56edo: Difference between revisions
KingHyperio (talk | contribs) →Intervals: bruh the step is like almost exactly a syntonic comma and you didn’t even put it in the right place tf Tags: Mobile edit Mobile web edit |
Dude if you want that kind of approximation plz make another column |
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'''56edo''' divides the octave into 56 parts of 21.429 cents each. It shares it's near perfect major third with [[28edo]], which it doubles, while also adding a superpythagorean 5th that is a convergent towards the [[ | '''56edo''' divides the octave into 56 parts of 21.429 cents each. It shares it's near perfect major third with [[28edo]], which it doubles, while also adding a superpythagorean 5th that is a convergent towards the [[Metallic harmonic series|bronze metallic mean]], following [[17edo]] and preceding [[185edo]]. | ||
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 [[ | 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 #Septimal sycamore|sycamore]], and the 11-limit 56d val is close to the [[POTE tuning]] for 11-limit pajara. | ||
== Intervals == | == Intervals == | ||
The following table assumes the [[patent val]] {{val| 56 89 130 157 194 207 }}. Other approaches are possible. | |||
{| class="wikitable center-all right-2 left-3" | {| class="wikitable center-all right-2 left-3" | ||
! # | ! # | ||
| Line 15: | Line 17: | ||
| 1 | | 1 | ||
| 21.429 | | 21.429 | ||
| [[49/48]], [[64/63 | | [[49/48]], [[64/63]] | ||
|- | |- | ||
| 2 | | 2 | ||
| 42.857 | | 42.857 | ||
| [[28/27]], [[50/49]] | | [[28/27]], [[50/49]], [[81/80]] | ||
|- | |- | ||
| 3 | | 3 | ||
| Line 131: | Line 133: | ||
== Commas == | == Commas == | ||
* 5-limit commas: 2048/2025, |-5 -10 9 | * 5-limit commas: 2048/2025, {{monzo| -5 -10 9 }}; | ||
* 7-limit commas: 686/675, 875/864, 1029/1024 | * 7-limit commas: 686/675, 875/864, 1029/1024 | ||
* 11-limit commas: 100/99, 245/242, 385/384, 686/675 | * 11-limit commas: 100/99, 245/242, 385/384, 686/675 | ||
== Scales == | == Scales == | ||
* [[ | * [[Supra7]] | ||
* [[ | * [[Supra12]] | ||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||