31edo modes

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

See Strictly proper 7-tone 31edo scales

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
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