Theory
ResearchFrontier structures and internal systems
OverviewSymmetryAsymmetrySet TheoryFormula LabUnified Model

3-12

Augmented triad

Cardinality
3

Prime Form

Prime form pitch class clockC0C#DD#E4FF#GG#8AA#B[0,4,8]3 pitch classes
T0

Interval Vector

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

Step Pattern

4-4-4
Intervals: 4-4-4

Complement

9-12card 9
[0,1,2,4,5,6,8,9,10]

All Transpositions

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