Theory
ResearchFrontier structures and internal systems
OverviewSymmetryAsymmetrySet TheoryFormula LabUnified Model

9-1

Chromatic nonachord

Cardinality
9

Prime Form

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

Interval Vector

<8,7,6,6,6,3> (sum: 36)
8
ic1
7
ic2
6
ic3
6
ic4
6
ic5
3
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]
Interval Vector
<8,7,6,6,6,3>
T-Symmetry
1
I-Symmetry
1 (inversionally symmetric)
Invariant at I: 8

Step Pattern

1-1-1-1-1-1-1-1-4
Intervals: H-H-H-H-H-H-H-H-4

Complement

3-1card 3
[0,1,2]
Chromatic trichord

All Transpositions

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