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 |