Strictly proper 7-tone 31edo scales

This is a list of 7-tone scales in 31edo which are strictly proper with regard to the Rothenberg propriety.

The "type" of a scale is defined by the linear temperament supported by 31edo in which it has the least span. "Breed type" means it is a tie between miracle and hemiwuerschmidt.

Meantone type

step pattern	name	example(s)
5 5 3 5 5 5 3	Meantone[7]; diatonic scale
5 3 5 5 5 5 3	Melodic minor scale
5 3 5 5 3 7 3	Harmonic minor scale; inverse harmonic major
5 5 3 5 3 7 3	Harmonic major scale; inverse harmonic minor
5 5 3 3 5 5 5	Major locrian scale
3 7 1 7 3 5 5	Diminished diatonic scale	Strange Diatonic by Chris Vaisvil play Omega centauri[dead link] by Zach Curley
5 5 3 5 6 4 3	Enharmonic major; inverse enharmonic minor
5 3 4 6 5 3 5	Enharmonic minor; inverse enharmonic major
5 5 3 5 6 2 5	Enharmonic mixolydian
5 5 2 6 5 3 5	Inverse enharmonic mixolydian
5 5 2 6 3 5 5	Enharmonic major-minor
5 5 5 3 6 2 5	Inverse enharmonic major-minor
6 4 3 5 6 2 5	Major doubleflat; inverse minor doubleflat
5 3 4 6 5 2 6	Minor doubleflat; inverse major doubleflat
5 5 5 3 6 5 2	Ping
3 5 5 5 2 5 6	Inverse ping
3 7 2 6 3 5 5	Alhijaz; inverse ambika
6 2 7 3 5 5 3	Ambika; inverse alhijaz
6 4 5 3 6 5 2	Kung; inverse ousak
3 5 4 6 2 5 6	Ousak; inverse kung

Valentine

schema	name
6 4 4 6 2 7 2	Silver
6 4 4 4 4 7 2	Harmonia
4 4 4 6 2 7 4	Inverse harmonia
6 4 4 4 5 6 2	Pendragon
4 6 2 6 5 4 4	Inverse pendragon
6 2 6 4 4 6 3	Hipop
4 6 2 6 3 6 4	Inverse Hipop
4 6 2 6 4 4 5	Malakon
4 6 2 6 4 5 4	Inverse malakon
4 4 6 4 5 2 6	Bagpipe
4 6 4 4 6 2 5	Inverse bagpipe
6 4 4 4 6 2 5	Pitu
6 4 4 4 6 5 2	Inverse pitu
6 4 4 4 4 4 5	Porch
4 4 4 6 5 4 4	Inverse porch

Miracle type

schema	name
5 4 3 6 3 4 6	Subdom scale; inverse superton
5 6 4 3 6 3 4	Superton scale; inverse subdom
5 4 3 6 3 6 4	Nudia; neutral diatonic
5 4 6 3 6 3 4	Inverse nudia
3 6 3 6 3 4 6	Nurow; Neutral triads in row
6 3 6 3 6 4 3	Inverse nurow

Mohajira type

schema	name
4 5 5 4 4 5 4	Sikah; Rast; Neutral Diatonic Hypolydian
4 4 4 4 5 5 5	Sheimanic
4 5 5 4 4 4 5	Thaiic
4 5 4 4 4 5 5	Inverse thaiic
4 5 4 5 4 5 4	Mohajira; Neutral Dorian

Hemiwuerschmidt type

schema	name
5 5 5 5 5 1 5	Hemiwuerschmidt/Hemithirds[7]
5 5 4 4 6 5 2	Hemaj; inverse hemin
4 4 5 5 2 5 6	Hemin; inverse hemaj
4 5 2 5 5 4 6	Gypsi; 11/9-10/7-7/4 chord on tonic
4 5 5 2 5 4 6	Inverse gypsi; 11/9-10/7-7/4 chord on tonic
5 5 5 5 5 4 2	Leadhole
5 5 5 5 5 2 4	Inverse leadhole

Mothra type

schema	name
5 5 5 3 6 4 3	Lydic
5 5 5 3 4 6 3	Inverse lydic
5 5 3 5 4 6 3	Ionic
5 3 6 4 5 3 5	Aeolic; inverse ionic
4 6 4 4 4 6 3	Quahog
6 4 4 4 6 4 3	Inverse quahog
6 4 5 3 6 4 3	Higasi
4 6 3 5 4 6 3	Inverse higasi

Orwell type

schema	name
5 3 6 4 4 6 3	Orminor
4 6 4 4 6 4 3	Ormed
4 6 4 4 3 6 4	Augton
4 6 4 4 6 3 4	Inverse augton

Breed type

schema	name
3 4 5 6 2 6 5	Hemisub
4 3 5 6 2 6 5	Inverse hemisub
6 3 5 4 5 3 5	Heminewt
4 5 3 6 5 3 5	Inverse heminewt

See also

• 31edo modes
• Strictly proper 19edo scales