Tone Clock · Set classes · 8 notes
Two shapes, each the other’s mirror
Interval content
| ic1 | ic2 | ic3 | ic4 | ic5 | ic6 |
|---|---|---|---|---|---|
| 5 | 6 | 5 | 5 | 5 | 2 |
Every set in the class holds five semitones, six whole tones, five minor thirds, five major thirds, five fourths and two tritones.
Common tones
| T0 | T1 | T2 | T3 | T4 | T5 | T6 | T7 | T8 | T9 | T10 | T11 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 8 | 5 | 6 | 5 | 5 | 5 | 4 | 5 | 5 | 5 | 6 | 5 |
Notes a set keeps when transposed by n.
| T0I | T1I | T2I | T3I | T4I | T5I | T6I | T7I | T8I | T9I | T10I | T11I |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 5 | 4 | 6 | 4 | 7 | 6 | 6 | 6 | 5 | 6 | 5 | 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.
01234579
- 01234579C C# D D# E F G A
- 1234568tC# D D# E F F# G# Bb
- 2345679eD D# E F F# G A B
- 0345678tD# E F F# G G# Bb C
- 1456789eE F F# G G# A B C#
- 0256789tF F# G G# A Bb C D
- 136789teF# G G# A Bb B C# D#
- 024789teG G# A Bb B C D E
- 013589teG# A Bb B C C# D# F
- 012469teA Bb B C C# D E F#
- 012357teBb B C C# D D# F G
- 0123468eB C C# D D# E F# G#
02456789
- 02456789C D E F F# G G# A
- 1356789tC# D# F F# G G# A Bb
- 246789teD E F# G G# A Bb B
- 035789teD# F G G# A Bb B C
- 014689teE F# G# A Bb B C C#
- 012579teF G A Bb B C C# D
- 012368teF# G# Bb B C C# D D#
- 0123479eG A B C C# D D# E
- 0123458tG# Bb C C# D D# E F
- 1234569eA B C# D D# E F F#
- 0234567tBb C D D# E F F# G
- 1345678eB C# D# E F F# G G#
Relations
- Complement
- 4-11 0135
- Z-partner
- none: no other class has this interval vector
- Symmetry
- none: only T0 maps it onto itself
- Inside it
2 notes: 2-1 ×5 · 2-2 ×6 · 2-3 ×5 · 2-4 ×5 · 2-5 ×5 · 2-6 ×2
3 notes: 3-1 ×4 · 3-2 ×7 · 3-3 ×6 · 3-4 ×5 · 3-5 ×4 · 3-6 ×4 · 3-7 ×7 · 3-8 ×6 · 3-9 ×4 · 3-10 ×2 · 3-11 ×6 · 3-12
4 notes: 4-1 ×3 · 4-2 ×5 · 4-3 ×2 · 4-4 ×4 · 4-5 ×3 · 4-6 ×2 · 4-7 · 4-10 ×2 · 4-11 ×4 · 4-12 ×3 · 4-13 ×2 · 4-14 ×4 · 4-Z15 ×3 · 4-16 ×3 · 4-17 ×2 · 4-18 ×2 · 4-19 ×3 · 4-20 · 4-21 ×2 · 4-22 ×5 · 4-23 ×3 · 4-24 ×2 · 4-25 · 4-26 ×2 · 4-27 ×3 · 4-Z29 ×3
5 notes: 5-1 ×2 · 5-2 ×3 · 5-3 ×2 · 5-4 ×2 · 5-5 ×3 · 5-8 · 5-9 ×2 · 5-10 · 5-11 ×3 · 5-13 ×2 · 5-14 ×3 · 5-15 · 5-16 ×2 · 5-Z17 · 5-Z18 · 5-21 · 5-23 ×3 · 5-24 ×2 · 5-25 · 5-26 ×2 · 5-27 ×2 · 5-28 ×2 · 5-29 ×2 · 5-30 ×2 · 5-32 ×2 · 5-33 · 5-34 · 5-35 ×2 · 5-Z36 ×2 · 5-Z37 · 5-Z38
6 notes: 6-1 · 6-2 · 6-8 · 6-9 ×2 · 6-Z10 · 6-Z11 · 6-14 · 6-15 · 6-21 · 6-22 · 6-Z24 · 6-31 · 6-32 · 6-33 · 6-34 · 6-Z36 ×2 · 6-Z37 · 6-Z39 · 6-Z40 · 6-Z41 ×2 · 6-Z46 · 6-Z47 ×2 · 6-Z48 · 6-Z49
7 notes: 7-2 · 7-3 · 7-9 · 7-Z12 · 7-23 · 7-24 · 7-26 · 7-27
- Around it
- 9-2 · 9-4 · 9-6 · 9-7 · and 7 larger classes