Just intonation subgroup: Difference between revisions

Xenwolf (talk | contribs)
m order in cat changed
Xenwolf (talk | contribs)
7-limit subgroups: added a bit of structure and EDO links
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=7-limit subgroups=
=7-limit subgroups=


2.3.7
; 2.3.7:
* {{EDOs|legend=1| 5, 17, 31, 36, 135, 571 }}
* Archytas Diatonic [8/7, 32/27, 4/3, 3/2, 12/7, 16/9, 2/1]
* Safi al-Din Septimal [8/7, 9/7, 4/3, 32/21, 12/7, 16/9, 2/1]


Ets: 5, 17, 31, 36, 135, 571
; 2.5.7:
* {{EDOs|legend=1| 6, 25, 31, 35, 47, 171, 239, 379, 410, 789 }}


Archytas Diatonic [8/7, 32/27, 4/3, 3/2, 12/7, 16/9, 2/1]
; 2.3.7/5:
* {{EDOs|legend=1| 10, 29, 31, 41, 70, 171, 241, 412 }}


Safi al-Din Septimal [8/7, 9/7, 4/3, 32/21, 12/7, 16/9, 2/1]
; 2.5/3.7:
* {{EDOs|legend=1| 12, 15, 42, 57, 270, 327 }}


2.5.7
; 2.5.7/3:
* {{EDOs|legend=1| 9, 31, 40, 50, 81, 90, 171, 261 }}


Ets: 6, 25, 31, 35, 47, 171, 239, 379, 410, 789
; 2.5/3.7/3:
* {{EDOs|legend=1| 27, 68, 72, 99, 171, 517 }}


2.3.7/5
; 2.27/25.7/3:
* {{EDOs|legend=1| 9 }}
* In effect, equivalent to 9EDO, which has a 7-limit version given by [27/25, 7/6, 63/50, 49/36, 72/49, 100/63, 12/7, 50/27, 2]


Ets: 10, 29, 31, 41, 70, 171, 241, 412
; 2.9/5.9/7:
 
* {{EDOs|legend=1| 6, 21, 27, 33, 105, 138, 171, 1848, 2019, 2190, 2361, 2532, 2703, 2874, 3045, 3216, 3387, 3558 }}
2.5/3.7
* ''Terrain temperament'' subgroup, see [[Chromatic pairs #Terrain]]
 
Ets: 12, 15, 42, 57, 270, 327
 
2.5.7/3
 
Ets: 9, 31, 40, 50, 81, 90, 171, 261
 
2.5/3.7/3
 
Ets: 27, 68, 72, 99, 171, 517
 
2.27/25.7/3
 
Ets: 9
 
In effect, equivalent to 9EDO, which has a 7-limit version given by [27/25, 7/6, 63/50, 49/36, 72/49, 100/63, 12/7, 50/27, 2]
 
2.9/5.9/7
 
Ets: 6, 21, 27, 33, 105, 138, 171, 1848, 2019, 2190, 2361, 2532, 2703, 2874, 3045, 3216, 3387, 3558
 
The [[Chromatic_pairs|Terrain temperament]] subgroup.


=11-limit subgroups=
=11-limit subgroups=