8-1

One shape, its own mirror

Interval content

Every set in the class holds seven semitones, six whole tones, five minor thirds, four major thirds, four fourths and two tritones.

Common tones

Notes a set keeps when transposed by n.

Notes a set keeps when inverted about n.

Its 12 sets

Set theory treats D# and Eb as one pitch class; the names under each set use one fixed spelling, sharps except Bb.

01234567

• 01234567C C# D D# E F F# G
• 12345678C# D D# E F F# G G#
• 23456789D D# E F F# G G# A
• 3456789tD# E F F# G G# A Bb
• 456789teE F F# G G# A Bb B
• 056789teF F# G G# A Bb B C
• 016789teF# G G# A Bb B C C#
• 012789teG G# A Bb B C C# D
• 012389teG# A Bb B C C# D D#
• 012349teA Bb B C C# D D# E
• 012345teBb B C C# D D# E F
• 0123456eB C C# D D# E F F#

Relations

Complement

4-1 0123

Z-partner

none: no other class has this interval vector

Symmetry

T0 and one inversion map it onto itself

Inside it

2 notes: 2-1 ×7 · 2-2 ×6 · 2-3 ×5 · 2-4 ×4 · 2-5 ×4 · 2-6 ×2

3 notes: 3-1 ×6 · 3-2 ×10 · 3-3 ×8 · 3-4 ×6 · 3-5 ×6 · 3-6 ×4 · 3-7 ×6 · 3-8 ×4 · 3-9 ×2 · 3-10 ×2 · 3-11 ×2

4 notes: 4-1 ×5 · 4-2 ×8 · 4-3 ×4 · 4-4 ×6 · 4-5 ×4 · 4-6 ×2 · 4-7 ×3 · 4-8 ×2 · 4-9 · 4-10 ×3 · 4-11 ×6 · 4-12 ×4 · 4-13 ×4 · 4-14 ×2 · 4-Z15 ×4 · 4-16 ×2 · 4-17 · 4-18 ×2 · 4-21 ×2 · 4-22 ×2 · 4-23 · 4-Z29 ×2

5 notes: 5-1 ×4 · 5-2 ×6 · 5-3 ×6 · 5-4 ×4 · 5-5 ×2 · 5-6 ×4 · 5-7 ×2 · 5-8 ×2 · 5-9 ×4 · 5-10 ×4 · 5-11 ×2 · 5-Z12 ×2 · 5-14 ×2 · 5-16 ×2 · 5-Z18 ×2 · 5-19 ×2 · 5-23 ×2 · 5-24 ×2 · 5-Z36 ×2

6 notes: 6-1 ×3 · 6-2 ×4 · 6-Z3 ×4 · 6-Z4 ×2 · 6-5 ×2 · 6-Z6 · 6-8 · 6-9 ×2 · 6-Z10 ×2 · 6-Z11 ×2 · 6-Z12 ×2 · 6-Z13 · 6-Z36 ×2

7 notes: 7-1 ×2 · 7-2 ×2 · 7-4 ×2 · 7-5 ×2

Around it

9-1 ×2 · 9-2 ×2 · and 5 larger classes