Theory
ResearchFrontier structures and internal systems
OverviewSymmetryAsymmetrySet TheoryFormula LabUnified Model

8-20

Cardinality
8

Prime Form

Prime form pitch class clockC0C#1D2D#E4F5F#G7G#8A9A#B[0,1,2,4,5,7,8,9]8 pitch classes
T0

Interval Vector

<5,4,5,6,6,2> (sum: 28)
5
ic1
4
ic2
5
ic3
6
ic4
6
ic5
2
ic6
ic1: m2/M7
ic2: M2/m7
ic3: m3/M6
ic4: M3/m6
ic5: P4/P5
ic6: TT
Prime Form
[0,1,2,4,5,7,8,9]
Interval Vector
<5,4,5,6,6,2>
T-Symmetry
1
I-Symmetry
1 (inversionally symmetric)
Invariant at I: 9

Step Pattern

1-1-2-1-2-1-1-3
Intervals: H-H-W-H-W-H-H-3

Complement

4-20card 4
[0,1,5,8]
Major seventh chord

All Transpositions

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