5-Z38

Two shapes, each the other’s mirror

Interval content

Every set in the class holds two semitones, one whole tone, two minor thirds, two major thirds, two fourths and one tritone.

Common tones

Notes a set keeps when transposed by n.

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.

01258

• 01258C C# D F G#
• 12369C# D D# F# A
• 2347tD D# E G Bb
• 3458eD# E F G# B
• 04569E F F# A C
• 1567tF F# G Bb C#
• 2678eF# G G# B D
• 03789G G# A C D#
• 1489tG# A Bb C# E
• 259teA Bb B D F
• 036teBb B C D# F#
• 0147eB C C# E G

03678

• 03678C D# F# G G#
• 14789C# E G G# A
• 2589tD F G# A Bb
• 369teD# F# A Bb B
• 047teE G Bb B C
• 0158eF G# B C C#
• 01269F# A C C# D
• 1237tG Bb C# D D#
• 2348eG# B D D# E
• 03459A C D# E F
• 1456tBb C# E F F#
• 2567eB D F F# G

Relations

Complement

7-Z38 0124578

Z-partner

5-Z18, the same interval vector in another class

Symmetry

none: only T0 maps it onto itself

Inside it

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

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

4 notes: 4-4 · 4-5 · 4-18 · 4-20 · 4-27

Around it

6-15 · 6-18 · 6-Z40 · 6-Z42 · 6-Z43 · 6-Z44 · 6-Z46 · and 62 larger classes