Xenharmonic Wiki

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

← Older edit
VisualWikitext
Wikispaces>FREEZE
No edit summary
Sintel (talk | contribs)
autopatrolled, emailconfirmed
1,547 edits
use 'step pattern' as column name
 
(7 intermediate revisions by 5 users not shown)
Line 1: Line 1:
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.
This is a list of [[:Category:7-tone scales|7-tone]] scales in [[31edo]] which are strictly proper with regard to the [[Rothenberg propriety]].


===Meantone type===
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 ==


{| class="wikitable"
{| class="wikitable"
|-
|-
! | schema
! step pattern
! | name
! name
! | 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|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]<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
| |  
|
|}
|}


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


{| class="wikitable"
{| class="wikitable"
|-
|-
| | '''<tt>6446272</tt>'''
! schema
| | Silver
! name
|-
|-
| | '''<tt>6444472</tt>'''
| '''<tt>6 4 4 6 2 7 2</tt>'''
| | Harmonia
| Silver
|-
|-
| | '''<tt>4446274</tt>'''
| '''<tt>6 4 4 4 4 7 2</tt>'''
| | Inverse harmonia
| Harmonia
|-
|-
| | '''<tt>6444562</tt>'''
| '''<tt>4 4 4 6 2 7 4</tt>'''
| | Pendragon
| Inverse harmonia
|-
|-
| | '''<tt>4626544</tt>'''
| '''<tt>6 4 4 4 5 6 2</tt>'''
| | Inverse pendragon
| Pendragon
|-
|-
| | '''<tt>6264463</tt>'''
| '''<tt>4 6 2 6 5 4 4</tt>'''
| | Hipop
| Inverse pendragon
|-
|-
| | '''<tt>4626364</tt>'''
| '''<tt>6 2 6 4 4 6 3</tt>'''
| | Inverse Hipop
| Hipop
|-
|-
| | '''<tt>4626445</tt>'''
| '''<tt>4 6 2 6 3 6 4</tt>'''
| | Malakon
| Inverse Hipop
|-
|-
| | '''<tt>4626454</tt>'''
| '''<tt>4 6 2 6 4 4 5</tt>'''
| | Inverse malakon
| Malakon
|-
|-
| | '''<tt>4464526</tt>'''
| '''<tt>4 6 2 6 4 5 4</tt>'''
| | Bagpipe
| Inverse malakon
|-
|-
| | '''<tt>4644625</tt>'''
| '''<tt>4 4 6 4 5 2 6</tt>'''
| | Inverse bagpipe
| Bagpipe
|-
|-
| | '''<tt>6444625</tt>'''
| '''<tt>4 6 4 4 6 2 5</tt>'''
| | Pitu
| Inverse bagpipe
|-
|-
| | '''<tt>6444652</tt>'''
| '''<tt>6 4 4 4 6 2 5</tt>'''
| | Inverse pitu
| Pitu
|-
|-
| | '''<tt>6444445</tt>'''
| '''<tt>6 4 4 4 6 5 2</tt>'''
| | Porch
| Inverse pitu
|-
|-
| | '''<tt>4446544</tt>'''
| '''<tt>6 4 4 4 4 4 5</tt>'''
| | Inverse porch
| Porch
|-
| '''<tt>4 4 4 6 5 4 4</tt>'''
| Inverse porch
|}
|}


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


{| class="wikitable"
{| class="wikitable"
|-
|-
| | '''<tt>5436346</tt>'''
! schema
| | Subdom scale; inverse superton
! name
|-
| '''<tt>5 4 3 6 3 4 6</tt>'''
| 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
|}
|}


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


{| class="wikitable"
{| class="wikitable"
|-
|-
| | '''<tt>4554454</tt>'''
! schema
| | Sikah; Rast; Neutral Diatonic Hypolydian
! name
|-
| '''<tt>4 5 5 4 4 5 4</tt>'''
| 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
|}
|}


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


{| class="wikitable"
{| class="wikitable"
|-
|-
| | '''<tt>5555515</tt>'''
! schema
| | Hemiwuerschmidt/Hemithirds[7]
! name
|-
|-
| | '''<tt>5544652</tt>'''
| '''<tt>5 5 5 5 5 1 5</tt>'''
| | Hemaj; inverse hemin
| Hemiwuerschmidt/Hemithirds[7]
|-
|-
| | '''<tt>4455256</tt>'''
| '''<tt>5 5 4 4 6 5 2</tt>'''
| | Hemin; inverse hemaj
| Hemaj; inverse hemin
|-
|-
| | '''<tt>4525546</tt>'''
| '''<tt>4 4 5 5 2 5 6</tt>'''
| | Gypsi; 11/9-10/7-7/4 chord on tonic
| Hemin; inverse hemaj
|-
|-
| | '''<tt>4552546</tt>'''
| '''<tt>4 5 2 5 5 4 6</tt>'''
| | Inverse gypsi; 11/9-10/7-7/4 chord on tonic
| Gypsi; 11/9-10/7-7/4 chord on tonic
|-
|-
| | '''<tt>5555542</tt>'''
| '''<tt>4 5 5 2 5 4 6</tt>'''
| | Leadhole
| Inverse gypsi; 11/9-10/7-7/4 chord on tonic
|-
|-
| | '''<tt>5555524</tt>'''
| '''<tt>5 5 5 5 5 4 2</tt>'''
| | Inverse leadhole
| Leadhole
|-
| '''<tt>5 5 5 5 5 2 4</tt>'''
| Inverse leadhole
|}
|}


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


{| class="wikitable"
{| class="wikitable"
|-
|-
| | '''<tt>5553643</tt>'''
! schema
| | Lydic
! name
|-
| '''<tt>5 5 5 3 6 4 3</tt>'''
| 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
|}
|}


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


{| class="wikitable"
{| class="wikitable"
|-
|-
| | '''<tt>5364463</tt>'''
! schema
| | Orminor
! name
|-
| '''<tt>5 3 6 4 4 6 3</tt>'''
| 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
|}
|}


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


{| class="wikitable"
{| class="wikitable"
|-
|-
| | '''<tt>3456265</tt>'''
! schema
| | Hemisub
! name
|-
|-
| | '''<tt>4356265</tt>'''
| '''<tt>3 4 5 6 2 6 5</tt>'''
| | Inverse hemisub
| Hemisub
|-
|-
| | '''<tt>6354535</tt>'''
| '''<tt>4 3 5 6 2 6 5</tt>'''
| | Heminewt
| Inverse hemisub
|-
|-
| | '''<tt>4536535</tt>'''
| '''<tt>6 3 5 4 5 3 5</tt>'''
| | Inverse heminewt
| Heminewt
|-
| '''<tt>4 5 3 6 5 3 5</tt>'''
| Inverse heminewt
|}
|}


{| class="wikitable"
== See also ==
|-
* [[31edo modes]]
| | 
* [[Strictly proper 19edo scales]]
| |
 
|}
[[Category:Lists of scales]]
[[Category:7-tone scales| ]]
[[Category:31edo]]
[[Category:31edo]]
[[Category:7-tone]]
[[Category:Listen]]
[[Category:edo]]
[[Category:listen]]
[[Category:scale]]
[[Category:theory]]
Retrieved from "https://en.xen.wiki/w/Strictly_proper_7-tone_31edo_scales"