Strictly proper 7-tone 31edo scales

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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

schema 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