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. There is also a dedicated page about strictly proper 7-tone 31edo scales.
Nothing special
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
|
MOS
| 4 5 4 5 4 5 4
|
Neutral[7]
|
| 4 1 4 4 4 1 4 4 1 4
|
Breed 10-tone / Neutral[10]
|
| 7 7 7 7 3
|
Orwell[5]
|
| 4 3 4 3 4 3 4 3 3
|
Orwell[9]
|
| 3 1 3 3 1 3 3 1 3 3 1 3 3
|
Orwell[13]
|
| 9 9 2 9 2
|
Squares[5]
|
| 2 7 2 7 2 2 7 2
|
Squares[8]
|
| 2 5 2 2 2 5 2 2 2 5 2
|
Secor/Barton no-fives / Squares[11]
|
| 5 5 5 5 5 6
|
Whole Tone / Tutone[6]
|
| 4 1 4 1 4 1 4 1 4 1 4 1 1
|
Tutone[13]
|
| 6 6 6 6 1 6
|
Mothra[6]
|
| 5 1 5 1 5 1 5 1 5 1 1
|
de Vries 11-tone / Mothra[11]
|
| 3 4 3 3 3 3 3 3 3 3
|
Miracle[10]
|
| 3 4 4 4 4 4 4 4
|
Greeley[8]
|
| 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3
|
Pseudo-Porcupine 15-note / Nusecond[15]
|
| 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2
|
Semi-Equalized Armodue / Valentine[15]
|
| 5 7 5 7 7
|
A-Team[5]
|
| 5 5 2 5 5 2 5 2
|
Oneirotonic / A-Team[8]
|
| 3 2 3 2 2 3 2 2 3 2 3 2 2
|
A-Team[13]
|
| 11 3 11 3 3
|
Joan[5]
|
| 8 3 3 8 3 3 3
|
Hypermavila / Joan[7]
|
| 5 3 3 3 3 5 3 3 3
|
Rothenberg Generalized Diatonic / Joan[9]
|
| 3 2 3 3 3 3 2 3 3 3 3
|
Joan[11]
|
| 8 1 1 8 1 1 8 1 1 1
|
Würschmidt[10]
|
| 1 1 6 1 1 6 1 1 6 1 6
|
Myna[11]
|
| 1 1 12 1 1 1 1 12 1
|
Tritonic[9]
|
MODMOS
| 3 4 3 4 4 3 4 3 3
|
Graham Orwell
|
| 5 4 4 5 5 4 4
|
Maqam Rast
|
| 4 4 5 5 3 5 5
|
Maqam Bayati
|
| 5 5 3 5 4 5 4
|
Turkish Major
|
| 4 5 5 4 4 4 5
|
Thaiic
|
| 7 2 7 2 7 2 2 2
|
Onydim
|
| 5 5 2 2 2 2 5 2 2 2 2
|
Squares Major
|
| 5 5 4 6 5 6
|
Harmonic Whole Tone
|
| 5 5 5 2 5 2 5 2
|
Dylydian
|
| 5 2 5 2 5 2 8 2
|
Harmonic Mnarian
|
| 7 6 5 7 6
|
Subminor Pentatonic
|
| 5 6 7 6 7
|
Supermajor Pentatonic
|
Cradle MOS
| 1 7 1 2 1 7 1 2 1 7 1
|
Nested Bees
|
| 3 1 6 1 3 3 1 6 1 3 3
|
Arc Aurelius
|
| 5 4 5 4 2 5 4 2
|
Xenosquare
|
| 4 2 4 2 4 2 4 3 3 3
|
Lumma Decatonic
|
Hexany
| 5 5 8 5 5 3
|
1-3-5-9
|
| 5 6 7 6 5 2
|
1-3-7-9
|
| 3 7 6 2 6 7
|
1-3-5-7
|
| 9 4 1 4 9 4
|
1-3-9-11
|
| 4 4 6 4 4 9
|
1-3-5-11
|
| 4 7 7 7 4 2
|
1-3-7-11
|
| 8 4 6 4 8 1
|
1-3-5-13
|
Harmonic Series
| 8 7 6 5 5
|
Mode 5
|
| 7 6 5 5 4 4
|
Mode 6
|
| 6 5 5 4 4 4 3
|
Mode 7
|
| 5 5 4 4 4 3 3 3
|
Mode 8
|
| 4 4 4 3 3 3 3 2 3 2
|
Mode 10
|
| 4 3 3 3 3 2 3 2 2 2 2 2
|
Mode 12
|
| 3 3 3 2 3 2 2 2 2 2 2 2 1 2
|
Mode 14
|
| 3 2 3 2 2 2 2 2 2 2 1 2 2 1 2 1
|
Mode 16
|
| 4 4 5 5 6 7
|
Mode 6-over
|
| 2 3 3 3 3 4 4 4 5
|
Mode 9-over
|
| 1 2 2 1 2 2 2 2 2 2 2 3 2 3 3
|
Mode 15-over
|
Euler-Fokker genera
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
| 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
| 6 6 7 6 6
|
Quasi-equal Pentatonic
|
| 3 3 2 3 3 3 3 3 2 3 3
|
near 11edo
|
Dimension scales
(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)
|
Miscellaneous
| 4 1 4 1 3 4 1 4 1 4 1 3
|
Iceface
|
| 1 4 2 3 3 1 4 2 3 2 3 3
|
Centaurus
|
| 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
|
| 2 5 3 5 3 5 2 6
|
Subminor Diminished
|
| 2 5 3 5 5 5 6
|
Subminor Altered
|
| 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
|
| 8 5 2 3 6 2 5
|
Hyperblue Dorian
|
| 8 5 2 3 2 9 2
|
Hyperblue harmonic
|
| 3 2 3 2 2 2 2 2 2 3 2 3 3
|
Major Miniscale (Mode 16 x Mode 15-over)
|
| 7 3 4 4 7 6
|
Graham Hexatonic
|
| 3 7 8 8 5
|
Aurora
|
Nonoctave
| 4 2 4 2 4 2 4 2 4 2
|
Blackwood
|
| 4 4 6 4 4 4 6
|
Mavila
|
| 8 2 8 2 8 2
|
Suboctave Augmented
|
| 2 6 2 6 2 6 2 6
|
Superoctave Diminished
|
| 4 4 3 7 3 5 3 (7)
|
Saba
|
| 5 5 5 3 5 5 5
|
Superlydian
|
