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''56edo'' divides the octave into 56 parts of 21.429 cents each. It can be used to tune hemithirds, superkliesmic, sycamore and keen temperaments, and using <56 89 130 158| as the equal temperament val, for pajara. It provides the optimal patent val for 7-, 11- and 13-limit [[Sycamore_family#Sycamore|sycamore]], and the 11-limit 56d val is close to the POTE tuning for 11-limit pajara.
'''56edo''' divides the octave into 56 parts of 21.429 cents each.  


=Commas=
56edo can be used to tune [[hemithirds]], [[superkleismic]], [[sycamore]] and [[keen]] temperaments, and using {{val|56 89 130 158}} (56d) as the equal temperament val, for [[pajara]]. It provides the optimal patent val for 7-, 11- and 13-limit [[Sycamore_family #Sycamore|sycamore]], and the 11-limit 56d val is close to the POTE tuning for 11-limit pajara.
5-limit commas: 2048/2025, |-5 -10 9>


7-limit commas: 686/675, 875/864, 1029/1024
== Intervals ==
{| class="wikitable center-all right-2 left-3"
! #
! Cents
! Approximate Ratios
|-
| 0
| 0.000
| [[1/1]]
|-
| 1
| 21.429
| [[49/48]], [[64/63]]
|-
| 2
| 42.857
| [[81/80]], [[28/27]], [[50/49]]
|-
| 3
| 64.286
| [[25/24]], [[36/35]], [[33/32]]
|-
| 4
| 85.714
| [[21/20]], [[22/21]]
|-
| 5
| 107.143
| [[16/15]]
|-
| 6
| 128.571
| [[15/14]], [[13/12]], [[14/13]]
|-
| 7
| 150.000
| [[12/11]]
|-
| 8
| 171.429
| [[10/9]], [[11/10]]
|-
| 9
| 192.857
| [[28/25]]
|-
| 10
| 214.286
| [[9/8]]
|-
| 11
| 235.714
| [[8/7]]
|-
| 12
| 257.143
| [[7/6]], [[15/13]]
|-
| 13
| 278.571
| [[75/64]], [[13/11]]
|-
| 14
| 300.000
| [[25/21]]
|-
| 15
| 321.429
| [[6/5]]
|-
| 16
| 342.857
| [[11/9]], [[39/32]]
|-
| 17
| 364.286
| [[27/22]], [[16/13]], [[26/21]]
|-
| 18
| 385.714
| [[5/4]]
|-
| 19
| 407.143
| [[14/11]]
|-
| 20
| 428.571
| [[32/25]], [[33/26]]
|-
| 21
| 450.000
| [[9/7]], [[13/10]]
|-
| 22
| 471.429
| [[21/16]]
|-
| 23
| 492.857
| [[4/3]]
|-
| 24
| 514.286
|
|-
| 25
| 535.714
| [[27/20]], [[15/11]]
|-
| 26
| 557.143
| [[11/8]]
|-
| 27
| 578.571
| [[7/5]]
|-
| 28
| 600.000
| [[45/32]], [[64/45]]
|-
| …
| …
| …
|}


11-limit commas: 100/99, 245/242, 385/384, 686/675
== Commas ==
* 5-limit commas: 2048/2025, |-5 -10 9>
* 7-limit commas: 686/675, 875/864, 1029/1024
* 11-limit commas: 100/99, 245/242, 385/384, 686/675


=Some scales=
== Scales ==
[[supra7|supra7]]
* [[supra7|supra7]]
 
* [[supra12|supra12]]    
[[supra12|supra12]]     [[Category:edo]]
[[Category:hemithirds]]
[[Category:Edo]]
[[Category:keen]]
[[Category:Hemithirds]]
[[Category:pajara]]
[[Category:Keen]]
[[Category:superkleismic]]
[[Category:Pajara]]
[[Category:sycamore]]
[[Category:Superkleismic]]
[[Category:Sycamore]]
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