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Jazz Harmony, Transformations, and ii–V SpaceMichael McClimon
“All the Things You Are” (bridge)
A small portion of ii–V space
ii7 V7 FÂTF TF
ii7 V7 CÂTF TF
3rd 7thT5
ii7 V7 GÂTF TF
3rd 7thT5
The underlying transformation graph of a single ii–V progression
S1 S2 S3TF TF
f
Two instantiations of a ii–V–I in C major
Voice-leading in the TF transformation
A nonsensical TF transformation
?
The underlying transformation graph of a larger portion of ii–V space
S1 S2 S3TF TF
TF TF
3RD 7THT5
S1 S2 S3
T5T5
ii7 V7 G@Â
ii7 V7 D@Â
ii7 V7 A@Â
ii7 V7 E@Â
ii7 V7 B@Â
ii7 V7 FÂ
ii7 V7 CÂ
12, 12, 20 3, 21
4
5 67
8, 16 9, 17
10, 14, 18 11, 19
13
15
A� B�– E�7 A� E�– A�7
D� D– G7 C– F7�9
B�– E�7 C– F7
D– G7 C– F7 B�– E�7
Lee Morgan, “Ceora”Cornbread (1965)
Complete ii–V space
Möbius strip of V7s at the center of ii–V space
C7
G�7
B7
G�7
C7
F7
E7
A7
D7
B�7
E�7
A�7
T6
T5T11
G7D�7
The TFT transformation
ii7 V7 G@Âii7 V7 CÂ
TFT TFT
Voice leadings of TF and TFT, compared
� ÆÆÆ ÆÆÆ ÆÆÆ ÆÆÆ ÆÆÆ@@ ÆÆÆD– G7 CÂ D– CÂD @7
0
5
2
5
11
7
11
4
0
0
5
2
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x3x2x1
TF TF TFT TFT
A substituted ii–V–I in C major
ii7 V7 G@Âii7 V7 CÂ
TF
TFT
A tritone-substituted portion of ii–V space
ii7 V7 FÂTF TF
ii7 V7 CÂTF TFT
7THT11
ii7 V7 GÂTFT TFT
3RDSLIDE7T5
The SLIDE7 transformation
SLIDE7 in “Ceora”
T6
T6
ii7 V7 G@Â
ii7 V7 D@Â
ii7 V7 CÂ
ii7 V7 GÂSLIDE
7
“Blues for Alice” – Charlie Parker
FÂ E ø A7 C– F7
B�7 B�– E�7
D– G7
G– C7A– D–
A– D7 A�– D�7
G– C7
ii7 V7 A@Â
D@Â
ii7 V7
ii7 V7
G @Â
ii7 V7
ii7 V7
ii7 V7
A@Â
ii7 V7
E@Â
ii7 V7
B@Â
ii7 V7
FÂ
ii7 V7
CÂ
DÂ
GÂ
TF T5 T6
FÂ E ø A7 C– F7
B�7 B�– E�7
D– G7
G– C7A– D–
A– D7 A�– D�7
G– C7
“Lo-Joe” – George Coleman
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A standard “Rhythm” bridge
“Lo-Joe,” bridge
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“Lo-Joe” – George Coleman
A “horizontal” hearing
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“Lo-Joe” – George ColemanEmphasizing T5
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Compared with ii–V space
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“Lo-Joe” – George Coleman
Emphasizing T6
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“Lo-Joe” – George Coleman
Emphasizing T11
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“Lo-Joe” – George Coleman
Emphasizing F–B tritone axis
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“Lo-Joe” – George ColemanTwo less good analyses
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