Theory
ResearchFrontier structures and internal systems
OverviewSymmetryAsymmetrySet TheoryFormula LabUnified Model

8-3

Cardinality
8

Prime Form

Prime form pitch class clockC0C#1D2D#3E4F5F#6GG#A9A#B[0,1,2,3,4,5,6,9]8 pitch classes
T0

Interval Vector

<6,5,6,5,4,2> (sum: 28)
6
ic1
5
ic2
6
ic3
5
ic4
4
ic5
2
ic6
ic1: m2/M7
ic2: M2/m7
ic3: m3/M6
ic4: M3/m6
ic5: P4/P5
ic6: TT
Prime Form
[0,1,2,3,4,5,6,9]
Interval Vector
<6,5,6,5,4,2>
T-Symmetry
1
I-Symmetry
1 (inversionally symmetric)
Invariant at I: 6

Step Pattern

1-1-1-1-1-1-3-3
Intervals: H-H-H-H-H-H-3-3

Complement

4-3card 4
[0,1,3,4]

All Transpositions

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