31edo modes: Difference between revisions

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Taken originally from Scala, Manuel Op De Coul, this is a user-editable list of modes of [[31edo|31edo]]. The numbers indicate successive intervals, in dieses. Strictly proper scales of seven notes can be found [[Strictly_proper_7-note_31edo_scales|here]].
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-note 31edo scales]].
 
== Nothing special ==


=Nothing special=
Or, to some, the only important thing.
Or, to some, the only important thing.


{| class="wikitable"
{| class="wikitable"
|-
|-
| | <tt>'''2 3 3 2 3 2 3 2 3 3 2 3'''</tt>
| <tt>'''2 3 3 2 3 2 3 2 3 3 2 3'''</tt>
| | Meantone Chromatic (53/220-comma)
| Meantone Chromatic (53/220-comma)
|-
|-
| | <tt>'''5 5 3 5 5 5 3'''</tt>
| <tt>'''5 5 3 5 5 5 3'''</tt>
| | Thirty-one tone Major, Intense Diatonic Lydian, M.Ionian
| Thirty-one tone Major, Intense Diatonic Lydian, M.Ionian
|-
|-
| | <tt>'''5 3 5 5 3 5 5'''</tt>
| <tt>'''5 3 5 5 3 5 5'''</tt>
| | Thirty-one tone Natural Minor, Intense Diatonic Hypodorian, Aeolian
| Thirty-one tone Natural Minor, Intense Diatonic Hypodorian, Aeolian
|-
|-
| | <tt>'''5 3 5 5 5 5 3'''</tt>
| <tt>'''5 3 5 5 5 5 3'''</tt>
| | Thirty-one tone Melodic Minor
| Thirty-one tone Melodic Minor
|-
|-
| | <tt>'''5 3 5 5 3 7 3'''</tt>
| <tt>'''5 3 5 5 3 7 3'''</tt>
| | Thirty-one tone Harmonic Minor
| Thirty-one tone Harmonic Minor
|-
|-
| | <tt>'''5 5 3 5 3 7 3'''</tt>
| <tt>'''5 5 3 5 3 7 3'''</tt>
| | Thirty-one tone Harmonic Major
| Thirty-one tone Harmonic Major
|-
|-
| | <tt>'''5 5 3 5 3 5 5'''</tt>
| <tt>'''5 5 3 5 3 5 5'''</tt>
| | Thirty-one tone Major-Minor
| Thirty-one tone Major-Minor
|-
|-
| | <tt>'''5 2 6 5 2 5 6'''</tt>
| <tt>'''5 2 6 5 2 5 6'''</tt>
| | "Septimal" Natural Minor
| "Septimal" Natural Minor
|}
|}


=Euler-Fokker genera=
== Euler-Fokker genera ==


Boxy shapes from the [3,5,7] lattice.
Boxy shapes from the [3,5,7] lattice.
Line 37: Line 38:
{| class="wikitable"
{| class="wikitable"
|-
|-
| | <tt>'''5 8 5 13'''</tt>
| <tt>'''5 8 5 13'''</tt>
| | Genus primum
| Genus primum
|-
|-
| | <tt>'''10 3 5 5 5 3'''</tt>
| <tt>'''10 3 5 5 5 3'''</tt>
| | Genus secundum
| Genus secundum
|-
|-
| | <tt>'''8 2 8 3 7 3'''</tt>
| <tt>'''8 2 8 3 7 3'''</tt>
| | Genus tertium
| Genus tertium
|-
|-
| | <tt>'''10 10 10 1'''</tt>
| <tt>'''10 10 10 1'''</tt>
| | Genus quartum
| Genus quartum
|-
|-
| | <tt>'''5 7 6 7 5 1'''</tt>
| <tt>'''5 7 6 7 5 1'''</tt>
| | Genus quintum
| Genus quintum
|-
|-
| | <tt>'''4 6 2 6 4 3 3 3'''</tt>
| <tt>'''4 6 2 6 4 3 3 3'''</tt>
| | Genus sextum
| Genus sextum
|-
|-
| | <tt>'''4 6 5 6 4 6'''</tt>
| <tt>'''4 6 5 6 4 6'''</tt>
| | Genus septimum
| Genus septimum
|-
|-
| | <tt>'''6 6 6 1 6 6'''</tt>
| <tt>'''6 6 6 1 6 6'''</tt>
| | Genus octavum
| Genus octavum
|-
|-
| | <tt>'''4 6 9 6 4 2'''</tt>
| <tt>'''4 6 9 6 4 2'''</tt>
| | Genus nonum
| Genus nonum
|-
|-
| | <tt>'''13 6 6 6'''</tt>
| <tt>'''13 6 6 6'''</tt>
| | Genus decimum
| Genus decimum
|-
|-
| | <tt>'''5 5 3 5 5 3 2 3'''</tt>
| <tt>'''5 5 3 5 5 3 2 3'''</tt>
| | Genus diatonicum
| Genus diatonicum
|-
|-
| | <tt>'''3 5 2 3 5 3 2 5 3'''</tt>
| <tt>'''3 5 2 3 5 3 2 5 3'''</tt>
| | Genus chromaticum
| Genus chromaticum
|-
|-
| | <tt>'''5 5 2 1 5 5 2 3 3'''</tt>
| <tt>'''5 5 2 1 5 5 2 3 3'''</tt>
| | Genus diatonicum cum septimis
| Genus diatonicum cum septimis
|-
|-
| | <tt>'''3 4 3 3 2 1 4 1 4 1 2 3'''</tt>
| <tt>'''3 4 3 3 2 1 4 1 4 1 2 3'''</tt>
| | Genus enharmonicum vocale
| Genus enharmonicum vocale
|-
|-
| | <tt>'''2 2 4 2 2 3 3 3 1 3 3 3'''</tt>
| <tt>'''2 2 4 2 2 3 3 3 1 3 3 3'''</tt>
| | Genus enharmonicum instrumentale
| Genus enharmonicum instrumentale
|-
|-
| | <tt>'''3 2 3 2 3 2 3 3 2 3 2 3'''</tt>
| <tt>'''3 2 3 2 3 2 3 3 2 3 2 3'''</tt>
| | Genus diatonico-chromaticum
| Genus diatonico-chromaticum
|-
|-
| | <tt>'''5 2 1 2 5 3 2 1 4 1 2 3'''</tt>
| <tt>'''5 2 1 2 5 3 2 1 4 1 2 3'''</tt>
| | Genus bichromaticum
| Genus bichromaticum
|-
|-
| | <tt>'''3 1 2 4 2 4 2 4 2 1 3 3'''</tt>
| <tt>'''3 1 2 4 2 4 2 4 2 1 3 3'''</tt>
| | Genus [3577] (Joel Mandelbaum ''Andante cantabile'')
| Genus [3577] (Joel Mandelbaum ''Andante cantabile'')
|}
|}


=Greek/tetrachord modes=
== Greek/tetrachord modes ==


{| class="wikitable"
{| class="wikitable"
|-
|-
| | <tt>'''4 4 5 4 4 5 5'''</tt>
| <tt>'''4 4 5 4 4 5 5'''</tt>
| | Neutral Diatonic Mixolydian
| Neutral Diatonic Mixolydian
|-
|-
| | <tt>'''4 5 4 4 5 5 4'''</tt>
| <tt>'''4 5 4 4 5 5 4'''</tt>
| | Neutral Diatonic Lydian
| Neutral Diatonic Lydian
|-
|-
| | <tt>'''5 4 4 5 5 4 4'''</tt>
| <tt>'''5 4 4 5 5 4 4'''</tt>
| | Neutral Diatonic Phrygian
| Neutral Diatonic Phrygian
|-
|-
| | <tt>'''4 4 5 5 4 4 5'''</tt>
| <tt>'''4 4 5 5 4 4 5'''</tt>
| | Neutral Diatonic Dorian
| Neutral Diatonic Dorian
|-
|-
| | <tt>'''4 5 5 4 4 5 4'''</tt>
| <tt>'''4 5 5 4 4 5 4'''</tt>
| | Neutral Diatonic Hypolydian
| Neutral Diatonic Hypolydian
|-
|-
| | <tt>'''5 5 4 4 5 4 4'''</tt>
| <tt>'''5 5 4 4 5 4 4'''</tt>
| | Neutral Diatonic Hypophrygian
| Neutral Diatonic Hypophrygian
|-
|-
| | <tt>'''5 4 4 5 4 4 5'''</tt>
| <tt>'''5 4 4 5 4 4 5'''</tt>
| | Neutral Diatonic Hypodorian
| Neutral Diatonic Hypodorian
|-
|-
| | <tt>'''4 5 4 4 5 4 5'''</tt>
| <tt>'''4 5 4 4 5 4 5'''</tt>
| | Neutral Mixolydian
| Neutral Mixolydian
|-
|-
| | <tt>'''5 4 4 5 4 5 4'''</tt>
| <tt>'''5 4 4 5 4 5 4'''</tt>
| | Neutral Lydian
| Neutral Lydian
|-
|-
| | <tt>'''4 4 5 4 5 4 5'''</tt>
| <tt>'''4 4 5 4 5 4 5'''</tt>
| | Neutral Phrygian
| Neutral Phrygian
|-
|-
| | <tt>'''4 5 4 5 4 5 4'''</tt>
| <tt>'''4 5 4 5 4 5 4'''</tt>
| | Neutral Dorian
| Neutral Dorian
|-
|-
| | <tt>'''5 4 5 4 5 4 4'''</tt>
| <tt>'''5 4 5 4 5 4 4'''</tt>
| | Neutral Hypolydian
| Neutral Hypolydian
|-
|-
| | <tt>'''4 5 4 5 4 4 5'''</tt>
| <tt>'''4 5 4 5 4 4 5'''</tt>
| | Neutral Hypophrygian
| Neutral Hypophrygian
|-
|-
| | <tt>'''5 4 5 4 4 5 4'''</tt>
| <tt>'''5 4 5 4 4 5 4'''</tt>
| | Neutral Hypodorian
| Neutral Hypodorian
|-
|-
| | <tt>'''2 2 9 2 2 9 5'''</tt>
| <tt>'''2 2 9 2 2 9 5'''</tt>
| | Hemiolic Chromatic Mixolydian
| Hemiolic Chromatic Mixolydian
|-
|-
| | <tt>'''2 9 2 2 9 5 2'''</tt>
| <tt>'''2 9 2 2 9 5 2'''</tt>
| | Hemiolic Chromatic Lydian
| Hemiolic Chromatic Lydian
|-
|-
| | <tt>'''9 2 2 9 5 2 2'''</tt>
| <tt>'''9 2 2 9 5 2 2'''</tt>
| | Hemiolic Chromatic Phrygian
| Hemiolic Chromatic Phrygian
|-
|-
| | <tt>'''2 2 9 5 2 2 9'''</tt>
| <tt>'''2 2 9 5 2 2 9'''</tt>
| | Hemiolic Chromatic Dorian
| Hemiolic Chromatic Dorian
|-
|-
| | <tt>'''2 9 5 2 2 9 2'''</tt>
| <tt>'''2 9 5 2 2 9 2'''</tt>
| | Hemiolic Chromatic Hypolydian
| Hemiolic Chromatic Hypolydian
|-
|-
| | <tt>'''9 5 2 2 9 2 2'''</tt>
| <tt>'''9 5 2 2 9 2 2'''</tt>
| | Hemiolic Chromatic Hypophrygian
| Hemiolic Chromatic Hypophrygian
|-
|-
| | <tt>'''5 2 2 9 2 2 9'''</tt>
| <tt>'''5 2 2 9 2 2 9'''</tt>
| | Hemiolic Chromatic Hypodorian
| Hemiolic Chromatic Hypodorian
|-
|-
| | <tt>'''2 3 8 2 3 8 5'''</tt>
| <tt>'''2 3 8 2 3 8 5'''</tt>
| | Ratio 2:3 Chromatic Mixolydian
| Ratio 2:3 Chromatic Mixolydian
|-
|-
| | <tt>'''3 8 2 3 8 5 2'''</tt>
| <tt>'''3 8 2 3 8 5 2'''</tt>
| | Ratio 2:3 Chromatic Lydian
| Ratio 2:3 Chromatic Lydian
|-
|-
| | <tt>'''8 2 3 8 5 2 3'''</tt>
| <tt>'''8 2 3 8 5 2 3'''</tt>
| | Ratio 2:3 Chromatic Phrygian
| Ratio 2:3 Chromatic Phrygian
|-
|-
| | <tt>'''2 3 8 5 2 3 8'''</tt>
| <tt>'''2 3 8 5 2 3 8'''</tt>
| | Ratio 2:3 Chromatic Dorian
| Ratio 2:3 Chromatic Dorian
|-
|-
| | <tt>'''3 8 5 2 3 8 2'''</tt>
| <tt>'''3 8 5 2 3 8 2'''</tt>
| | Ratio 2:3 Chromatic Hypolydian
| Ratio 2:3 Chromatic Hypolydian
|-
|-
| | <tt>'''8 5 2 3 8 2 3'''</tt>
| <tt>'''8 5 2 3 8 2 3'''</tt>
| | Ratio 2:3 Chromatic Hypophrygian
| Ratio 2:3 Chromatic Hypophrygian
|-
|-
| | <tt>'''5 2 3 8 2 3 8'''</tt>
| <tt>'''5 2 3 8 2 3 8'''</tt>
| | Ratio 2:3 Chromatic Hypodorian
| Ratio 2:3 Chromatic Hypodorian
|-
|-
| | <tt>'''3 5 5 3 5 5 5'''</tt>
| <tt>'''3 5 5 3 5 5 5'''</tt>
| | Intense Diatonic Mixolydian, M.Locrian
| Intense Diatonic Mixolydian, M.Locrian
|-
|-
| | <tt>'''5 3 5 5 5 3 5'''</tt>
| <tt>'''5 3 5 5 5 3 5'''</tt>
| | Intense Diatonic Phrygian, M.Dorian
| Intense Diatonic Phrygian, M.Dorian
|-
|-
| | <tt>'''3 5 5 5 3 5 5'''</tt>
| <tt>'''3 5 5 5 3 5 5'''</tt>
| | Intense Diatonic Dorian, M.Phrygian
| Intense Diatonic Dorian, M.Phrygian
|-
|-
| | <tt>'''5 5 5 3 5 5 3'''</tt>
| <tt>'''5 5 5 3 5 5 3'''</tt>
| | Intense Diatonic Hypolydian, M.Lydian
| Intense Diatonic Hypolydian, M.Lydian
|-
|-
| | <tt>'''5 5 3 5 5 3 5'''</tt>
| <tt>'''5 5 3 5 5 3 5'''</tt>
| | Intense Diatonic Hypophrygian, M.Mixolydian
| Intense Diatonic Hypophrygian, M.Mixolydian
|-
|-
| | <tt>'''2 5 6 2 5 6 5'''</tt>
| <tt>'''2 5 6 2 5 6 5'''</tt>
| | Soft Diatonic Mixolydian
| Soft Diatonic Mixolydian
|-
|-
| | <tt>'''5 6 2 5 6 5 2'''</tt>
| <tt>'''5 6 2 5 6 5 2'''</tt>
| | Soft Diatonic Lydian
| Soft Diatonic Lydian
|-
|-
| | <tt>'''6 2 5 6 5 2 5'''</tt>
| <tt>'''6 2 5 6 5 2 5'''</tt>
| | Soft Diatonic Phrygian
| Soft Diatonic Phrygian
|-
|-
| | <tt>'''2 5 6 5 2 5 6'''</tt>
| <tt>'''2 5 6 5 2 5 6'''</tt>
| | Soft Diatonic Dorian
| Soft Diatonic Dorian
|-
|-
| | <tt>'''5 6 5 2 5 6 2'''</tt>
| <tt>'''5 6 5 2 5 6 2'''</tt>
| | Soft Diatonic Hypolydian
| Soft Diatonic Hypolydian
|-
|-
| | <tt>'''6 5 2 5 6 2 5'''</tt>
| <tt>'''6 5 2 5 6 2 5'''</tt>
| | Soft Diatonic Hypophrygian
| Soft Diatonic Hypophrygian
|-
|-
| | <tt>'''5 2 5 6 2 5 6'''</tt>
| <tt>'''5 2 5 6 2 5 6'''</tt>
| | Soft Diatonic Hypodorian
| Soft Diatonic Hypodorian
|-
|-
| | <tt>'''1 2 10 1 2 10 5'''</tt>
| <tt>'''1 2 10 1 2 10 5'''</tt>
| | Enharmonic Mixolydian
| Enharmonic Mixolydian
|-
|-
| | <tt>'''2 10 1 2 10 5 1'''</tt>
| <tt>'''2 10 1 2 10 5 1'''</tt>
| | Enharmonic Lydian
| Enharmonic Lydian
|-
|-
| | <tt>'''10 1 2 10 5 1 2'''</tt>
| <tt>'''10 1 2 10 5 1 2'''</tt>
| | Enharmonic Phrygian
| Enharmonic Phrygian
|-
|-
| | <tt>'''1 2 10 5 1 2 10'''</tt>
| <tt>'''1 2 10 5 1 2 10'''</tt>
| | Enharmonic Dorian
| Enharmonic Dorian
|-
|-
| | <tt>'''2 10 5 1 2 10 1'''</tt>
| <tt>'''2 10 5 1 2 10 1'''</tt>
| | Enharmonic Hypolydian
| Enharmonic Hypolydian
|-
|-
| | <tt>'''10 5 1 2 10 1 2'''</tt>
| <tt>'''10 5 1 2 10 1 2'''</tt>
| | Enharmonic Hypophrygian
| Enharmonic Hypophrygian
|-
|-
| | <tt>'''5 1 2 10 1 2 10'''</tt>
| <tt>'''5 1 2 10 1 2 10'''</tt>
| | Enharmonic Hypodorian
| Enharmonic Hypodorian
|}
|}


=Of particular [[interscalar|interscalar]] interest=
== Of particular [[interscalar]] interest ==


{| class="wikitable"
{| class="wikitable"
|-
|-
| | <tt>'''6 6 7 6 6'''</tt>
| <tt>'''6 6 7 6 6'''</tt>
| | Quasi-equal Pentatonic
| Quasi-equal Pentatonic
|-
|-
| | <tt>'''3 3 2 3 3 3 3 3 2 3 3'''</tt>
| <tt>'''3 3 2 3 3 3 3 3 2 3 3'''</tt>
| | near [[11edo|11edo]]
| near [[11edo|11edo]]
|}
|}


=Miscellaneous=
== Miscellaneous ==


{| class="wikitable"
{| 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>
| | Fokker 12-tone
| Fokker 12-tone
|-
|-
| | <tt>'''5 3 5 3 5 2 5 3'''</tt>
| <tt>'''5 3 5 3 5 2 5 3'''</tt>
| | Modus conjunctus
| Modus conjunctus
|-
|-
| | <tt>'''3 5 2 5 3 5 3 5'''</tt>
| <tt>'''3 5 2 5 3 5 3 5'''</tt>
| | Octatonic
| Octatonic
|-
|-
| | <tt>'''3 3 4 3 5 3 4 3 3'''</tt>
| <tt>'''3 3 4 3 5 3 4 3 3'''</tt>
| | Hahn symmetric pentachordal
| Hahn symmetric pentachordal
|-
|-
| | <tt>'''3 4 3 3 5 3 4 3 3'''</tt>
| <tt>'''3 4 3 3 5 3 4 3 3'''</tt>
| | Hahn pentachordal
| Hahn pentachordal
|-
|-
| | <tt>'''4 4 2 5 3 3 4 3 3'''</tt>
| <tt>'''4 4 2 5 3 3 4 3 3'''</tt>
| | Hahn Nonatonic
| Hahn Nonatonic
|-
|-
| | <tt>'''5 3 3 3 3 5 3 3 3'''</tt>
| <tt>'''5 3 3 3 3 5 3 3 3'''</tt>
| | Rothenberg Generalized Diatonic
| Rothenberg Generalized Diatonic
|-
|-
| | <tt>'''(5) 3 1 4 (5) (5)'''</tt>
| <tt>'''(5) 3 1 4 (5) (5)'''</tt> <br> <tt>'''3 1 4'''</tt>
 
| Michael Sheiman's "Dimension" scale (Maqam Rast mixed with Meantone Diatonic...lattice (ratio/chord map) available below <br> [[File:dimensionscale.jpg|alt=dimensionscale.jpg|512x197px|dimensionscale.jpg]]
<tt>'''3 1 4'''</tt>
| | Michael Sheiman's "Dimension" scale (Maqam Rast mixed with Meantone Diatonic...lattice (ratio/chord map) available below
 
[[File:dimensionscale.jpg|alt=dimensionscale.jpg|512x197px|dimensionscale.jpg]]
|-
|-
| | <tt>'''(3 2)3 1 4 (3 2)(3 2)'''</tt>
| <tt>'''(3 2)3 1 4 (3 2)(3 2)'''</tt> <br> <tt>'''3 1 4'''</tt>
 
| 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)
<tt>'''3 1 4'''</tt>
| | 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)
|}
|}


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


{| class="wikitable"
{| class="wikitable"
|-
|-
| | <tt>'''4 5 4 5 4 5 4'''</tt>
| <tt>'''4 5 4 5 4 5 4'''</tt>
| | Neutral scale 7-note
| Neutral scale 7-note
|-
|-
| | <tt>'''4 1 4 4 1 4 4 4 1 4'''</tt>
| <tt>'''4 1 4 4 1 4 4 4 1 4'''</tt>
| | Neutral scale 10-note
| Neutral scale 10-note
|-
|-
| | <tt>'''4 1 4 4 4 1 4 4 1 4'''</tt>
| <tt>'''4 1 4 4 4 1 4 4 1 4'''</tt>
| | Breed 10-tone
| Breed 10-tone
|-
|-
| | <tt>'''4 3 4 3 4 3 4 3 3'''</tt>
| <tt>'''4 3 4 3 4 3 4 3 3'''</tt>
| | Orwell[9]
| Orwell[9]
|-
|-
| | <tt>'''5 1 5 1 5 1 5 1 5 1 1'''</tt>
| <tt>'''5 1 5 1 5 1 5 1 5 1 1'''</tt>
| | de Vries 11-tone
| de Vries 11-tone
|-
|-
| | <tt>'''3 1 3 1 3 1 3 1 3 1 3 1 3 1 3'''</tt>
| <tt>'''3 1 3 1 3 1 3 1 3 1 3 1 3 1 3'''</tt>
| | Pseudo-Porcupine 15-note
| Pseudo-Porcupine 15-note
|-
|-
| | <tt>'''1 7 1 2 1 7 1 2 1 7 1'''</tt>
| <tt>'''1 7 1 2 1 7 1 2 1 7 1'''</tt>
| | Nested Bees
| Nested Bees
|-
|-
| | <tt>'''4 2 4 2 4 2 4 3 3 3'''</tt>
| <tt>'''4 2 4 2 4 2 4 3 3 3'''</tt>
| | Lumma Decatonic
| Lumma Decatonic
|-
|-
| | <tt>'''2 5 2 2 5 2 2 2 5 2 2'''</tt>
| <tt>'''2 5 2 2 5 2 2 2 5 2 2'''</tt>
| | Secor/Barton no-fives
| Secor/Barton no-fives
|}
|}
[[Category:31edo]]
[[Category:31edo]]
[[Category:modes]]
[[Category:Modes]]

Revision as of 00:38, 2 January 2021

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-note 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

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

Miscellaneous

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
(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)

MOS and Cradle MOS

4 5 4 5 4 5 4 Neutral scale 7-note
4 1 4 4 1 4 4 4 1 4 Neutral scale 10-note
4 1 4 4 4 1 4 4 1 4 Breed 10-tone
4 3 4 3 4 3 4 3 3 Orwell[9]
5 1 5 1 5 1 5 1 5 1 1 de Vries 11-tone
3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 Pseudo-Porcupine 15-note
1 7 1 2 1 7 1 2 1 7 1 Nested Bees
4 2 4 2 4 2 4 3 3 3 Lumma Decatonic
2 5 2 2 5 2 2 2 5 2 2 Secor/Barton no-fives
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