Tone Clock · Set classes · 6 notes
Two shapes, each the other’s mirror
Interval content
| ic1 | ic2 | ic3 | ic4 | ic5 | ic6 |
|---|---|---|---|---|---|
| 2 | 3 | 3 | 2 | 4 | 1 |
Every set in the class holds two semitones, three whole tones, three minor thirds, two major thirds, four fourths and one tritone.
Common tones
| T0 | T1 | T2 | T3 | T4 | T5 | T6 | T7 | T8 | T9 | T10 | T11 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 6 | 2 | 3 | 3 | 2 | 4 | 2 | 4 | 2 | 3 | 3 | 2 |
Notes a set keeps when transposed by n.
| T0I | T1I | T2I | T3I | T4I | T5I | T6I | T7I | T8I | T9I | T10I | T11I |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 4 | 4 | 2 | 5 | 2 | 3 | 2 | 3 | 4 | 2 | 4 |
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.
012479
- 012479C C# D E G A
- 12358tC# D D# F G# Bb
- 23469eD D# E F# A B
- 03457tD# E F G Bb C
- 14568eE F F# G# B C#
- 025679F F# G A C D
- 13678tF# G G# Bb C# D#
- 24789eG G# A B D E
- 03589tG# A Bb C D# F
- 1469teA Bb B C# E F#
- 0257teBb B C D F G
- 01368eB C C# D# F# G#
023479
Relations
- Complement
- 6-Z25 013568
- Z-partner
- 6-Z25, the same interval vector in another class
- Symmetry
- none: only T0 maps it onto itself
- Inside it
2 notes: 2-1 ×2 · 2-2 ×3 · 2-3 ×3 · 2-4 ×2 · 2-5 ×4 · 2-6
3 notes: 3-1 · 3-2 · 3-3 ×2 · 3-4 · 3-5 ×2 · 3-6 · 3-7 ×4 · 3-8 · 3-9 ×3 · 3-10 · 3-11 ×3
4 notes: 4-2 · 4-4 · 4-6 · 4-13 · 4-14 · 4-Z15 · 4-16 · 4-17 · 4-18 · 4-22 ×2 · 4-23 ×2 · 4-26 · 4-27
- Around it
- 7-Z12 · 7-20 · 7-23 · 7-25 · 7-27 · 7-29 · and 29 larger classes