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Just intonation subgroup: Difference between revisions

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== List of selected subgroups ==
== List of selected subgroups ==
=== 7-limit subgroups ===
=== 7-limit subgroups ===
{{See also| 2.3.7 subgroup }}
* [[2.3.7 subgroup]]
* [[2.5.7 subgroup]]
* [[3.5.7 subgroup]]


; 2.3.7:
Others:  
* {{EDOs|legend=1| 5, 17, 31, 36, 135, 571 }}
* 2.3.7/5
* Archytas Diatonic [8/7, 32/27, 4/3, 3/2, 12/7, 16/9, 2/1]
** {{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| 6, 25, 31, 35, 47, 171, 239, 379, 410, 789 }}
** {{EDOs|legend=1| 9, 31, 40, 50, 81, 90, 171, 261 }}
 
* 2.5/3.7/3
; 2.3.7/5:
** {{EDOs|legend=1| 27, 68, 72, 99, 171, 517 }}
* {{EDOs|legend=1| 10, 29, 31, 41, 70, 171, 241, 412 }}
* 2.27/25.7/3
 
** {{EDOs|legend=1| 9 }}
; 2.5/3.7:
** 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]
* {{EDOs|legend=1| 12, 15, 42, 57, 270, 327 }}
* 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 }}
; 2.5.7/3:
** The [[terrain]] temperament subgroup
* {{EDOs|legend=1| 9, 31, 40, 50, 81, 90, 171, 261 }}
 
; 2.5/3.7/3:
* {{EDOs|legend=1| 27, 68, 72, 99, 171, 517 }}
 
; 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]
 
; 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 }}
* ''Terrain temperament'' subgroup, see [[Subgroup temperaments #Terrain]]
 
; 3.5.7:
* Does not have octaves, commonly used for non-octave [[EDT]]s


=== 11-limit subgroups ===
=== 11-limit subgroups ===
{{See also| 2.3.7.11 subgroup }}
* [[2.3.11 subgroup]]
{{See also| Alpharabian tuning }}
* [[2.3.5.11 subgroup]]
 
* [[2.3.7.11 subgroup]]
; 2.3.11:
* {{EDOs|legend=1| 7, 15, 17, 24, 159, 494, 518, 653 }}
* Zalzal, al-Farabi's version [9/8, 27/22, 4/3, 3/2, 18/11, 16/9, 2/1]
 
; 2.5.11:
* {{EDOs|legend=1| 6, 7, 9, 13, 15, 22, 37, 87, 320 }}


; 2.7.11:
Others:  
* {{EDOs|legend=1| 6, 9, 11, 20, 26, 135, 161, 296 }}
* 2.5.11
 
** {{EDOs|legend=1| 6, 7, 9, 13, 15, 22, 37, 87, 320 }}
; 2.3.5.11:
* 2.7.11
* {{EDOs|legend=1| 7, 15, 22, 31, 65, 72, 87, 270, 342, 407, 494 }}
** {{EDOs|legend=1| 6, 9, 11, 20, 26, 135, 161, 296 }}
 
* 2.5.7.11
; 2.3.7.11:
** {{EDOs|legend=1| 6, 15, 31, 35, 37, 109, 618, 960 }}
* {{EDOs|legend=1| 9, 17, 26, 31, 41, 46, 63, 72, 135 }}
* 2.5/3.7/3.11/3
* The [[Gamelismic clan#Radon|Radon temperament]] subgroup, generated by the Ptolemy Intense Chromatic [22/21, 8/7, 4/3, 3/2, 11/7, 12/7, 2/1]
** {{EDOs|legend=1| 33, 41, 49, 57, 106, 204, 253 }}
* See: [[Gallery of 2.3.7.11 Subgroup Scales]]
** The [[indium]] temperament subgroup.
 
; 2.5.7.11:
* {{EDOs|legend=1| 6, 15, 31, 35, 37, 109, 618, 960 }}
 
; 2.5/3.7/3.11/3:
* {{EDOs|legend=1| 33, 41, 49, 57, 106, 204, 253 }}
* The [[Subgroup temperaments#Indium|Indium temperament]] subgroup.


=== 13-limit subgroups ===
=== 13-limit subgroups ===
* [[2.3.5.13 subgroup]]
* [[2.3.5.7.13 subgroup]]
* [[2.3.7.11.13 subgroup]]


; 2.3.13:
Others:
* {{EDOs|legend=1| 7, 10, 17, 60, 70, 130, 147, 277, 424 }}
* 2.3.13
* Mustaqim mode, Ibn Sina [9/8, 39/32, 4/3, 3/2, 13/8, 16/9, 2/1]
** {{EDOs|legend=1| 7, 10, 17, 60, 70, 130, 147, 277, 424 }}
 
** Mustaqim mode, Ibn Sina [9/8, 39/32, 4/3, 3/2, 13/8, 16/9, 2/1]
; 2.3.5.13:
* 2.3.5.13
* {{EDOs|legend=1| 15, 19, 34, 53, 87, 130, 140, 246, 270 }}
** {{EDOs|legend=1| 15, 19, 34, 53, 87, 130, 140, 246, 270 }}
* The [[Kleismic family#Cata|Cata]], [[The Archipelago#Trinidad|Trinidad]] and [[The Archipelago#Parizekmic|Parizekmic]] temperaments subgroup.
** The [[cata]], [[trinidad]] and [[parizekmic]] temperaments subgroup
 
* 2.3.7.13
; 2.3.7.13:
** {{EDOs|legend=1| 10, 26, 27, 36, 77, 94, 104, 130, 234 }}
* {{EDOs|legend=1| 10, 26, 27, 36, 77, 94, 104, 130, 234 }}
** Buzurg [14/13, 16/13, 4/3, 56/39, 3/2]
* Buzurg [14/13, 16/13, 4/3, 56/39, 3/2]
** Safi al-Din tuning [8/7, 16/13, 4/3, 32/21, 64/39, 16/9, 2/1]
* Safi al-Din tuning [8/7, 16/13, 4/3, 32/21, 64/39, 16/9, 2/1]
** Ibn Sina tuning [14/13, 7/6, 4/3, 3/2, 21/13, 7/4, 2]
* Ibn Sina tuning [14/13, 7/6, 4/3, 3/2, 21/13, 7/4, 2]
* 2.3.5.11.13
 
* 2.5.7.13
; 2.5.7.13:
** {{EDOs|legend=1| 7, 10, 17, 27, 37, 84, 121, 400 }}
* {{EDOs|legend=1| 7, 10, 17, 27, 37, 84, 121, 400 }}
** The [[huntington]] temperament subgroup
* The [[No-threes subgroup temperaments#Huntington|Huntington temperament]] subgroup.
* 2.5.7.11.13
 
** {{EDOs|legend=1| 6, 7, 13, 19, 25, 31, 37 }}
; 2.5.7.11.13:
** The [[roulette]] temperament subgroup
* {{EDOs|legend=1| 6, 7, 13, 19, 25, 31, 37 }}
* 2.3.13/5
* The [[Hemimean clan#Roulette|Roulette temperament]] subgroup
** {{EDOs|legend=1| 5, 9, 14, 19, 24, 29, 53, 82, 111, 140, 251, 362 }}
 
** The [[barbados]] temperament subgroup.
; 2.3.13/5:
* 2.3.11/5.13/5
* {{EDOs|legend=1| 5, 9, 14, 19, 24, 29, 53, 82, 111, 140, 251, 362 }}
** {{EDOs|legend=1| 5, 9, 14, 19, 24, 29 }}
* The [[The Archipelago#Barbados|Barbados temperament]] subgroup.
** The [[bridgetown]] temperament subgroup
 
* 2.3.11/7.13/7
; 2.3.11/5.13/5:
** {{EDOs|legend=1| 5, 7, 12, 17, 29, 46, 75, 196, 271 }}
* {{EDOs|legend=1| 5, 9, 14, 19, 24, 29 }}
** The [[pepperoni]] temperament subgroup.
* The [[Subgroup temperaments#Bridgetown|Bridgetown temperament]] subgroup.
* 2.7/5.11/5.13/5
 
** {{EDOs|legend=1| 5, 8, 21, 29, 37, 66, 169, 235 }}
; 2.3.11/7.13/7:
** The [[tridec]] temperament subgroup.
* {{EDOs|legend=1| 5, 7, 12, 17, 29, 46, 75, 196, 271 }}
* The [[Subgroup temperaments#Pepperoni|Pepperoni temperament]] subgroup.
 
; 2.7/5.11/5.13/5:
* {{EDOs|legend=1| 5, 8, 21, 29, 37, 66, 169, 235 }}
* The [[Subgroup temperaments#Tridec|Tridec temperament]] subgroup.


=== Higher-limit subgroups ===
=== Higher-limit subgroups ===
* [[2.11.13.17.19 subgroup]]
* [[2.3.5.7.11.13.19 subgroup]]
* [[2.17/13.19/13 subgroup]]
* [[2.3.5.7.11.13.19.29 subgroup]]
 
; 8.9.5.7.11.13.17.23:
* [[143ed11]]


=== Irrational subgroups ===
=== Irrational subgroups ===
Retrieved from "https://en.xen.wiki/w/Just_intonation_subgroup"