not issueforth from the nearest chord tone but by skip from some othermember of th e chord .
With the following exercises for sequences , the attempt at fi vepart wri ting will be made . Th e five parts a re to remain within thesame total compass retained throughout this text—book . Th e twolower parts may occa siona l ly be distan t a n octave from the threeupper or the three lower from the two upper . D oubling of thirdsand fi fths will happen more o ften
,but the former rules regarding
them hold good . Th e following example may ser ve a s a n i l lustration .
T DZ T S E? S r
E x . 148 .
1 19
E XE RCI SE S . (I n five pa rts . )
Because i t a ffords good practice in reading score,the s tuden t
ought to work out these exercises on five staves every pa rt is to beon a separa te staff.
a sc .
3 1 71 1
w a s.
M r ?
L A l — l I
TTc Tr S S r D r Tr S r D T f_l
mT m aD mS mT e mTr m aD e
I l l ‘w I
mTc mTr mS e
j: r
de sc .
” _Wl I f
”
(ma g:TD 7 T S6 Tr
u
miS ID i g7
| T r
m aD mT m aD mT mS m aD7 mTc mD r
0
u n a'
mTr msg<maD e7<
msn r ”1 5 mS6. m aD mD D maD
mT mS c ma f,> g7 mT l
'
— 120
5
(147) T D T Tr Tr S r3_Q
3
D D 3> m iS6 T m iS c m iS S
6 D 7 T 9
f—
1 r r
(148 ) 2:mT m aD7 mT
0 0 3 1
I I 6 o
-1
I
m S m aD mT0 0 0 0 9 9 .
I I I I I I I I
74 . INTE RM E D IATE CAD E N CE S . S ome st-udents‘
mayo ften have felt the avoidance of familia r chromatic alterations in theexerc ises a s a restra in t . M any of the successions developed in thefollowing
,may by experience have frequently en tered their minds .
But our a im wa s to develop the bounda ries of the key to the utmostexten t . A key is a circ le of chords , and the studen t wa s taught tounderstand
,in their relation to the tonic
,chords apparen tly very
remote from it . In this paragraph chord successions a re in troducedwhich a re generally called transitions
,not modulations . Amodula
tion is the process o f pass ing out of one key into another , mean ing,an actual change of ton ic . M odula tions
,a fter a ll
,a re to be j udged
a s ha rmony steps (chord connections ) o f which they a re the reflex ,
that is the new ton ics reached by modulation must always be understood similar ly a s chords within the key . Amodula tion is close whenthe new ton ic reached is c losely rela ted to the ton ic of the old key
,a
modulation is remote when the new ton ic reached is remotely rela tedto the ton ic of the old key . M odulations h ave tonal functions in ahigher degree or sense . I n transi tions
,which we ca ll I ntermediate
Cadences (or M iddle Ca dences ) there is no change of any tonalfunction . Th e T remains the main center of the key , but in in termedia te ca dences the other chords (functions ) of the key a re madesubordina te cen ters
, surrounded by their circles o f chords . I t is
simila r to the solar system . Th e sun is the cen ter of our planeta rysystem
,but some planets have their sa tellites , a nd these revolve
around the planets a s their cen ter . Th e simplest forms of ca dence,
the connection of the ton ic with its dominants of the same mode , are
T— S— D — T and mT— mD — mS — mT.
These will appear differen tly when we chromatical ly change atone of a chord or add a tone foreign to the scale so tha t each chordbecomes the domina n t of the next
— 122
D r D'7 T T (mS maD7 ) miS (S 6 D ) m iS r miS c D ID
9> D
mT (mS maD 7 ) mS (S D ) e mS 6 m aD 7 mT
W agne r . L oh engr in ,Act I , S cene 3 .
E x . 152 .
(s'
ss misE'
S ch ubert . Impromp tu , Op . 9 0 , I I I .
E x . 153 .
am iS r
— 123
Tsch a ikowsky . Op . 37 , N o“
. I 2. Ch ristmas.
E x . 154 .
155 .
W agne r . M e iste rsinger , Act I I I , S cene 2 .
W a l th e r . S a ch s.
What rul e wi l l mycommencement fi t ? Firstmakeyour rul e, then fol - lowit.
7
r 7 -1
IbIZIZ a I IDfi ) [e enh f I2 | miS c
Isa t }3 2 dfl
ICIZ enh b _J
Your dream a l one l et 0 c cu py
124
E x ..156 .
S ch ubert . M omen ts M usica l s . Op . 9 4 , N o . 1 .
pg 7 TD T D Trt (D73 1
E x 157 .
W agne r . L oh engrin ,Act I
, S cene 2 .
93>
aD D (D2
S e e E ssa y , pag e 15 .
aD D r
126
T 86 D7 T(mS6 7 T mT(mS6 maD) [mD]c m86 maDmT
S7 <
W agne r . M eiste rsinge r . S e cond Act , second scene .
E x . 1 61 .
(D 7 ) [S c] (D 7< 7 ) miss 6>
5 m iS c 4 3 7 ) [S r] ss 4 s s'
D 7 4 3
Al l this shows tha t a ny tona l chord can be embellished harmonica l ly ( intermediate cadences a re finally nothing but ha rmon icembel lishmen ts ) by a D ominan t with a 7 or a S ubdominan t with a 6like the Ton ic ; and can also be treated like in a deceptive close ,S e e E x . 161 , measure 6 , or measure 7 .
In order to read quickly the chord signs enriched by thesenew resources
,a nd to have in mind a t once the chord successions
ca lled for,the studen t must , whenever he comes to round brackets
look directly to the chord after them (un less a n arrow pointsbackwards ) , and consider i t a s th e ton ic (center ) of the inte rmediate cadence . Th e abbreviation enh in some of the exercisesindicates an enharmonic ti e .
127
E XE RCIS E S .
( I n four pa rts . Free use of figuration tones e tc . permitted . )
T I mi86 Tr (D
7
) m iS c D2 D D7
3 3>
T (D7
) s D ”D Tr m isr m iS T
mT mTr mD (D7
) m S (D7
) m aD (D7
)
(D7
) [111 5 ] mS c m aD g>7
56 D 2 2 S I D r (ms fi m aD )
S r S (111n m aD mS 3 < xm aD ) Tr .
6
(D ) S D i7 T (
9
(152) g ; ml
T 3< mS K D 7 mTv -mT mD (ms6
maD7
) mS mS2< m aD7 mTv
(153) a :T | s5
| m aD 7
) ITr D D 7
D T D c D T 23 T
(154 ) E :mS mT. mD (12386
) mD (D ) mD mT
(ms6 maD ) [m aD r] (D ) [mTvr](D
e) m aD D 7 m aD ImT
(155 ) E :T Tv D D - (D ) [D r] I D3>
(D7) I 5
6 5
I
(mS6 maD ) ITo Tr ID lfi
9> D 7
IT
128
I
(156) if:D IZ)9> D (D
9>) mTr (DDr S ) m S (D
9>) mS
m aD (m iS6 D ) I mD r (8
6D 7
) [mTc] (mS rna i>7
)
1n S6
(D ) rnaD I mT
I
(15 7) E :T (D7
) [Tr] S [D r] Tr9
) D D7
T 5 D D7
(D7
) D r S r D 27 T
3
(158 )”3 mT mS (D
7
) maD mT maD (D D7
0 9 5> 5>I I
D 7
) [mTr] mS6 m aD 1nT mTr (1115
6
3 e nh 3
(159m:D 159
(D7
) [D r] Tvc m iS c-
I(S ) D 7 mg g
5 > e nh 3
D (miSG D 7
) D D D 7 T
1nT m aD D m aD (m iS c DD95) [maD ]
w I I
m aD r 1nT (D‘
) mS c (D7
) [mS] e mTr (11186
D 7
)3
mTr (mS6
m aD ) mD r ( 111 56 m aD
7
) [ms]
msc mS§< ma i> 7
0 O
— 130
M e nde l ssoh n . S ong W ith ou t words , N o . 9 .
E X . 1 65 .
(D7) D
In instrumen ta l music the ton ic chord is sometimes trea ted a s a
sort of resolution in a lump of the mass o f a ny of the discords builtupon a major D omina n t . Th e ma ss of harmony that follows is regula r
,although the progression of individua l parts is free .
Haydn . Sona ta in D .
E x . 1 66 .
Here the 7 o f the D is not reso lved by degrees to the T butthe ma ss of ha rmony of the T fo llows the ma ss of ha rmony of
the D 7
76 . In M odern Ha rmon y a ny concord (major or minor ) ca nbe succeeded by a ny o ther concord , un i ting especia lly well whenthere is a tone in common , but they can follow ea ch other also whenthere is no tone in common .
The ultimate resolution o f a discord in to a concord can be constant l y postponed ,
although the harmon ies change . Any seven thchord (or other discord ) can follow a ny o ther seventh chord (orother discord ) . E specially well
, when there is a tone in common .
Besides,the second chord may be resolved in ano ther octave
,or in
a ny posi tion whatever , that is irregula rly .
” This is one of themost modern devices for sta rtling effects
,
S ometimes the chordsa re chained by enharmonic modula tion ,
that is,a sharp in one chord
may be tied over to a fl a t in the following chord , or vice versa ,because the two notes represen t the same sound . S uccessions of
discords will na tura lly lengthen the periods of unquietude . I n
connecting discords the shi fting of dissonan t tones must proceed inhal f a nd whole tone steps . Th e dissonan t tones , instead of resolvingdiaton ical ly may either remain stationary , forming part of the newchord , or may progress chroma tica lly . Sometimes the enharmon iccha nges a re expressed in wri ting ,
a nd sometimes not .
- 131
77 . S ome a ltered forms of the D 7,D D 7
a nd D ID9 > have beengiven special names:“
I ta lian S ixth chord , ” French S ixth chord ”
and“ German S ixth ch
‘
ord .
” These “
na tiona l ” terms a re unrationa l a nd useless .
I ta l ian S ixth . French S ixth . Ge rm a n S ixth .
E x . 1 67
D IDZ> D 131752? I?)T)
78 . M OD U L ATI ON (Con tinued ) D IM IN ISHE DTRIAD S . I n 33 i t wa s poin ted out that the omission of theprime in the D ominan t S eventh chord (10 7 ) and the omission Of thefifth in the minor Subdominan t sixth chord (mSg, mn ) producesthe so- called “
d imin ished _tr ia d .
” When the pr ime of a ny ma jorchord is ra ised or when the fifth Of a minor chord is lowered thesame chord forma tion of a dimin ished triad arises
c1 <c jI e g , c e .
E XE RCISE . Change by chromatic altera tion every major a ndminor . chord ( the principa l , rela tive a nd correlative chords ) in thekey in to dimin ished tria ds , a nd let them proceed once a s mSS; a ndonce a s 1237 . There will be two modulations from each dimin ishedtr iad and each modulation again ,
can go to a . major or minor key.
A few wi ll not lea d out of the key ,a nd the thoughtful studen t will
pe rceive _why such is the case . W ork in three part harmony .
D7 I n C major :c 1 < — fl 7 leads to d or dm key .
I n C major c emgleads to b or bm key .
1157 In A minor am leads to bIz or bIzm key .
ImSgIn A minor am leads to g or gm key .
HIT 5>
A dimin ished triad is a symmetrically constructed chord in tha ti t consists of two minor thirds . L ike al l symmetrically constructedchords i t is adapted for enharmon ic changes and consequent ly
'
can '
produce modulations . Th e D iminished S even th chord 79 ) isthe greatest favori te for such enharmonic modulations . E nharmon icchanges a re frequen tly used in modern harmony , but they ought notbe indulged in to excess .
E X . 168 .
T T 1133z T T 5 enh 9> T 10 5 enh 3 T
7 enh 3 (mT) 12) (mT) E 7 10 (mT) (mT)f? 5 71
— 1 32
79 . M OD UL ATI ON (Continued ) . D IM I N ISHE DSE VE NTH CHORD S .
” These chords a re characteristic a nd veryeffective forms O f
“ the D . Altogether the D a nd all chords derivedfrom i t a re great favori tes . Th e diminished seven th chord is usuallya D 9> with the prime omitted . Th e chord consists then of threeminor thirds on top of ea ch other
,a nd is termed “ diminished
seven th chord ” beca use that in terva l is found between its lowesta nd highest notes .
D iminished seventh chords ca n be made to arise by raising theprime of a D 7
or by lower ing the fi fth of a minor S 6 chord . I n
C-major D 7(g
7 lea ds to a or am key . mnlea ds to eIz or e Izm key . In A minor
mSg5> —
ID9> (d — g9> ) l e ads to c or cm key . maD 7 K
D.” (e 7 leads to fII or fIIm key .
D iminished seventh chords may be formed a t a ny t ime bymerely ra ising the prime of a ma jor chord a nd adding the seventhor by lowering the fifth of a minor chord a nd adding the s ixth .
c e g — cII e g bbz cka c e — fg a c e Iz z am 5>
(i
Th e studen t should thus alter every principa l , relative and cor
rela tive chord in the key a nd fi nd out to which major or minor keyit l e ads .
Th e dimin ished seven th chords ha ve especia l importa nce fromtheir chameleon like quali ties
,that is the possibili ty O f numerous
enha rmonic changes Of mea n ing of single notes . E nharmonicchanges a re greatly indulged in in modern harmony . These chords ,
being built of three minor thirds On top Of ea ch other , a re cer tain lyvery symmetrica lly constructed chords . This very symmetry makesthem pa rticularly ada pted for enha rmonic changes . Th e followingwill show that every dimin ished seven th chord equals four otherdimin ished seven th chords .
E x . 1 69
¢ 9>E F 3 lpg> enh 5 s enh 9> 7 enh-
5 3 ant:s
m9> m9>m9> ID 12597 1259 115n
To th e e a r the a bove chords sound all a like , but the enha rmon icchanges induce difi e ren t progressions o f the harmon y . There a reon ly three difi e re n t ly sounding dimin ished seven th chords
E x . 1 7 0 .
134
Often the D9> seems to be but a.
leading tone chord .
” Th efollowing excerpt i llustrates where a n apparent D ID9> is but alea ding tone chord and where i t is a true D 10 9 ?\Vagne r . Tannh
'
ause r Ove rt ure .
E x . 1 73 .
D ID9>z l e ading tone ch ord to T(th e g ough t to b e re ad a s f x
l e ading to gfi , th e afi l eads tob
, and CI:to b . )
S v a .
Th e chords most common ly used for intermediate cadences a re
the D 7,miS 6 , S
6a nd Wagner h a s even embellished chords
by the correlative of the subdominant .
W agne r . Fl ying D u tchman. Act I I I , I ntroduction .
E x . 174 .
miS r (mS c ) mis (mS B)bfl ischromaticpassing tone.
‘
Th e fol lowing excerpt contains in measure 8 a suspension (orleading tone ”
) chord to the ID” . Observe the chromaticallydescending melody from measure 5
,and h ow the most distantly
related chords a re brought in succession .
— 185
W agne r . W a lkure, Act I I I , S cene 3 .
E x . 175 .
D e (mis ams maD
amD (m9> ) mTv ffi=gI2 to fa(E 9>) mTc77> 7 «w ! ea to d
3< an bIZIZ to a lz
bt? a# to bh
L isz t h as wri tten a rema rka ble scale of whole tones in h is
Traurige M Onch .
”
E x . 176 .
Th e piece ends in C-minor,the Tv . Th e scale of whole tones
moves through the D 1 3> chord in wh ole tone steps . According tosound c is a whole tone from b a nd a whole tone from eIz, but goingto e lz the cIIought to be thought a s dIz. Altogether a highly interesting piece to analyse . Compare E x . 86
,from L isz t’s D ante Sym
phony ,where the ba ss moves in a whole tone scale .
- 136
8 0 . M OD UL ATI ON (Con tinued ) . AU GM E NTE DTRIAD S .
” Th e augmented tr iad is the opposi te of the dimin ishedtria d . I n regard to its capa bili ty of inducing surprising modulations
,i t nearly equals the diminished seven th chord . I t consists or
two ma jor thirds,the tones stand at equal distances
.from one
another . W hen the fifth O f a ny major chord is raised,or when the
prime O f any minor chord is lowered then a n Augmen ted Triad isformed . I t derives its name from the augmented interval found .
between the lowest a nd highest notes .
E XE RCIS E . Change every ma jor a nd minor chord of a keyinto an augmen ted triad .
Th e symmetrica l construction O f the chord makes i t pa rticularlyadapted for enharmonic modulations . Th e fol lowing enharmonicallychanged chords sound alike to the e a r , but at a) the a ugmented fifthis in the highest part
,at b) in the middle part , a nd at c) in the
lowest part
E x . 1 77 .
There a re on ly four differently sounding augmen ted tria ds , a l lthe rest a re inversions or enha rmon ic changes of these
(1 )
E x . 1 78 .
Th e studen t should change them enha rmon ica lly a nd fi nd to
wha t chords they would lea d . Th e fo llowing will serve a s a n i l lus‘
t ra t ion .
a ) Th e ba ss tone is the dissona n t tone ( the tone tha t h a s to
move ) :
E x . 179 .
b ) Th e third is the dissonan t tone
E x . 18 0 .
— 138
XVague r . Tristan and I sol de . Act 1, Scene 5 .
E x . 1 86 .
mTr with 5 <a sc . sequence .
z a II
S e e a lso the examples N OS . 146 , 147 a nd 143 .
This chord h a s certainl y a n almost endless va ri ety of possibi lities and a wonderful flexibi li ty .
§ 81 . PE DAL PO INT or ORGAN POI NT is the name fora prolonged bass tone , upon which is formed a series of chordswhich can also include passing chords foreign to that tone . S tanding among themselves in correct connection the chords move moreor less independen tly from the bass tone . Organ point formationsa re a n extension O f the ha rmonic apparatus a nd consequently thisparagraph concludes the explanation of the most complicated tonecombinations . I ts name h a s been derived from organ music
,where
deep tones long sustained a re played on the peda l key- board by theplayer ’s feet . Th e harmon ic domain wa s in time extended
,and
long sustained tones (pedal poin ts ) a re now also found in the middleand higher regions . Th e pedal tone when first sounded
,or finally
quitted,must be a member of the chord above i t . Th e pedal poin t
wa s undoubtedly developed from the D 2, which may be looked upona s the germ o f the peda l point .
7
D2 8 8 r D 7 T if1 1 8
D 1 1 T
139
Th e most effective tone of the peda l poin t is the prime of thetonic ,
a s an auricular i llustration that a ll ha rmon ies a re thought ofin connection with the tonic . Th e 1 of the D is a fa vori te bass fororgan poin ts . And sometimes the prime a nd fifth o f the ton ic a re
used,producing a so — ca lled Double Pedal . Amost exquisi te ex
ample of this is Chopin ’s Berceuse
,Op . 57 . E ven the 1 and 5 of
the T a nd 5 of the D have already been employed a s a Triple Pedal .I n this manner even the D 7 h a s been used . Th e 1 of the S mayalso be used a s ba ss . Apeda l may Occur in ei ther an upper
,middle
or lower part . I t is most eff ective a s a bass . Th e‘
oth e r posi tionsa re named “ inverted pedal . ” Then the famous passa ge in Beethoven ’
s E roica ”
Symphony may be ca lled a D 7 inverted peda l,
wi th the T tones below it
E x . 188 .
T
Th e spiri t of uni ty pervades in the peda l point . Th e pedalpoint need not be merely sustained or repeated but may have anyornamen tal figure . I n Analysiswe separate the pedal
,a nd indicate
chords above i t a s we always did . Th e following example con tainsintermediate cadences .
miS 11
32 (D 7 ) Tr (D 7 ) S r (D 7 ) D 7
T(D7 ) S mis T
1 1
Amodulating sequence (see E xamples N OS . 141,143 and 144 )
can be combined with a pedal point . This taxes the power for tonalperception to the utmost .
asc.Mod. seq.
E x . 190 .
7 3’
v 1
S miS 6 D 4 3 T miS r miS 6 D T
— 14 0
I n a modula ting sequence not on ly the melodic pattern but al sothe harmon ic one is imita ted , by ha ving successions of functions t ep ea ted in other keys .
E XE RCI SE .
JJ. J JJJJ(165 ) g ; T Tc Tr(mS “ S r (D
7
) e7 T S
1 1
Tr (ID9>) Tr m is
6 7 7 T (D7
) SS (mSS D )
1
2< 3
S m iS6 D2 aTc 8 6 D DT D (D
7
)1 1
Th e u5 (unde rfi fth ) o f the D is the prime O f the T. I n thesecond la st measure of the above exercise the D 7
can be considereda suspension chord delaying tones O f the ton ic .
82 . M OD UL ATI ON (Concluded ) N ot on ly singlechords but a lso single tones can be ma de the pivoting poin ts Of mod
ul a tion . Th e different possibili ties a re
1 ) a dissonan t tone becomes a member of a concord,for ex
5 < 5
ample :cfim
2 ) a member of a concord becom es a dissonan t tone,for ex
ample6 >
e3 ) a member of a chord turns in to a diff eren t member o f a nother
chord,for example :
(2:5 , (b is 8 a nd becomes se e g 79 .
4 ) the dissona n t tone turns in to som e other dissona n t tone , for5 < 7 <
example
There is a n endless field of possibi li ties . Al l we have to re
member is,that it is possible to cha nge the mean ing of a single tone
(with or without enharmon ic modulation ) and make i t the mea ns Ofa modulation . Th e single tone can be (normal , raised or lowered)prime
,second
,third
,fourth ,
fifth, sixth , seventh
,even octave ,
S ch ub e r t . D ying S tra ins, N O . 2 , VVa rrior’s Foreboding .
E x . 191 .
E
2 ) Consecutive fifths can recur upon the accented beat or a c
cent ed parts of bea ts . They point to sequen tial forma tions .
S ch ube r t.
E x . 192 .
3) Conse cii tive fifthsmay be disguised by rests,suspensions e tc .
but they must be considered faul ty where no relationship exists .
M oza r t . BIZ-m a jor M e nde l ssoh n . Op . 19,N O . 6 . Ba rca ro l l e .
E x . 1 93 .
4 ) Consecutive fifths can occur in arpeggio ’d chords in sequences .
Ba ch . Tocca ta ,D -rninor .
E x . 194
5 ) Consecutive fifths can occur by mea ns O f gra ce notes (a ppogg ia tura s ) auxiliary , passing tones , e tc . Very numerous
,usually
unnoticabl e on accoun t of the tones swiftly passing the e a r .
W eber . I nvita tion to D a nce . Haydn . M il i ta ry Symph ony .
E x . 1 95 .
M oza r t . O ve rt ure . M ag ic Fl ute .
E x . 196 .
G l uck . Arm ide ,Act I I
, S ce ne 3 .
E x . 197 .
S ch umann . Op . 28,N O . 1 , Roma nce .
E x . 198 .
S ch umann . Op . 39,N O . 6 . Sch one Fremde .
E x . 199 .
144
E x . 20 0 .
Ch opin . Op . 40 , Pol ona ise .
0 4 3 -1 }4 4 4— 0 -4— 1: 4!
6 ) Consecutive fifths ca n occur when a certa in figura tion motiveis persisted upon .
Ba ch . S t . Joh n-Pa ssion , N O . 25 , Ch orus .
Be e th ove n . Op . 1 0 , N O . 3 , Sona ta .
E x . 2 0 2 .
4 ) Consecutive fifths can occur between the D omina n ts a nd
their Ton ic .
M ende l ssoh n . O ve rture . M idsumme r N igh t ’s D ream .
E x . 2 0 3 .
— 146
9 ) Consecutive fifths a re a llowed between the principals and
their relatives . Consecutive fifths by leap ca n occur when the S 6 isbrought in a broken form thus This sounds wel l because the e a r does not perceive successions O f fi fths
,
but merely a rhythmical fi gura tion Of the entireS 6
chord
E x . 20 8 .
S ch uma nn . Pa radise a nd th e Pe ri . L a Romanesca .
II -a - x x x x
X X X X X X X X
Chromatic consecutive fifths between T and aT or mT and amTcan be seen in E xamples 79 ,
80 a nd 81 . Th e fa ct is tha t consecutivescan occur between any related chords Of a key ,
provided they do not
con tradict a rational leading Of parts (voices ) . S ee also half toneconsecutive fifths in E x . 84 b ) a D r to SS .
1 0 ) Some consecutive fifths a nd octaves a re to be looked atmerely a s fi l l ing
- in parts .
Be e th oven . Op . 53 , Sona ta .
E x . 20 9 .
Take awa y in al l the chords the three upper notes in the basssta ff a nd the lowest note in the treble , a nd the consecutive fifths a ndoctaves will disappear . Th e fo llowing extract is merely one melody(part ) strengthened in octaves a nd fifths .
Gounod . Fa ust,Fina l e .
E X 0 1 0Al l wh o h a ve sin ned h e re .
- 147
11 ) Consecutive fi fths have been used a s a means for expressionand co loring . F or instance in imitating the bagpipe
Haydn . Symph ony , C-ma jor .
E x r 2 l 1 .
A bea uti ful piece O f coloring of this kind is to be found inPucc in i ’s “ Th e Bohemians ,
” where descending staccato fifths ad
mirably represent the falling of snowflakes a nd the bleak winterwinds .
§ 84 . CON CL U D I N G RE MARKS . Th e elabora tion Of Ha r
mony is the work a nd thought of cen turies . Th e masters withdelicate artistic sensibi li ty a re the ones wh o make the advances inmusic by their refinemen t of feeling for Harmony a nd a boldness inaccepting tha t feeling a s a guide in contradiction to existing p ractice . Theorists endeavor to expla in the results when
'
al l is a ccom
p l ish ed . On ly those rules that the masters themselves Observe canbe rules
,and there a re but a few absolute rules above time a nd
taste . S tudying the works of the master musicians and the worksof the theorists of many schools a nd times
,I have collected every
thing that might help the ha rmony pupi l to better understand a nd
en joy the endless world Of Harmony . I have aimed to select thebest and most advanced idea s out of a l l methods , always searchingfor the most practical , the s implest
,yet most compreh ensive . I
owe a great deal to the works of al l distinguished,O l d a nd modern
,
theorists . Where I wen t farther than a ny ,I did so upon the prin
cipl e Of analogy a nd the practice of modern composers . There isnot a single statemen t made in this book which is not corrobora tedby scientific research of some great theorist
,or by the practice of
some master composer . Al though diff eren t from the curren t bookson Harmony
,this method is , nevertheless , founded upon the most
advanced ideas ever developed and scattered among many systems .
Amethod which is to expla in the intricacies of modern Harmonymust naturally possess a dvanced ideas . I hope that my work O f
un i ting the va rious advanced ideas (and some of my own ) into aconsisten t method wa s not a labor in vain . Th e book i tself willexplain everything of the method . Should my work be considereda successful effort toward simplify ing the system of Harmony
,and
o f making the study of i t profitable and an intellectual enjoyment .then I shal l be happy to have contributed my share towards improving the teaching O f one of the most fasc inating subj ects of music .
CARL W . GRI M M .
Cincinna z‘i, j u ly 2 0
,1 90 1 .
ALPHABETICAL INDEX .
(Th e numbe r s z
'
ndica fe t/ze p ag es . )
Added tone s , 96 .
Additions to th e D ,1 0 1 .
Al te ra tion ,12 1 .
O f th e ma jor S , 1 0 2 .
minor S , 1 0 3 .
Al te red Ch ords, 96 , 1 0 0 .
m inor T, 8 1 .
tone en te ring fre e l y , 1 0 1 .
ton e s in D ,1 0 2 .
T, 8 1 .
Ana lysis , 1 0 3 , 121 , 139 .
An ticipa tion ,1 0 8— 110 .
Arrow poin ting ba ck 125 .
Augmen ted in te rva l s , 3 , 30 .
Augme n ted S e cond S tep ,m a j . to m a j . 92ma j . to m in 69
7 1 , 9 2
m in . to m a j . 92
min tom in 92
Th ird S te p , m a j . toma j .
, 93
m a j . to m in .
,93
m in, to m a j . , 93
min . tomin . 93
triad , 136 .
Auxil ia ry tone s , 48 , 50 , 1 11 , 1 12 .
susta ined a s susp e n
sions , 10 0 .
Ba ch, 88 ,
1 0 3 .
S t . Joh n — Pa ssion,144 .
Tocca ta D m inor , 142 .
Viol in S ona ta I V , 57 .
Be e th oven , 1 0 3 , 141 .
Anda n te in F , 67 , 68 .
O ve rture ,
“
L e onora”N O . 3 ,
Sona ta , Op . 1 0 , N o . 3 , 144 .
Op . 27 , N O . 2, 58 .
Op . 53 , 77 , 146 .
S ymph ony E roica” 117 , l 39 .
N O . 9 , 11 0 .
Bize t Ca rme n,1 14 .
Cadence s , 43 , 84 , 120 .
Ca nce l l ing of fig ure s , 54 .
C(an tus ) f(irmus ) , 24 .
Ch a in of fifth s . 8 .
Ch anged re so l utions of D 3, 25 .
Ch ange ofme a n ing of sing le tone s , 140 .
mode (Of ch ords )position ,21 .
Ch opin, Op . 24 ,
N o . 2 M a zurka,145 .
Op . 30 , No . 2 89 .
Op . 30 , N O . 3 79 .
Op . 30,No . 4 1 17 .
Op . 40 , Po lona ise , 1 44 .
Op . 57 , Be rce use ,139 .
inte rva l s , 37 .
se venth ch ord ,131. 132 , 136
Th ird S tep , ma j . toma j . 92ma j . tomin . 92
m in . toma j . 697 1 92
min . to min . 92
Ch ord g roups, 55 .
of fi ve -six,45 .
th e second,45 .
sixth,1 1 .
th ird a nd sixt h,l l .
th ree -four , 45 .
signs , 24 .
Ch ord tone s , 48 .
Ch rom a tic a l te ra tion,
conse cutive fifth s , 146 .
h a l f step , 7pa ssing ton es , 1 1 1 , 1 12 .
sca l e , 1 12 .
S tep , m ajor to ma jor , 92 .
ma j . tom in .
m1nor to m a jor, 92 .
m inor to m inor , 92 .
Circl e s O f chords ,1 20 .
Circuitous modu la tion,141 .
Circumscriptive pa ssing tone s , 1 11 .
Cl a ssifica tion of ch ord conne ctions,18 ,
58 , 68 , 90 .
conse cutive fifth s , 141 .
in te rva l s , 3 .
Close position,1 1 .
Cl ose s , 84 .
Coa l e scence of ch ord tone s , 8 .
Combine d modu la tion ,141 .
Comp l e te Cl ose , 84.
Conse cutive fifth s , 30 , 37 , 47 , 10 4 ,
1 17 , 141- 147 .
octa ve s,20 , 30 , 37 , 47 ,
Consonant ch ords, 7 .
Contra ction of in te rva l s , 3 .
Con tra ry motion,16 , 30 .
Corre l a tive ch ords , 55 .
Coun terpoin t , 141 .
Crossing of pa rts , 17 .
Cross re l a tion,38 .
D e ceptive cl ose , 60 , 69 , 84, 87
D e l ayed p i ogre ssions , 1 12 .
D ia toni c h a l f ste p , 7 .
D im inish ed Fourth S tep ,ma j . toma j . 93ma j . to mm . 93
m in . to ma j . 6970 , 93
m in . tomin . 93
15 0 AL PHAB E TICAL I N D E X .
M inor Ton ic va ria n t , 78 .
corre l a tive, 79 .
re l a tive, 79 .
M ixed keys or mode s,13 .
M ixo l ydian mode, 77 .
M ode rn h a rm ony, 12 , 130 — 132 , 141 , 147
M odified in te rva l s, 6 .
M odul a ting sequence , 139 , 140 .
M odu la tion , 40 , 50 , 62— 64
,72
,1 20 , 131
— 133,136
,140 ,
M oza rt , 1 0 3 .
D on Jua n Ove r ture, 1 0 0 .
Fa n ta sia (e S ona ta ) C m inor ,
Ove rture M ag ic Fl ute , 1 43 .
Symph ony , E IZ, 142 .
M usica l Form , 141 .
N e a pol ita n sixth,57
N ota Cambia ta , 1 0 9 .
Ob l ique mo tion,16 .
Octa ve s in con tra ry motion,1 7 .
Omission of tone s, 14 , 6 0 .
Open position ,
Orga n poin t , 29 , 1 0 7 , 138 .
O rg an um , 141 .
Ornamen ta tion,48 .
of th e disson a nce,98 .
O ute r pa rts,2 1 .
O ve r—D om inan t,12.
Pa ra l le l fifth s,16 .
mo tion, 16 .
octa ve s,16
, 20 .
Pa ssing ch o rds, 138 .
discords or dissonance s,9 6 .
h a rmonie s ,96 . 99 , 1 17 .
tone s, 48 ,
99 , 1 1 0 , 1 11 , 1 18 .
by skip,1 1 1
,1 12 .
e n te ring fre e l y , 1 0 0 .
Peda l poin t , 29 , 138 .
Pe rcussion ,9 7 .
Po lyph onic m usic , 88 ,141 .
Postponeme n t Of re so l u tion of a dis
cord,130 .
Pra ctica l work on th e piano,43 .
Pre pa ra tion O f th e dissona nce, 97 , 1 0 3 .
Prepa red suspe nsion,9 7 .
Pucini, Th e Boh emians
,1 13 , 147 .
Re l a tionsh ip by th e Fifth 55 .
Th ird 55 .
of ch ords, 5 1 .
Re l a tive ch ords , 55 .
Re so l u tion, 97 .
7
by prog re ssion ,9 9 .
in a l ump,130 .
of th e dom inan t se ve n thch ord
, 45 ,1 29 .
of th e subdom in a nt six thCh ord ,
47 .
Re ta rda tion s, 97 .
Re t urning Fifth S tep , 27 .
Re turn m odu l a tion, 141 .
Re vo l ving ch a rts O f h a rmony,40 ,
64 .
Rh ythm ,3 .
S ca r la tti, 57 .
S ch ube rt , 61 , 1 0 3 .
Am M e ere , 98 .
D ying S tra ins N o . 2 , W ar
rior’s Foreboding , 142 .
D ying S tra ins N O . 6 ,Afa r , 81 .
Op . 1 0 3 ,Fa nta sie , 82 .
Op .9 0 , N o . 2,Impromptu
,88 .
Op . 9 0,N O . 3 , Impromp tu ,
122 .
Op . 9 0 ,N o . 4 , Impromptu , 89 .
Op . 142 , N o . 3 , Impromptu ,113 .
Op . 94 , N o . 1 , M omen ts M u
sica l s, 124 .
Op . 94, N O . 4 , M om en ts M u
sica l s,8 0 .
S on a ta Ama jor , 143 .
S ch um a nn, 10 3 .
O ve rture Ge nove va,10 6 .
Op . 15 , N O . 4,Kinde rsce
nen,89 .
Op . 15,N o . 7 , Traum e re i
,
145 .
Op . 15 , N o . 9 , Kinde r sce
nen,145 .
Op . 7 , Kre is l eria na ,9 0 .
Pa radise Pe ri,146 .
Op . 39 , N O . 6, S ch oene
Fremde ,143 .
Op . 28,N O . 1
, Romance .
143 .
Op . , 7 Tocca ta , 85 .
S e quence s ,1 14 .
S e rie s of fifth s , 8 .
S e ven th ch ords,1 14 , 130 .
S e ven th S tep , 9 1 .
S ign o f equa lity (z ) , 4 0 .
S ix - four ch ord ,1 1 , 17 .
S im i la r motion, 1 6 .
S ubdominan t , 12 .
corre l a tive , 56 .
h a rm onie s , 9 0 .
of th e subdom ina n t, 78 .
re la tive ,. 56 .
sixth ch ord , 44 , 47 .
S uspensions , 2 1 , 22 , 96 — 98 , 1 0 2 , 1 0 8 ,
S uspe nsion ch ord , 137 , 140 .
Syncopa tionTh e ory O f di scords , 96 .
Th ird -doub l ing ,46 .
Th ird S tep , m a j . to m a j . ,69 ,
7 0 ,93
ma j . to m in . , 68 , 93 .
m in . to ma j ., 93 .
m in . to min .,69 , 70 , 93 .
Th re e -pa r t h a rmony , 131 .
Tie rce de Pica rdie,88 .
Tona l functions , 12 .
Tonic , 1 1 .
AL PHAB E TI CAL I N D E X . 15
Ton ic corre l a tive , 56 .
h a rmonie s, 9 0 .
re l a tive, 56 .
va rian t, 78 .
corre la tive , 78 .
re la tive , 78 .
Transitions,120 .
Triads, 7 .
Trip l e peda l,139 .
Tritone, 30 . 91 .
S tep,m a j . to m a j . ,
69 , 71 , 93 .
m a j . to m in .,
m inor to m a jor, 93 .
mm . to m in .,69
, 7 1 , 93 .
Tsch a ikowsky , Op . 37 , Ch ristm a s, 99 ,
1 23 .
U nde r D ominan t , 1 2 .
in te rva l s , 5 .
U pper D ominan t , 12 .
U pwa rd motion of seven th ,45
,129 .
W agne r , 1 0 3 .
Flying D utchman,67 , 83 , 134 .
L oh engrin , 77 , 8 1 ,83 , 84 , 88 ,
122 , 124, 125 , 133.
W agne r , M e istersing e r , 78 , 82 , 84 , 1 18d o ,
Pa rsifa l:78 .
Rh e ingol d , 83 .
S ieg fr ied ,1 16 .
Tannh ause r , 1 15 , 134 .
Trista n and I so lde , 1 0 0 , 1 0 7
1 0 8 , 133 ,138
W a l ku re, 135 .
VVebe r,1 0 3 .
‘C I nvita tion to D ance ,14
Ronde a u bri l l ian t , 1 1 1 .
W h o l e tone sca l e,
S t
S tep , 62 , 91 .
ma jor to m a jor,
ma jor to m inor ,
18
92
58
m inor to ma jor ,19 , 37 ,
m inor to m inor,
30 ,58
,
18
92
19
92
RL W .
6170 V111 211 of 2111110 11
N O. 1 .
N ingen ious device to help the student in learn ing and theteacher 111 i llustrat ing Ha rmony . especially M odula tion a nd
Harmon ic Analysis .
Th e chart h a s a perforated part and a revolving disc.
”
Overthe perforations a re ma rks indicating the key mode a nd the funct ions the chords have therein .
T means the major Tonic th e major key .
D D ominantS Subdominan tmS minor Subdom inan tmTmeans the minor Ton ic chord Of the minor key .
mS“
5
Subdominan tmD D ominan tmaD maj or D ominant
This chart shows 0 11 the one half the pr inc ipal chords of al lthe major keys (from CIZ to CII) , on the other half i t shows all theminor keys (from A12 to Ag) .
Th e keys succeed each other in fifths . Turning the disc to
the r ight will make the lower (fi a t) keys appear , turning to the leftwil l show the higher (sharp) keys .
Th e cha rt shows all th e principal functions any chord can havein the various ma jor a nd minor keys .
Chart N O . 1 is to be used in conn ection with P a r t One of theHa rmony .
9 1.5 115t by THE W IL L IS MUSIC CO .
CINCINNATI, OHIO .
MODERN HARMONY
I s truly a wonderful worl d in itself . Th e more we explore i t andthe closer we examine i t , the greater does its bri lliant splendorappear . And yet i t is bu t the revelation of nature’s laws govern ingthe relationship of tones:they a re the same laws that a re to befound in t h e smallest a s wel l a s in the greatest in the ' un iverse .
These laws have always been in existence . but it wa s for man to
discover them. Th e progress Of constructing the now marvelouslyr ich and complicated edifice of Harmony h a s been very slow
, and
h as extended over a wide stretch Of t ime . Th e condition of h ar
mon ic progress is a process of accustoming and train ing the e a r todiscern between agreeable a nd disagreeable , reasonable and unre a
sonable sounds . This is men tal work , but the mental organ ismdepends upon the laws of the universe . There is always a progressfrom imperfection to perfection , a str iving towards development ,because developmen t is the order of the world . Th e idea of evolution is a universal process swaying alike nature’s physical a ndman ’
s a rt world .
There is un ity in the M odern Harmony system . I t developedby a natural growth ; and , if there be a ny complexity of thoughtin i t . i t is a s the structure of a tree or a human body is complex , on lytil l the l ines by natural growth in each a re discerned ,
a nd then theidea of th e whole becomes s imple and plain .
E volution— the process of becoming— is also mostly attendedby a revo lution . Th e ascending scale of progress from the simpleto the complex is a rrived
‘
a t on ly by"
successive stages . And i t isinertia in many to consider a past
,
stage of mus ic (be it Palestrina ,Bach or Beethoven ) the most perfect , and all later stages a succession of degradations . M any of the progress ions which Beethovenused outraged the fixed notions of theorists of h is day , wh o did notunderstand them
,and thought he was violat ing their orthodox
principles of key . Y e t Beethoven ’
s whole system wa s founded on
h is very acute feel ing for Harmony . He expanded the range of
key a s much a s he could , and Wagner wen t farther on the samepath . Th e typica l conservative mind regards a ny eff ort to changeh is habits of thinking or mode of feeling a s a species of heresy .
Th e stronger and more practical mind soon cultivates such heresieswith much success . N aturally
,growth implies also decay , that is
the work of clearing the useless rubbish . N o new teacher comes onlyto destroy , but also to build up . F or that reason we ought alwaysrespect our predecessors for the preparatory work they have done .
Jus t now ,so ma ny a re discontented with the curren t harmony
teaching . But this disconten t is a token of a higher thing , the( 2 )
en trance of a new spiri t at strife with the O l d the darkness whichm ay herald the dawn .
Th e mas ters , with delicate , art istic sensibility , a re the ones wh omake the advances in music . Correct progressions come to theminst inct ively , but i t must not be forgotten that th is instinct is inpart also th e result of acquired knowledge . Th e artists select andrej ect by e a r ; they use tones and chords according to their innersense of the relation which every combination of tones and succession of chords bears to th e feeling . M any human beings understandeven modern music , through their feeling for tonality , before theya re capable of explain ing it . S cience , theory , always follows longway behind
, on ly to confirm th e progress achieved by the masters .
Th e masters f ee l the inner bond of un ity Of new relationships of
chords , long before science sees them . Th e possibilities Of trainingthe e a r a re un limited . Th e ear is educated by exercising its p ercep tion Of tonal relationships . Pra tice and good will a re necessaryto thoroughly understand a great and complicated modern musicala rt work .
Th e guide through this seeming labyrinth of possible relationships of tones is the l aw of unity in the manifoldness
,which is the
greatest law of a l l a rt creations. Th e harmonic center of al l chordrelationships is their centraliz ing point , the chord of repose , cal ledthe Tonic . Akey is but a family or kinsh ip of chords.
M ajor chord and minor chord are the two foundation stonesof harmon ic structure . They a re the only two consonant chordsand a re of Oppos ite natures , the one sounds bright and strong , theother sad and serious .
I f we look closely at the intervals of these chords , we fi nd inthe major chord a minor third above the maj or third :
g) minor third .
C) ma jor third .
In the minor chord we fi nd i t reversed , namely a major thirdabove the minor third g
) major thirde
z) m inor third .
Th e major chord consists Of a major third and perfect fifth,the
minor chord shows the same intervals i f measured downwardAg g
major third (A
g)perfect fifth maj or th 1rd V
? v) perfect fifth .
Th e minor chord is in its construction,the exact opposi te and
counterpart of th e major chord . These t wo kinds of chords a re
co -equal in value and importance ; they express contrasting moods .
Th e tones forming these chords coalesce (blend ) in to a perfectunity , and around these two chords al l music revolves. Al l dissonan tchords are to be conceived a s modifications of major or minor chords.
Instead of regarding chords as capable of arrangement in one
series l ike the steps of a ladder or like the alphabet ical arrangementof words in a dictionary a s al l those Harmony systems built uponthe thorough bass signature h ave done , the results of moderninvestigation compel us to d ispose of them as i f they were the twigsand branches O f a tree . Th e source of all those everbranch ing and
beauti fu l ramifications of the main branch is the tonic chord of thekey . Th e ton ic is the common root , whence spring
,governed by
the law of contrast , two main trunks , one representing the higher(D ominan t) side and one the lower (Subdominant) side Of the toneregion ; each dividing into a few main branches , these subdivide intomultitudes of branchlets , and these into smaller groups Of twigs , e tc .
S ince there a re only two fundamental harmon ies , the major andminor chord ,
and either one of them ca n be the ton ic chord,i t is
plain , that there can be on ly two kinds Of key systems , maj or and
minor .
M odern harmony un ifies , and in this sense it is one of thetokens of the modern spirit , which is that of central ization . I f
teachers seek to interpret What modern masters have accomplished,
they will naturally arrive at new ideas and methods .
I n a rational tonality (key-system) every chord , by the law Of
relativi ty,bears a certain relation to the tonal center of gravity ,
cal led’
ton ic , and thereby h a s a certain quality of inheren t emotionalforce and meaning . Awhol ly new treatmen t of elaboration h a s
begun by classi fying these chord successions , and pointing out to
the student their various techn ical difficulties .
Th e new system of Harmony is founded en tirely upon therelationship o f chords by the Fi fth and the Third . Th e relation of
the chord to the key is called function ,
”and every chord h a s a
function in the key . There a re on ly three k inds of functions(offices) within a key , namely , Ton ic , D ominan t , and Subdominant .
Al l the other ch ords will have to be considered as modifications(relatives) of them .
C-MAJOR KE vT
g
Th e three principal chords , T,D a nd S ,
give the signature ofthe major key .
A-M I N OR KE Y . (Pure M inor Key
mT
g
Th e three principal chords , mT,mS and mD
, give the signatureof the minor key .
of the augmen ted second , 1% steps) the sixth degree is ra ised , andin this manner the M elodic M inor S cale is produced :
Asce nding . D e scending .
Th e descending M elodic M inor S cale is the pure minor scalespoken of before ; i t is ,
therefore , sti l l in use . Th e maj or key isbright and cheerful . Th e minor key is dark a nd sorrowful . Th eminor key is brightened by intensifying (brighten ing) its D ominan tside by using a major D ominant chord instead o f a minor . Just so ,
the major key is darkened (made sombre) by intensifying (darkening ) its S ubdominant side by using a minor Subdominan t chord instead of a maj or . M ajor a nd minor a re Opposi tes , not on ly in theconstruction of chords
,but a lso in the construction Of keys ; couse
quently , i f we wan t to fi nd the corresponding chord in the majorkey we -must look for i t on the reverse S ide o f that of the minorkey , a nd vice versa .
S
f
These a re the pr incipal chords of the key and represent theessentia l conten ts of i t . Before we wil l point out the other concordsof the key we wil l explain its most importan t discords . They a re
the dominants with additional tones , which help to mark them morepointedly a s S or D . Th e added tones a re tones borrowed fromthe other dominan t . Th e M ajor Over-dominan t adds the prime ofthe Subdominant (in C-major
,g b d If ; in A-minor , e gII b d) . I t
is called D omina n t seventk efi om’(D
7) .
T
f Ia c e I g b d d [f a c] e gII b
S D mS m aD
Th e M a jor S ubdomina n t adds the fi fth Of the D ominan t (inC-major
,f a c
i
d) .
f a c [e g b] d
S D
I t is called S uédomz’
na nt sz’
x t/z cil ar a’
(Se) .
Th e M inor S ubdominan t adds the fi fth of the m inor or maj orOver-D ominant (in A-minor , d f a b ; in C-m a j or , f 3 12 c d ) .
d f a [c e g] b f arc e g bI d
mS mD m iS D
I t is called minor S ubdomina nt sz’
x t/z e/zora’ (mS S , m iS 6
Th e M inor Over-D ominan t adds the prime of the minor S ubdominan t (ih A-minor , e g b Id) .
d [f a c] e g b
mS mD
I t is called minor D omina nt sevent/z clzor a’ (mD 7) .
Adding a tone of one dominant to the dominant lying on theother side c ircumscribes the key in the same way a s does the succession of two dominan ts— it points to their ton ic . O f these princip a l discords the D 7 holds the most prominent posit ion
, and fromit develop the N inth , E leven th and Thirteenth chords . Th e mechamical idea that such chords a s the D 9
,11 and 13 must , but can
not always be inverted with good eff ect , h a s caused much con fusionin the minds of some theorists , a nd h a s led some to rej ect e rroneousl y such chords altogether .
I t is cer tain ly a step forward if theory begins to free itsel f fromthe notion that the acoustical phenomenon of the overtone seriescan explain the nature Of the major and minor chords. Acousticsh a s merely helped us to improve the construction of some of our
instruments and concert halls . Perhaps the overtone series may belooked upon a s the model for the D 7
,9,1 1 a nd 13 chords
, and givein music n ew mean ing to the anc ien t theory that “ the harmony of
the wor ld arises out of discord .
”
Th e pr incipal chords of a key a re related to each other by theFifth . Th ere exists another relationship of chords , and that is therelationship by the Third . F or example , around C-maj or chordgroup themselves A-minor and E -minor chords:
C
We call A-minor chord th e re lative chord of C-major . E -minoris a lso a relative chord of C-major , but to dist inguish i t from the
— 8
other relative chord (A-minor) , we‘
call i t the cor re l a tive enora’ of
C-major . When the pr incipal chord is maj or then the relative andcorrelat ive chords a re always minor . Th e relative chord is si tuateda minor third below the prime of the pr incipal (major ) chord , a ndcontains the pr ime a nd third of the latter
Th e correlat ive chord is s ituated a major third above the primeO f the principal (maj or) chord , and a fifth above the relat ive chord .
Th e correlative con tains the third and fifth of the principal chord .
Th e dominan t and subdomina n t chords a re a whole tone step(double fifth step , f— c—
g ) apart , and move around the ton ic a s
their central point . Th e relative a nd correlative chords imitatethis relat ionship within a sma l ler c ircle ; they a re on ly a fifth stepapart
,move around their principal chord , and can be used a s sub
stitutes for i t .This unfolding of a few simple laws is noticeable throughout
the realm of harmony . E volution ,therefore
,considers the higher
or more complex forms of a key a s fo llowing and depending on thelower or simpler forms Of key .
Around A-minor chord group themselves C-major and F-majorchords .
f
Here we fi nd another proof that major and minor a re opposi tesin al l things . I t h as alrea dy been stated
,that when the pr inc ipa l
chord is major , then the rela tive and correlative chords a re minor ;consequen tly
,when the principal chord is minor
,then the relative
and correlative chords a re always major . With the maj or chord wefound the relative s ituated a minor third below ; here the relative Ofa minor chord is situated a minor th ird above the principal (minor )chord . C-major is the relative chord of A-minor chord . I t con
tains th e third and fifth of th e principa l chord
1 0
Th e relative a nd correlative chords of the m iS in the major keya re called minor S ubdominan t relative and minor S ubdominantcorrelative . I n C-major key they a re :
Th e relative and correlative chords of the maD in the minorkey a re called m aD r and maDc . I n A-minor key they a re :
Th e third of the 11 15 in the minor key can be chromaticallyraised , and the third O f the D in the major key can be chroma ticallyl owered . Appa rent ly th is g ives the major key a minor D ,
a nd theminor key a m a jor S . N evertheless
,they must be looked upon
m erely a s l icenses , and not a s key -ma king (principal ) chords . Th ea rtificial tones a re supposed to lead to the third of the m aD or m iS ;when they do not do this , then the progressions as musical ell ipsesrequire leaps in the concept ion . Th e raised third of the m8(mS
3<,the short crescendo sign means “
raised i f used withoutmodulation and without p rogressing to the 3 O f the maD , w i l l p roduce eff ects peculiar to the “
D orian mode ” of the fi fteenth to theseven teen th centuries . Th e lowered third of the D (D 3>
, the shortdecrescendo sign means if used without modulationa nd without progressing to the 3 of the miS ,
will rep roduce thechara cteristics of the M ixolydian mode .
” Th e mS 3< i l lumines theminor key and the D 3> c louds the major key , even when the n a t
ura l l y expected chords do not appear .
Keys have grown l ike the big c i ties , by a nd by they absorb thesurrounding terr itory and extend beyond the original boundaries .
I t is the process of lumping ”or kn itting together into a larger
un i ty . A key can branch (reach) out above the dominan t and
below the subdominant and use the chords beyond without inducinga modulation .
— 1 1
C-M AJOR KE Y
512 f 5
SS S TbIZm f m
m 1SS m 1S
A-M I N OR KE Y .
b
m aD D
g m dm a m 5 771
mSS mS mT mD D
Th e extension of the key to the S S , and espec ially to the misS ,
br ings darker shades in to the majo r key . Th e same holds good of
the mS S in the minor key ,whereas the mDD ,
and especial ly themaDD , bring brighter shades in to the minor key .
Th e chromatic alteration of the third of the T produces a chordof the opposi te mode ; in C-major the c-minor chord , in A-minorkey the a -major chord . This va r iation of the tonic puts i t intoanother mood . M ost beautiful e ffects a re Obtained by the use O f
the variants O f the ton ic . F or the major key i t is s imilar in effectto a cheerful landscape made dark a nd gloomy by a passing cloud .
In the minor key the eff ect is the reverse . l ike a desolate scenemade entrancing by sunshine . By using the variant O f the ton ic ,
the darkness in major , or brightness in minor ,is cast over the entire
key , and does not spread on ly over a part O f the key , a s with otherchords , l ike the m iS , S S ,
maD,e tc . Th e tonic variants have rela
tive s and correlatives .
C-M AJOR KE Y
A-M I N OR KE Y
/mTvc
mTvr
12
I n C-major key the Tvc (aQ-maj or) is frequen tly used for decep tive closes .
As the sense for chord relationship developed , a new ser ies of
chords was evolved within the key by a certain simultaneous alteration of the tones forming the fifths of the principal chords . F or
example , a major chord is changed into a minor by chromaticallyra is ing the tones forming the in terval Of the fifth (the pr ime a ndfi fth
,the “
outer ” tones) ; a minor chord is changed in to a maj orchord by chromatical ly lowering the tones forming the fifth .
mT amT
F or short , we call these chords a ltered ” Ton ic and alteredminor Ton ic chords . Th e tone which is the third of each chordforms the bond (connecting link) of the two chords .
These chords have their relatives a nd correlatives a lso ,a nd
appear more frequen tly than some would suppose .
C-M AJOR KE Y .
i t afforded sumcientl y accurate suggestions of the value and relationO f the different chromatic tones . Thus i t came that the piano h a shad a great influence in the developmen t of ha rmony .
N ow when we wil l explain the utmost extens ion of the key , theresult wil l show that any key contains all the chords in existence .
This does not mean that the bounds of the key have been brokenon the contrary , the feel ing for key h a s been strengthened .
We know that Fetis, in a n essay , read in 1832,put forth the
hypothesis that some day the proo f could be given that al l chordswere to be found in every key . This system of chord a fli l ia tion heca l led “
ordre omn itonique .
”
L isz t wa s presen t and was deeply impressed with the thought . S O he began to ma ke original innovations in this direct ion
,and he h a s contributed a good many bold
and character istic harmonies , exquisi tely tender and noble , demon iacal and religious . He made frequen t use of enharmon ic changes ,and divulged the endless va rieties Of possibilities and wonderfulflexibili ty Of the augmen ted triad .
What I disclose now ,I have omitted in my text book , M odern
Harmony ,published in 190 1
,because I wan ted convincing proofs
in the master works to sat isfy me o f the correctness Of the theory .
S ince then I have found numerous examples O f such chords in theworks of Berl ioz
, L isz t and W agner , substan t iating my ideas .
I t h a s been pointed out that the keys branch out upwards tothe dominan t of the dominant
, a nd downwards to the subdominantof the subdominant . These chords have re latives and correlativesissuing from them .
C-M AJOR KE Y .
SS C
{12
SS
g m
S S r
d iz
m iSS r
A-M I N OR KE Y .
m aD D r
oIZ
/ mS S r
g m
mS S mS mT mD mD D
6 ?
mSS c
F or the last we need on ly apply the pr inciple of the Variationtheory , ” a s shown in the explanation of the “
a ltered ” ton ic , dom ~
inant and subdominan t chords , to arrive at the extreme limits of
chord relationsh ip . S ti ll there is fundamen tal un ity among al l theseeming diversi t ies .
C-M AJOR KE Y .
d
/ a S S r a D D r
bin
a S S
g
a SS c
(1 12m
/am iSS c
blzIzamiSS
am iS S r
A-M I N OR KE Y .
/am aD D r
amaD D
am aD D c
bIZm dm
Q/ amSS c
bk/ amD D c
/g
amS S /
b
amD D
L’IZ172
amS S r amD D r
g m om
mSS mD mD D
Amodulat ion is a change O f key . I t occurs whenever a newchord is ma de the cen tral po in t of the tonal system . We break thebounds of the key , when we change the funct ions of harmon ies ; tha tis ,when we trea t any one of them a s having a new mean ing (func
t ion) . Th e change of mean ing of a chord can be made to occuralso by means of dissonan t tones, chromatic alteration Of tones , emharmonic changes , e tc .
There a re chord success ions which a re generally called transitions
,not modulations . I n trans itions , which we call I n termediate
Cadences , there is no change of any tonal function . Th e T remainsthe main cen ter of the key , but in intermediate cadences theother chords (functions) of the key a re made subordinate cen ters ,surrounded by thei r c ircles Of chords , constructed on the same plana s the pla in keys .
I t is s imilar to the solar system . Th e sun is the cen ter of ourplanetary sy stem , but some planets have their satell ites , and theserevolve around the planets a s their cen ter . E very a nd any tonalfunction can have its own dominan t and subdominan t , a nd a greatvariety o f chord successions results . Th e chords can circumscr ibethe chord immedia tely following it . Sometimes an in termediatecadence follows a chord instead of preceding it . Then in place of
the chord embellished (circumscribed ) and expected to fol low ,
ano ther comes in . There a re cases where the chord circumscr ibedby a n in termediate cadence neither precedes '
nor fol lows , but isskipped a nd a nother chord comes in . U sually a chord nea r lyrela ted to the skipped one fol lows .
I n modern mus ic a ny concord ca n fol low any other concord ,even when on ly distantly rela ted . D isson an t chords empha size theharmon ic movemen t and add to the appea l ing qua l ities O f music.
— 18
Th e theory O f the relationship of chords by the Fifth a nd theThird and the theory of their va r iation ”
(which is a n indisputablefact) , give us a s imple a nd yet perfectly organ ized system , and formsthe j ust ification of the key-extension of modern harmony .
Amethod or system is , after al l , but an instrument or a techn ica l appara tus , and a s this is the country where the geni us of
machinery dwells , i t may not be wrong to expect from theAmer ica nteachers the very best of methods yet to come .
We have come to this convention with the desire to learnsomething . Th e person wh o learns is the one wh o desires to learn ,
and the person wh o improves is the one who desires to improve .
1, too ,
have come to learn whether you have a simpler and bettersystem of modern harmony than I have expounded . I f you havenot anything better
, or a s good . then I wi ll be glad to have beena ble to Show you something ,
a nd to have contributed m y litt le mitetowards improving the teaching of one of th e most fascinating sub
j e cts of music .
Th e following is a list of chords in Wagner’s Parsifal
(Kl e inm ich e l’s piano score) , i llustrating the extreme limits of chord
relationship
M AJOR KE Y
m e a sure
aD D r
M I N OR
amS S r
amS S
mSS r
amaD D
F or oth er,nume rous e xampl e s from th e works of th e m a ste rs
, with g ive na na lysis , see AS imp l e M e th od of M odern Harmony .
m e a sure 12
4
1
5
3
3
5
2
4
5
1
(written enh . a s amTc,but
fol lowed by m aD D e nh .
writte n . )
CARL W . GRIMM ’S
Revolving Chart of Harmony, No. 2 .
An inge n iou s device to h e l p th e s tud e n t in l e a rn i ng a nd t h e te a ch e r in i l lu s t r a t ingH a rm ony
,e spe c ia l l y M odul a t ion a nd H a rm on ic An a lys i s .
Th e ch a r t h a s a pe rfora te d pa r t a nd a r e v 0 1v 1n g d i sc . Ove r th e pe r fo r a t i on s a rc
m a rk s ind ica t ing t h e k ey m od e a nd th e function s th e ch ord s h a ve t h e re in .
I N THE M AJOR KE YTon ic ch ord .
T0 7ZZC r e l a ti ve ch ord s i t ua t ed a m i n or th i rd be low th e Ton ic .
Ton i c cor r e l a t zve ch ord s i tua t ed a m a j o r th i rd a bove t h e Ton i c.
D om in a n t ch ord .
D om zn a n t r e l a t zve ch o rd s i tu a t ed a m inor th i rd be low th e D om i n a n t .
D om i n a n t cor r e l a tive ch ord s i tua ted a m a j o r th i rd a bove th e D om in a n t.S ubdom i n a n t Ch ord .
S ubdom zn a n t r e l a t i ve ch ord s i tua t e d a m inor th i rd be low th e S ubdom in a n t .
S ubdom in a n t co r r e l a t i ve ch ord s i tua te d a m a j or t h i rd a bove t h e S ubdom in a n t .
m vn or S ubdom in a n t ch ord .
m i nor S ubdom i n a n t r e l a tive ch ord s i tua ted a m inor th i rd a bove th e m inorS ubdom i n a n t .
msc minor S ubdom zna n t cor r e l a t ive ch ord s i tua ted a m a jo r th i rd be low th e m i norS ubdom i na n t .
Ton ic va r i a n t,t h e ton i c ch ord of th e op p osrt e m ode .
Ton ic va r i a n t r e l a t i ve , th e ch ord s i t u a t e d a m ino r t h i rd a bove th e Tv .
Ton ic va r ia n t co r r e l a t ive , t h e ch o rd s i tu a t e d a m a jor th i rd be low th e Tv.
D om in a n t ch ord wi th low e re d th i rd .
D om in a n t Ch ord of th e D om in a n t .
S ubdom i n a n t ch ord of th e S ubdom in a n t .
mznor S ubdom i n a n t of th e S ubdom i na n t .
I N THE M I N OR K E Y
m Tm e a n s th e mm o r Ta n ve ch o rd .
mm o r To n ic r e l a t i ve ch ord s i tu a t e d a m i n or th i rd a bove th e Ton ic .
m inor Ton i c co r r e l a tive ch ord S i t ua t e d a m a jor t h i rd be low th e Ton ic .
m inor S ubdom in a n t ch ordm i nor S ubdom in a n t r e l a t i ve ch o rd s i tua te d a m inor th i rd a bove th e S ubdom
in a u t
m sc m inor S ubdom i n a n t cor r e l a t i ve ch ord s i tua t e d 3 m a jor th i rd be low th e S ubdom in a n t .
m inor D om in a n t ch ord .
m inor D om in a n t r e l a tzve ch ord s i tua t e d a m inor th i rd a bove th e D om in a n t .
m znor D om zn a n t cor r e l a t ive ch ord s i tua ted a m a jo r th i rd be low th e D om i na n t.m aj o r D om i n a n t ch o rd .
m a j or D om in a n t r e l a t ive ch ord S i tua ted a m in or th i rd be low th e D om in a n t.m a jor D om in a n t cor r e l a t i ve ch ord s i tua te d a m a jo r th i rd a bove th e D om in a n t .m in or Ton i c va r i a n t , t h e ton i c ch ord o f t h e O ppos i t e m ode .
m inor Ton i c r e l a t i ve , th e ch ord s i tua t ed a m ino r th i rd be low th e mTv .
mzn'or Ton ic cor r e l a tzve ,
th e ch ord s i tua te d a m a jor th i rd a bove th e m ’
Iw.
m in or S ubdom i n a n t ch ord wi th ra i sed th i rd .
m i nor S ubdom ina n t ch ord of t/ze S ubdom in a n t .m i nor D om in a n t ch ord of th e D omin a n t .
maj or D om i n a n t of th e D omina n t .
Th i s ch a rt con ta i n s a l l ch ord s r e l a ted to e a ch o th e r in a l l t h e M a j or a nd M in o r K eys ,
a ccord i n g to M ode rn H a rm ony t e a ch i ng .
Th i s ch a rt sh ow s on th e on e h a l f a l l th e m a j or keys (from C12 to C11) , on th e o th e r h a l fi t sh ow s a l l t h e m in o r k ey s ( from A12 t o Aft)
Th e key s succe e d e a ch o th e r in fi ft h s . Turn ing th e d i sc to th e r i gh t w i l l m a ke th elowe r (fl a t) k e ys a ppe a r , tu rn ing to th e l e ft wi l l sh ow th e h i gh e r (s h a rp) k eys .
Th i s ch a r t exh i b i ts th e d i ff e re n t pos i t ion s (fun c tion s ) a ny ch ord ca n h a ve in th e
v a r ious ke ys ; by m e re l y turn ing th e d isc to a ny ke y d e s i re d , a l l th e ch ord s be longing to
it ca n b e se e n a t a gl a n ce .
Ch a r t N O . 2 is to b e u se d 1 11 conn e ction W i th P a r t Tw o o f t h e Ha r mony .
Publ ish ed by THE W IL L IS M U SIC CO .
CIN CIN NATI, OHIO .
— i i
G i ve t h e unde r - four th of b fi a t .
Wh a t k ind of in te rva l is b fi a t — e fi a t ?
N a m e t h e unde r — fi f t h of a - fi a t .
Th r e e a nd on e - h a l f ste ps form wh a t norma l in te rva l ?N a m e t h e ove r - s i xth o f f sh a rp . Th e und e r - s ixth of f sha rp.G i ve t h e und e r — se ve nth of a - sh a rp .
Wh a t in te rva l is a w h o l e - ton e s te p sma l le r th a n t h e oc ta ve ?N a m e t h e in te rva l a wh o l e s te p la rge r th a n t h e oc ta ve .
Wh a t is t h e und e r - n in th of 0 fl a t ?
How m uch la rge r is t h e te n th th a n t h e n inth ?N a m e t h e ove r - te n th of 0 fl a t .
N a m e t h e und e r - ten th of e s h a r p .
I s th e r e a ny d iff e r e nc e in s iz e be twe en a n ove r - inte rva l a nd a n unde rin te rva l of t h e sa m e na m e ?
I f not , in wh a t doe s t h e m ode of th ink ing th em e ss e n t ia l l y d iff e r ?
3, 4How a re in te rva ls m od ifie d ?
Wh a t is t h e s ign use d w ith t h e figur e s t o e xpr e s s ra ise d ton e s ?Wh a t s ign is use d t o e xpre ss lowe r e d tone s ?Wh a t is t h e d iff e r e nce be tw e e n a ch rom a t ic h a l f - s te p a nd d ia ton ic h a l f
s te p ?
Wh a t sort of a n in te rva l is d -
g sh a rp ?Ca n d iff e r en t l y n am e d in te rva ls h a ve t h e sam e num be r o f s te ps ?Y
V
h a t k ind of in te rva l is d a - fi a t ?
D oe s t h e n am ing o f in te r va ls d e pe nd e n t ir e l y upon s te ps , or m us t oth e rth ings b e cons ide red ?
I f w e wou ld h a ve to ind ica te doubl y e xte nd e d or con tra c te d in te rva l s ,
h ow would w e do i t ? G ive e xam pl e s .
Wh a t is t h e a ugm e n te d pr im e o f a - sh a rp ?G i ve t h e low e r e d unde r - pr im e of 0 fl a t .
N a m e t h e ra ise d se cond of d sh a rp .
Wh a t note is e nh a rm on ica l ly id e n t ica l w i th e doub l e sh a rp ?Wh a t ove r - in te rva l wou ld f sh a rp produce w ith d sh a rp ?G i ve t h e ra ise d und e r - th ird of d sh a r p .
N a m e t h e low e re d unde r - th ird of g sh a rp .
Wh a t oth e r unde r - in te rva l is t h e sam e , re ga rd ing t h e n um be r of s te ps ,
a s t h e low e re d un de r - th ird ?Wh a t is t h e a ugm e n te d fou rth of d fi a t ?
Wh a t is t h e ra ise d und e r - fourth of a - fi a t ?
G i ve t h e lowe re d f ourth of g sh a rp .
G i ve t h e lowe re d und e r - four th of c sh a rp .
D oe s i t m a ke a ny d i ff e re n ce in figur ing in te rva l s t o sound t h e ton e s compr is ing th em S im u lta n e ous l y or succ e ss i ve l y ?
Wh a t is t h e lowe re d und e r - fi f t h of c sh a rp ?Wh a t und e r - s i xth h a s t h e sa m e num be r of s te ps a s t h e lowe r e d un d e r
fi f th ?
G ive t h e a ugm e n te d fi f th of f sh a rp .
Wh a t is t h e m inor s ixth of f sh a r p ?How m uch do w e e n la rge a n in te rva l wh en w e a ugm e n t i t ?How much sm a l le r do w e m a k e a n in te rva l wh e n w e con tra ct i t ?Wh a t doe s t h e ra is ing of t h e uppe r tone of a n ove r - in te rva l do t o t h e la tte r ?Wh a t doe s t h e ra is ing of t h e low e r ton e o f a n und e r - in te rva l d o t o t h e
la tte r ?N am e t h e low e r e d un de r — s ixth of b .
Wh a t se ven th corr e spond s in S i z e t o t h e a ugm en te d s ixth of e ?
Wh a t k ind of a s e cond is g a - fi a t ?
G ive t h e lowe re d unde r - pr im e of f ; w ith wh a t und e r - se cond doe s i t a gre ein num b e r of ste ps ?
“rh a t is t h e d iff e r e n ce be tw e e n g a — fi a t a nd g g
— sh a r p ? fl'
h y h a ve th e s ein te rva ls d iff e r e n t nam e s ?
I f a - fi a t is pr im e ,wh a t would you ca l l a - doub l e - fi a t be low it ?
I f f sh arp is pr im e ,wh a t wou ld you ca l l e fi a t b e low i t ?
G i ve t h e m inor s i xth o f a - fi a t .
Wh a t is t h e ra ised unde r - fi f t h of c sh a rp ?Wh a t int e rva l doe s a - sh a r p form a bove b ?Wh a t in te rva l doe s a - fi a t f orm b e low g ?Wh a t in te rva l doe s a form be low g fi a t ?
I f a doub le fi a t t e d n ote h a d t o b e lowe re d , h ow wou ld you ind ica te i t ?N am e two in te rva ls r e qu ir ing th re e fold fi a t t ed note s , a nd one in te rva l
re qu ir ing a th re e fo ld sh a rpe d note .
(Tr ip le fi a t s or sh a rps a re n e ve r used in pra ct ica l mus ic . beca use e n
h a rmon ic ch a nge s a re r e sorted to , but th eor e t ica l ly th e y h a veto be a dm i t ted .)
12 0 .
12 1 .
122 .
123 .
124 .
133 .
139 .
140 .
14 1 .
142 .
143 .
144.
— i i i
Q5How ma ny k inds of con son a nt ch ords a re th e re ?Wh a t a re d issona n t ch ords ?
N am e t h e c h ord s th a t form t h e founda t ion of h a rmon ic s tructur e .
D e scr i be t h e sound a nd cons truct ion of t h e m a j or ch ord .
D e scr ibe it s oppos i te .
Wh e re is a m inor th ird to b e found in a m a jor ch ord ?
Wh e re is a ma jor th ird to b e found in a m inor ch ord ?
O f wh a t k ind of a th ird a nd fi f th doe s a m a jor ch ord cons ist ?Wh e n t h e m inor ch ord is m e a sure d downwa rd , wh a t k ind of in te rva ls
a ppe a r ?I s t h e m inor ch ord of t h e sam e va l ue a nd im porta nce a s t h e m a jor ch ord ?
Around wh a t ch ord s doe s a l l mus ic re vo l ve ?
é GG i ve t h e a scend ing ch a in of fi f th s produce d by th e na tura l note s .
G i ve t h e d e scend ing ch a in o f fi f th s produce d by t h e na tura l note s .
I n wh a t do t h e pe r f e ct fif th s de r ive d f rom b - f d is t ingu ish th em se l ve sf rom a l l oth e rs ?
G i ve t h e a sc e nd ing ch a in _of fi f th s p roduce d by sh a rpe d no te s .
G i ve t h e de scend ing ch a in of fi f th s produc e d by fi a t t e d note s .
N a m e t h e a sce nd ing ch a in of fi f th s produce d by doubl e sh a r pe d note sN a m e t h e d e sce nd ing ch a in of fif th s produc ed by double fi a t t e d note s .
G iv e a com ple te ch a in of fif th s , sta r t ing w ith f double fl a t , a nd e nd ingw ith b double sh a rp .
Wh a t a re t h e m a in p i l la rs o f a l l m a jor a nd m inor ch ords ?
N am e t h e m a jor th irds th a t h a v e no ch roma t ic s igns , th ose th a t h a veboth note s sh a rpe d , th ose th a t h a ve th em fi a t t e d , th os e th a t h a veth em double sh a rpe d a nd th ose th a t h a ve th em doubl e fi a t t e d .
G ive t h e m inor th irds th a t h a ve n o ch rom a t ic s ign s .
H ow ca n you m a ke m a jor th i rds out of m inor th ird s h a v ing na tura l note s ;th ose h a v ing sh a rpe d note s a nd th ose h a v ing fi a t t e d n ote s ?H ow m a ny wa ys a re th e r e t o turn m a jor th ird s in to m inor ? G ive i l lus
t ra t ions .
How do w e ind ica te m a jor ch ords by l e tte rs ?Wh a t would you a dd t o turn th em in to m inor ?How would you ind ica te e fi a t m inor , f sh a rp m inor , a nd 0 double sh a rp
m inor ch ords ?
Q7O f h ow m a ny m a jor a nd m inor ch ords is a ny ton e a m embe r ?I f a g ive n tone is t h e th ird of a ma jor ch ord , wh a t und e r - in te rva l w i l l
t h e pr im e form w ith 1t ?
I f a give n ton e is t h e th ird of a m inor ch ord , h ow do you fi nd t h e pr im e ?
I f you know t h e fif th of a m a jor ch ord , h ow w i l l you fi nd it s th ird ?Wh en a give n ton e is t h e fi f th of a m inor ch ord , h ow do you figure it s
th ird a nd pr im e ?
§ 8
Wh en is a ch ord in it s fundam en ta l pos i t ion ?
Wh a t do w e ca l l a ch ord , wh en i t , is not in it s fun dam en ta l pos i t ion ?
I f a ch ord is in it s fundam en ta l pos i t ion a nd in c los e pos i t ion , wh a tin te rva ls w i l l t h e note s com pr is ing i t form ?
E xpla in t h e d i ffe rence be twe e n c lose pos i t ion a nd ope n pos i t ion .
D e fin e a ch ord in it s firs t inve rs ion .
Wh a t in te rva ls do it s note s form , wh en i t is in c lose pos i t ion ?Wh a t nam e is of te n give n t o a ch ord in it s first inve r s ion ?
Wh a t is m e a n t by t h e se cond inve rs ion of a ch ord ?
Wh en i t is in c lose pos i t ion , wh a t in te rva ls wi l l t h e ton e s of a ch ord init s se cond in ve rs ion form ?
G i ve t h e n a m e comm on ly a ppl ie d to a ch ord in it s se cond inve rs ion .
Wh en a ch ord is in ope n pos i t ion , h ow do you br ing i t t o its c lose pos i t ion ?Wh e re a r e inve rs ion s of ch ord s found in com pos i t ions ?Ca n a compos i t ion end w ith a ch ord in open pos i t ion ?
Wh a t is a ch ord ?
Wh a t is m e a n t by K e y in Ha rm ony ?N am e t h e pr in c i pa l ch ord of a ke y .From wh ich ch ord doe s t h e ke y bra n ch out ?
D oe s th e key bra nch out downwa rds a s we l l a s upwa rds ?Wh a t is t h e n e a re s t re la te d ch ord on t h e uppe r s ide ca l led ?W h a t is a n U nde r D om ina n t ?
1 55 .
156 .
157 .
1 58 .
1 59 .
1 6 0 .
17 0 .
17 1 .
172 .
173 .
174 .
17 5 .
17 6 .
177 .
— iV
W h a t is a S ubdom ina n t ?How m a ny k ind s of f unc t ions (or office s ) a r e th er e w ith in a ke y ?
How fa r a pa r t is t h e pr im e of t h e D om ina n t f rom t h e pr im e o f t h eHow f a r a wa y f rom t h e pr im e of t h e S ubdom ina n t is t h e pr im e
Ton ic ch ord ?
Wh a t ton e of t h e Ton ic is id e n t ica l w ith t h e pr im e of t h e D omina n tWh a t tone of t h e S ubdom ina n t is a lwa ys ide n t 1ca l wi th t h e pr im e
Ton ic ch ord ?
Wh en is a ke y m a jor ?Wh e n is a ke y m inor ?Wh ich ch ord s d e te rm in e t h e s igna tu r e of a m a jor ke y
?
Wh ich ch ords d e te rm ine t h e s igna ture of a m inor k e y?
é 1 0
Ge ne ra l l y spe a k ing , wh a t is a sca le ?As wh a t doe s m od e rn h a rm ony con s id e r sca le s ?I f you use t h e a rpeggio of a m a jor ch ord a nd fi l l up t h e ga ps wi th oth e r
note s of a m a jor key , wh a t w i l l you produce ?Wh a t ch ord form s t h e f ram ework of t h e 0 m inor sca le ?Wh e r e a r e t h e h a l f s te ps to b e found in a m a jor sca le ?Wh e re a re t h e h a lf s te ps in t h e pure m inor sca le ?
fi l l
W h y . is mode rn ta ste not sa t isfie d w ith t h e ol d pure m inor sca le ?Wh a t is t h e d i ff e re nce be twe e n t h e pur e m inor sca le a nd t h e h a rmon ic
m inor sca le ?Wh a t note no t in t h e s igna ture doe s t h e h a rm on ic m inor sca le in troduce ?Wh a t h a ppe ns to t h e mD ?
D e scr ibe t h e e ff e ct t h e m a D h a s upon t h e key .
How m a ny dom ina n t ch ords ca n b e used in a m inor k e y?
M en t ion t h e fa c t th a t s ta m ps t h e m a D ch ord a s a fore ign ch ord .
H ow o l d a re t h e m ixe d m od e s ?
Wh a t k ind of ste p is th e r e be twe e n t h e s ix th a nd se ve n th d e gr e e s of t h e
h a rmon ic m inor sca le ?Q 1 2
W h y is t h e progr e ss ion f rom t h e s ixth t o t h e s e ve n th d egre e s of t h e
Ha rm on ic m inor sca le d ifficu l t t o s ing ?E xpla in h ow t h e unm e lod ic s te p in t h e H a rmon ic m inor sca le is ch a nged
in t h e M e lod ic m inor sca le .
W h a t is t h e d e sce nd ing M e lod ic m inor sca l e ?
§ 1 3
D e s cr ibe th e ch a ra c te r of th e m a jor key a nd it s oppos i te , t h e m inor .
H ow is a m inor k e y br i gh te n e d ?Ca n a ma jor k e y b e da rke n e d ? I f so , h ow ?
Wh e r e m us t w e look in t h e m a jor k ey for t h e ch ord corre spond ing t o t h e
m a D in t h e m inor ke y?
Wil l t h e re ve rse of t h e a bove h old good ? I f so , w h y ?
§ 14
I n pra ct ic ing t h e wr i t ing of ch ord conn e ct ion s , wh a t numbe r of pa rts is
con s id e r ed t h e be s t ?N a m e t h e h igh e s t vo ice .
Wh a t is t h e lowe s t pa r t ca l l ed ?G i ve t h e na m e of t h e low e s t pa r t of t h e f ema le vo ice s .
Wh a t is t h e h igh m a le vo ice ca l le d ?
B e twe en wh a t pa r ts is t h e a l to t o b e found ?Wh a t pa r t com e s be twe e n t h e a l to a nd t h e ba ss ?Wh a t pa r t usua l l y ca r r ie s t h e m e lody ?N am e t h e pa r t ne xt in im por ta n ce to t h e s 0 p ra no .
H ow h igh ca n t h e studen t of th is text —book go w ith t h e sopra no pa rt ?U nde r wh a t note sh ould you not g o in t h e ba ss pa r t ?I f you h a ve on l y th re e ton e s in a ch ord , a nd four pa r ts to wr i te , wh a t
must you do ?
Wh ich is t h e b e st note for doubl ing ?N ext to th is ,
wh ich note is t h e be s t t o doubl e ?Ca n t h e fundam en ta l e ve r b e tr e bl ed ?Wh a t note of t h e ch ord sh ou ld ge n e ra l ly not b e doubled ?Wh ich note ca n b e om i tte d ?Ca n t h e doubl ing occu r in t h e same tone — reg1ou , or must it occur in
a noth e r octa ve ?W h a t note is n e ve r om i t ted ?
253 .
254 .
2 5 5 .
2 56 .
2 57 .
2 58 .
2 59 .
2 6 0 .
2 6 1 .
272 .
27 3 .
27 4 .
27 5 .
2 7 6 .
287 .
2 88 .
289 .
2 9 0 .
29 1 .
2 92 .
293 .
2 94 .
2 9 5 .
2 9 6 .
2 97 .
2 9 8 .
299 .
3 0 0 .
30 1 .
30 2 .
3 0 3 .
3 0 4 .
I n h ow m a ny keys ca n th e se e xe rc ise s b e worke d out ?Wh a t pa r ts a re ca l le d t h e oute r pa r ts ?Wh a t m u st t h e m idd l e pa r ts pr inc i pa l l y do ?Wh a t is a dom ina n t s ix - four c h ord ?
Wh a t a re suspe n s ion s ?Are d issona n t tone s a l lowe d t o b e doubl e d ?I n re so l vm g t h e D ? in to D 3, is i t good t o doubl e t h e 5 of t h e la tte r ?Wh a t ton e sh ould r em a in doub led in th is r e so l u t ion ?
I n‘th e se e xe rc is e s , wh a t do t h e note s unde r t h e le tte rs m e a n ?
I s i t be t te r t o re pe a t note s or t ie a nd w r i te th em a s long note s wi th in t h esa m e m e a su re ?
E xpla in th e t e i m ca n tus fi rmus .
H ow do w e ind ica te t h e ch ord s ?
Wh en do w e d i s pe nse e ve n w ith l e tte rs ?NV h a t do t h e figure s ind ica te ?Wh e n do t h e figure s re f e r to t h e sopra no pa r t ?G i ve t h e m e a n ing o f in und e r a note .
Wh ere sh ou ld you wr i te t h e ch ord s igns wh en t h e sopra no is give n ?Wh e n t h e a l to or t e nor is given ? YV h e n t h e ba ss is give n ?Wh a t is t h e d i ff e re nce in m e a n ing of figure s a bove a nd be low t h e le tte rs ?How do you unm is ta ka bl y ind ica te t h e give n vo ice ?M us t t h e s ixth a nd fourth o f a D 2 in va r ia bl y progr e s s by s t e ps of a
s e cond w h e n go ing t o D 3 G i ve ch a nged r e so l u t ions , if you ca n .
£2 1
E xplain t h e F our th ste p in th e m a jor k e y a nd in t h e m inor .
With wh a t oth e r s te p doe s t h e Fourth ste p s e em to b e t h e sam e ?
Te l l t h e d i ff e r e nce of e ff e c t b e twe e n t h e tw o ch ord conne ct ion s a ppa re n tl ya l ike .
Wh en ca n t h e th i rd of t h e S or t h e mD b e doubl e d ?
H ow do w e m a rk t h e p e da l ~ p oint?
§ 22
G i ve a n expla n a t ion of t h e Wh ol e - tone s te p in both m a jor a nd m inor ke ys .
W h y do w e m e e t con s e cut ive fi f th s a nd octa ve s so re a d i l y in th is ch o rd
conne c t ion ?How ca n th e s e conse cut i ve s b e a vo ide d ?Wh a t obj e c t ions a re th e r e to t h e a ugm e n te d fourth ?
Wh e n is i t e ve r a l low ed ?
Wh a t pe rm iss i bl e in te rva l ca n w e wr i te in st e a d of t h e a ugm e n te d f ou rth ,
a nd h ow do you ma n a ge i t ?I n wr i t ing e a ch pa r t on a s e pa ra te sta ff , wh a t rul e s sh ould b e obse rve d
a s rega rd s t h e s tem s o f t h e note s ?Wh a t ta booe d sk i p in t h e ba s s is of te n a l lowe d in th is ch ord conn e ct ion ?
D oe s t h e D in a ny DOS it n a f te r t h e S d e fine t h e k e y su ffic ie n tl y ?Wh a t is t h e D 2 re a l ly be tw e e n t h e S a nd D ?
E xpla in t h e Fourth s te p wh e re on e ch ord is m a jor a nd t h e oth e r m inor .
Wh a t a bou t t h e a ugm e n te d fi f th ?
Wh a t fo l lows t h e d im in is h e d four th ?
Wh e re sh ould t h e d im in ish e d four th not b e u se d ?
W h y m ust t h e D om ina n t s ix — four o f t h e m inor ke y h a ve a lowe r e d s ixth ?
Ca n w e h a ve t h e sa m e ch a nge d r e so l ut ion s of t h e D 51 in t h e m inorkey a s in t h e m a jor ke y
?
Q24
E xpla in t h e Wh o l e - tone s te p wh e r e on e ch ord is m a jor a nd th e oth e r m inor .
Wh a t obj e ct ions a re th e re t o t h e a ugm e nte d se cond ?
H ow do you remove t h e sa m e ?
Q2S
Wh a t is m e a n t by Ch a nge of M ode (of ch ords ) ?
I l l us tra te wh e re i t occurs in t h e ke y so fa r e x p lam e d .
Wh e re is t h e ch rom a t ic s te p to b e f ound ?Wh a t a re you obl ige d to obs e rve conce rn ing i t in th is ch ord conn e ct ion ?Wh a t is m e a n t by c ross - re la t ion ?
I s fa lse re la t ion f e l t in oth e r ch ord conne ct ions th a n th is ?Q26
Wh a t is modula t ionHow on l y ca n i t b e m a de t o occur ?
0
W h a t s ign do w e use to ind ica te a modula t ion ?
vi i
5 2 7
Q2SWh a t ch ords a re t h e pr inc i pa l d iscords of t h e ke y ?
How m a ny subdom ina n t s ixth c h ords h a s a m a jor ke y?
How m a ny dom ina nt se ven th ch ord s a r e th e re in t h e ma jor ke y ?How m a ny dom ina n t se ve n th c h ord s a r e con ta in e d in t h e m inor ke y ?
Ha s t h e m inor ke y more th a n on e subdom ina n t S ixth ch ord ?
Wh a t tone o f a no th e r ch ord doe s t h e dom ina n t se ve nth ch ord a lwa ys a dd ?
Wh a t tone of a noth e r c h ord doe s t h e subdom ina n t s ixth ch ord a lwa ys a dd ?
How wou ld t h e th oroug h ba ss figur ing coun t t h e in te rva ls of a l l ch ords ?
Wh a t d id t h e th orough ba ss m e a n byWh e n is t h e 8 6 in 1ts fundam enta l
Q29How doe s th e s e ve n th a lwa ys m ove ?I n wh a t d ire ct ion doe s t h e sev e nth ge ne ra l ly g o
?
Wh e n toncs h a ppen to form a n in te rva l of a se cond , wh a t do th e y do ?
Wh e n on l y is t h e m e rging of on e ton e in to a noth e r cons id e re d good ?
Wh e n is t h e upwa rd m ovem e n t of t h e se ve n th a l low ed ?Ca n t h e fi f th of a s e ve n th ch ord b e om i tte d ?Wh e n doe s t h e Ton ic a ppe a r w ith out its fi f th ?
Wh e n is th ird doub l ing in four pa rt h a rmony con s id e re d fa u lty , a nd wh e non ly is i t good ?
I s i t poss ibl e to h a ve t h e se v e n th a s ba ss no te for t h e se cond la s t c h ord ?
Wh e n n e e d t h e se ve n th of a D 7 not progre ss by s te p of a se cond ?
D oe s t h e mD 7 progre ss l ike t h e ma D 7 ?
Wh en doe s t h e se ve n th o f a ch ord , in t h e m inor k e y , not n e e d to m ove ?Ca n t h e r e so lut 1on s o f t h e mD 7 b e d isg u is e d by m e a ns of int e rm e d ia te
ch ords ?
Q 3 0How a re t h e movem e n ts of pa rts influ ence d wh en t h e fi f th a nd s ixth of
a subdom ina nt s ixth ch ord a r e sound e d toge th e r ?I s i t n e ce ssa ry to susta in in t h e ba ss pa r t t h e 6 o f a S 6 wh e n t h e D fo l lows ?
Wh e n ca n t h e 6 of a S a ct l ike t h e pr im e o f a D 7 of t h e D ?
How ca n you turn a S 6 in to a D 7 o f t h e D ?
D oe s t h e use of a dde d (d issona nt ) ton e s w ith t h e dom ina n ts inc re a s e or
l e s se n t h e da nge r of con s e cut i ve fi f th s a nd octa ve s ? W h y?
How ca n you ch a nge a m inor 8 6 in to a D 7 o f t h e D ?
Wh a t doe s t h e 6 or 7 b e s id e a ch ord s ign or ch ord le tte r m e a n ?
Wh a t do th e se figure s be low or a bove t h e s igns ind ica te ?
Q3 1
Wh a t a re ca dences ?
Wh a t is m e a n t by figura t ion ?
E xpla in c h ord tone s .
Wh a t is m e a n t by pa ss ing tone s ?To wh a t c la ss do r e pe a te d ton e s be long ?I l lustra te a ux i l ia ry ton e s .
Ca n t h e se ve n th of a D b e use d in figu ra t ion a t a ny t im e ?
Wh a t a bout t h e use of t h e 6 in t h e S or m S ?
Ar e th e re a ny ob j e ct ion s to sk i pp ing in t h e ba ss pa r t f rom t h e fi fth o f
on e c h ord to t h e fi f th o f a noth e r ?Ca n a d issona n t tone b e d roppe d wi th out be ing re so l ve d ?Wh a t is m e a n t by d i v ide d figu ra t ion ?
Q 32Wh a t doe s t h e a dd i t ion of a 7 do t o a Ton ic ?Wh a t be com e s o f a Ton ic t o wh ic h a 6 is a dd e d ?
Wh a t tona l func t ion is sugge ste d wh e n t h e th ird of a T is ch rom a t ica l l ylowe re d ?How ca n you ch a nge t h e mT in to a m sG, a nd conse que n tl y ch a nge t h e
m e a n ing of t h e ch ord a nd m odu la te ?Wh a t m e a n ing doe s i t g ive t o a mT t o ch rom a t ica l l y ra ise its th ird ?
Q33How doe s a d im in i sh e d tr ia d g e t its nam e ?From w h a t d iscord s ca n t h e d im in ish e d tr ia d b e d e r i ve d ?
I s t h e d im in ish e d tr ia d a concord ?
Wh a t note m a y b e double d in t h e d im in ish e d tr ia d wh e n i t is pa rt of D 7 ,
a nd wh a t note wh e n i t is pa rt o f a m sG? E xpla in with e xa m ple s ine fl a t ma jor a nd g m inor k e ys .
Q34Wh a t is t h e re la t ion sh i p o f t h e pr inc i pa l ch ords ?Wh
‘a t o t h e r re la t ionsh i p e x ists th a n th a t of t h e F i fth ?
393 .
3 94 .
39 5 .
39 6 .
3 97 .
3 9 8 .
399 .
4 0 0 .
vii i
E xpla in a re la t ive ch ord .
D e fine a cor r e la t ive ch ord .
Wh en t h e pr inc i pa l ch ord is ma jor , of wh a t mode a re its re la t ive a ndcorr e la t ive ch ords ?
Wh e re is. t h e r e la t ive of a pr inc i pa l c h ord (m a jor ) s i tua te d ?Wh e re is t h e corre la t ive of a m a jor ch ord s i tua te d ?Wh a t m embe r s of t h e pr inc i pa l (ma jor ) c h ord doe s t h e r e la t ive conta in ?
Wh a t m em be rs of t h e pr inc i pa l (m inor ) ch ord doe s t h e corr e la t ive poss e ss ?F or wh a t ch ord ca n t h e re la t i ve a nd corre la t ive ch ord s b e used a s a
subst itute ?Wh a t re la t ionsh i p do t h e r e la t ive a nd corre la t ive ch ord s im i ta te ?Wh a t proof doe s t h e r e la t ions h i p by t h e Th ird f urn ish th a t m a jor a nd ,
m inor a re oppos i te s ?Wh en t h e pr inc i pa l ch ord is m inor , of wh a t m ode a re it s re la t i ve a nd cor
r e la t ive ch ords ?
Wh e re is t h e r e la t ive of a m inor ch ord s i tua te d ?XV h e re is t h e corre la t i ve o f a m inor ch ord s i tua te d ?How fa r a pa r t a re t h e re la t i ve a nd corre la t ive ch ords ?
é 35G i ve t h e Tr of B m a jor , a nd th e Tc of D fl a t m a jor key .
N a m e t h e S r of E m a jor , a nd t h e S c of A fl a t m a jor key .
Wh a t re la t ive ch ord doe s t h e 8 6 wi th ca nce l led fi f th produce ?Wh a t ch ord is t h e D r o f G ma jor , a nd wh a t ch ord is D c of F m a jor key ?Wh ich cor re la t ive ch ord of t h e ma jor k e y r e qu i re s a n a cc ide nta l ?Wh a t corre la t i ve s a nd re la t i ve s a re re pre se n ted by t h e sa m e ch ords in
t h e m a jor ke y ?How sh ould you de c ide th e ir re la t ion sh i p wh en a na lyz ing ?Ca n a ch ord h a ve mor e th a n one r e la t ionsh i p ?
§ 36N am e t h e mTr of E m inor , a nd mTc of D m inor key ,G ive t h e mD r of F - sh a rp m inor , a nd t h e c o f C ‘
m inor ke y .
Wh a t re la t i ve ch ord do w e g e t wh en w e ca nce l t h e pr im e o f t h e mD 7 ?N a m e t h e m S i of G - sh a rp m inor , a nd t h e m sc of F m inor k e y .
E xpla in t h e c h ord of t h e N e a po l i ta n s ixth .
N a m e t h e corr e la t ive s a nd r e la t i ve s r e pre sen te d by t h e sam e ch ords int h e m inor k e y .
Wh a t corre la t ive n e e ds a n a cc ide n ta l in t h e m inor ke y?
§ 3 7How do w e fi nd t h e e qu iva l en t ch ord conne ct ion s in m a jor a nd m inor keys ?
é 38“ Th a t is t h e spe c ia l f e a tur e of t h e r e la t ive a nd corre la t ive ch ords ?
I s sk i pp ing t o t h e fi f th in t h e ba ss pa r t a l lowe d for r e la t ive a nd corre la t ive ch ord s ?
Wh e re in t h e ca de nce is t h e na tu ra l pos i t ion o f t h e Tr . S r a nd D r ?
Wh e r e do t h e corre la t iv e s ta ke th e ir pla ce s in t h e ca de nce ?
Ca n t h e doubl ing of t h e th ird s of re la t i ve s a nd corre la t ive s occur in
pa ra l le l m ot ion ?
é 39Wh a t is m e a n t by a de ce pt i ve c lose ?F or wh a t ch ord ca n t h e r e la t i ve a nd corre la t ive ch ords b e subst i tuted ?O f wh ose na ture do t h e r e la t i ve a nd corre la t ive ch ords pa rta ke ?Wh a t is ch a ra cte r is t ic a bout t h e d e ce pt iv e c lose ?Wh e n is t h e d ista nce of a n oc ta v e be twe en a l to a nd tenor a l lowed in t h e
d e c e pt ive c lose ?G i ve . in t h e m inor k e y , t h e e qu iva le n t of t h e d e cept ive c lose D 7 -Tr in
th e ma jor ke y .
40 .
I l l ustra te t h e ch ord conn e c t ion of a M inor Th ird s te p , de scend ing f rom
m a jor t o m inor ch ord , or t h e r e ve rse a sce nd ing ; use F m a jor a nd
E m inor ke ys .
Are,t h e re a ny
‘spe c ia l d i fficul t ie s ?
4 1
I l l u stra te t h e ch ord conne ct ion of a Th ird s te p , a sce nd ing f rom ma jor t o
m inor ch ord or t h e re ve rse de s ce nd ing ; use G m a j or a nd D m inor
ke ys .
G i ve som e e xce pt iona l le a d ing of pa r ts not v io la t ing a ny rul e s .
Q 42I l l u stra te th e ch ord conne c t ion o f a “ f h o l e ' ton e s te p , a sce nd ing f rom
m a jor t o m inor ch ord , or t h e r e ve rse d e sce nd ing ; em ploy D m a jora nd G m inor ke ys .
H ow is t h e da nge r of con se cut ive fi fth s a nd oc ta ve s a vo id ed ?
437 .
438 .
439 .
440 .
441 .
Wh e r e is t h e a ugm e n ted se cond t o b e found ?Wh ich is t h e be s t w a y t o a vo id a l l t h e da nge rs of con se cut ives ?
5 55I l l ustra te t h e ch ord conn e ct ion of a n Augm en te d S e cond s te p , a sc end ing
f rom m a jor to m inor ch ord or t h e r e ve r se d e sce nd ing ; use F - sh a rpm a jor a nd D m inor ke ys .
Wh e r e is t h e d eba rr e d a ugm e n te d s ixth t o b e found ?Wh a t oth e r a ugm e n te d in t e rva ls ca n b e encoun te re d h e r e ?
%56I l lustra te t h e ch ord conn e ct ion of a Tr i ton e s te p , f rom m a jor to m a jor
1
(
ih ord , a nd f rom m inor to m inor ch ord ; us e G — fi a t m a jor a nd E m inor
e y s .
Wh a t is m e a n t by tr i tone ?O f wh a t a ugm e n te d s te p is t h e d im in ish ed th ird ste p t h e inve rs ion ?
é 5 7I l l ustra t e t h e ch ord conn e c t ion of a D im in ish e d Th ird ste p , de scend ing
from m a jor t o m inor ch ord or t h e r e ve rse a sce nd ing ; use G m a jora nd C - s h a rp m inor k e ys .
I Vh e re ca n t h e in te rva l of a n a ugm e n te d four th occur ?How a r e t h e a ugm e n te d s ixth s a vo id e d ?
W h y a r e th e s e ch ord s so d is ta n t ly re la te d ?
§ 5 8D oe s t h e use of t h e r e la t ive s a nd corre la t ive s of t h e m is a nd maD a fford
m a ny m e a n s of m odula t ion ?
How long sh ou ld you ke e p t o t h e o l d k e y wh en a na lyz ing ?Wh e r e a re po in ts of m odu la t ion t o b e loca te d ?
é 59Wh a t doe s t h e m a D do to t h e m inor sca l e ?Wh a t doe s t h e m iS do t o t h e m a jor sca le ?How is t h e a ugm e n te d in te rva l in sca le s ch a nge d ?Ca n t h e th ird o f t h e D of t h e ma jor k e y b e low e re d ?Ca n t h e th ird of t h e m 8 of t h e - m inor ke y b e ra ise d ?How is th i s ind ica te d in t h e ch ord s ign s o f tona l func t ions ?Wh e r e is t h e lowe re d th ird of a D suppose d t o l e a d t o ?
Wh e r e ough t t h e ra ise d th i rd of a m S g o t o ?
Ar e th e s e tw o ch ord s pr inc i pa l (ke y -m a k ing ) ch ords ?
Wh a t a n 0 1en t ch ur ch m od e doe s t h e m S 3 < re produce wh en it s th ird doe snot progr e ss t o t h e 3 o f t h e ma D ?
Wh a t ch a ra cte r is t ic ch urch m od e doe s t h e D 3 > re produce wh en it s th irddoe s not g o t o th a t of t h e m is ?
Wh ich of t h e two ch ord s , m S 3< a nd D 3 > i l lum in e s it s key?
Q 6 0Ca n a k ey bra nch ou t a nd r e a ch a bove th e dom ina n t or be low th e sub
dom ina n t w i th out induc ing a m odula t ion ?
Wh a t is t h e e ff e ct o f t h e D D ?
Wh a t a r e t h e r e sul ts of t h e S S a nd m iss ?E xpla in t h e e ff e cts of t h e m ss , mD D a nd ma D D in t h e m inor key .
‘
é 6 1Wh a t do you ca l l t h e ch ord re su l t ing from th e ch rom a t ic a l te ra t ion of th e
th ird of t h e T ?
D e scr ibe t h e e ff e ct t h e Tv h a s upon t h e m a jor ke y .
D e scr i be t h e e ff e c t of t h e mTv .
N am e t h e Tvc a n d Tvr of G . D - fi a t , B a nd E - fi a t m a jor ke ys .
N a m e t h e mTvr a nd mTvc of E - fi a t , B . C - sh a rp a nd D m inor ke ys .
W h y do com pos e rs som e t im e s wr i te c h ords e nh a rmon ica l l y ch a nged ?
Q 62(W ith th is p a ra grap h , the a uthor
’s E ssay on the Key-ex tension of Modern Ha rmony should
be stud ied . Therej ore , th ese questions refer to the essa y as wel l a s to the tex t-book. )
I s th e r e a noth e r a l te ra t ion of ch ords poss ib le b e s id e s th a t of ch a ngingth e ir th i rd s ?
Wh a t do w e ca l l such ch ords ?
I n to wh a t m od e is a m a jor ( pr in c i pa l ) ch ord a lwa ys ch a nge d wh en a l te re d ?Wh a t e ff e c t h a s t h e s im ul ta n e ous a l te ra t ion of t h e pr im e a nd fi f th of a
m inor ch ord ?
D oe s t h e a l t e ra t ion ra i se or lowe r th e oute r note s of a m a j or ch ord ?
Wh a t doe s t h e a l te ra t ion d o t o t h e oute r note s of a m inor ch ord ?QG i ve t h e ton e th a t a lwa ys forms t h e conn e c t ing l ink be twe e n t h e pr inc ipa l
a nd it s a l te re d form .
— xi
Ha ve t h e a s , aD, a T , am is , amT, a ms , a mD a nd a m a D a ny r e la t ive a ndcor r e la t i ve ch ord s ?
Ar e th e y use d exten s i ve ly ?Wh a t s e r ie s of ch ord s g iv e s mos t e xqu is i te t in ts t o tona l h a rmony ?E xpla in t h e te rm “
Va r ia t ion Th eory.”D oes Wa gne r ignore tona l i ty ?W h o m a y b e looke d upon a s t h e fa th e r of m od e rn h a rm ony ?W h o v ir tua l ly se tt led t h e qu e st ion of e qua l t em pe ra m e n t ?Wh a t in strum en t h a s h a d a gr e a t influe nce upon t h e de ve lopm en t of
m ode rn h a rmony ?Ca n a ny ke y con ta in a l l e x is t ing ch ord s ?
Wh a t d id Fe t is proph e sy ?I f a l l ch ords could b e con ta in ed in a l l ke ys , h ow would on e key r e a l ly
d iff e r f rom a noth e r ?Ca n t h e S S , D D , a nd m iS S h a ve r e la t ive a nd corr e la t i ve ch ord s ?
I s i t poss ib le to h a ve r e la t ive a nd corr e la t ive ch ords of t h e m ss , mD Da nd m a D D ?
Ca n t h e“ va r ia t ion th e ory b e a pp l ie d t o t h e S S , D D , m iss , mD D , mss ,
a nd m a D D c h ords ?1Wh a t ch ord s r e pr e s en t t h e e xtr em e l im i ts of ch ord re la t ionsh i p ?Wh en doe s a m odula t ion occur ?Wh a t ch ord m ust a lwa ys rem a in t h e ton a l cen te r ?E xpla in t h e l aw of re la t iv i ty .
To wh a t c la ss of ch ord s m us t a l l d i scords b e tra ce d ?D oe s a l l m e lody r e s t upon a n h a rm on ic ba s is , given or im pl ied ?Wh a t is pol yph ony ?
D e fin e a ca dence .
E xpla in a com pl e te c los e .
Wh a t is a h a l f c lose ?D e scr ibe t h e d e ce pt iv e c lose .
D oe s m od e rn th eory l im i t h a l f c los e s t o t h e dom ina n ts ?Are d e ce pt ive c lose s poss ib le f rom t h e subdom ina n t s ide a s we l l a s from
t h e dom ina n t ?G i ve t h e m e a n ing of T ie rce d e P ica rd i e .
I s i t poss ib le to c lose a p i e ce of mus ic in t h e ma jor ke y w ith its ton icva r ia n t ?
Could a pi e ce end ing in ma jor begin wi th it s ton ic va r ia n t ?D o com pose rs e ve r e nd p i e c e s on h a l f c lose s ?Ha s e ve r a nyth ing e lse but t h e pr im e of a ch ord been use d in th e ba ss
for a c lose ?Wh en m us t t h e l istene r fi nd th e c lose for h im se l f ?
é 6 4Wh a t a re th e gu id ing po in ts for a l l ch ord conn e ct ion s ?H ow m a ny ch ord groups a re th e re ?How d id w e na m e t h e ch ord conne ct ions ?With in wh a t ' in te rva l ca n a l l ch ord conn e ct ion s b e in c luded ?Wh a t is m e a n t by t h e inve rs ion of a n in te rva l ?How m a n y d i ff e ren t k inds of - s te ps a re con ta in e d w i th in e a ch ch ord
conn e c t ion ?
Wh a t co in c ide s w ith a double fif th ste p ?Wh ich is t h e m os t r e a d i l y und e rs tood s te p of a l l ?
Wh a t a r e ch ords for e ign t o t h e sca le ” ?
D oe s t h e gr e a te s t pow e r of e xpre ss ion in h a rm ony con s ist in frequen tch a nge s o f ke y or in extend ing t h e bounda r ie s of t h e key
?
é 6 5E xpla in wh a t d issona nce is .
How is t h e consona n ce of a m a jor or m inor ch ord d isturbe d ?Wh a t form s t h e ba s is o f e ve ry d iscord ?H a s t h e ton ic ch ord a ny ch a ra cte r is t ic a dd i t iona l ton e ?Are d iscords e ve r prod uce d by a dd ing tone s to t h e ton ic ?How ca n you expla in such forma t ions ?Wh a t is a suspe n s ion ?
Ca n a suspen s ion ton e b e t h e subst i tut ion of a n e igh bor ton e , m ore th a na wh o le ton e a bove or b e low , in p la ce of a ton e be longing t o a con
sona n t ch ord ?I n conn e ct ion with wh a t a re suspens ion ch ords a lwa ys th ough t of ?
Wh en is a suspe n s ion pre pa re d ?Wh en is a suspens ion unpr e pa r ed ?Wh a t is t h e
“ pe rcuss ion of a d iscord ?E xpla in t h e re so lu t ion ”
of a d iscord .
Wh a t a re r e ta rda t ion s ” ?
D oe s i t produce a good e ff e ct t o wr i te t h e su sta in ed note s imul ta ne ous lyin t h e s a m e octa ve pos i t ion a s t h e ch ord ton e wh ich i t re ta rd s or
suspends ?
5 9 1 .
59 8 .
599 .
— xii
N am e th e four poss ib i l i t ie s of suspens ions be fore a ny ch ord ton e .Wh ich a re t h e mos t r e a d i l y und e rs tood suspens ions f rom be low ?
N am e t h e be st suspens ion s f rom a bove .
H ow ca n t h e re so lu t ion of a d iscord b e d e f e rre d ?Wh a t is a re so lu t ion by progre ss ion ?
Wh a t is a n orna m en ta t ion of a d issona nce ?E xpla in pa ss ing h a rmon ie s .
M a y a pa ss ing tone e n te r f re e l y on a h e a vy b ea t ?Wh a t a re le a d ing tone s ?Ca n l e a d ing tone s b e u se d with out re f e rence t o wh a t pre cede s a nd a t a nypla ce in t h e m e a sure ?Wh a t doe s ch roma t ic a l te ra t ion of ch ord tone s m e a n ?
Ca n a n a l te re d ton e en te r fr e e ly on a h ea vy bea t ?Are a dde d a nd suspe ns ion ton e s t o b e found in t h e sa m e ch ord ?
I s i t poss ible t o h a ve a dde d a nd a l te re d tone s in th e sam e ch ord ?
Ca n suspe n s ion a nd a l te re d tone s b e com b in e d in t h e sa m e ch ord ?
Ca n a
h
l t e
rie
o
d ton e s b e un i te d w ith a dde d a nd suspens ion t on e s in t h e se m e
c or
N am e som e a dded ton e s to t h e dom ina n t of E a nd A m a jor ke ys .
G i ve s ix i l lus tra t ions of suspe n s ion s in t h e D 7 a nd D 9 of B - fi a t ma j or .ke y .
G i ve s ix i l lustra t ions of a l te r a t ions , e t c in t h e D 7 , a nd D 9 of D m a jor k e yG i ve s ix i l lustra t ions o f a l te ra t ion s , e t c . , of t h e S S in A- fi a t m a jor ke y .
G i ve six i l lustra t ions of a l te ra t ions , e tc . , of t h e m inor subdom ina n t o f
B m a jor ke y .
Ca n a ny ch ord of a ny tona l funct ion b e ch a nged by a dd i t ions , e t c .
?
Wh a t m us t you se a rch for wh en you unra ve l puzz l ing ch ord forma t ions ?Wh a t ton e s form t h e pre pa ra t ion of a d issona nce ?On wh a t pa r t of a be a t doe s t h e suspens ion tone a ppea r ?H ow m us t d iss ona nce s a lwa ys m ove ?E xpla in syncopa t ion .
Are syncopa te d con se cut ive fif th s or octa ve s a l lowed ?
Q6 6Wh a t a re D om ina n t N in th ch ords ?
“ Th e r e do oth e r s e v en th ch ord s th a n t h e D 7 occur ?Wh e r e doe s t h e dom ina n t
‘
w it h lowe re d n in th borrow its 7 a nd 9 f rom ?
How m a ny dom ina n t n in th ch ord s h a s t h e m inor ke y ?How m a n y dom ina n t n in th ch ords h a s t h e m a jor ke y
?
Ca n t h e 9 o f a D be dropped a nd th e n not re qu ire a re solu t ion ?
Wh ich n ote of t h e D 9 is t h e mos t re a d i l y om i tte d in four pa r t h a rm ony ?Ca n t h e 3 or 7 b e le f t out in t h e D 9 ?
I s t h e pr im e o f a D 9 e ve r om i t te d ?Are t h e ton e s of a D 9 usua l ly ke pt c lose toge th e r ?Wh a t ton e s of a D 9 a re be st for t h e ba ss ?
6 7Te l l wh a t you ca n a bout t h e D 1 1 .
I Vh a t h a ve som e th e or is ts don e w ith th is ch ord ?
Ca n t h e 1 1 d isa ppe a r W ith out re so lut ion ?
Ar e a l l of it s tone s a lwa ys pre sen t ?6 8
How m a n y D 13 ch ords ca n you nam e in th e ma jor key ?
How m a ny D 13 ch ord s a re th e re in t h e m inor k ey?
D o th e s e ch ords usua l ly a ppe a r in th e i r com pl e te form ?
I Vh e n m us t t h e D 13 b e looke d upon a s a funda m e n ta l ch ord ?
O f wh a t is a n t ic i pa t ion th e r e ve rse ?On
‘
w h a t pa r t of a m e a sure doe s t h e a n t ic i pa t ion occu r ?D oe s a nt ic i pa t ion occur on ly in c e rta in pa r ts of t h e h a rmony ?Ca n a n t ic i pa t ion a pp e a r in a l l pa rts s im u l ta n e ous l y ?Ca n ton e s b e in te rpo la te d be tw e e n t h e a nt ic i pa t ion a nd its subs e qu en tton e ?
Are suspe n s ions a nd a n t ic i pa t ion s a l lowe d s im ul ta n e ous l y in t h e sam e
ch ord ?
Ca n a ny ton e of t h e fo l lowing ch ord b e u se d a s a n a n t ic i pa t ion ton e ?Ca n ch ord ton e s ,
wh ich do not a ppe a r in t h e fo l low ing ch ord but couldbe long to i t , b e u se d a s a n t ic i pa t ion ton e s ?
Wh a t ca n you sa y a bout t h e N ota Ca mb ia ta ?Ca n a n t ic i pa t ion b e use d in a syncopa te d m a nn e r ?
G i ve t h e d iff e re nce be twe e n a n t ic i pa t ions . sus pe n s ion s a nd syncopa t ion s .
Ca n suspen s ion or pa ss ing ton e s e ve r b e a n t ic1p a t ed?
Wh a t is th e d i ffe re nc e b e twe en a d ia ton ic a nd a ch rom a t ic pa ss ing ton e ?Ca n pa ss ing ton e s'
occur in se ve ra l pa rts S im ul ta n e ous l y ?
655 .
6 5 6 .
6 57 .
6 58 .
659 .
67 0 .
67 1 .
6 72 .
673 .
6 74 .
6 7 5 .
67 6 .
677 .
xiv
§ 75I n wh ich d irec t ion doe s th e th ird of a D 7 g o t o th e ton ic ?D oe s t h e th ird of a D 7 e ve r d e sc en d to t h e fif th o f t h e ton ic ?I s t h e th ird o f a D 7 e ve r om i tt ed ?Wh a t h a ppe ns t o t h e se v e n th wh e n t h e D 7 r e so l ve s to t h e ton ic with t h eth ird of th i s c h ord in t h e ba ss ?E xpla in h ow t h e r e so lu t ion of a ch ord ca n b e r e gu la r a l th ough t h e p ro
g re ssmns a re fre e .
6 76Ca n a ny m a jor or m inor ch ord fo l low a ny oth e r (ma jor or m inor ) ch ord ?
M us t th e r e b e a conn e c t ing ton e ?Ca n a ny d i scord fo l low a ny oth e r d iscord ?
Wh en do d iscords conn e c t e spe c ia l l y w e l l ?Ca n d iscord s b e r e sol ved in oth e r octa ve s ?I V h a t 18 a n i rr e gula r r e sol ut ion ?
Wh a t is m e a n t by e n h a rm on ic modula t ion ?
Ar e e nh a rm on ic ch a nge s e ve r und e rstood but le f t unma rke d in t h e m us ica ln ota t ion ?
H ow sh ould t h e d issona n t ton e s proc e ed in ch a in s of d iscords ?Ca n d issona n t ton e s r em a in s ta t iona ry a nd form pa r t o f t h e n ew ch ord ?
7 7
Wh a t form s of t h e dom ina n t h a ve be e n give n spe c ia l na t iona l na m e s , a ndwh a t a re th e se na m e s ?
5"8I
Wh a t is a d im in i sh e d tr ia d ?H ow ca n a m a jor c h ord b e ch a nge d in to a d im in ish e d tr ia d ?Wh a t w i l l ch a nge a
' m inor ch ord in to a d im in ish e d tr ia d ?
W h y ca n th e r e b e a lwa ys four m odu la t ion s f rom e a ch d im in ish e d tr ia d ?H ow doe s i t com e th a t a f ew wi l l not l e a d out of t h e key a nd conse qu en t ly
produce n o m odula t ion ?
Wh a t m a ke s t h e d im in is h e d tr ia d a symm e tr ica l l y construc te d ch ord ?
I s t h e d im in i sh ed ch ord a da pte d for e n h a rmon ic c h a nge s ?
“ 9
Wh a t a re d im in ish e d se venth ch ord s ?
W h y is th is c h ord ca l le d a d im in ish e d se ven th ch ord ?
How ca n a d im in ish e d se v e n th ch ord b e m a de t o a r ise f rom a D 7 ?
H ow1ca n
d‘ad im in ish e d s e ve n th ch ord b e m a d e t o a r ise f rom a m inor S B
0 or
H ow ca n a d im in ish ed se ve n th ch ord b e form e d ou t of a m a jor ch ord ?
H ow ca n a d im in ish e d se ve n th c h ord b e f orm e d out of a minor c h ord ?
Ca n a ny pr inc ipa l , r e la t ive or c orre la t ive ch ord of t h e k e y b e ch a nge din to a d im in i sh e d se ve n th ch ord ?
W h y h a ve d im in ish e d se ve n th ch ord s ch a m e l e on - l ike qua l i t i e s ?Wh a t p i oduce s t h e symm e tr ica l con struc t ion o f th e se ch ord s ?
How m a ny oth e r d im in ish e d se v e n th ch ord s wi l l a ny d im in ish e d ch ord
e qua l wh e n e nh a i m on ic ch a nge s a r e em ploye d ?How m a ny d i ff e re n t ly s ound ing d im in ish e d se ven th ch ords a r e th e i c ?W h y a r e th e r e no m or e ?
Wh e n a re t h e doubl e pa r e n th e se s use d in t h e ch ord n ota t ion ?
Wh e n is t h e d im in ish e d se ve n th ch ord on l y a le a d ing ton e ch ord ?
I s i t ob l iga tory th a t a l l t h e ton e s o f a l e a d ing t one ch ord m us t f ormh a l f ton e s te ps t o t h e fo l lowing ch ord ?
Ca n oth e r ch ords t h a n t h e pr inc ipa l d iscord s b e used for in te rm e d ia teca d e nce s ?
W'
h a t is a wh ol e ton e sca le ?
Wh a t is a n a ugm e n t e d tr ia d ?O f wh a t ch ord is it t h e oppos i t e ?Wh a t ch ord d oe s i t n e a r l y e qua l . a s r ega rds surpr is ing modula t ions ?H ow is a m a jor ch ord tu rne d in to a n a ugm e n te d tr ia d ?Wh a t ch a nge s. a m inor c h ord in to a n a ugm e n te d tr ia d ?
From w h a t doe s t h e a ugm e n t ed tr ia d d e r ive it s na m e ?
E xpla in h ow t h is c h ord i s symm e tr ica l l y cons t i uc t e d .
How ca n e nh a rm on ica l l y ch a nge d form s of t h e a ugm e n te d tr ia d sounda l ike a nd y e t ea ch h a ve t h e a ugm e n t ed fi f th in t h e h igh e s t , in t h e
m idd le or in t h e lowe s t pa r t ?N a m e t h e numbe r of d i ff e re nt l y sound ing a ugm e n te d t r ia ds .
W h y a re th e re n o m ore ?
Wh ich ton e is t h e on e th a t h a s t o m ove ?Wh a t ton e s o f a n a ugm e n t e d tr ia d ca n b e doubl e d ?
Ca n you om i t a ny ton e o f t h e a ugm e n te d tr i a d a nd s t i l l pre se rve i ts
m e a n ing ?I s i t poss ibl e t o use a noth e r d iscm d a ft e i t h e a ugm e n te d t i ia d ?
7 62 .
7 63 .
7 64 .
7 65 .
7 66 .
Ca n any dom ina n t se ve n th ch ord fo l low a n a ugm e n ted tr ia d ?Could a ny d im in is h ed s e ve n th ch ord com e a f te r a ny a ugm en te d tr ia d ?Ca n th e a ugm e n te d tr ia d b e embe l l ish e d by suspe n s ion s , e tc.
I s i t prope r to l e t one a ugm ente d tr ia d fo l low a noth e r ?
G i ve t h e m ea n ing of pe da l poin t or orga n po in t .Wh a t m a y b e cons id e re d t h e ge rm of t h e pe da l po in t ?Wh ich i s t h e m ost e ff e c t ive ton e for a pe da l po in t ?O f wh a t is t h e pe da l po in t a n a ur icu la r i l lu stra t ion ?
I s t h e D e ve r m a d e t h e ba ss for orga n po in ts ?Wh a t is a doub l e pe da l ?G ive t h e m e a n ing of tr ip le peda l .I s t h e S used for pe da l po in ts ?Ca n a pe da l po in t occur in e i th e r uppe r or m idd le pa r t ?Wh en is t h e pe da l po in t m os t e ff e c t ive ?W h a t is a n inve rted pe da l ?M us t t h e peda l a lwa ys b e a susta in ed tone ?Wh a t spir i t pe rva d e s in t h e pe da l po in t ?Wh a t sp ir i t pe rva d e s in a se que nc e ?How do w e ind ica te t h e pe da l po in t in a na lys is ?Ca n a m odula t ing s e quence b e com b ined W i th a peda l po in t ?Wh en t h e pr im e of t h e T is be low t h e D 7 ch ord , h ow do you ind ica te i t
in a na lys is ?Ca n t h e D 7 e ve r b e cons ide red a s a sus pen s ion ch ord d e la ying th e tones
of t h e ton ic ?Q 82
Ca n s ingle tone s b e m a de t h e pivot ing po in ts of modula t ions ?Wh en doe s a d issona n t ton e be com e a m em be r of a concord ?
Wh e n doe s a m embe r of a concord be com e a d issona n t ton e ?Wh en doe s t h e m em be r of one ch ord t urn _into a d iff e re n t m embe r of
a noth e r ?Wh en doe s a d issona n t tone of one d iscord turn in to a d issona n t ton e of
a noth e r d iscord ?I s i t poss ib le to ch a nge t h e m e a n ing of a s ingl e ton e a nd ma ke i t t h e
m e a ns of a m odu la t ion ?
Ca n enh a rm on ic ch a nge s b e em ploye d wh en ch a nging th e m e a n ing of a
s ingle tone for t h e sa ke of m odula t ion ?
Wh a t is m e a n t by a ch a in of m odula t ion s ?Wh a t is t h e pr inc i pa l th ing t o b e obse rv e d in a comb ined m odula t ion ?
assHow ol d is t h e proh ib it ion of conse cut ive fif th s ?Wh a t w a s t h e orga num ?
Are th e re d is t inc t ions m a de be twe en t h e a l lowa ble a nd una l lowa bl e con
se cut ive fi f th s ?Wh e re a re conse cut i ve fif th s m os t ob je ct iona bl e ?F or wh om is t h e r igorous rule of conse cut i ve s ind ispensa ble ?U nd e r wh a t cond i t ions w i l l fi f th s occur , th ough or ig ina l ly not so wr i t ten ?
To wh a t form a t ions do fi f th s po in t wh en th e y re cur upon t h e a ccen tedpa rts of be a ts ?M a y conse cut i ve fif th s b e d isgu ise d by re s ts , suspen s ions , e tc .
?
Are con se cut i ve fif th s a l low e d in a rp e g g io’
d ch ord s in se quence s ?Are gra ce note s , a ux i l ia ry , pa ss ing ton e s , e t c . , e ve r t h e ca use of con
se cut ive fif th s ?How ca n a figura t ion m ot ive produce conse cut ive fi f th s ?B e twe en wh a t c lose ly re la te d h a rm on ie s a re pa ra l le l fi f th s a l lowe d ?Wh a t ce rta in form s of t h e D a l low con se cu t i ve fif th s ?Wh e n a re con se cut iv e fi f t h s pe rm i t te d be tw e e n a S a nd D 7 ?
Wh en ca n con se cut i ve fi f th s occur be twe e n se ve n th ch ord s ?
Wh en a re conse cut ive fi f t h s occa s iona l ly e xcus ed be twe e n t h e subdom ina n ta nd dom in a n t ?
Are pa ra l le l fi f th s a l lowe d b e twe en t h e pr inc i pa l ch ords a nd th e i r rela t ive sa nd corr e la t ive s ?
Ha ve ch roma t ic con se cut ive fi f th s e ve r be en wr i tten by gre a t m a ste rs ?
Ar e th e re conse cut ive s progr e ss ing by a d ia ton ic h a l f - s te p ?Wh a t m us t b e obse rve d a bove a l l in a l l conse cut ive s ?Ca n con se cut ive s b e produce d by m e re fi l l ing - ih pa r ts ?Are conse cut ive fif th s e ver use d a s a m e a ns of expre ss ion a nd color ing ?
§ 84I s t h e e la bora t ion of h a rmony t h e work of one man ?
W h o m a ke t h e a dva nce s in m us ic ?Wh a t h a ve th eor is ts to do ?
Wh a t rul e s a r e trul y rule s ?Ar e th e re ma ny ru le s a bove t im e a nd ta ste ?
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