The Circle of Fifths - utsc.utoronto.camarksch/psyc56/Key Finding - OVs.pdf · The Circle of Fifths...

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