Maximally Even

5-35

(02479)
Pentatonic

7-35

(013568t)
Diatonic

8-28

(0134679t)
Diminished (Oct.)

9-12

(01245689t)
Enneatonic

8 Notes

8-28

(0134679t)
Diminished (Oct.)

8-25

8-9

8 Notes

8-28

(0134679t)
Diminished (Oct.)

Cluster-free, 8 Notes

8 Notes

8-28

(0134679t)
Diminished (Oct.)

8-28, (0134679t), Diminished (Oct.)

Set Class

The double diminished (octatonic) scale refers to the set class (unordered collection) of eight notes consisting of alternating semitone and whole-tone intervals. This scale is a mode of limited transposition and can be thought of as two interlocking fully-diminished seventh chords. More

The diminished scale is the maximally even scale of cardinality eight, a symmetric set class which only has two modes, one starting with a semitone then a whole-tone, and one starting with a whole-tone followed by a semitone. There are only three transpositions of the scale, and they are closer in voice leading distance to transpositions of the acoustic scale (two semitones away from four of the transpositions of the acoustic scale) than to one another (four semitones away from the nearest transposition of the diminished scale).

See Beyond Diatonic for more on the set class for this scale.

Less

OPTC equiv: (0134679t)

Interval-content vector <448444>

Distance √(4/8)*

the minimum Euclidean distance from this set to any transposition of the perfectly even 8 note chord, in semitones

Ancohemitonic chromatic-cluser-free

Hemitonic set contains one or more semitones

Maximally Even divides the octave maximally evenly (for cardinality of 5, 7, 8 or 9, no set can be perfectly even)

Mode of Limited Transposition this set has fewer than 12 unique transpositions

Self-M-Related the M-relation (replace semitone intervals with perfect fourths) maps this set to itself

Symmetric the involution of this set is the same set

Tritonic set contains one or more tritones

Complement

4-28

Voice leading distance: 1

8-27

9-10

Has Modes

Half/Whole Diminished

Whole/Half Diminished

Transpositions

C/E♭/F♯/A Diminished

D♭/E/G/B♭ Diminished

D/F/A♭/B Diminished

Scale Contains

4-18

(0147)
X7(♯9)noR

(0367)
XM11(♯5)no3/9

4-17

(0347)
Dom ♯9

4-9

(0167)
Maj 11 ♭5

5-32

(01469)
X13(♯9)no♭7

(02569)
X7(♯9)

5-31

(01369)
XM11(♯5)no3

(02369)
X7(♭9)

5-19

(01367)
X13(♯9)♭5noR

(01467)
X♯11(♭9)no3

5-16

(01347)
Diminished-5

(03467)
Diminished-5

6-30

(013679)
X13(♯9)♭5

(023689)
X♯11(♭9)

6-Z50

(014679)
X13(♯9)
X13♯11(♭9)no♭7

6-Z49

(013479)
X♯11(♯9)
X13♯11(♭9)no5

6-27

(013469)
XAlt13♯11no3/5

(023569)
X7(♭9♯9)
X13(♭9)

6-Z13

(013467)
Diminished-6

7-31

(0134679)
Diminished-7

(0235689)
Diminished-7