Musical Set Theory

By Evenness

Index

Nearly even or maximally even chords and scales are much more common in harmony because they are related to their involutions and transpositions by short voice leadings, whereas perfectly even chords and scales are limited in their voice leading possibilities. More

Examples of perfectly even chords and scales are the diminished seventh, augmented triad, and hexatonic whole-tone scale. Examples of nearly even or maximally even chords and scales are major and minor triads, dominant seventh, half-diminished seventh, pentatonic scale, diatonic scale, etc.

See Evenness & Clusters and Tymoczko 2006 and 2011 for extended explanations of this.

Less

Perfectly Even

Interval

3-12

4-28

6-35

(02468t)
Whole-Tone Scale

Maximally Even

5-35

(02479)
Pentatonic

7-35

(013568t)
Diatonic

8-28

(0134679t)
Diminished (Oct.)

9-12

(01245689t)
Enneatonic

Nearly Even

Interval

3-11

4-27

(0258)
min 7 ♭5
min 6

(0368)
Dom 7
Gr. 6

5-34

(02469)
Dom 9
min ♭13 ♭5

6-34

(013579)
Aug 9 ♯11
Alt 7 ♭9

(024689)
Dom 9 ♯11
Alt 7 ♯9

7-34

(013468t)
Acoustic

8-27

9-11