52edo: Difference between revisions
→Theory: ''It is recommended to read the page regular temperament first to understand this section.'' Tag: Reverted |
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== Theory == | == Theory == | ||
52edo has [[26edo]]'s very flat [[meantone]] [[perfect|fifth]] and a very sharp fifth close to 1/2-[[64/63|septimal-comma]] [[superpyth]]. The [[patent val]] has the same mapping for [[3/1|3]], [[7/1|7]], [[11/1|11]] and [[13/1|13]] as 26 does, but its [[5/1|5]] is sharp rather than flat. From this it tempers out [[648/625]] rather than [[81/80]] in the 5-limit, and [[225/224]] and [[1029/1024]] in the 7-limit, showing it [[support]]s [[miracle]], albeit badly, and may be defined by the tempering out of both 648/625 and miracle. In the 11-limit it tempers out [[99/98]] and [[176/175]] and in the 13-limit [[78/77]], [[144/143]] and [[169/168]]. It supplies the [[optimal patent val]] for then 12 & 40 temperament of the diminished family in the 7- and 11-limit, and also in the 13-limit where it can be defined as tempering out 78/77, 99/98, 176/175, 567/550 rather than by two patent vals. It also gives the 13-limit patent val for the {{nowrap|21 & 52}} variant of miracle. | 52edo has [[26edo]]'s very flat [[meantone]] [[perfect|fifth]] and a very sharp fifth close to 1/2-[[64/63|septimal-comma]] [[superpyth]]. The [[patent val]] has the same mapping for [[3/1|3]], [[7/1|7]], [[11/1|11]] and [[13/1|13]] as 26 does, but its [[5/1|5]] is sharp rather than flat. From this it tempers out [[648/625]] rather than [[81/80]] in the 5-limit, and [[225/224]] and [[1029/1024]] in the 7-limit, showing it [[support]]s [[miracle]], albeit badly, and may be defined by the tempering out of both 648/625 and miracle. In the 11-limit it tempers out [[99/98]] and [[176/175]] and in the 13-limit [[78/77]], [[144/143]] and [[169/168]]. It supplies the [[optimal patent val]] for then 12 & 40 temperament of the diminished family in the 7- and 11-limit, and also in the 13-limit where it can be defined as tempering out 78/77, 99/98, 176/175, 567/550 rather than by two patent vals. It also gives the 13-limit patent val for the {{nowrap|21 & 52}} variant of miracle. | ||
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! Degrees | ! Degrees | ||
! [[Cents]]s | ! [[Cents]]s | ||
! colspan="3" | [[Ups and | ! colspan="3" | [[Ups and downs notation]] | ||
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| 0 | | 0 | ||
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== Music == | == Music == | ||
; [[Bryan Deister]] | |||
* [https://www.youtube.com/shorts/lNJCZz7EjL0 ''microtonal improvisation in 52edo''] (2025) | |||
* [https://www.youtube.com/watch?v=3uo24YpEN0E ''Waltz in 52edo''] (2025) | |||
; [[Claudi Meneghin]] | ; [[Claudi Meneghin]] | ||
* [https://www.youtube.com/watch?v=5HkEM0ZchP0 ''5-in-1 Canon on Happy Birthday''] (2020) | * [https://www.youtube.com/watch?v=5HkEM0ZchP0 ''5-in-1 Canon on Happy Birthday''] (2020) | ||