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

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Below are listed scales which are [http://en.wikipedia.org/wiki/Rothenberg_propriety 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.
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.


===Meantone type===
== Meantone type ==


{| class="wikitable"
{| class="wikitable"
|-
|-
! | schema
! schema
! | name
! name
! | example(s)
! example(s)
|-
|-
| | '''<tt>5535553</tt>'''
| '''<tt>5535553</tt>'''
| | Meantone[7]; diatonic scale
| Meantone[7]; diatonic scale
| |  
|
|-
|-
| | '''<tt>5355553</tt>'''
| '''<tt>5355553</tt>'''
| | Melodic minor scale
| Melodic minor scale
| |  
|
|-
|-
| | '''<tt>5355373</tt>'''
| '''<tt>5355373</tt>'''
| | Harmonic minor scale; inverse harmonic major
| Harmonic minor scale; inverse harmonic major
| |  
|
|-
|-
| | '''<tt>5535373</tt>'''
| '''<tt>5535373</tt>'''
| | Harmonic major scale; inverse harmonic minor
| Harmonic major scale; inverse harmonic minor
| |  
|
|-
|-
| | '''<tt>5533555</tt>'''
| '''<tt>5533555</tt>'''
| | Major locrian scale
| Major locrian scale
| |  
|
|-
|-
| | '''<tt>3717355</tt>'''
| '''<tt>3717355</tt>'''
| | Diminished diatonic scale
| Diminished diatonic scale
| | [http://chrisvaisvil.com/?p=142 Strange Diatonic] by [[Chris_Vaisvil|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|Zach Curley]]
| [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]]
|-
|-
| | '''<tt>5535643</tt>'''
| '''<tt>5535643</tt>'''
| | Enharmonic major; inverse enharmonic minor
| Enharmonic major; inverse enharmonic minor
| |  
|
|-
|-
| | '''<tt>5346535</tt>'''
| '''<tt>5346535</tt>'''
| | Enharmonic minor; inverse enharmonic major
| Enharmonic minor; inverse enharmonic major
| |  
|
|-
|-
| | '''<tt>5535625</tt>'''
| '''<tt>5535625</tt>'''
| | Enharmonic mixolydian
| Enharmonic mixolydian
| |  
|
|-
|-
| | '''<tt>5526535</tt>'''
| '''<tt>5526535</tt>'''
| | Inverse enharmonic mixolydian
| Inverse enharmonic mixolydian
| |  
|
|-
|-
| | '''<tt>5526355</tt>'''
| '''<tt>5526355</tt>'''
| | Enharmonic major-minor
| Enharmonic major-minor
| |  
|
|-
|-
| | '''<tt>5553625</tt>'''
| '''<tt>5553625</tt>'''
| | Inverse enharmonic major-minor
| Inverse enharmonic major-minor
| |  
|
|-
|-
| | '''<tt>6435625</tt>'''
| '''<tt>6435625</tt>'''
| | Major doubleflat; inverse minor doubleflat
| Major doubleflat; inverse minor doubleflat
| |  
|
|-
|-
| | '''<tt>5346526</tt>'''
| '''<tt>5346526</tt>'''
| | Minor doubleflat; inverse major doubleflat
| Minor doubleflat; inverse major doubleflat
| |  
|
|-
|-
| | '''<tt>5553652</tt>'''
| '''<tt>5553652</tt>'''
| | Ping
| Ping
| |  
|
|-
|-
| | '''<tt>3555256</tt>'''
| '''<tt>3555256</tt>'''
| | Inverse ping
| Inverse ping
| |  
|
|-
|-
| | '''<tt>3726355</tt>'''
| '''<tt>3726355</tt>'''
| | Alhijaz; inverse ambika
| Alhijaz; inverse ambika
| |  
|
|-
|-
| | '''<tt>6273553</tt>'''
| '''<tt>6273553</tt>'''
| | Ambika; inverse alhijaz
| Ambika; inverse alhijaz
| |  
|
|-
|-
| | '''<tt>6453652</tt>'''
| '''<tt>6453652</tt>'''
| | Kung; inverse ousak
| Kung; inverse ousak
| |  
|
|-
|-
| | '''<tt>3546256</tt>'''
| '''<tt>3546256</tt>'''
| | Ousak; inverse kung
| Ousak; inverse kung
| |  
|
|}
|}


===Valentine===
== Valentine ==


{| class="wikitable"
{| class="wikitable"
|-
|-
| | '''<tt>6446272</tt>'''
| '''<tt>6446272</tt>'''
| | Silver
| Silver
|-
|-
| | '''<tt>6444472</tt>'''
| '''<tt>6444472</tt>'''
| | Harmonia
| Harmonia
|-
|-
| | '''<tt>4446274</tt>'''
| '''<tt>4446274</tt>'''
| | Inverse harmonia
| Inverse harmonia
|-
|-
| | '''<tt>6444562</tt>'''
| '''<tt>6444562</tt>'''
| | Pendragon
| Pendragon
|-
|-
| | '''<tt>4626544</tt>'''
| '''<tt>4626544</tt>'''
| | Inverse pendragon
| Inverse pendragon
|-
|-
| | '''<tt>6264463</tt>'''
| '''<tt>6264463</tt>'''
| | Hipop
| Hipop
|-
|-
| | '''<tt>4626364</tt>'''
| '''<tt>4626364</tt>'''
| | Inverse Hipop
| Inverse Hipop
|-
|-
| | '''<tt>4626445</tt>'''
| '''<tt>4626445</tt>'''
| | Malakon
| Malakon
|-
|-
| | '''<tt>4626454</tt>'''
| '''<tt>4626454</tt>'''
| | Inverse malakon
| Inverse malakon
|-
|-
| | '''<tt>4464526</tt>'''
| '''<tt>4464526</tt>'''
| | Bagpipe
| Bagpipe
|-
|-
| | '''<tt>4644625</tt>'''
| '''<tt>4644625</tt>'''
| | Inverse bagpipe
| Inverse bagpipe
|-
|-
| | '''<tt>6444625</tt>'''
| '''<tt>6444625</tt>'''
| | Pitu
| Pitu
|-
|-
| | '''<tt>6444652</tt>'''
| '''<tt>6444652</tt>'''
| | Inverse pitu
| Inverse pitu
|-
|-
| | '''<tt>6444445</tt>'''
| '''<tt>6444445</tt>'''
| | Porch
| Porch
|-
|-
| | '''<tt>4446544</tt>'''
| '''<tt>4446544</tt>'''
| | Inverse porch
| Inverse porch
|}
|}


===Miracle type===
== Miracle type ==


{| class="wikitable"
{| class="wikitable"
|-
|-
| | '''<tt>5436346</tt>'''
| '''<tt>5436346</tt>'''
| | Subdom scale; inverse superton
| Subdom scale; inverse superton
|-
|-
| | '''<tt>5643634</tt>'''
| '''<tt>5643634</tt>'''
| | Superton scale; inverse subdom
| Superton scale; inverse subdom
|-
|-
| | '''<tt>5436364</tt>'''
| '''<tt>5436364</tt>'''
| | Nudia; neutral diatonic
| Nudia; neutral diatonic
|-
|-
| | '''<tt>5463634</tt>'''
| '''<tt>5463634</tt>'''
| | Inverse nudia
| Inverse nudia
|-
|-
| | '''<tt>3636346</tt>'''
| '''<tt>3636346</tt>'''
| | Nurow; Neutral triads in row
| Nurow; Neutral triads in row
|-
|-
| | '''<tt>6363643</tt>'''
| '''<tt>6363643</tt>'''
| | Inverse nurow
| Inverse nurow
|}
|}


===Mohajira type===
== Mohajira type ==


{| class="wikitable"
{| class="wikitable"
|-
|-
| | '''<tt>4554454</tt>'''
| '''<tt>4554454</tt>'''
| | Sikah; Rast; Neutral Diatonic Hypolydian
| Sikah; Rast; Neutral Diatonic Hypolydian
|-
|-
| | '''<tt>4444555</tt>'''
| '''<tt>4444555</tt>'''
| | Sheimanic
| Sheimanic
|-
|-
| | '''<tt>4554445</tt>'''
| '''<tt>4554445</tt>'''
| | Thaiic
| Thaiic
|-
|-
| | '''<tt>4544455</tt>'''
| '''<tt>4544455</tt>'''
| | Inverse thaiic
| Inverse thaiic
|-
|-
| | '''<tt>4545454</tt>'''
| '''<tt>4545454</tt>'''
| | Mohajira; Neutral Dorian
| Mohajira; Neutral Dorian
|}
|}


===Hemiwuerschmidt type===
== Hemiwuerschmidt type ==


{| class="wikitable"
{| class="wikitable"
|-
|-
| | '''<tt>5555515</tt>'''
| '''<tt>5555515</tt>'''
| | Hemiwuerschmidt/Hemithirds[7]
| Hemiwuerschmidt/Hemithirds[7]
|-
|-
| | '''<tt>5544652</tt>'''
| '''<tt>5544652</tt>'''
| | Hemaj; inverse hemin
| Hemaj; inverse hemin
|-
|-
| | '''<tt>4455256</tt>'''
| '''<tt>4455256</tt>'''
| | Hemin; inverse hemaj
| Hemin; inverse hemaj
|-
|-
| | '''<tt>4525546</tt>'''
| '''<tt>4525546</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>4552546</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>5555542</tt>'''
| | Leadhole
| Leadhole
|-
|-
| | '''<tt>5555524</tt>'''
| '''<tt>5555524</tt>'''
| | Inverse leadhole
| Inverse leadhole
|}
|}


===Mothra type===
== Mothra type ==


{| class="wikitable"
{| class="wikitable"
|-
|-
| | '''<tt>5553643</tt>'''
| '''<tt>5553643</tt>'''
| | Lydic
| Lydic
|-
|-
| | '''<tt>5553463</tt>'''
| '''<tt>5553463</tt>'''
| | Inverse lydic
| Inverse lydic
|-
|-
| | '''<tt>5535463</tt>'''
| '''<tt>5535463</tt>'''
| | Ionic
| Ionic
|-
|-
| | '''<tt>5364535</tt>'''
| '''<tt>5364535</tt>'''
| | Aeolic; inverse ionic
| Aeolic; inverse ionic
|-
|-
| | '''<tt>4644463</tt>'''
| '''<tt>4644463</tt>'''
| | Quahog
| Quahog
|-
|-
| | '''<tt>6444643</tt>'''
| '''<tt>6444643</tt>'''
| | Inverse quahog
| Inverse quahog
|-
|-
| | '''<tt>6453643</tt>'''
| '''<tt>6453643</tt>'''
| | Higasi
| Higasi
|-
|-
| | '''<tt>4635463</tt>'''
| '''<tt>4635463</tt>'''
| | Inverse higasi
| Inverse higasi
|}
|}


===Orwell type===
== Orwell type ==


{| class="wikitable"
{| class="wikitable"
|-
|-
| | '''<tt>5364463</tt>'''
| '''<tt>5364463</tt>'''
| | Orminor
| Orminor
|-
|-
| | '''<tt>4644643</tt>'''
| '''<tt>4644643</tt>'''
| | Ormed
| Ormed
|-
|-
| | '''<tt>4644364</tt>'''
| '''<tt>4644364</tt>'''
| | Augton
| Augton
|-
|-
| | '''<tt>4644634</tt>'''
| '''<tt>4644634</tt>'''
| | Inverse augton
| Inverse augton
|}
|}


===Breed type===
== Breed type ==


{| class="wikitable"
{| class="wikitable"
|-
|-
| | '''<tt>3456265</tt>'''
| '''<tt>3456265</tt>'''
| | Hemisub
| Hemisub
|-
|-
| | '''<tt>4356265</tt>'''
| '''<tt>4356265</tt>'''
| | Inverse hemisub
| Inverse hemisub
|-
|-
| | '''<tt>6354535</tt>'''
| '''<tt>6354535</tt>'''
| | Heminewt
| Heminewt
|-
|-
| | '''<tt>4536535</tt>'''
| '''<tt>4536535</tt>'''
| | Inverse heminewt
| Inverse heminewt
|}
|}


{| class="wikitable"
|-
| | 
| |
|}
[[Category:31edo]]
[[Category:31edo]]
[[Category:7-tone]]
[[Category:7-tone]]
[[Category:listen]]
[[Category:Listen]]
[[Category:scale]]
[[Category:Scale]]
[[Category:theory]]
[[Category:Theory]]

Revision as of 00:17, 2 January 2021

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.

Meantone type

schema name example(s)
5535553 Meantone[7]; diatonic scale
5355553 Melodic minor scale
5355373 Harmonic minor scale; inverse harmonic major
5535373 Harmonic major scale; inverse harmonic minor
5533555 Major locrian scale
3717355 Diminished diatonic scale Strange Diatonic by Chris Vaisvil play Omega centauri by Zach Curley
5535643 Enharmonic major; inverse enharmonic minor
5346535 Enharmonic minor; inverse enharmonic major
5535625 Enharmonic mixolydian
5526535 Inverse enharmonic mixolydian
5526355 Enharmonic major-minor
5553625 Inverse enharmonic major-minor
6435625 Major doubleflat; inverse minor doubleflat
5346526 Minor doubleflat; inverse major doubleflat
5553652 Ping
3555256 Inverse ping
3726355 Alhijaz; inverse ambika
6273553 Ambika; inverse alhijaz
6453652 Kung; inverse ousak
3546256 Ousak; inverse kung

Valentine

6446272 Silver
6444472 Harmonia
4446274 Inverse harmonia
6444562 Pendragon
4626544 Inverse pendragon
6264463 Hipop
4626364 Inverse Hipop
4626445 Malakon
4626454 Inverse malakon
4464526 Bagpipe
4644625 Inverse bagpipe
6444625 Pitu
6444652 Inverse pitu
6444445 Porch
4446544 Inverse porch

Miracle type

5436346 Subdom scale; inverse superton
5643634 Superton scale; inverse subdom
5436364 Nudia; neutral diatonic
5463634 Inverse nudia
3636346 Nurow; Neutral triads in row
6363643 Inverse nurow

Mohajira type

4554454 Sikah; Rast; Neutral Diatonic Hypolydian
4444555 Sheimanic
4554445 Thaiic
4544455 Inverse thaiic
4545454 Mohajira; Neutral Dorian

Hemiwuerschmidt type

5555515 Hemiwuerschmidt/Hemithirds[7]
5544652 Hemaj; inverse hemin
4455256 Hemin; inverse hemaj
4525546 Gypsi; 11/9-10/7-7/4 chord on tonic
4552546 Inverse gypsi; 11/9-10/7-7/4 chord on tonic
5555542 Leadhole
5555524 Inverse leadhole

Mothra type

5553643 Lydic
5553463 Inverse lydic
5535463 Ionic
5364535 Aeolic; inverse ionic
4644463 Quahog
6444643 Inverse quahog
6453643 Higasi
4635463 Inverse higasi

Orwell type

5364463 Orminor
4644643 Ormed
4644364 Augton
4644634 Inverse augton

Breed type

3456265 Hemisub
4356265 Inverse hemisub
6354535 Heminewt
4536535 Inverse heminewt
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