Theory
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8-28

Octatonic scale / Diminished scale

Cardinality
8

Prime Form

Prime form pitch class clockC0C#1DD#3E4FF#6G7G#A9A#10B[0,1,3,4,6,7,9,10]8 pitch classes
T0

Interval Vector

<4,4,8,4,4,4> (sum: 28)
4
ic1
4
ic2
8
ic3
4
ic4
4
ic5
4
ic6
ic1: m2/M7
ic2: M2/m7
ic3: m3/M6
ic4: M3/m6
ic5: P4/P5
ic6: TT
Prime Form
[0,1,3,4,6,7,9,10]
Interval Vector
<4,4,8,4,4,4>
T-Symmetry
4 (limited transposition)
Invariant at T: 0, 3, 6, 9
I-Symmetry
4 (inversionally symmetric)
Invariant at I: 1, 4, 7, 10

Step Pattern

1-2-1-2-1-2-1-2
Intervals: H-W-H-W-H-W-H-W

Complement

4-28card 4
[0,3,6,9]
Diminished seventh chord

All Transpositions

LevelPitch ClassesNote Names
T0[0,1,3,4,6,7,9,10]C C# D# E F# G A A#
T1[1,2,4,5,7,8,10,11]C# D E F G G# A# B
T2[0,2,3,5,6,8,9,11]C D D# F F# G# A B
T3(invariant)[0,1,3,4,6,7,9,10]C C# D# E F# G A A#
T4[1,2,4,5,7,8,10,11]C# D E F G G# A# B
T5[0,2,3,5,6,8,9,11]C D D# F F# G# A B
T6(invariant)[0,1,3,4,6,7,9,10]C C# D# E F# G A A#
T7[1,2,4,5,7,8,10,11]C# D E F G G# A# B
T8[0,2,3,5,6,8,9,11]C D D# F F# G# A B
T9(invariant)[0,1,3,4,6,7,9,10]C C# D# E F# G A A#
T10[1,2,4,5,7,8,10,11]C# D E F G G# A# B
T11[0,2,3,5,6,8,9,11]C D D# F F# G# A B
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