31edo modes: Difference between revisions

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BudjarnLambeth (talk | contribs)
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m →Miscellaneous: Added 1 mode
KingHyperio (talk | contribs)
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Tried to revamp the page a bit, added a bunch of scales that definitely should've been there, as well as a few that I find interesting.
Line 30: Line 30:
| <tt>'''5 2 6 5 2 5 6'''</tt>
| <tt>'''5 2 6 5 2 5 6'''</tt>
| "Septimal" Natural Minor
| "Septimal" Natural Minor
|}
== MOS ==
{| class="wikitable"
|-
| <tt>'''4 5 4 5 4 5 4'''</tt>
| Neutral[7]
|-
| <tt>'''4 1 4 4 1 4 4 4 1 4'''</tt>
| Neutral[10]
|-
| <tt>'''7 7 7 7 3'''</tt>
| Orwell[5]
|-
| <tt>'''4 3 4 3 4 3 4 3 3'''</tt>
| Orwell[9]
|-
| <tt>'''3 1 3 3 1 3 3 1 3 3 1 3 3'''</tt>
| Orwell[13]
|-
| <tt>'''9 9 2 9 2'''</tt>
| Squares[5]
|-
| <tt>'''2 7 2 7 2 2 7 2'''</tt>
| Squares[8]
|-
| <tt>'''2 5 2 2 2 5 2 2 2 5 2'''</tt>
| Secor/Barton no-fives / Squares[11]
|-
| <tt>'''5 5 5 5 5 6'''</tt>
| Tutone[6]
|-
| <tt>'''4 1 4 1 4 1 4 1 4 1 4 1 1'''</tt>
| Tutone[13]
|-
| <tt>'''6 6 6 6 1 6'''</tt>
| Mothra[6]
|-
| <tt>'''5 1 5 1 5 1 5 1 5 1 1'''</tt>
| de Vries 11-tone / Mothra[11]
|-
| <tt>'''3 4 3 3 3 3 3 3 3 3'''</tt>
| Miracle[10]
|-
| <tt>'''3 4 4 4 4 4 4 4'''</tt>
| Nusecond[8]
|-
| <tt>'''3 1 3 1 3 1 3 1 3 1 3 1 3 1 3'''</tt>
| Pseudo-Porcupine 15-note / Nusecond[15]
|-
| <tt>'''2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2'''</tt>
| Semi-Equalized Armodue / Valentine[15]
|-
| <tt>'''5 7 5 7 7'''</tt>
| A-Team[5]
|-
| <tt>'''5 5 2 5 5 2 5 2'''</tt>
| A-Team[8]
|-
| <tt>'''3 2 3 2 2 3 2 2 3 2 3 2 2'''</tt>
| A-Team[13]
|-
| <tt>'''11 3 11 3 3'''</tt>
| Joan[5]
|-
| <tt>'''3 2 3 3 3 3 2 3 3 3 3'''</tt>
| Joan[11]
|-
| <tt>'''8 1 1 8 1 1 8 1 1 1'''</tt>
| Würschmidt[10]
|-
| <tt>'''1 1 6 1 1 6 1 1 6 1 6'''</tt>
| Myna[11]
|-
| <tt>'''1 1 12 1 1 1 1 12 1'''</tt>
| Tritonic[9]
|}
== MODMOS ==
{| class="wikitable"
|-
| <tt>'''3 4 3 4 4 3 4 3 3'''</tt>
| Graham Orwell
|-
| <tt>'''5 4 4 5 5 4 4'''</tt>
| Maqam Rast
|-
| <tt>'''4 4 5 5 3 5 5'''</tt>
| Maqam Bayati
|-
| <tt>'''7 2 7 2 7 2 2 2'''</tt>
| Onydim
|-
| <tt>'''5 5 4 6 5 6'''</tt>
| Harmonic Whole Tone
|-
| <tt>'''5 5 5 2 5 2 5 2'''</tt>
| Dylydian
|-
| <tt>'''5 2 5 2 5 2 8 2'''</tt>
| Harmonic Mnarian
|-
| <tt>'''7 6 5 7 6'''</tt>
| Subminor Pentatonic
|}
== Cradle MOS ==
{| class="wikitable"
|-
| <tt>'''1 7 1 2 1 7 1 2 1 7 1'''</tt>
| Nested Bees
|-
| <tt>'''3 1 6 1 3 3 1 6 1 3 3'''</tt>
| Arc Aurelius
|-
| <tt>'''5 4 5 4 2 5 4 2'''</tt>
| Xenosquare
|-
| <tt>'''4 2 4 2 4 2 4 3 3 3'''</tt>
| Lumma Decatonic
|}
== Hexany ==
{| class="wikitable"
|-
| <tt>'''5 5 8 5 5 3'''</tt>
| 1-3-5-9
|-
| <tt>'''5 6 7 6 5 2'''</tt>
| 1-3-7-9
|-
| <tt>'''3 7 6 2 6 7'''</tt>
| 1-3-5-7
|-
| <tt>'''9 4 1 4 9 4'''</tt>
| 1-3-9-11
|-
| <tt>'''4 4 6 4 4 9'''</tt>
| 1-3-5-11
|-
| <tt>'''4 7 7 7 4 2'''</tt>
| 1-3-7-11
|-
| <tt>'''8 4 6 4 8 1'''</tt>
| 1-3-5-13
|}
== Harmonic Series ==
{| class="wikitable"
|-
| <tt>'''8 7 6 5 5'''</tt>
| Mode 5
|-
| <tt>'''7 6 5 5 4 4'''</tt>
| Mode 6
|-
| <tt>'''6 5 5 4 4 4 3'''</tt>
| Mode 7
|-
| <tt>'''5 5 4 4 4 3 3 3'''</tt>
| Mode 8
|-
| <tt>'''4 4 4 3 3 3 3 2 3 2'''</tt>
| Mode 10
|-
| <tt>'''4 3 3 3 3 2 3 2 2 2 2 2'''</tt>
| Mode 12
|-
| <tt>'''3 3 3 2 3 2 2 2 2 2 2 2 1 2'''</tt>
| Mode 14
|}
|}


Line 260: Line 433:
|}
|}


== MOS and Cradle MOS ==
== Miscellaneous ==


{| class="wikitable"
{| class="wikitable"
|-
|-
| <tt>'''4 5 4 5 4 5 4'''</tt>
| <tt>'''4 1 4 1 3 4 1 4 1 4 1 3'''</tt>
| Neutral scale 7-note
| Iceface
|-
| <tt>'''4 1 4 4 1 4 4 4 1 4'''</tt>
| Neutral scale 10-note
|-
| <tt>'''4 1 4 4 4 1 4 4 1 4'''</tt>
| Breed 10-tone
|-
| <tt>'''4 3 4 3 4 3 4 3 3'''</tt>
| Orwell[9]
|-
| <tt>'''5 1 5 1 5 1 5 1 5 1 1'''</tt>
| de Vries 11-tone
|-
| <tt>'''3 1 3 1 3 1 3 1 3 1 3 1 3 1 3'''</tt>
| Pseudo-Porcupine 15-note
|-
| <tt>'''1 7 1 2 1 7 1 2 1 7 1'''</tt>
| Nested Bees
|-
|-
| <tt>'''4 2 4 2 4 2 4 3 3 3'''</tt>
| <tt>'''1 4 2 3 3 1 4 2 3 2 3 3'''</tt>
| Lumma Decatonic
| Centaurus
|-
| <tt>'''2 5 2 2 5 2 2 2 5 2 2'''</tt>
| Secor/Barton no-fives
|}
 
== Miscellaneous ==
 
{| class="wikitable"
|-
|-
| <tt>'''3 2 2 3 3 2 3 3 2 2 3 3'''</tt>
| <tt>'''3 2 2 3 3 2 3 3 2 2 3 3'''</tt>
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| <tt>'''8 5 2 3 2 9 2'''</tt>
| <tt>'''8 5 2 3 2 9 2'''</tt>
|Hyperblue harmonic
|Hyperblue harmonic
|-
| <tt>'''3 2 3 2 2 2 2 2 2 3 2 3 3'''</tt>
| Major Miniscale (Mode 16 x Mode 15-over)
|-
|-
| <tt>'''3 7 8 8 5'''</tt>
| <tt>'''3 7 8 8 5'''</tt>
|[[Aurora scale|Aurora]]
|[[Aurora scale|Aurora]]
|}
== Nonoctave ==
{| class="wikitable"
|-
| <tt>'''4 2 4 2 4 2 4 2 4 2'''</tt>
| Blackwood
|-
| <tt>'''4 4 6 4 4 4 6'''</tt>
| Mavila
|-
| <tt>'''8 2 8 2 8 2'''</tt>
| Suboctave Augmented
|-
| <tt>'''2 6 2 6 2 6 2 6'''</tt>
| Superoctave Diminished
|-
| <tt>'''4 4 3 7 3 5 3 (7)'''</tt>
| Saba
|-
| <tt>'''5 5 5 3 5 5 5'''</tt>
| Superlydian
|}
|}


Revision as of 03:52, 19 February 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 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 1 4 4 4 1 4 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 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 Nusecond[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 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]
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
7 2 7 2 7 2 2 2 Onydim
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

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

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
dimensionscale.jpg
(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
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
5 3 3 3 3 5 3 3 3 Rothenberg Generalized Diatonic
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)
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
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