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MUSIC 105Dmitri Tymoczko
Handout 6 (2010)
SCALES, SCALES, SCALES
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4&5).&- $,6 1&/-76)*8 17-)./0 4)-'/*.&9 '(&* -./0&- 4, *,' *&&4 ', (/5& :$)6-'; *,'&-?@?A?=?B?C?D?E>F< GH(& I6/.+&'- /6,7*4 '(& 0/-' > )*4)./'& '(/' %&
(/5& / .)6.70/6 ,64&6)*8 '(/' (/- 6&'76*&4 ', )'- -'/6')*8 2,)*' 4)/',*). -./0& >?@?A?=?B?C?D?E>F )- 4)$$&6&*' $6,1 '(& B 4)/',*). -./0&
B?C?D?>?@?A?=!?EBF9 -)*.& '(& $,61&6 (/- /* ="%()0& '(& 0/''&6 (/- /* =!< D7' '(& '%,-./0&- /6& 6&0/'&4 I3 .(6,1/'). '6/*-2,-)'),*P &5&63 *,'& )* '(& B 1/M,6 -./0& )- -&5&*
-&1)',*&- /I,5& '(& .,66&-2,*4)*8 *,'& )* '(& > 1/M,6 -./0&< =,6 '()- 6&/-,*9 '(&3 -,7*4
5&63 -)1)0/6< H%, -./0&- I&0,*8 ', '(& -/1&*(+,$ %01$)$ '(&3 /6& 6&0/'&4 I3 .(6,1/').
'6/*-2,-)'),*< H(& > /*4 B 4)/',*). -./0&- I,'( I&0,*8 ', '(& #'+%"&'( *(+,$ %01$)
Q)1)0/6039 '%, 1,4&- ', '(& -/1& !"#$ %01$)$ '(&3 /6& 6&0/'&4 I3 .(6,1/').
'6/*-2,-)'),*K $,6 &N/120& '(& @ 4,6)/* 1,4& @?A?=?B?C?D?>?@ /*4 '(& B 4,6)/* 1,4&
B?C?D#?>?@?A?=?B I&0,*8 ', '(& #"/'+& !"#$ %01$)2345!567 R7-).)/*- /6& *,' /0%/3- .,*-)-'&*' )* '(&)6 7-& ,$ '&61)*,0,83P
-,1&')1&- '(&3 7-& :-./0&; ', 1&/* :1,4&; G/- )* :'(& C */'76/0 1)*,6 -./0&;J9 /*4-,1&')1&- '(&3 7-& )' ', 1&/* :-./0& '32&; G/- )* :'(& 4)/',*). -./0&;J< Q,1&')1&-
:1,4&; 1&/*- :1,4& '32&; G:'(& 4,6)/* 1,4&;J< C- 0,*8 /- .,*'&N' 1/+&- 3,76
1&/*)*8 .0&/69 /*4 )' )- 2&6$&.'03 $)*& ', %6)'& /*4 -2&/+ )* '()- G-,1&%(/' )*$,61/0J
%/3
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"
#$%&%&'%( )*+) )*% +,-./)0,+112 3.(% 404)* 0/ /105*)12 6044%(%7) 4(-& )*% %8.+1 )%&3%(%6
404)* -4 )*% -(607+(2 30+7-9: ;*0/ &%+7/ -4
404)*/ ?@A@B@C@D@E
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"
#$% !"#$%&'#(% *+,$%&'('&%) *$% +,*-(% '.*+ )'/ 01%,')%23 %(%. 0-1*) -.& ,+.*-'.)
-) 4-.3 4-5+1 *$'1&) -) - *$1%%6.+*% ),-2% ,-. $-(%7 8#$-* ')9 %(%13 .+*% '. *$% ),-2% $-)
- 4-5+1 *$'1& -:+(% '*7; '1)* ?)%& :3 @2'.A-9 -.& =-) 4-&% >-4+?) :3 B%:?))37 1%C?%.*23 -00%-1) '. 5-DD 8%)0%,'-223 #$%2+.'+?) E+.AF) 02-3'.G; -.& ') +>*%. ?)%& *+
)'G.'>3 &1%-4 )%C?%.,%) '. *%2%(')'+. -.& 4+('%)7
! #$%&' (%)'
3+? *1-.)0+)% *$% ),-2% :3 *=+ ,$1+4-*', )%4'*+.%)9 3+? %.& ?0 ='*$ *$% )-4% ),-2%
-G-'.H4%-.'.G *$-* *$%1% -1% 5?)* *=+ =$+2%6*+.% ),-2%)I J'.,% *$') ),-2% $-) (%13 2'**2%
'.*%1.-2 (-1'%*39 '* C?',A23 :%,+4%) :+1'.G7
K )%,+.& )'/6.+*% ),-2% ') *$% "%-,'#(.+ *+,$%L ,+.)')*'.G +> -2*%1.-*'.G +.%6
)%4'*+.% -.& *$1%%6)%4'*+.% )*%0)7 >%1%.* 0%1>%,* >'>*$) -.& ,+.*-'.'.G 4-.3
&'>>%1%.* 4-5+1 -.& 4'.+1 *1'-&) 8$+= 4-.39 '> 3+? 'G.+1% )0%22'.GM;
! $'*+(%),-K4+.G *$% '40+1*-.* )%(%.6.+*% ),-2%)9 =% $-(% *$% ,*+%(/.(0 1%$#/.+ 1.(#2+1
,+#3*'.+ *+,$%8-2)+ )+4%*'4%) ,-22%& *$% N23&'-. &+4'.-.*O;9 ='*$ 4-5+1 +1 4'.+1 *$'1&)
-:+(% %-,$ +> '*) .+*%)9 -.& =$',$ &'('&%) *$% +,*-(% >-'123 %(%.237 *$) -.& *1'-&) 8$+= 4-.3M;7
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"
" #$%&%#'($ #) " *(+('(,-.* /0&112
#$% &'()(&*+' ,')-% $), (.& ,+/%, &0 ,(%1 23 )*4 5 ,%6+(&*%,7 )*4 0&89($ 2: )*4 "
,%6+(&*%,7; +( $), &*-? &*% ,+/% &0 ($+94 2@ ,%6+(&*%,7 )*4 0+0($ 2A ,%6+(&*%,7;
B* ($+, ,%*,% +( +, *%)9-? ), ,?66%(9+')- ), ($% .$&-%C(&*% ,')-%D +0 .% (9)*,1&,% ($%&'()(&*+' ,')-% E? ($9%% ,%6+(&*%,> ($%* .% %*4 81 .+($ ($% ,)6% ,')-% )F)+*;
#$% 0&--&.+*F ()E-% ,866)9+/%, &89 ,')-%,;
345 6 7)(.8 -(,%#)9 #8 ,$&:., (' ;.,%.)' +.' D&E(+&::9
@&%. '#%., \%*()(&*+' \%90%'( 0+0($,
@(E '#%., X$&-% (&*%
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"
!"#$%& () !(*%+ ,-./% ,%0"%1-% () 21*%&3./+
453% #$%&'&(%)* +,+,-,+,-
./(0$ &(%$ +,+,+,+,+,+,56
1$2'&(%)* 3,-,3,-,3,-
4)'&(%)* +,+,3,+,+,+,3
5$0(6)* 5)%(7 89*$%6)%: +,3,+,+,+,+,3
1'7;(%)* ;)%(7 +,3,+,+,3,-,3
,%3%1
1'7;(%)* ;'
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"
cccccc
THE DIATONIC MODES
!"#$# &$# '#(#) *+,#' +- ."# ,/&.+)/0 '0&1#2 !"#3 &11 0+).&/) ."# '&*# )+.#'4 56. #*7"&'/8# & ,/--#$#).
)+.# /) ."# 0+11#0./+)2 !"# *&/) )+.# +- #&0" *+,# /' ."#tonic+- ."# *+,#2
92 : /+)/&) ;< *&=+$> C is tonic ? /+)/&)
@2 A ,+$/&) D is tonic ? ,+$/&)
B2 C 7"$3D/&) E is tonic ? 7"$3D/&)
E2 ? 13,/&) F is tonic ? 13,/&)
F2 G */H+13,/&) G is tonic ? */H+13,/&)
I2 J &+1/&) ;J )&.6$&1 */)+$> A is tonic ? &+1/&)
K2 L 1+0$/&) ;(#$3 $&$#> B is tonic ? 1+0$/&)
in this column, each mode is transposed
so that F is tonic
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!"# %&'#( &) !"# %#*&'+, %+-&.
#$%&% '&% (%)%* +,-%( ,. /$% '(0%*-1*2 +%3,-10 +1*,& (0'3%4 56%&% 78)% 31(/%- /$%+ 1*
/9, 9':(; .1&(/< '( -1..%&%*/ '&&'*2%+%*/( ,. /$% *,/%( =>?>@!>A>B>C>D< '*- (%0,*-< (,
/$'/ /$%: (/'&/ ,* =4E F,+% ,. /$%+ '&% )%&: 0,++,* 1* G'HH '*- ,/$%& +I(10(< 9$%&%
/$%: '&% I(%- 1* J,/$ /$%1& '(0%*-1*2 '*- -%(0%*-1*2 .,&+(4 K,/% /$'/ /$%(% +,-%( '&%,./%* 0'33%- L(0'3%(4M
!" $ %&'()*+ %*,(- ./+&,)*,0
1" ,(2 ,.%&) 3-.-&4
5" ,(2 ,.%&) 3-.-&4
6" 7 89)*., :(%*,.,2 /+.'& 3;.
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"#
?
?bbbbbbbbbbbbbb
bbbbbbbbbbbb
bbbbbbbbbb
bbbbbbbb
bbbbbb
bbbb
bb
C major G major D major A major E major B major Fsmajor Csmajor
A minor E minor B minor Fsminor Cs minor Gsminor Dsminor Asminor
Cfmajor Gfmajor Dfmajor Afmajor Efmajor Bfmajor F major C majorAfminor Efminor Bfminor F minor Cminor G minor D minor A minor
DIATONIC KEY SIGANTURES
$%&'( &)'*' +*' ,% -'. /01,+&2*'/ *'320*0,1 + 4%256' /)+*7 %* 4%256' 86+&9 :)0/ 0/ ;). ;' 4%,'= ?!@+A%*= ;)%/' ,%&'/ ?!= B!= C!= D!!= E!= F!= G!*'320*'/ + 4%256' 86+&9
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MUSIC 105
Dmitri Tymoczko
Handout 7 (2010)
!"#$% %'#(!$) $%$)*+,+
,- ./01123451 64374383617- "#$%& '()*+ ,-./$*),) 0*1*0.0 ,-. *2,.$1#%) *2,/ !"#$"#%#!&$
3(2*)/24 '*2/$ ,-*$04 '#5/$ ,-*$04 6.$7.+, 7/($,-4 #20 #%% ,-.*$ $.8*),$#% *21.$)*/2)9: #20
'($$"#%#!&$3.1.$&,-*28 .%).:; . # %//> #, ,-. ,-$..?2/,. +-/$0) +/2,#*2*28 /2%&
+/2)/2#2+.);
(a)
(b)
@-/). *2 3%: -#1. ,A/ +/6*.) /7 )/'. 2/,.; B) # $.)(%,4 ,-.& )/(20 # %*,,%. %.)) $*+- #20 7(%% ,-#2
,-/). *2 3):; C. +#%% ,-*) ).+/20 8$/(6 *+(%'$, )*2+. ,-.& -#1. ,-$.. 0*),*2+, 6*,+- +%#)).); D1.$
,-. +.2,($*.) '()*+*#2) 8$#1*,#,.0 '/$. #20 '/$. ,/A#$0 ,$*#0)4 6$.7.$$*28 ,-.*$ $*+-2.)) ,/ ,-.
.'6,& )/(20 /7 ,-. +-/$0) *2 3%:;
,,- 9:;877 7?@>4A7- D$*8*2#%%&4 ,$*#0) A.$. 2#'.0 E& 8*1*28 ,-.*$ E#)) 2/,.4 6%()
,-.*$ *2,.$1#%) #E/1. ,-. E#)); @-. )&'E/%!"
'.#2) ,-#, ,-.$. #$. # 7*7,- #20 ,-*$0 #E/1. ,-. E#))4$"
'.#2) ,-#, ,-.$. #$. # )*F,- #20 ,-*$0 #E/1. ,-. E#))4$%
'.#2) ,-#, ,-.$. #$. # )*F,- #20 7/($,-
#E/1. ,-. E#)); 3G.$. A. #8#*2 0*)$.8#$0 .F,$# /+,#1.)H I# 7*7,-J +/(%0 '.#2 I7*7,- 6%() #2
/+,#1.J /$ I7*7,- 6%() ,A/ /+,#1.)4J .,+;: K/ *2 ,-. '()*+ E.%/A4 ,-. 7*$), ,-$.. +-/$0) A/(%0 -#1.
E..2 +#%%.0 L!"
4 ,-. ).+/20 B$"
4 #20 ,-. ,-*$0 M$%
;
C
5eA6e
B6r
N, *) +(),/'#$& ,/ #EE$.1*#,. ,-.). )&'E/%) E& .%*'*2#,*28 ,-.!"
4 A$*,*28 O7/$$"
4 #20 >..6*28$%
(2+-#28.0;
9@-#, *)4 #%% ,-. 2/,.) &/( +/(%0 8., E& ),#$,*28 A*,- P4 'Q4 RQ4 ST #20 ,$#2)6/)*28 .*,-.$ 2/,.
E& #2& 2('E.$ /7 /+,#1.);
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"
!!!" $%%&'" #$%& '() *+,--./' *$(01- .& 2$.- 3,'4 2$%0% ,55%,0 2( 6% 2$0%% /)&1,7%&2,+
8.&1- (/ *(&-(&,&2 20.,1-9!"
4$"
,&1$%
: ;& 2$% %,0+' %..%,
ABC>)*&)2 RS T RS RS IU DE4 F4 G!H ETD-E%1 RS T 7S RS ?U DE4 F4 GH E
D3*%1 7S T RS 7S ?U DE4 F"4 GH *F3>3*3'0)2 7S T 7S 7S 1U DE4 F"4 G"H *V
;&
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"
#$%& %'(% %'& )*+*,*-'&) %.*() '(- ( )*--$,(,% *,%&./(01 %'& )*+*,*-'&) 2*2%'3 4'& (56+&,%&)
%.*()7- (56+&,%&) 2*2%' 8(- 9$,-*)&.&) )*--$,(,% (- 8&001 &/&, %'$56' *% -$5,)- :5-% 0*;& ( +*,$.
-*&0&) FF =2$. +(:$.B
$. ** =2$. +*,$.B1 (,) -$ $,3 G,9& (6(*,1 ( 9(@*%(0 0&%%&. 8*%' ( @05- -*6, =&363 FFFHB *,)*9(%&- (,
(56+&,%&) %.*()1 ( 9(@*%(0 0&%%&. =&363 FFFB *,)*9(%&- ( +(:$. %.*()1 ( -+(00 0&%%&. =***B *,)*9(%&-
+*,$.1 (,) ( -+(00 0&%%&. 8*%' ( )&6.&& -*6, =***IB *,)*9(%&- )*+*,*-'&)3 C& *,)*9(%& %'& ;&A %$
%'& 0&2% $2 %'& D$+(, ,5+&.(0-1 5-*,6 9(@*%(0 0&%%&.- 2$. +(:$. ;&A- (,) -+(00 0&%%&.- 2$. +*,$.
;&A-3
w w w w w w w w
w w w w w w w w
w w w w w w w w w w w w w w w w w w w w w w w
C: I ii iii IV V vi vii I
major
minor (harmonic minor scale)
c: i ii III+ iv V VI vii i
minor (melodic minor scale)
c: i ii III+ IV V vi vii i VII VI v iv III ii i
c: i ii III iv v VI VII i
minor (natural minor scale)
C& 9(, 5-& %'& -(+& -A-%&+ 2$. +$)(0 +5-*91 %'$56' A$5 -'$50) -@&9*2A %'& +$)& 9$+@0&%&0AJ
w w w w w w w wC mixolydian: I ii iii IV v vi VII I
mixolydian
D$+(, ,5+&.(0- 9(, (0-$ >& 5-&) 2$. 9'$.)- ,$% *, %'& -9(0&J (99*)&,%(0- >&2$.& %'& ,5+&.(0
(@@0A %$ %'& .$$%1 8*%' 9(@*%(0K-+(00 0&%%&.- .&2&..*,6 %$ +(:$.K+*,$. *, %'& -%(,)(.) 8(A3 4'5-
LFFFM .&2&.- %$ (, N +(:$. 9'$.) *, %'& ;&A $2 O +(:$. =*** 8*%' ( .(*-&) %'*.)B1 (,) L!PFM .&2&.- %$Q +(:$. *, %'& ;&A $2 E +(:$.3 R*+*0(.0A1 L"**IM *, S +(:$. *- (, E")*+*,*-'&) %.*()3
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"
!"# %&'&()* +*,-./# #$%&'$ () (*++ ,%- .) &/*,' /)0),-$ 1$%23/ 4%2 5 4)( 6%2) ())7/8
*-9/ (%2-$ :&--*,' -$)6 $)2);
0/)1+2 ,3 )*4-./5 6*4-. 743)* %&'&()* 891:;, *>
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!" $%&'( )*+',-.-) /*,0.11'- 23,3&&'&("
!" $%&'()*+,-( .(/0()+ ,&+(/-12'3-* 45* +*.6'( 63- 738' 2',/'64 *643+'( *- 45*
6*-('6%4.+' 69*,1(: *, 2',/'64 /./49( *- 45* 6*-('6%4.+' 69*,1(" ;? 4* @?: 59.&' 3&4* 7*+'( /,*7 A? 4* >B"
4" 5,6,&,'7(8 0,0+7 +% .(/0()+ 0,0+79 C/ (*7' +*.6' .( 3 1.7.-.(9'1 /./49 30*+' 49'
03((: 49'- .4 63--*4 738' 3 2',/'64 /./49 5.49 49' 03(( *- 49' -'2(8,''%&1&)(./ 49' 03(( .( -*4
.-+*&+'1G .-4*&',30&' *49',5.('
'+',F49.-) '&(' 1.((*-3-6'
U" K( 3 ,'(%&4: 4,.31( 63- 322'3, *-&F .- ,**4 2*(.4.*- *, /.,(4 .-+',(.*-" ?()%&8
,&-(/',%& +/,18' 1/( )%&',8(/(8 8,''%&1&+@
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!"# !%&'()*+%)# !"#$%&% %"()*+ ,&-./ $/+ &/+ 0.1" #((1 2(%.1.(/ 1#.$+%3 4&/$**56 #((1
2(%.1.(/ 7"(#+% $#& 1"& /(#89)%& 1"&8 $,()1 :;< (= 1"& 1.8&3 >.#%1 ./?%.(/ 1#.$+%
%"()*+ ,& )%&+ (/*5 0"&/ 1"&5 7(/1#.,)1& 1( $ %8((1"6 8&*(+.7 ,$%% *./&6 $,()1 @;< (= 1"&
1.8&3 A -((+ #)*& (= 1")8, .%B 0"&/ 1"& 1".#+ (= 1"& 7"(#+ .% ./ 1"& ,$%%6 .1 %"()*+ ,&
7(//&71&+ ,5 %1&2 1( &.1" 1"& /(1& 1"$1 7(8&% ,&=(#& .16 (# 1"& /(1& 1"$1 7(8&% $=1$#+3
CD(8&1.8&% (/& (= 1"&%& /(1&% 0.** ,& $ 2$%%./- 1(/&3E F(0&? 1".% .% G)%1 $ #)*& (=
1")8,91"& $#2&--.$1.(/ ./ 1"& 1".#+ 8&$%)#& ,&*(0 .% 2=&71*5 /(#8$*3
?
bad: leaping betweeninversions without aclear melodic or
harmonic purpose.
good: the stepwisebass is melodic
good: the bass arpeggiatesan A minor chord, which isalso the chord in the upper
voices
"# ,-.'%/')# H/ -&/$* 2"#$%&%6 %"()*+ ,&-./ $/+ &/+ 0.1" 1"& %$8& 7"(#+6 1"()-" 1".%
#)*& 7$/ (77$%.(/$**5 ,& ?.(*$1&+3
!" $%&'' (& )(&' *(+,'-.A1 &? 7$+&/7&6 10( ?(.7&% %"()*+ 8(?& ,5 %1&26 ./
7(/1#$#5 8(1.(/6 1( $ )/.%(/ (# (71$?&3 I"& 2.17" 7*$%% (/ 0".7" 1"&%& ?(.7&%
7(/?-& %"()*+ $*%( $22&$# ./ 1"& ,$%% (= 1"& =./$* 7"(#+3 I"& #&8$././- ?(.7&%
%"()*+ ,& +&2*(5&+ %( 1"$1 1"& 2&/)*1.8$1& 7"(#+ .% $ 7(82*&1& 1#.$+3 H/ =()#
?(.7&%6 1"& =./$* 7"(#+ 7$/ ,& &.1" $ #((1 2(%.1.(/ 1#.$+6 $ ,$#& 1".#+6 (# $ ,$#&
=.=1"3 H/ 1"#&& ?(.7&%6 .1 7$/ $*%( ,& $ )/.%(/3 JK$82*&B 1&/(# 8(?&% =#(8 L< 1(
MN6 0".*& $*1( 8(?&% =#(8 ON 1( MNP ,$%% 8(?&% =#(8 4< 1( M
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MUSIC 105
Dmitri Tymoczko
Handout 11 (2010)
!"#$%%&'(&)* ,(-./%$0'12%$ 3/."-)2 4&1( 5-)(/."-)&6 7-)$'
"#$%$ &%$ & '()*$% +, -&./ 0+ 0&1$ & /2)34$ 5+26$74$&82'9 /1$4$0+' &'8 $)*$442/# 20 0+ 6%$&0$
/+)$0#2'9 )+%$ /+3#2/026&0$8 &'8 )(/26&4: ;+/0 +, 0#$/$ 2'5+45$ !"!#$%&"!'( *"!+,-+% '+0$/
,+%$29' 0+ 0#$ ('8$%4.2'9 #&%)+'.: "#$%$ &%$ ,+(% )&2' 0.3$/ +, '+'#&%)+'26 0+'$/ 2'
2' 6#+%&4$ /0.4$= &4)+/0 &4-&./ 0#$ /$6+'8 $29#0# '+0$ 2' & *$&0E= &'8 (/(&44. 6+''$60 0-+6+'/+'&'6$/: R+-$5$%= .+( /+)$02)$/ ,2'8 0-+ 3&//2'9 0+'$/ 2' & %+-= &/ 2' 0#$ ,+(%0# $T&)34$
*$4+-: C+)$02)$/ 0#$ 3&//2'9 0+'$ +66(%/ +' & /0%+'9 *$&0= ,+%)2'9 &' $((+!*+2 .$,,'!/ *"!+5
F"#$%$ &%$ &60(&44. & ,$- +0#$%/ 0#&0 .+( -244 $5$'0(&44. '$$8 0+ 4$&%'K 2'6+)34$0$ '$29#*+%
0+'$/= 3$8&4 0+'$/= &'8U2, .+( 829 8$$3 2'0+
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"
PTPT
PT
PT, PT APT
two PTs in a row!
#$ %&'()*'+ ,-).+/ .0+1(+ *1//)23 %-()-24 )( )/ 1 3--5 )5+1 $-0 (6+ *1//)23 (-2+/ (- 7+ .-2/-212(
8)(6 +1.6 -(6+09 :10+ -0 -7,)-&/ *101''+' $-&0(6/4 .1&/+5 7; *1//)23 (-2+/ )2 (8- ,-).+/4 10+
$1)0'; 010+< weird
PTs don't sound veryconsonant together.
=-%+()%+/ 1 .-%*-/+0 8)'' 5+')7+01(+'; &/+ *1//)23 (-2+/ (- .0+1(+ 1 5)//-212( >.'1/64? 1/ )2 (6+
@ %)2-0 $&3&+ $0-% :--A # -$ (6+ !"## %"&'"(") *#+,-"(. B6)/ )/ 1 /*+.)1' +$$+.(4 (6-&364 125 )/
0+'1(),+'; &2&/&1'9 C-( 0+.-%%+25+5 &2()' ;-& 3+( (- DE="FG -0 /-9
!!!" $%&'()*+ ,*-%." H 2+)367-0 (-2+ %-,+/ 7; /(+* $0-% 1 .-2/-212.+ (- 1 5)//-212.+4 7+$-0+
0+,+0/)23 5)0+.()-2 125 0+(&02)23 7; /(+* (- (6+ /(-0-1+#.-2/-212.+9 C+)367-0 (-2+/ .12 7+
1..+2(+5 -0 &21..+2(+59
NT NT
accented
NT
!/" 0-,&1&23,&*-." H2().)*1()-2/ 10)/+ $0-% 06;(6%). 5)/*'1.+%+2(< 1 .6-05 (-2+ 1**+10/ 1 ')(('+
7)( 7+$-0+ (6+ .6-059 H2().)*1()-2/ %-/( -$(+2 -..&0 )2 (6+ %+'-5;4 125 &/&1''; %-,+ 7; /(+*9
I-8+,+04 -2+ 5-+/ $)25 (6+% )2 -(6+0 ,-).+/ 125J,+0; -..1/)-21'';J(6+; %1; )2,-',+ '+1*/9
A
A
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C: V I vi
Chord changes as suspensionresolves. The tone of resolution,
C, belongs to both chords on beat 2
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passing F4 does noteliminate sop/altoparallels
passing D5 createssop/alto parallels!
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ANT
PT
C: V I
for whatever reason, Bachallows this!
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(C4, C4) (D4, D4) (E4, E4) (F4, F4) (Fs4, Fs4)(Cs4, Cs4) (Ef4, Ef4)
(D4, D5) (E4, E5) (F4 , F5) (Fs4, Fs5)(Cs4, Cs5) (Ef4, Ef5)(Fs3, Fs4) (Gs3 Gs4) (Bf3, Bf4) (B3, B4) (C4, C5)(G3, G4) (A3, A4)
(Gs4, Gs4) (Bf4, Bf4) (B4, B4) (C5, C5)(G4, G4) (A4, A4)
(D5, D4) (E5, E4) (F5, F4) (Fs5, Fs4)(Cs5, Cs4) (Ef5, Ef4)(Fs4, Fs3) (Gs4, Gs3) (Bf4, Bf3) (B4, B3) (C5, C4)(G4, G3) (A4, A3)
(B3, Cs4) (C4, D4) (D4, E4) (E4, Fs4) (F4, G4)(Cs4, Ef4) (Ef4, F4) (Fs4, Gs4) (G4, A4) (A4, B4) (B4, Cs5)(Gs4, As4) (Bf4, C5)
(B4, Cs4) (C5, D4) (D5, E4) (E5, Fs4)(Cs5, Ef4) (Ef5, F4)(F4, G3) (Fs4, Gs3) (G4, A3) (A4, B3) (B4, Cs4)(Gs4, As3) (Bf4, C4)
(B3, D4) (C4, Ef4) (D4, F4) (E4, G4)(Cs4, E4) (Ef4, Gf4) (F4, Af4) (Fs4, A4) (Gs4, B4) (As4, Cs5)(G4, Bf4) (A4, C5)
(B4, D4) (C5, Ef4) (D5, F4) (E5, G4)(Cs5, E4) (Ef5, Gf4)(F4, Af3) (Fs4, A3) (Gs4, B3) (As4, Cs4)(G4, Bf3) (A4, C4)
(Bf3, D4) (B3, Ds4) (Df4, F4) (Ef4, G4) (E4, Gs4)(C4, E4) (D4, Fs4) (Fs4, As4) (Af4, C5) (Bf4, D5)(A4, Cs5)(F4, A4) (G4, B4)
(B4, Ds4) (Df5, F4) (Ef5, G4) (E5, Gs4)(C5, E4) (D5, Fs4)(E4, Gs3) (Fs4, As3) (Af4, C4) (Bf4, D4)(A4, Cs4)(F4, A3) (G4, B3)
(Bf3, E4)(A3, Ds4) (B3, F4) (Df4, G4) (Ef4, A4)(C4, Fs4) (D4, Gs4) (F4, B4)(E4, Bf4) (Fs4, C5) (Gs4, D5)(G4, Cs5) (A4, Ds5)
(Bf4, E4) (B4, F4) (Df5, G4) (Ef5 A4)(C5, Fs4) (D5, Gs4)(Ef4, A3) (F4, B3)(E4, Bf3) (Fs4, C4) (Gs4, D4)(G4, Cs4) (A4, Ds4)
(D4, B4) (Ef4, C5) (F4, D5) (G4, E5)(E4, Cs5) (Gf4, Ef5)(Bf3, G4)(A3, Fs4) (B3, Gs4) (Cs4, As4)(Af3, F4) (C4, A4)
(D4, B3) (Ef4, C4) (F4, D4) (G4, E4)(E4, Cs4) (Gf4, Ef4) (Bf4, G4)(A4, Fs4) (B4, Gs4) (Cs5, As4)(Af4, F4) (C5, A4)
(Ds4, B4) (F4, Df5) (G4, Ef5)(Gs4, E5)(E4, C5) (Fs4, D5)(Bf3, Gf4)(A3, F4) (B3, G4) (Cs4, A4)(Gs3, E4) (C4, Af4) (D4, Bf4)
(Bf4, Gf4)(A4, F4) (B4, G4) (Cs5, A4)(C5, Af4) (D5, Bf4)(Ds4, B3) (F4, Df4) (G4, Ef4)(Gs4, E4)(E4, C4) (Fs4, D4)(D4, Bf3)
(D4, C4) (E4, D4) (Fs4, E4) (G4, F4)(Ef4, Cs4) (F4, Ef4)(Cs4, B3) (Bf4, Af4)(A4, G4) (B4, A4) (Cs5, B4)(Af4, Gf4) (C5, Bf4)
(D4, C5) (E4, D5) (Fs4, E5) (G4, F5)(Ef4, Cs5) (F4, Ef5)(Bf3, Af4)(A3, G4) (B3, A4) (Cs4, B4)(Af3, Gf4) (C4, Bf4)(G3, F4)
(Cs4, C5) (Ef4, D5) (F4, E5) (Fs4, F5)(D4, Cs5) (E4, Ef5)(Bf3, A4)(A3, Gs4) (B3, As4)(Af3, G4) (C4, B4)(G3, Fs4)
(Cs4, C4) (Ef4, D4) (F4, E4) (Fs4, F4)(D4, Cs4) (E4, Ef4) (Bf4, A4)(A4, Gs4) (B4, As4)(Af4, G4) (C5, B4)(G4, Fs4)
(C4, Cs4) (D4, Ef4) (E4, F4) (F4, Fs4)(Cs4, D4) (Ef4, E4) (Bf4, B4)(A4, Bf4) (B4, C5)(Af4, A4)(G4, Af4)(Fs4, G4)
(C5, Cs4) (D5, Ef4) (E5, F4) (F5, Fs4)(Cs5, D4) (Ef5, E4)(Bf4, B3)(A4, Bf3) (B4, C4)(Af4, A3)(G4, Af3)(Fs4, G3)
(Bf3, F4)(A3, E4) (B3, Fs4) (Df4, Af4)(C4, G4) (D4, A4) (Ef4, Bf4) (E4, B4) (Gf4, Df5) (Af4, Ef5)(F4, C5) (G4, D5)
(Bf4, F4)(A4, E4) (B4, Fs4) (Df5, Af4)(C5, G4) (D5, A4)(Ef4, Bf3) (E4, B3) (Gf4, Df4) (Af4, Ef4)(F4, C4) (G4, D4)
(Bf3, Ef4) (B3, E4) (Df4, Gf4) (Ef4, Af4)(C4, F4) (D4, G4) (Fs4, B4) (G4, C5) (A4, D5)(Gs4, Cs5)(E4, A4) (F4, Bf4)
(Bf4, Ef4) (B4, E4) (Df5, Gf4) (Ef5, Af4)(C5, F4) (D5, G4)(Fs4, B3) (G4, C4) (A4, D4)(Gs4, Cs4)(E4, A3) (F4, Bf3)
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CDf
CC
CD
CEf
CE
CF
CFs
CG
CAf
CA
CBf
CB
[CC]
CsCs
CsD
CsDs
CsE
DfF
DfGf
CsG
DfAf
CsA
DfBf
[CsB]
BCs
BD
BDs
BE
BF
BFs
BG
BGs
BA
BAs
BB
DD
DEf
DE
DF
DFs
DG
DAf
DA
[DBf]
BfD
BfEf
BfE
BfF
BfGf
BfG
BfAf
BfA
BfBf
EfEf
DsE
EfF
EfGf
EfG
EfAf
[EfA]AEf
AE
AF
AFs
AG
AGs
AA
EE
EF
EFs
EG
[EGs]
GsE
AfF
AfGf
AfG
AfAf
FF
FGf
[FG]
GF
GFs
GG
[FsFs]
FsFs
unison
tritone
unison
minor second
minor second
major second
major second
minor third
minor third
major third
major third
perfect fourth
perfect fourth
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i VI iv ii vii6 V
S D
to VI, IV6, oriv6
to i6
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MUSIC 105
Dmitri Tymoczko
Handout 16 (2010)
APPLIED DOMINANTS
Consider the following chord progressions:
Whats new about these progressions is that we can no longer attribute all the chords to asingle key. The A7in progression (a) belongs to d minor, but the progression as a whole
belongs to C major. Likewise, the C7in progression (b) belongs to F, but the progression
as a whole is in the key of Bfminor.
These chords are called appliedor secondarydominants. Any major or minor triad in a
key can be preceded by its own dominant chord. It is as if the music shifts key for a very
brief time, making a subsidiary triad into a temporary tonic. (This is called
tonicization: the above examples tonicize D minor and F major, respectively.) Another
way to describe the phenomenon is that a dominant chord is borrowed from a closely
related key. The result of a secondary dominant is to create a hierarchically nested series
of tonalities: the local tonality (D minor in the first example) is embedded in a larger
tonality (C major, in this case). This is similar to the way an English clause can be
embedded in a larger clause: the boy who got bitten last week kicked the dog.
Secondary dominants add a lot of musical color, and help create a strong sense of
harmonic motion. It is possible to overuse them. But classical (and jazz) harmony
typically makes very frequent use of applied dominant chords. In fact, V7/V is one of
Beethovens favorite chordsit appears about as often as ii or IV.
Here are some basic principles governing the use of these chords.
1. The borrowed chord is usually always a dominant seventh chord. Borrowing a
major triad is less common the added dissonance of the seventh chord makes it want to
lead to the next chord all the more strongly. (In rock music, however, it is quite typical to
borrow a major triad rather than a seventh chord.) It is also possible to borrow a leading
tone triad (vii6) or seventh chord.
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2. Normal voice-leading rules apply to the borrowed dominant chord as if you had
changed key. You cannot double the leading tone of the applied dominant. You
should resolve the borrowed chords tendency tones normally. (But see the exception
listed as point 8 below.) You should also spell the chord correctly, as dominant of the
chord to which it resolves.
3. The applied dominant almost always resolves to the appropriate temporary
tonic chord, but it can occasionally participate in a deceptive progression, moving up by
step. For example, you might find V/vi moving to IV (aka VI/iv) rather than vi.
4.Beware the cross-relation! A cross-relation is a clash between two different
forms of a single note in consecutive chords in different registers. (Refer back to the
Style 1 handout!) In the first example below, the sopranos high Efconflicts with thebass Enin the next chord. This was felt to be an undesirable sort of dissonance. In (b)there is no cross relation, even though the high Efstill contrasts with the low En. Thereason is because the high Efis supported by a low Efin the bass. The bass Ef
neutralizes the cross-relation since it moves to En in the same register, and keeps us fromnoticing the sharp dissonance between soprano and bass.
Cross-relations are not always bad. Classical composers sometimes used them to add
expressive bite, or pungent dissonance, to their harmony. You should probably avoid
them however, unless its really clear that you know what youre doing.
5. In root position, dont move from an unaltered version of a chord to the
borrowed version of the chord. A lot of students tend to write banal progressions like (a)
below. This is not very stylistic. The progression from ii to V/V sounds clunky and
obvious. Here it would be better just to move from I to V/V.
(a) (b)
Note that the progression in (b) is OK. This is because the dramatic change in the bass
tones adds a lot of energy to the progression. For the same reason, you can move from I
to V2/IV, since there is a powerful change of bass in the progression.
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6. You cannot apply a dominant seventh chord to a diminished or augmented
triad, since these triads cannot serve as tonics, even temporary ones.1 This means you
cannot use V/vii in major, V/iiin minor, or V/vii in minor. In minor, it is also unusual
to use secondary dominants of the chords involving the raised sixth scale degree: V/ii and
V/IV.
Here are the normal chords which can support applied dominants.
MAJOR MINOR
ii -
iii III (note that V/III is just VII)
IV iv
V V or v
vi VI
- VII (i.e. the major chord based on the naturalseventh degree)
7. When a secondary dominant moves to another dominant seventh chord, the
leading tone often does notresolve by step. Instead, it becomes the seventhof the
following chord, as in the following progression:
Sometimes one finds long chains of applied dominants, as in the Mozartian chord
progression below. Here, the leading tone is always lowered semitonally, creating a
descending chromatic line.
C B7 E7 A7 D7 G7 C
I V7/V/V/V/V V7/V/V/V V7/V/V V7/V V7 I
8. The V#/V chord can come either before or after a I@. In the progressionV#/V!I@!V, the I@is inserted between the V#and its resolution. In the progression
I@!V#/V!V, the V#/V is inserted between I@and its resolution. Both of these work.
9. Occasionally an applied chord will be preceded by its own predominant, as in
the progressions I!iv6/ii!V7/ii!ii!V7!I.
1There is, so far as I know, only one possible exception in the Bach chorales: chorale 89,mm. 5.
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