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
|