31edo modes
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Taken originally from Scala, Manuel Op De Coul, this is a user-editable list of modes of 31edo. The numbers indicate successive intervals, in dieses. Strictly proper scales of seven notes can be found here.
Nothing special[edit]
Or, to some, the only important thing.
| 2 3 3 2 3 2 3 2 3 3 2 3 | Meantone Chromatic (53/220-comma) |
| 5 5 3 5 5 5 3 | Thirty-one tone Major, Intense Diatonic Lydian, M.Ionian |
| 5 3 5 5 3 5 5 | Thirty-one tone Natural Minor, Intense Diatonic Hypodorian, Aeolian |
| 5 3 5 5 5 5 3 | Thirty-one tone Melodic Minor |
| 5 3 5 5 3 7 3 | Thirty-one tone Harmonic Minor |
| 5 5 3 5 3 7 3 | Thirty-one tone Harmonic Major |
| 5 5 3 5 3 5 5 | Thirty-one tone Major-Minor |
| 5 2 6 5 2 5 6 | "Septimal" Natural Minor |
Euler-Fokker genera[edit]
Boxy shapes from the [3,5,7] lattice.
| 5 8 5 13 | Genus primum |
| 10 3 5 5 5 3 | Genus secundum |
| 8 2 8 3 7 3 | Genus tertium |
| 10 10 10 1 | Genus quartum |
| 5 7 6 7 5 1 | Genus quintum |
| 4 6 2 6 4 3 3 3 | Genus sextum |
| 4 6 5 6 4 6 | Genus septimum |
| 6 6 6 1 6 6 | Genus octavum |
| 4 6 9 6 4 2 | Genus nonum |
| 13 6 6 6 | Genus decimum |
| 5 5 3 5 5 3 2 3 | Genus diatonicum |
| 3 5 2 3 5 3 2 5 3 | Genus chromaticum |
| 5 5 2 1 5 5 2 3 3 | Genus diatonicum cum septimis |
| 3 4 3 3 2 1 4 1 4 1 2 3 | Genus enharmonicum vocale |
| 2 2 4 2 2 3 3 3 1 3 3 3 | Genus enharmonicum instrumentale |
| 3 2 3 2 3 2 3 3 2 3 2 3 | Genus diatonico-chromaticum |
| 5 2 1 2 5 3 2 1 4 1 2 3 | Genus bichromaticum |
| 3 1 2 4 2 4 2 4 2 1 3 3 | Genus [3577] (Joel Mandelbaum Andante cantabile) |
Greek/tetrachord modes[edit]
| 4 4 5 4 4 5 5 | Neutral Diatonic Mixolydian |
| 4 5 4 4 5 5 4 | Neutral Diatonic Lydian |
| 5 4 4 5 5 4 4 | Neutral Diatonic Phrygian |
| 4 4 5 5 4 4 5 | Neutral Diatonic Dorian |
| 4 5 5 4 4 5 4 | Neutral Diatonic Hypolydian |
| 5 5 4 4 5 4 4 | Neutral Diatonic Hypophrygian |
| 5 4 4 5 4 4 5 | Neutral Diatonic Hypodorian |
| 4 5 4 4 5 4 5 | Neutral Mixolydian |
| 5 4 4 5 4 5 4 | Neutral Lydian |
| 4 4 5 4 5 4 5 | Neutral Phrygian |
| 4 5 4 5 4 5 4 | Neutral Dorian |
| 5 4 5 4 5 4 4 | Neutral Hypolydian |
| 4 5 4 5 4 4 5 | Neutral Hypophrygian |
| 5 4 5 4 4 5 4 | Neutral Hypodorian |
| 2 2 9 2 2 9 5 | Hemiolic Chromatic Mixolydian |
| 2 9 2 2 9 5 2 | Hemiolic Chromatic Lydian |
| 9 2 2 9 5 2 2 | Hemiolic Chromatic Phrygian |
| 2 2 9 5 2 2 9 | Hemiolic Chromatic Dorian |
| 2 9 5 2 2 9 2 | Hemiolic Chromatic Hypolydian |
| 9 5 2 2 9 2 2 | Hemiolic Chromatic Hypophrygian |
| 5 2 2 9 2 2 9 | Hemiolic Chromatic Hypodorian |
| 2 3 8 2 3 8 5 | Ratio 2:3 Chromatic Mixolydian |
| 3 8 2 3 8 5 2 | Ratio 2:3 Chromatic Lydian |
| 8 2 3 8 5 2 3 | Ratio 2:3 Chromatic Phrygian |
| 2 3 8 5 2 3 8 | Ratio 2:3 Chromatic Dorian |
| 3 8 5 2 3 8 2 | Ratio 2:3 Chromatic Hypolydian |
| 8 5 2 3 8 2 3 | Ratio 2:3 Chromatic Hypophrygian |
| 5 2 3 8 2 3 8 | Ratio 2:3 Chromatic Hypodorian |
| 3 5 5 3 5 5 5 | Intense Diatonic Mixolydian, M.Locrian |
| 5 3 5 5 5 3 5 | Intense Diatonic Phrygian, M.Dorian |
| 3 5 5 5 3 5 5 | Intense Diatonic Dorian, M.Phrygian |
| 5 5 5 3 5 5 3 | Intense Diatonic Hypolydian, M.Lydian |
| 5 5 3 5 5 3 5 | Intense Diatonic Hypophrygian, M.Mixolydian |
| 2 5 6 2 5 6 5 | Soft Diatonic Mixolydian |
| 5 6 2 5 6 5 2 | Soft Diatonic Lydian |
| 6 2 5 6 5 2 5 | Soft Diatonic Phrygian |
| 2 5 6 5 2 5 6 | Soft Diatonic Dorian |
| 5 6 5 2 5 6 2 | Soft Diatonic Hypolydian |
| 6 5 2 5 6 2 5 | Soft Diatonic Hypophrygian |
| 5 2 5 6 2 5 6 | Soft Diatonic Hypodorian |
| 1 2 10 1 2 10 5 | Enharmonic Mixolydian |
| 2 10 1 2 10 5 1 | Enharmonic Lydian |
| 10 1 2 10 5 1 2 | Enharmonic Phrygian |
| 1 2 10 5 1 2 10 | Enharmonic Dorian |
| 2 10 5 1 2 10 1 | Enharmonic Hypolydian |
| 10 5 1 2 10 1 2 | Enharmonic Hypophrygian |
| 5 1 2 10 1 2 10 | Enharmonic Hypodorian |
Of particular interscalar interest[edit]
| 6 6 7 6 6 | Quasi-equal Pentatonic |
| 3 3 2 3 3 3 3 3 2 3 3 | near 11edo |
Miscellaneous[edit]
| 3 2 2 3 3 2 3 3 2 2 3 3 | Fokker 12-tone |
| 5 3 5 3 5 2 5 3 | Modus conjunctus |
| 3 5 2 5 3 5 3 5 | Octatonic |
| 3 3 4 3 5 3 4 3 3 | Hahn symmetric pentachordal |
| 3 4 3 3 5 3 4 3 3 | Hahn pentachordal |
| 4 4 2 5 3 3 4 3 3 | Hahn Nonatonic |
| 5 3 3 3 3 5 3 3 3 | Rothenberg Generalized Diatonic |
| (5) 3 1 4 (5) (5)
3 1 4 |
Michael Sheiman's "Dimension" scale (Maqam Rast mixed with Meantone Diatonic...lattice (ratio/chord map) available below |
| (3 2)3 1 4 (3 2)(3 2)
3 1 4 |
Michael Sheiman's extended 12 tone "Dimension ECT" scale (Maqam Rast mixed with Meantone Diatonic and Michael Sheiman's "6-factor" no wolves 12th harmonic scale) |
MOS and Cradle MOS[edit]
| 4 5 4 5 4 5 4 | Neutral scale 7-note |
| 4 1 4 4 1 4 4 4 1 4 | Neutral scale 10-note |
| 4 1 4 4 4 1 4 4 1 4 | Breed 10-tone |
| 4 3 4 3 4 3 4 3 3 | Orwell[9] |
| 5 1 5 1 5 1 5 1 5 1 1 | de Vries 11-tone |
| 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 | Pseudo-Porcupine 15-note |
| 1 7 1 2 1 7 1 2 1 7 1 | Nested Bees |
| 4 2 4 2 4 2 4 3 3 3 | Lumma Decatonic |
| 2 5 2 2 5 2 2 2 5 2 2 | Secor/Barton no-fives |