Tone Clock · Set classes · 8 notes
Two shapes, each the other’s mirror
Interval content
| ic1 | ic2 | ic3 | ic4 | ic5 | ic6 |
|---|---|---|---|---|---|
| 5 | 5 | 5 | 5 | 6 | 2 |
Every set in the class holds five semitones, five whole tones, five minor thirds, five major thirds, six fourths and two tritones.
Common tones
| T0 | T1 | T2 | T3 | T4 | T5 | T6 | T7 | T8 | T9 | T10 | T11 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 8 | 5 | 5 | 5 | 5 | 6 | 4 | 6 | 5 | 5 | 5 | 5 |
Notes a set keeps when transposed by n.
| T0I | T1I | T2I | T3I | T4I | T5I | T6I | T7I | T8I | T9I | T10I | T11I |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 4 | 6 | 6 | 4 | 5 | 4 | 7 | 6 | 5 | 6 | 5 | 6 |
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.
01245679
- 01245679C C# D E F F# G A
- 1235678tC# D D# F F# G G# Bb
- 2346789eD D# E F# G G# A B
- 0345789tD# E F G G# A Bb C
- 145689teE F F# G# A Bb B C#
- 025679teF F# G A Bb B C D
- 013678teF# G G# Bb B C C# D#
- 0124789eG G# A B C C# D E
- 0123589tG# A Bb C C# D D# F
- 123469teA Bb B C# D D# E F#
- 023457teBb B C D D# E F G
- 0134568eB C C# D# E F F# G#
02345789
- 02345789C D D# E F G G# A
- 1345689tC# D# E F F# G# A Bb
- 245679teD E F F# G A Bb B
- 035678teD# F F# G G# Bb B C
- 0146789eE F# G G# A B C C#
- 0125789tF G G# A Bb C C# D
- 123689teF# G# A Bb B C# D D#
- 023479teG A Bb B C D D# E
- 013458teG# Bb B C C# D# E F
- 0124569eA B C C# D E F F#
- 0123567tBb C C# D D# F F# G
- 1234678eB C# D D# E F# G G#
Relations
- Complement
- 4-14 0237
- 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 ×5 · 2-3 ×5 · 2-4 ×5 · 2-5 ×6 · 2-6 ×2
3 notes: 3-1 ×3 · 3-2 ×5 · 3-3 ×6 · 3-4 ×7 · 3-5 ×6 · 3-6 ×3 · 3-7 ×8 · 3-8 ×4 · 3-9 ×4 · 3-10 ×2 · 3-11 ×7 · 3-12
4 notes: 4-1 · 4-2 ×3 · 4-3 · 4-4 ×5 · 4-5 ×3 · 4-6 ×2 · 4-7 ×2 · 4-8 ×2 · 4-9 · 4-10 ×2 · 4-11 ×4 · 4-12 · 4-13 ×3 · 4-14 ×4 · 4-Z15 ×4 · 4-16 ×3 · 4-17 ×2 · 4-18 ×3 · 4-19 ×4 · 4-20 ×2 · 4-21 · 4-22 ×5 · 4-23 ×3 · 4-24 · 4-26 ×3 · 4-27 ×3 · 4-Z29 ×2
5 notes: 5-2 ×2 · 5-3 ×2 · 5-4 · 5-5 · 5-6 ×3 · 5-7 ×2 · 5-9 ×2 · 5-10 · 5-11 ×3 · 5-Z12 · 5-13 · 5-14 ×3 · 5-Z17 · 5-Z18 · 5-19 ×2 · 5-20 · 5-21 ×2 · 5-22 · 5-23 ×3 · 5-24 · 5-25 ×2 · 5-26 · 5-27 ×3 · 5-29 ×2 · 5-30 ×2 · 5-32 ×3 · 5-34 · 5-35 ×2 · 5-Z36 ×2 · 5-Z37 ×2 · 5-Z38 ×2
6 notes: 6-Z3 · 6-Z4 · 6-5 · 6-Z6 · 6-8 · 6-9 · 6-Z11 · 6-Z12 · 6-14 ×2 · 6-16 · 6-Z17 · 6-18 · 6-Z24 · 6-Z25 · 6-31 · 6-32 · 6-33 · 6-Z39 · 6-Z40 · 6-Z44 ×2 · 6-Z46 ×2 · 6-Z47 ×2 · 6-Z48 · 6-Z50
7 notes: 7-5 · 7-11 · 7-Z17 · 7-Z18 · 7-20 · 7-23 · 7-27 · 7-29
- Around it
- 9-2 · 9-4 · 9-9 · 9-11 · and 7 larger classes