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
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Meantone Chromatic (53/220-comma)
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5 5 3 5 5 5 3
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Thirty-one tone Major, Intense Diatonic Lydian, M.Ionian
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5 3 5 5 3 5 5
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Thirty-one tone Natural Minor, Intense Diatonic Hypodorian, Aeolian
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5 5 8 5 8
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Thirty-one tone Major Pentatonic
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5 3 5 5 5 5 3
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Thirty-one tone Melodic Minor
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5 3 5 5 3 7 3
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Thirty-one tone Harmonic Minor
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5 5 3 5 3 7 3
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Thirty-one tone Harmonic Major
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5 5 3 5 3 5 5
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Thirty-one tone Major-Minor
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8 2 8 2 8 3
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Thirty-one tone Augmented
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3 5 2 5 3 5 3 5
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Thirty-one tone Diminished
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5 2 6 5 2 5 6
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"Septimal" Natural Minor
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MOS
4 5 4 5 4 5 4
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Neutral[7]
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4 1 4 4 4 1 4 4 1 4
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Breed 10-tone / Neutral[10]
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7 7 7 7 3
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Orwell[5]
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4 3 4 3 4 3 4 3 3
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Orwell[9]
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3 1 3 3 1 3 3 1 3 3 1 3 3
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Orwell[13]
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9 9 2 9 2
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Squares[5]
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2 7 2 7 2 2 7 2
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Squares[8]
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2 5 2 2 2 5 2 2 2 5 2
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Secor/Barton no-fives / Squares[11]
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5 5 5 5 5 6
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Whole Tone / Tutone[6]
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4 1 4 1 4 1 4 1 4 1 4 1 1
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Tutone[13]
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6 6 6 6 1 6
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Mothra[6]
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5 1 5 1 5 1 5 1 5 1 1
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de Vries 11-tone / Mothra[11]
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3 4 3 3 3 3 3 3 3 3
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Miracle[10]
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1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1
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Blackjack / Miracle[21]
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3 4 4 4 4 4 4 4
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Greeley[8]
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3 1 3 1 3 1 3 1 3 1 3 1 3 1 3
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Pseudo-Porcupine 15-note / Nusecond[15]
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2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2
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Semi-Equalized Armodue / Valentine[16]
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5 7 5 7 7
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A-Team[5]
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5 5 2 5 5 2 5 2
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Oneirotonic / A-Team[8]
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3 2 3 2 2 3 2 2 3 2 3 2 2
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A-Team[13]
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11 3 11 3 3
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Joan[5]
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8 3 3 8 3 3 3
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Hypermavila / Joan[7]
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5 3 3 3 3 5 3 3 3
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Rothenberg Generalized Diatonic / Joan[9]
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3 2 3 3 3 3 2 3 3 3 3
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Joan[11]
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8 1 1 8 1 1 8 1 1 1
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Würschmidt[10]
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1 1 6 1 1 6 1 1 6 1 6
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Myna[11]
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1 1 12 1 1 1 1 12 1
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Tritonic[9]
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MODMOS
3 4 3 4 4 3 4 3 3
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Graham Orwell
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5 4 4 5 5 4 4
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Maqam Rast
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4 4 5 5 3 5 5
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Maqam Bayati
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5 5 3 5 4 5 4
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Turkish Major
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4 5 5 4 4 4 5
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Thaiic
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4 4 4 4 5 5 5
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Sheimanic
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5 5 4 4 5 5 3
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Screamapillar
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5 3 5 5 5 4 4
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Altered Dorian
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3 5 5 5 5 4 4
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Altered Neapolitan Major
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7 2 7 2 7 2 2 2
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Onydim
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5 5 2 2 2 2 5 2 2 2 2
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Squares Major
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5 5 4 6 5 6
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Harmonic Whole Tone
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5 5 5 2 5 2 5 2
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Dylydian / Archeodim
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5 2 5 2 5 2 8 2
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Harmonic Mnarian
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3 4 3 2 3 3 3 4 3 3
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Miracle Major
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3 4 3 4 4 5 4 4
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Greeley Major
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7 6 5 7 6
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Subminor Pentatonic
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5 6 7 6 7
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Supermajor Pentatonic
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1 6 1 1 1 6 1 1 6 1 6
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Submyna
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Cradle MOS
1 7 1 2 1 7 1 2 1 7 1
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Nested Bees
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3 1 6 1 3 3 1 6 1 3 3
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Arc Aurelius
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5 4 5 4 2 5 4 2
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Xenosquare
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5 4 5 3 5 4 5
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Scorp
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5 6 2 5 5 6 2
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Harrison Major
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4 2 4 2 4 2 4 3 3 3
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Lumma Decatonic
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8 2 8 2 8 2 1
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AugmentedPlus
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Hexany
5 5 8 5 5 3
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1-3-5-9
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5 6 7 6 5 2
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1-3-7-9
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3 7 6 2 6 7
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1-3-5-7
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9 4 1 4 9 4
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1-3-9-11
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4 4 6 4 4 9
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1-3-5-11
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4 7 7 7 4 2
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1-3-7-11
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8 4 6 4 8 1
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1-3-5-13
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Harmonic Series
8 7 6 5 5
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Mode 5
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7 6 5 5 4 4
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Mode 6
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6 5 5 4 4 4 3
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Mode 7
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5 5 4 4 4 3 3 3
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Mode 8
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4 4 4 3 3 3 3 2 3 2
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Mode 10
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4 3 3 3 3 2 3 2 2 2 2 2
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Mode 12
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3 3 3 2 3 2 2 2 2 2 2 2 1 2
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Mode 14
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3 2 3 2 2 2 2 2 2 2 1 2 2 1 2 1
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Mode 16
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4 4 5 5 6 7
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Mode 6-over
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2 3 3 3 3 4 4 4 5
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Mode 9-over
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1 2 2 1 2 2 2 2 2 2 2 3 2 3 3
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Mode 15-over
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Euler–Fokker genera
Boxy shapes from the [3, 5, 7] lattice.
5 8 5 13
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Genus primum
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10 3 5 5 5 3
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Genus secundum
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8 2 8 3 7 3
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Genus tertium
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10 10 10 1
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Genus quartum
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5 7 6 7 5 1
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Genus quintum
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4 6 2 6 4 3 3 3
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Genus sextum
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4 6 5 6 4 6
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Genus septimum
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6 6 6 1 6 6
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Genus octavum
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4 6 9 6 4 2
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Genus nonum
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13 6 6 6
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Genus decimum
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5 5 3 5 5 3 2 3
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Genus diatonicum
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3 5 2 3 5 3 2 5 3
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Genus chromaticum
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5 5 2 1 5 5 2 3 3
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Genus diatonicum cum septimis
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3 4 3 3 2 1 4 1 4 1 2 3
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Genus enharmonicum vocale
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2 2 4 2 2 3 3 3 1 3 3 3
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Genus enharmonicum instrumentale
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3 2 3 2 3 2 3 3 2 3 2 3
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Genus diatonico-chromaticum
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5 2 1 2 5 3 2 1 4 1 2 3
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Genus bichromaticum
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3 1 2 4 2 4 2 4 2 1 3 3
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Genus [3577] (Joel Mandelbaum Andante cantabile)
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Strictly proper modes
See Strictly proper 7-tone 31edo scales
Greek/tetrachord modes
4 4 5 4 4 5 5
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Neutral Diatonic Mixolydian
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4 5 4 4 5 5 4
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Neutral Diatonic Lydian
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5 4 4 5 5 4 4
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Neutral Diatonic Phrygian
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4 4 5 5 4 4 5
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Neutral Diatonic Dorian
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4 5 5 4 4 5 4
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Neutral Diatonic Hypolydian
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5 5 4 4 5 4 4
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Neutral Diatonic Hypophrygian
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5 4 4 5 4 4 5
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Neutral Diatonic Hypodorian
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4 5 4 4 5 4 5
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Neutral Mixolydian
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5 4 4 5 4 5 4
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Neutral Lydian
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4 4 5 4 5 4 5
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Neutral Phrygian
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4 5 4 5 4 5 4
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Neutral Dorian
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5 4 5 4 5 4 4
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Neutral Hypolydian
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4 5 4 5 4 4 5
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Neutral Hypophrygian
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5 4 5 4 4 5 4
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Neutral Hypodorian
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2 2 9 2 2 9 5
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Hemiolic Chromatic Mixolydian
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2 9 2 2 9 5 2
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Hemiolic Chromatic Lydian
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9 2 2 9 5 2 2
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Hemiolic Chromatic Phrygian
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2 2 9 5 2 2 9
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Hemiolic Chromatic Dorian
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2 9 5 2 2 9 2
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Hemiolic Chromatic Hypolydian
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9 5 2 2 9 2 2
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Hemiolic Chromatic Hypophrygian
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5 2 2 9 2 2 9
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Hemiolic Chromatic Hypodorian
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2 3 8 2 3 8 5
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Ratio 2:3 Chromatic Mixolydian
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3 8 2 3 8 5 2
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Ratio 2:3 Chromatic Lydian
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8 2 3 8 5 2 3
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Ratio 2:3 Chromatic Phrygian
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2 3 8 5 2 3 8
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Ratio 2:3 Chromatic Dorian
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3 8 5 2 3 8 2
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Ratio 2:3 Chromatic Hypolydian
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8 5 2 3 8 2 3
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Ratio 2:3 Chromatic Hypophrygian
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5 2 3 8 2 3 8
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Ratio 2:3 Chromatic Hypodorian
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3 5 5 3 5 5 5
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Intense Diatonic Mixolydian, M.Locrian
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5 3 5 5 5 3 5
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Intense Diatonic Phrygian, M.Dorian
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3 5 5 5 3 5 5
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Intense Diatonic Dorian, M.Phrygian
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5 5 5 3 5 5 3
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Intense Diatonic Hypolydian, M.Lydian
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5 5 3 5 5 3 5
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Intense Diatonic Hypophrygian, M.Mixolydian
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2 5 6 2 5 6 5
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Soft Diatonic Mixolydian
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5 6 2 5 6 5 2
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Soft Diatonic Lydian
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6 2 5 6 5 2 5
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Soft Diatonic Phrygian
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2 5 6 5 2 5 6
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Soft Diatonic Dorian
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5 6 5 2 5 6 2
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Soft Diatonic Hypolydian
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6 5 2 5 6 2 5
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Soft Diatonic Hypophrygian
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5 2 5 6 2 5 6
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Soft Diatonic Hypodorian
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1 2 10 1 2 10 5
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Enharmonic Mixolydian
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2 10 1 2 10 5 1
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Enharmonic Lydian
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10 1 2 10 5 1 2
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Enharmonic Phrygian
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1 2 10 5 1 2 10
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Enharmonic Dorian
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2 10 5 1 2 10 1
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Enharmonic Hypolydian
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10 5 1 2 10 1 2
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Enharmonic Hypophrygian
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5 1 2 10 1 2 10
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Enharmonic Hypodorian
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Of particular interscalar interest
Dimension scales
(5) 3 1 4 (5) (5)
3 1 4
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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
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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)
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Miscellaneous
4 1 4 1 3 4 1 4 1 4 1 3
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Iceface
|
1 4 2 3 3 1 4 2 3 2 3 3
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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
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2 5 3 5 3 5 2 6
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Subminor Diminished
|
2 5 3 5 5 5 6
|
Subminor Altered
|
2 8 3 5 2 5 6
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Phrygian Harmonic
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5 5 3 5 5 2 3 3
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Bebop Harmonic
|
5 7 1 5 7 5 1
|
Tropical Major
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3 3 4 3 5 3 4 3 3
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Hahn symmetric pentachordal
|
3 4 3 3 5 3 4 3 3
|
Hahn pentachordal
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4 4 2 5 3 3 4 3 3
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Hahn Nonatonic
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8 5 2 3 6 2 5
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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
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