Theory
ResearchFrontier structures and internal systems
OverviewSymmetryAsymmetrySet TheoryFormula LabUnified Model

7-Z12

Cardinality
7

Prime Form

Prime form pitch class clockC0C#1D2D#3E4FF#G7G#A9A#B[0,1,2,3,4,7,9]7 pitch classes
T0

Interval Vector

<4,4,4,3,4,2> (sum: 21)
4
ic1
4
ic2
4
ic3
3
ic4
4
ic5
2
ic6
ic1: m2/M7
ic2: M2/m7
ic3: m3/M6
ic4: M3/m6
ic5: P4/P5
ic6: TT
Prime Form
[0,1,2,3,4,7,9]
Interval Vector
<4,4,4,3,4,2>
T-Symmetry
1
I-Symmetry
1 (inversionally symmetric)
Invariant at I: 4

Step Pattern

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

Complement

5-Z12card 5
[0,1,3,5,6]

Z-Related Set

7-Z36Same IC Vector
[0,1,2,3,5,6,8]

All Transpositions

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