musical tonality existence of multiple tonalities raises a variety of questions what is the relation...

Musical Tonality

• Existence of multiple tonalities raises a variety of questions

• What is the relation of one tonality to another?• Can we measure relatedness?

• How do we represent relatedness?

• Questions regarding perception of tonality• How do we find our sense of key?

• Are we accurate in sense of key?

• What models do we have for determining key?

Theoretical Maps of Interkey Distances

• Are there ways of deriving interkey distances?

• Put differently, can we determine key maps?

• Key distance an important issue in music-theoretic descriptions of tonal music because of key modulation

• Musical composition written in home key

• Compositions move to other keys, or modulate

• Usually return to home key

• Practice codified in interkey distances – key distances considered close if modulations are frequent

Interkey Distances

The Circle of Fifths

Interkey Distances, con’t

Diatonic set overlaps


Diatonic set overlaps

•The problem of minor keys•Different forms of the minor

•Relation between the major and minor keys•The Relative Minor (C major and A minor)

•Identical scale degrees•C Major: C D E F G A B •A Minor: A B C D E F G

•The Parallel Minor (C major and C minor)•Common tonic and 5th scale degree•C Major: C D E F G A B•C Minor: C D Eb F G Ab B


Krumhansl & Kessler (1982)


Interkey correlations


Interkey correlations, graphed



Multidimensional scaling solution


The four-dimensional torus



Map of key space


Schoenberg (1954/1969)

Chart of key distance


Werts (1983)

•Analyzed key progressions between compositions•Expressed as movement from one key to neighboring keys•Produced a multidimensional scaling solution based on number of times keys moved from one to another•Similar to MDS solution just seen

Models of Key Finding

Longuet-Higgens & Steedman (1971)

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

Models of Key Finding, con’t


Map of key space

A E B F# C# G# D# A# F C G D AF C G D A E B F# C# G# D# A# FC# G# D# A# F C G D A E B F# C#


A E B F# C# G# D# A# F C G D AF C G D A E B F# C# G# D# A# FC# G# D# A# F C G D A E B F# C #

9 4 11 6 1 8 3 10 5 0 7 2 95 0 7 2 9 4 11 6 1 8 3 10 51 8 3 10 5 0 7 2 9 4 11 6 19 4 11 6 1 8 3 10 5 0 7 2 95 0 7 2 9 4 11 6 1 8 3 10 51 8 3 10 5 0 7 2 9 4 11 6 19 4 11 6 1 8 3 10 5 0 7 2 95 0 7 2 9 4 11 6 1 8 3 10 51 8 3 10 5 0 7 2 9 4 11 6 1



Notes in Fugue Subject: E F# B C# D# E D# E F# G# A4 6 11 1 3 4 3 4 6 8 9

C# D# E F# G# A# B1 3 4 6 8 9 11



Map of key space




Possible Keys:Note 1 (E) : B, E, A, D, G, C, F#



Map of key space




Possible Keys:Note 1 (E) : B, E, A, D, G, C, F#Note 2 (E, F#) : B, E, A, D, G



Map of key space




Possible Keys:Note 1 (E) : B, E, A, D, G, C, F#Note 2 (E, F#) : B, E, A, D, GNote 3 (E, F#, B) : B, E, A, D, G



Map of key space




Possible Keys:Note 1 (E) : B, E, A, D, G, C, F#Note 2 (E, F#) : B, E, A, D, GNote 3 (E, F#, B) : B, E, A, GNote 4 (E, F#, B, C#) : B, E, A



Map of key space




Possible Keys:Note 1 (E) : B, E, A, D, G, C, F#Note 2 (E, F#) : B, E, A, D, GNote 3 (E, F#, B) : B, E, A, GNote 4 (E, F#, B, C#) : B, E, ANote 5 (E, F#, B, C#, D#) : B, E



Map of key space




Possible Keys:Note 1 (E) : B, E, A, D, G, C, F#Note 2 (E, F#) : B, E, A, D, GNote 3 (E, F#, B) : B, E, A, GNote 4 (E, F#, B, C#) : B, E, ANote 5 (E, F#, B, C#, D#) : B, E

. . . Note 10 (E, F#, B, C#, D#, G#) : B, ENote 11 (E, F#, B, C#, D#, G#, A) :E



Notes in Fugue Subject: C Db C B E F Bb A Ab G0 1 0 11 4 5 10 9 8 7

(0 1 4 5 7 8 9 10 11)


Krumhansl-Schmuckler

Key-Finding Algorithm (Krumhansl & Schmuckler, 1986,

Schmuckler & Tomovski, 1995)

Schubert, Op. 94, no. 1 – Tone durations



Key-Finding Algorithm (Krumhansl & Schmuckler, 1986)

Bach, C Minor Prelude – Tone durations



Key-Finding Algorithm (Schmuckler & Tomovski, 2005)


Brown & Butler (1981)

Intervals of the diatonic set

Major Scale



Trichords and the rare interval



Intervals of the diatonic set

Minor Scale

musical tonality existence of multiple tonalities raises a variety of questions what is the relation...

Documents

b c minor

b c d e f g

c d eb f g ab b slide

parallel minor c major

relative minor c major

c major diatonic scale

c minor common tonic

map of key space slide