8-9

One shape, its own mirror

Interval content

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

Common tones

Notes a set keeps when transposed by n.

Notes a set keeps when inverted about n.

Its 6 sets

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

01236789

• 01236789C C# D D# F# G G# A
• 1234789tC# D D# E G G# A Bb
• 234589teD D# E F G# A Bb B
• 034569teD# E F F# A Bb B C
• 014567teE F F# G Bb B C C#
• 0125678eF F# G G# B C C# D

Relations

Complement

4-9 0167

Z-partner

none: no other class has this interval vector

Symmetry

2 transpositions and 2 inversions map it onto itself

Inside it

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

3 notes: 3-1 ×4 · 3-2 ×4 · 3-3 ×4 · 3-4 ×8 · 3-5 ×12 · 3-7 ×4 · 3-8 ×8 · 3-9 ×4 · 3-10 ×4 · 3-11 ×4

4 notes: 4-1 ×2 · 4-4 ×4 · 4-5 ×8 · 4-6 ×4 · 4-7 ×2 · 4-8 ×4 · 4-9 ×3 · 4-12 ×4 · 4-13 ×4 · 4-14 ×4 · 4-Z15 ×4 · 4-16 ×8 · 4-18 ×4 · 4-20 ×2 · 4-23 ×2 · 4-25 ×2 · 4-27 ×4 · 4-28 · 4-Z29 ×4

5 notes: 5-4 ×4 · 5-5 ×4 · 5-6 ×4 · 5-7 ×8 · 5-14 ×4 · 5-15 ×4 · 5-Z18 ×4 · 5-19 ×4 · 5-20 ×4 · 5-28 ×4 · 5-29 ×4 · 5-31 ×4 · 5-Z38 ×4

6 notes: 6-5 ×4 · 6-Z6 ×2 · 6-7 ×2 · 6-18 ×4 · 6-Z29 ×2 · 6-30 ×2 · 6-Z38 ×2 · 6-Z41 ×4 · 6-Z42 ×2 · 6-Z43 ×4

7 notes: 7-7 ×4 · 7-19 ×4

Around it

9-5 ×4 · and 5 larger classes