Tone Clock · Set classes · 7 notes
Two shapes, each the other’s mirror
Interval content
| ic1 | ic2 | ic3 | ic4 | ic5 | ic6 |
|---|---|---|---|---|---|
| 3 | 3 | 5 | 4 | 4 | 2 |
Every set in the class holds three semitones, three whole tones, five minor thirds, four major thirds, four fourths and two tritones.
Common tones
| T0 | T1 | T2 | T3 | T4 | T5 | T6 | T7 | T8 | T9 | T10 | T11 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 7 | 3 | 3 | 5 | 4 | 4 | 4 | 4 | 4 | 5 | 3 | 3 |
Notes a set keeps when transposed by n.
| T0I | T1I | T2I | T3I | T4I | T5I | T6I | T7I | T8I | T9I | T10I | T11I |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 6 | 4 | 3 | 4 | 5 | 4 | 4 | 4 | 3 | 6 | 4 | 2 |
Notes a set keeps when inverted about n.
Its 24 sets
Set theory treats D# and Eb as one pitch class; the names under each set use one fixed spelling, sharps except Bb.
0134689 · harmonic minor scale
- 0134689C C# D# E F# G# A
- 124579tC# D E F G A Bb
- 23568teD D# F F# G# Bb B
- 034679eD# E F# G A B C
- 014578tE F G G# Bb C C#
- 125689eF F# G# A B C# D
- 023679tF# G A Bb C D D#
- 13478teG G# Bb B C# D# E
- 024589eG# A B C D E F
- 013569tA Bb C C# D# F F#
- 12467teBb B C# D E F# G
- 023578eB C D D# F G G#
0135689 · harmonic major scale
Relations
- Complement
- 5-32 01469
- Z-partner
- none: no other class has this interval vector
- Symmetry
- none: only T0 maps it onto itself
- Inside it
2 notes: 2-1 ×3 · 2-2 ×3 · 2-3 ×5 · 2-4 ×4 · 2-5 ×4 · 2-6 ×2
3 notes: 3-2 ×4 · 3-3 ×4 · 3-4 ×4 · 3-5 ×3 · 3-6 · 3-7 ×4 · 3-8 ×3 · 3-9 ×2 · 3-10 ×4 · 3-11 ×5 · 3-12
4 notes: 4-3 · 4-7 · 4-8 · 4-10 · 4-11 ×2 · 4-12 ×3 · 4-13 ×3 · 4-14 ×3 · 4-Z15 · 4-16 ×2 · 4-17 · 4-18 ×3 · 4-19 ×3 · 4-20 · 4-22 · 4-23 · 4-24 · 4-26 · 4-27 ×3 · 4-28 · 4-Z29
5 notes: 5-10 · 5-Z12 · 5-16 · 5-Z17 · 5-Z18 ×2 · 5-20 · 5-21 · 5-22 · 5-23 · 5-25 · 5-26 ×2 · 5-27 · 5-29 ×2 · 5-30 · 5-31 ×3 · 5-32
6 notes: 6-Z19 · 6-Z24 · 6-Z25 · 6-27 · 6-Z28 · 6-Z29 · 6-31
- Around it
- 8-Z15 · 8-17 · 8-18 · 8-26 · 8-27 · and 14 larger classes