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 5 8 5 8 Thirty-one tone Major Pentatonic
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
8 2 8 2 8 3 Thirty-one tone Augmented
3 5 2 5 3 5 3 5 Thirty-one tone Diminished
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]
1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 Blackjack / Miracle[21]
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[16]
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
4 4 4 4 5 5 5 Sheimanic
5 5 4 4 5 5 3 Screamapillar
5 3 5 5 5 4 4 Altered Dorian
3 5 5 5 5 4 4 Altered Neapolitan Major
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 / Archeodim
5 2 5 2 5 2 8 2 Harmonic Mnarian
3 4 3 2 3 3 3 4 3 3 Miracle Major
3 4 3 4 4 5 4 4 Greeley Major
7 6 5 7 6 Subminor Pentatonic
5 6 7 6 7 Supermajor Pentatonic
1 6 1 1 1 6 1 1 6 1 6 Submyna
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
5 4 5 3 5 4 5 Scorp
5 6 2 5 5 6 2 Harrison Major
4 2 4 2 4 2 4 3 3 3 Lumma Decatonic
8 2 8 2 8 2 1 AugmentedPlus
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 )
Strictly proper modes 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 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
2 5 3 5 3 5 2 6 Subminor Diminished
2 5 3 5 5 5 6 Subminor Altered
2 8 3 5 2 5 6 Phrygian Harmonic
5 5 3 5 5 2 3 3 Bebop Harmonic
5 7 1 5 7 5 1 Tropical Major
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 (this is the original/default tuning)
8 5 2 3 2 9 2 Hyperblue harmonic (this is the original/default tuning)
5 5 4 8 3 6 Harmonic Prometheus
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 Magnetosphere
5 4 1 3 5 2 3 6 2 Oclock
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
See main article The Erose-McClain double modes
