Theory
ResearchFrontier structures and internal systems
OverviewSymmetryAsymmetrySet TheoryFormula LabUnified Model

10-1

Chromatic decachord

Cardinality
10

Prime Form

Prime form pitch class clockC0C#1D2D#3E4F5F#6G7G#8A9A#B[0,1,2,3,4,5,6,7,8,9]10 pitch classes
T0

Interval Vector

<9,8,8,8,8,4> (sum: 45)
9
ic1
8
ic2
8
ic3
8
ic4
8
ic5
4
ic6
ic1: m2/M7
ic2: M2/m7
ic3: m3/M6
ic4: M3/m6
ic5: P4/P5
ic6: TT
Prime Form
[0,1,2,3,4,5,6,7,8,9]
Interval Vector
<9,8,8,8,8,4>
T-Symmetry
1
I-Symmetry
1 (inversionally symmetric)
Invariant at I: 9

Step Pattern

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

Complement

2-1card 2
[0,1]
Minor second

All Transpositions

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