the circle of fifths - university of torontomarksch/psyc56/key finding - ovs.pdf · the circle of...
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The Circle of Fifths
Diatonic Set Overlaps
Key Profiles
C Major, A Minor, & F< Major
Interkey Correlations
Interkey Correlations, Graphed
Krumhansl & Kessler (1982)
Multidimensional Scaling Solution
The Four-Dimensional Torus
Krumhansl & Kessler (1982)
Key Space
Schoenberg (1954/1969)
Chart of Key Distance
C Major Diatonic Scale: C D E F G A B Major Chords: C E G F A C G B D
E A B C G F C G D
C Major 0 Major A E B 9 4 11 F C G D 5 0 7 2
C Minor 0 Minor
B 11 F C G D 5 0 7 2 G# D# 8 3
Longuet-Higgins & Steedman (1971)
Map of Key Space A E B F# C# G# D# A# F C G D A F C G D A E B F# C# G# D# A# F C# G# D# A# F C G D A E B F# C#
A E B F# C# G# D# A# F C G D A F C G D A E B F# C# G# D# A# F C# G# D# A# F C G D A E B F# C#
A E B F# C# G# D# A# F C G D A F C G D A E B F# C# G# D# A# F C# G# D# A# F C G D A E B F# C#
9 4 11 6 1 8 3 10 5 0 7 2 9 5 0 7 2 9 4 11 6 1 8 3 10 5 1 8 3 10 5 0 7 2 9 4 11 6 1 9 4 11 6 1 8 3 10 5 0 7 2 9 5 0 7 2 9 4 11 6 1 8 3 10 5 1 8 3 10 5 0 7 2 9 4 11 6 1 9 4 11 6 1 8 3 10 5 0 7 2 9 5 0 7 2 9 4 11 6 1 8 3 10 5 1 8 3 10 5 0 7 2 9 4 11 6 1
Notes in Fugue Subject:
E F< B C< D< G< 4 6 8 1 3 9
(1 3 4 6 8 9)
Notes in Fugue Subject:
C D= C B E F B= A A= G 0 1 0 11 4 5 10 9 8 7 (0 1 4 5 7 8 9 10 11)
Tone Durations
Schubert, Op. 94, no. 1
Krumhansl & Schmuckler (1986)
Bach C Minor Prelude Tone Durations
Intervals of the Diatonic Set
Major Scale
Brown & Butler (1981)
Intervals of the Diatonic Set
Minor Scale
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