Tone Clock · Set classes · 6 notes
Two shapes, each the other’s mirror
Interval content
| ic1 | ic2 | ic3 | ic4 | ic5 | ic6 |
|---|---|---|---|---|---|
| 3 | 2 | 2 | 2 | 4 | 2 |
Every set in the class holds three semitones, two whole tones, two minor thirds, two major thirds, four fourths and two tritones.
Common tones
| T0 | T1 | T2 | T3 | T4 | T5 | T6 | T7 | T8 | T9 | T10 | T11 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 6 | 3 | 2 | 2 | 2 | 4 | 4 | 4 | 2 | 2 | 2 | 3 |
Notes a set keeps when transposed by n.
| T0I | T1I | T2I | T3I | T4I | T5I | T6I | T7I | T8I | T9I | T10I | T11I |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 3 | 4 | 4 | 4 | 2 | 2 | 2 | 4 | 4 | 4 | 3 | 0 |
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.
012578
- 012578C C# D F G G#
- 123689C# D D# F# G# A
- 23479tD D# E G A Bb
- 3458teD# E F G# Bb B
- 04569eE F F# A B C
- 01567tF F# G Bb C C#
- 12678eF# G G# B C# D
- 023789G G# A C D D#
- 13489tG# A Bb C# D# E
- 2459teA Bb B D E F
- 0356teBb B C D# F F#
- 01467eB C C# E F# G
013678
Relations
- Complement
- 6-18 012578
- 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 ×2 · 2-3 ×2 · 2-4 ×2 · 2-5 ×4 · 2-6 ×2
3 notes: 3-1 · 3-2 · 3-3 · 3-4 ×3 · 3-5 ×5 · 3-7 ×2 · 3-8 ×2 · 3-9 ×2 · 3-10 · 3-11 ×2
4 notes: 4-4 · 4-5 · 4-6 · 4-8 · 4-9 · 4-13 · 4-14 · 4-Z15 · 4-16 ×2 · 4-18 · 4-20 · 4-23 · 4-27 · 4-Z29
- Around it
- 7-7 · 7-14 · 7-19 · 7-20 · 7-29 · 7-Z38 · and 32 larger classes