Theory
ResearchFrontier structures and internal systems
OverviewSymmetryAsymmetrySet TheoryFormula LabUnified Model

8-1

Chromatic octachord

Cardinality
8

Prime Form

Prime form pitch class clockC0C#1D2D#3E4F5F#6G7G#AA#B[0,1,2,3,4,5,6,7]8 pitch classes
T0

Interval Vector

<7,6,5,4,4,2> (sum: 28)
7
ic1
6
ic2
5
ic3
4
ic4
4
ic5
2
ic6
ic1: m2/M7
ic2: M2/m7
ic3: m3/M6
ic4: M3/m6
ic5: P4/P5
ic6: TT
Prime Form
[0,1,2,3,4,5,6,7]
Interval Vector
<7,6,5,4,4,2>
T-Symmetry
1
I-Symmetry
1 (inversionally symmetric)
Invariant at I: 7

Step Pattern

1-1-1-1-1-1-1-5
Intervals: H-H-H-H-H-H-H-5

Complement

4-1card 4
[0,1,2,3]
Chromatic tetrachord

All Transpositions

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