Strictly proper 7-tone 31edo scales: Difference between revisions

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Below are listed scales which are [[strictly proper]], in the sense the term is used by music theorist David Rothenberg. The "type" of a scale is defined by the linear temperament supported by 31et in which it has the least span. "Breed type" means it is a tie between miracle and hemiwuerschmidt.
This is a list of 7-note scales in [[31edo]] which are strictly proper with regard to the [[Rothenberg propriety]].
 
The "type" of a scale is defined by the linear temperament supported by 31edo in which it has the least span. "Breed type" means it is a tie between miracle and hemiwuerschmidt.


== Meantone type ==
== Meantone type ==
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! example(s)
! example(s)
|-
|-
| '''<tt>5535553</tt>'''
| '''<tt>5 5 3 5 5 5 3</tt>'''
| Meantone[7]; diatonic scale
| Meantone[7]; diatonic scale
|
|
|-
|-
| '''<tt>5355553</tt>'''
| '''<tt>5 3 5 5 5 5 3</tt>'''
| Melodic minor scale
| Melodic minor scale
|
|
|-
|-
| '''<tt>5355373</tt>'''
| '''<tt>5 3 5 5 3 7 3</tt>'''
| Harmonic minor scale; inverse harmonic major
| Harmonic minor scale; inverse harmonic major
|
|
|-
|-
| '''<tt>5535373</tt>'''
| '''<tt>5 5 3 5 3 7 3</tt>'''
| Harmonic major scale; inverse harmonic minor
| Harmonic major scale; inverse harmonic minor
|
|
|-
|-
| '''<tt>5533555</tt>'''
| '''<tt>5 5 3 3 5 5 5</tt>'''
| Major locrian scale
| Major locrian scale
|
|
|-
|-
| '''<tt>3717355</tt>'''
| '''<tt>3 7 1 7 3 5 5</tt>'''
| Diminished diatonic scale
| Diminished diatonic scale
| [http://chrisvaisvil.com/?p=142 Strange Diatonic] by [[Chris Vaisvil]] [http://micro.soonlabel.com/strange-diatonic/strange-diatonic-1.mp3 play] [http://micro.soonlabel.com/gene_ward_smith/Others/Curley/Zach%20Curley%20-%20Omega%20Centauri.mp3 Omega centauri] by [[Zach Curley]]
| [http://chrisvaisvil.com/?p=142 Strange Diatonic] by [[Chris Vaisvil]] [http://micro.soonlabel.com/strange-diatonic/strange-diatonic-1.mp3 play]<br>[http://micro.soonlabel.com/gene_ward_smith/Others/Curley/Zach%20Curley%20-%20Omega%20Centauri.mp3 Omega centauri]{{dead link}} by [[Zach Curley]]
|-
|-
| '''<tt>5535643</tt>'''
| '''<tt>5 5 3 5 6 4 3</tt>'''
| Enharmonic major; inverse enharmonic minor
| Enharmonic major; inverse enharmonic minor
|
|
|-
|-
| '''<tt>5346535</tt>'''
| '''<tt>5 3 4 6 5 3 5</tt>'''
| Enharmonic minor; inverse enharmonic major
| Enharmonic minor; inverse enharmonic major
|
|
|-
|-
| '''<tt>5535625</tt>'''
| '''<tt>5 5 3 5 6 2 5</tt>'''
| Enharmonic mixolydian
| Enharmonic mixolydian
|
|
|-
|-
| '''<tt>5526535</tt>'''
| '''<tt>5 5 2 6 5 3 5</tt>'''
| Inverse enharmonic mixolydian
| Inverse enharmonic mixolydian
|
|
|-
|-
| '''<tt>5526355</tt>'''
| '''<tt>5 5 2 6 3 5 5</tt>'''
| Enharmonic major-minor
| Enharmonic major-minor
|
|
|-
|-
| '''<tt>5553625</tt>'''
| '''<tt>5 5 5 3 6 2 5</tt>'''
| Inverse enharmonic major-minor
| Inverse enharmonic major-minor
|
|
|-
|-
| '''<tt>6435625</tt>'''
| '''<tt>6 4 3 5 6 2 5</tt>'''
| Major doubleflat; inverse minor doubleflat
| Major doubleflat; inverse minor doubleflat
|
|
|-
|-
| '''<tt>5346526</tt>'''
| '''<tt>5 3 4 6 5 2 6</tt>'''
| Minor doubleflat; inverse major doubleflat
| Minor doubleflat; inverse major doubleflat
|
|
|-
|-
| '''<tt>5553652</tt>'''
| '''<tt>5 5 5 3 6 5 2</tt>'''
| Ping
| Ping
|
|
|-
|-
| '''<tt>3555256</tt>'''
| '''<tt>3 5 5 5 2 5 6</tt>'''
| Inverse ping
| Inverse ping
|
|
|-
|-
| '''<tt>3726355</tt>'''
| '''<tt>3 7 2 6 3 5 5</tt>'''
| Alhijaz; inverse ambika
| Alhijaz; inverse ambika
|
|
|-
|-
| '''<tt>6273553</tt>'''
| '''<tt>6 2 7 3 5 5 3</tt>'''
| Ambika; inverse alhijaz
| Ambika; inverse alhijaz
|
|
|-
|-
| '''<tt>6453652</tt>'''
| '''<tt>6 4 5 3 6 5 2</tt>'''
| Kung; inverse ousak
| Kung; inverse ousak
|
|
|-
|-
| '''<tt>3546256</tt>'''
| '''<tt>3 5 4 6 2 5 6</tt>'''
| Ousak; inverse kung
| Ousak; inverse kung
|
|
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{| class="wikitable"
{| class="wikitable"
|-
|-
| '''<tt>6446272</tt>'''
! schema
! name
|-
| '''<tt>6 4 4 6 2 7 2</tt>'''
| Silver
| Silver
|-
|-
| '''<tt>6444472</tt>'''
| '''<tt>6 4 4 4 4 7 2</tt>'''
| Harmonia
| Harmonia
|-
|-
| '''<tt>4446274</tt>'''
| '''<tt>4 4 4 6 2 7 4</tt>'''
| Inverse harmonia
| Inverse harmonia
|-
|-
| '''<tt>6444562</tt>'''
| '''<tt>6 4 4 4 5 6 2</tt>'''
| Pendragon
| Pendragon
|-
|-
| '''<tt>4626544</tt>'''
| '''<tt>4 6 2 6 5 4 4</tt>'''
| Inverse pendragon
| Inverse pendragon
|-
|-
| '''<tt>6264463</tt>'''
| '''<tt>6 2 6 4 4 6 3</tt>'''
| Hipop
| Hipop
|-
|-
| '''<tt>4626364</tt>'''
| '''<tt>4 6 2 6 3 6 4</tt>'''
| Inverse Hipop
| Inverse Hipop
|-
|-
| '''<tt>4626445</tt>'''
| '''<tt>4 6 2 6 4 4 5</tt>'''
| Malakon
| Malakon
|-
|-
| '''<tt>4626454</tt>'''
| '''<tt>4 6 2 6 4 5 4</tt>'''
| Inverse malakon
| Inverse malakon
|-
|-
| '''<tt>4464526</tt>'''
| '''<tt>4 4 6 4 5 2 6</tt>'''
| Bagpipe
| Bagpipe
|-
|-
| '''<tt>4644625</tt>'''
| '''<tt>4 6 4 4 6 2 5</tt>'''
| Inverse bagpipe
| Inverse bagpipe
|-
|-
| '''<tt>6444625</tt>'''
| '''<tt>6 4 4 4 6 2 5</tt>'''
| Pitu
| Pitu
|-
|-
| '''<tt>6444652</tt>'''
| '''<tt>6 4 4 4 6 5 2</tt>'''
| Inverse pitu
| Inverse pitu
|-
|-
| '''<tt>6444445</tt>'''
| '''<tt>6 4 4 4 4 4 5</tt>'''
| Porch
| Porch
|-
|-
| '''<tt>4446544</tt>'''
| '''<tt>4 4 4 6 5 4 4</tt>'''
| Inverse porch
| Inverse porch
|}
|}
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{| class="wikitable"
{| class="wikitable"
|-
|-
| '''<tt>5436346</tt>'''
! schema
! name
|-
| '''<tt>5 4 3 6 3 4 6</tt>'''
| Subdom scale; inverse superton
| Subdom scale; inverse superton
|-
|-
| '''<tt>5643634</tt>'''
| '''<tt>5 6 4 3 6 3 4</tt>'''
| Superton scale; inverse subdom
| Superton scale; inverse subdom
|-
|-
| '''<tt>5436364</tt>'''
| '''<tt>5 4 3 6 3 6 4</tt>'''
| Nudia; neutral diatonic
| Nudia; neutral diatonic
|-
|-
| '''<tt>5463634</tt>'''
| '''<tt>5 4 6 3 6 3 4</tt>'''
| Inverse nudia
| Inverse nudia
|-
|-
| '''<tt>3636346</tt>'''
| '''<tt>3 6 3 6 3 4 6</tt>'''
| Nurow; Neutral triads in row
| Nurow; Neutral triads in row
|-
|-
| '''<tt>6363643</tt>'''
| '''<tt>6 3 6 3 6 4 3</tt>'''
| Inverse nurow
| Inverse nurow
|}
|}
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{| class="wikitable"
{| class="wikitable"
|-
|-
| '''<tt>4554454</tt>'''
! schema
! name
|-
| '''<tt>4 5 5 4 4 5 4</tt>'''
| Sikah; Rast; Neutral Diatonic Hypolydian
| Sikah; Rast; Neutral Diatonic Hypolydian
|-
|-
| '''<tt>4444555</tt>'''
| '''<tt>4 4 4 4 5 5 5</tt>'''
| Sheimanic
| Sheimanic
|-
|-
| '''<tt>4554445</tt>'''
| '''<tt>4 5 5 4 4 4 5</tt>'''
| Thaiic
| Thaiic
|-
|-
| '''<tt>4544455</tt>'''
| '''<tt>4 5 4 4 4 5 5</tt>'''
| Inverse thaiic
| Inverse thaiic
|-
|-
| '''<tt>4545454</tt>'''
| '''<tt>4 5 4 5 4 5 4</tt>'''
| Mohajira; Neutral Dorian
| Mohajira; Neutral Dorian
|}
|}
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{| class="wikitable"
{| class="wikitable"
|-
|-
| '''<tt>5555515</tt>'''
! schema
! name
|-
| '''<tt>5 5 5 5 5 1 5</tt>'''
| Hemiwuerschmidt/Hemithirds[7]
| Hemiwuerschmidt/Hemithirds[7]
|-
|-
| '''<tt>5544652</tt>'''
| '''<tt>5 5 4 4 6 5 2</tt>'''
| Hemaj; inverse hemin
| Hemaj; inverse hemin
|-
|-
| '''<tt>4455256</tt>'''
| '''<tt>4 4 5 5 2 5 6</tt>'''
| Hemin; inverse hemaj
| Hemin; inverse hemaj
|-
|-
| '''<tt>4525546</tt>'''
| '''<tt>4 5 2 5 5 4 6</tt>'''
| Gypsi; 11/9-10/7-7/4 chord on tonic
| Gypsi; 11/9-10/7-7/4 chord on tonic
|-
|-
| '''<tt>4552546</tt>'''
| '''<tt>4 5 5 2 5 4 6</tt>'''
| Inverse gypsi; 11/9-10/7-7/4 chord on tonic
| Inverse gypsi; 11/9-10/7-7/4 chord on tonic
|-
|-
| '''<tt>5555542</tt>'''
| '''<tt>5 5 5 5 5 4 2</tt>'''
| Leadhole
| Leadhole
|-
|-
| '''<tt>5555524</tt>'''
| '''<tt>5 5 5 5 5 2 4</tt>'''
| Inverse leadhole
| Inverse leadhole
|}
|}
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{| class="wikitable"
{| class="wikitable"
|-
|-
| '''<tt>5553643</tt>'''
! schema
! name
|-
| '''<tt>5 5 5 3 6 4 3</tt>'''
| Lydic
| Lydic
|-
|-
| '''<tt>5553463</tt>'''
| '''<tt>5 5 5 3 4 6 3</tt>'''
| Inverse lydic
| Inverse lydic
|-
|-
| '''<tt>5535463</tt>'''
| '''<tt>5 5 3 5 4 6 3</tt>'''
| Ionic
| Ionic
|-
|-
| '''<tt>5364535</tt>'''
| '''<tt>5 3 6 4 5 3 5</tt>'''
| Aeolic; inverse ionic
| Aeolic; inverse ionic
|-
|-
| '''<tt>4644463</tt>'''
| '''<tt>4 6 4 4 4 6 3</tt>'''
| Quahog
| Quahog
|-
|-
| '''<tt>6444643</tt>'''
| '''<tt>6 4 4 4 6 4 3</tt>'''
| Inverse quahog
| Inverse quahog
|-
|-
| '''<tt>6453643</tt>'''
| '''<tt>6 4 5 3 6 4 3</tt>'''
| Higasi
| Higasi
|-
|-
| '''<tt>4635463</tt>'''
| '''<tt>4 6 3 5 4 6 3</tt>'''
| Inverse higasi
| Inverse higasi
|}
|}
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{| class="wikitable"
{| class="wikitable"
|-
|-
| '''<tt>5364463</tt>'''
! schema
! name
|-
| '''<tt>5 3 6 4 4 6 3</tt>'''
| Orminor
| Orminor
|-
|-
| '''<tt>4644643</tt>'''
| '''<tt>4 6 4 4 6 4 3</tt>'''
| Ormed
| Ormed
|-
|-
| '''<tt>4644364</tt>'''
| '''<tt>4 6 4 4 3 6 4</tt>'''
| Augton
| Augton
|-
|-
| '''<tt>4644634</tt>'''
| '''<tt>4 6 4 4 6 3 4</tt>'''
| Inverse augton
| Inverse augton
|}
|}
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{| class="wikitable"
{| class="wikitable"
|-
|-
| '''<tt>3456265</tt>'''
! schema
! name
|-
| '''<tt>3 4 5 6 2 6 5</tt>'''
| Hemisub
| Hemisub
|-
|-
| '''<tt>4356265</tt>'''
| '''<tt>4 3 5 6 2 6 5</tt>'''
| Inverse hemisub
| Inverse hemisub
|-
|-
| '''<tt>6354535</tt>'''
| '''<tt>6 3 5 4 5 3 5</tt>'''
| Heminewt
| Heminewt
|-
|-
| '''<tt>4536535</tt>'''
| '''<tt>4 5 3 6 5 3 5</tt>'''
| Inverse heminewt
| Inverse heminewt
|}
|}


[[Category:Lists of scales]]
[[Category:7-tone scales| ]]
[[Category:31edo]]
[[Category:31edo]]
[[Category:7-tone]]
[[Category:Listen]]
[[Category:Listen]]
[[Category:Scale]]
[[Category:Theory]]

Revision as of 17:23, 14 August 2021

This is a list of 7-note scales in 31edo which are strictly proper with regard to the Rothenberg propriety.

The "type" of a scale is defined by the linear temperament supported by 31edo in which it has the least span. "Breed type" means it is a tie between miracle and hemiwuerschmidt.

Meantone type

schema name example(s)
5 5 3 5 5 5 3 Meantone[7]; diatonic scale
5 3 5 5 5 5 3 Melodic minor scale
5 3 5 5 3 7 3 Harmonic minor scale; inverse harmonic major
5 5 3 5 3 7 3 Harmonic major scale; inverse harmonic minor
5 5 3 3 5 5 5 Major locrian scale
3 7 1 7 3 5 5 Diminished diatonic scale Strange Diatonic by Chris Vaisvil play
Omega centauri[dead link] by Zach Curley
5 5 3 5 6 4 3 Enharmonic major; inverse enharmonic minor
5 3 4 6 5 3 5 Enharmonic minor; inverse enharmonic major
5 5 3 5 6 2 5 Enharmonic mixolydian
5 5 2 6 5 3 5 Inverse enharmonic mixolydian
5 5 2 6 3 5 5 Enharmonic major-minor
5 5 5 3 6 2 5 Inverse enharmonic major-minor
6 4 3 5 6 2 5 Major doubleflat; inverse minor doubleflat
5 3 4 6 5 2 6 Minor doubleflat; inverse major doubleflat
5 5 5 3 6 5 2 Ping
3 5 5 5 2 5 6 Inverse ping
3 7 2 6 3 5 5 Alhijaz; inverse ambika
6 2 7 3 5 5 3 Ambika; inverse alhijaz
6 4 5 3 6 5 2 Kung; inverse ousak
3 5 4 6 2 5 6 Ousak; inverse kung

Valentine

schema name
6 4 4 6 2 7 2 Silver
6 4 4 4 4 7 2 Harmonia
4 4 4 6 2 7 4 Inverse harmonia
6 4 4 4 5 6 2 Pendragon
4 6 2 6 5 4 4 Inverse pendragon
6 2 6 4 4 6 3 Hipop
4 6 2 6 3 6 4 Inverse Hipop
4 6 2 6 4 4 5 Malakon
4 6 2 6 4 5 4 Inverse malakon
4 4 6 4 5 2 6 Bagpipe
4 6 4 4 6 2 5 Inverse bagpipe
6 4 4 4 6 2 5 Pitu
6 4 4 4 6 5 2 Inverse pitu
6 4 4 4 4 4 5 Porch
4 4 4 6 5 4 4 Inverse porch

Miracle type

schema name
5 4 3 6 3 4 6 Subdom scale; inverse superton
5 6 4 3 6 3 4 Superton scale; inverse subdom
5 4 3 6 3 6 4 Nudia; neutral diatonic
5 4 6 3 6 3 4 Inverse nudia
3 6 3 6 3 4 6 Nurow; Neutral triads in row
6 3 6 3 6 4 3 Inverse nurow

Mohajira type

schema name
4 5 5 4 4 5 4 Sikah; Rast; Neutral Diatonic Hypolydian
4 4 4 4 5 5 5 Sheimanic
4 5 5 4 4 4 5 Thaiic
4 5 4 4 4 5 5 Inverse thaiic
4 5 4 5 4 5 4 Mohajira; Neutral Dorian

Hemiwuerschmidt type

schema name
5 5 5 5 5 1 5 Hemiwuerschmidt/Hemithirds[7]
5 5 4 4 6 5 2 Hemaj; inverse hemin
4 4 5 5 2 5 6 Hemin; inverse hemaj
4 5 2 5 5 4 6 Gypsi; 11/9-10/7-7/4 chord on tonic
4 5 5 2 5 4 6 Inverse gypsi; 11/9-10/7-7/4 chord on tonic
5 5 5 5 5 4 2 Leadhole
5 5 5 5 5 2 4 Inverse leadhole

Mothra type

schema name
5 5 5 3 6 4 3 Lydic
5 5 5 3 4 6 3 Inverse lydic
5 5 3 5 4 6 3 Ionic
5 3 6 4 5 3 5 Aeolic; inverse ionic
4 6 4 4 4 6 3 Quahog
6 4 4 4 6 4 3 Inverse quahog
6 4 5 3 6 4 3 Higasi
4 6 3 5 4 6 3 Inverse higasi

Orwell type

schema name
5 3 6 4 4 6 3 Orminor
4 6 4 4 6 4 3 Ormed
4 6 4 4 3 6 4 Augton
4 6 4 4 6 3 4 Inverse augton

Breed type

schema name
3 4 5 6 2 6 5 Hemisub
4 3 5 6 2 6 5 Inverse hemisub
6 3 5 4 5 3 5 Heminewt
4 5 3 6 5 3 5 Inverse heminewt
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