Tone Clock · Set classes · 8 notes
Two shapes, each the other’s mirror
Interval content
| ic1 | ic2 | ic3 | ic4 | ic5 | ic6 |
|---|---|---|---|---|---|
| 5 | 4 | 5 | 7 | 5 | 2 |
Every set in the class holds five semitones, four whole tones, five minor thirds, seven major thirds, five fourths and two tritones.
Common tones
| T0 | T1 | T2 | T3 | T4 | T5 | T6 | T7 | T8 | T9 | T10 | T11 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 8 | 5 | 4 | 5 | 7 | 5 | 4 | 5 | 7 | 5 | 4 | 5 |
Notes a set keeps when transposed by n.
| T0I | T1I | T2I | T3I | T4I | T5I | T6I | T7I | T8I | T9I | T10I | T11I |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 4 | 6 | 7 | 4 | 4 | 6 | 7 | 4 | 5 | 6 | 7 | 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.
01245689
- 01245689C C# D E F F# G# A
- 1235679tC# D D# F F# G A Bb
- 234678teD D# E F# G G# Bb B
- 0345789eD# E F G G# A B C
- 0145689tE F F# G# A Bb C C#
- 125679teF F# G A Bb B C# D
- 023678teF# G G# Bb B C D D#
- 0134789eG G# A B C C# D# E
- 0124589tG# A Bb C C# D E F
- 123569teA Bb B C# D D# F F#
- 023467teBb B C D D# E F# G
- 0134578eB C C# D# E F G G#
01345789
- 01345789C C# D# E F G G# A
- 1245689tC# D E F F# G# A Bb
- 235679teD D# F F# G A Bb B
- 034678teD# E F# G G# Bb B C
- 0145789eE F G G# A B C C#
- 0125689tF F# G# A Bb C C# D
- 123679teF# G A Bb B C# D D#
- 023478teG G# Bb B C D D# E
- 0134589eG# A B C C# D# E F
- 0124569tA Bb C C# D E F F#
- 123567teBb B C# D D# F F# G
- 0234678eB C D D# E F# G G#
Relations
- Complement
- 4-19 0148
- 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 ×4 · 2-3 ×5 · 2-4 ×7 · 2-5 ×5 · 2-6 ×2
3 notes: 3-1 ×2 · 3-2 ×4 · 3-3 ×9 · 3-4 ×9 · 3-5 ×4 · 3-6 ×3 · 3-7 ×4 · 3-8 ×6 · 3-9 ×2 · 3-10 ×2 · 3-11 ×9 · 3-12 ×2
4 notes: 4-2 ×3 · 4-3 ×2 · 4-4 ×4 · 4-5 ×3 · 4-7 ×4 · 4-8 ×2 · 4-11 ×3 · 4-12 ×3 · 4-14 ×4 · 4-Z15 ×3 · 4-16 ×3 · 4-17 ×4 · 4-18 ×4 · 4-19 ×8 · 4-20 ×4 · 4-21 ×2 · 4-22 ×3 · 4-24 ×2 · 4-25 · 4-26 ×2 · 4-27 ×3 · 4-Z29 ×3
5 notes: 5-3 ×3 · 5-6 ×3 · 5-8 · 5-9 ×2 · 5-11 ×3 · 5-13 ×2 · 5-15 · 5-16 ×3 · 5-Z17 ×2 · 5-Z18 ×3 · 5-20 ×3 · 5-21 ×7 · 5-22 ×2 · 5-24 ×2 · 5-26 ×2 · 5-27 ×3 · 5-28 ×2 · 5-30 ×2 · 5-32 ×3 · 5-33 · 5-34 · 5-Z37 ×2 · 5-Z38 ×3
6 notes: 6-Z4 · 6-Z10 ×2 · 6-14 ×3 · 6-15 ×2 · 6-16 ×2 · 6-Z19 ×3 · 6-20 · 6-21 · 6-22 · 6-Z26 · 6-31 ×2 · 6-34 · 6-Z43 ×2 · 6-Z44 ×3 · 6-Z46 ×2 · 6-Z49
7 notes: 7-13 · 7-Z17 · 7-21 ×2 · 7-22 · 7-26 · 7-30 · 7-Z37
- Around it
- 9-3 · 9-4 · 9-11 · 9-12 · and 6 larger classes