31edo modes: Difference between revisions
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| <tt>''See main article''</tt> | |||
| The [[Erose-McClain double mode]]s | |||
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Revision as of 07:37, 11 December 2024
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 3a | 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 |
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 |