Tone Clock · Set classes · 6 notes
Two shapes, each the other’s mirror
Interval content
| ic1 | ic2 | ic3 | ic4 | ic5 | ic6 |
|---|---|---|---|---|---|
| 3 | 2 | 2 | 3 | 3 | 2 |
Every set in the class holds three semitones, two whole tones, two minor thirds, three major thirds, three fourths and two tritones.
Common tones
| T0 | T1 | T2 | T3 | T4 | T5 | T6 | T7 | T8 | T9 | T10 | T11 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 6 | 3 | 2 | 2 | 3 | 3 | 4 | 3 | 3 | 2 | 2 | 3 |
Notes a set keeps when transposed by n.
| T0I | T1I | T2I | T3I | T4I | T5I | T6I | T7I | T8I | T9I | T10I | T11I |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 3 | 2 | 4 | 4 | 4 | 2 | 2 | 2 | 5 | 4 | 2 | 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.
012478
- 012478C C# D E G G#
- 123589C# D D# F G# A
- 23469tD D# E F# A Bb
- 3457teD# E F G Bb B
- 04568eE F F# G# B C
- 015679F F# G A C C#
- 12678tF# G G# Bb C# D
- 23789eG G# A B D D#
- 03489tG# A Bb C D# E
- 1459teA Bb B C# E F
- 0256teBb B C D F F#
- 01367eB C C# D# F# G
014678
Relations
- Complement
- 6-Z43 012568
- Z-partner
- 6-Z43, the same interval vector in another class
- Symmetry
- none: only T0 maps it onto itself
- Inside it
2 notes: 2-1 ×3 · 2-2 ×2 · 2-3 ×2 · 2-4 ×3 · 2-5 ×3 · 2-6 ×2
3 notes: 3-1 · 3-2 · 3-3 ×2 · 3-4 ×2 · 3-5 ×5 · 3-6 · 3-7 · 3-8 ×2 · 3-9 · 3-10 · 3-11 ×2 · 3-12
4 notes: 4-2 · 4-5 · 4-6 · 4-8 · 4-9 · 4-13 · 4-Z15 · 4-16 · 4-18 ×2 · 4-19 ×2 · 4-22 · 4-24 · 4-Z29
- Around it
- 7-6 · 7-15 · 7-Z18 · 7-20 · 7-28 · 7-Z38 · and 31 larger classes