57edo: Difference between revisions
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Using the full prime-limit [[patent val]], the equal temperament tempers out [[81/80]], [[1029/1024]], and [[3125/3072]] in the 7-limit; and [[99/98]], [[385/384]], [[441/440]], and [[625/616]] in the [[11-limit]]. A good generator to exploit the 2.5/3.7.11.13.17.19 aspect of 57 is the approximate [[11/8]], which is 26\57. This gives the [[19-limit]] 46 & 57 temperament [[heinz]]. It can also be used to tune [[mothra]] as well as [[trismegistus]]. | Using the full prime-limit [[patent val]], the equal temperament tempers out [[81/80]], [[1029/1024]], and [[3125/3072]] in the 7-limit; and [[99/98]], [[385/384]], [[441/440]], and [[625/616]] in the [[11-limit]]. A good generator to exploit the 2.5/3.7.11.13.17.19 aspect of 57 is the approximate [[11/8]], which is 26\57. This gives the [[19-limit]] 46 & 57 temperament [[heinz]]. It can also be used to tune [[mothra]] as well as [[trismegistus]]. | ||
57edo is interesting in that it is a [[dual-fifth]] system where both fifths are somewhat plausible. The 57b val uses the alternative fifth of 715.789 cents. While not very accurate in the 5 and 7-limits (being even worse than 19edo), it does support some interesting temperaments like [[sixix]] and a near-perfect 1/2-comma [[archy]] (such that the diatonic minor seventh is almost exactly [[7/4]]). | |||
=== Odd harmonics === | === Odd harmonics === | ||
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== Music == | == Music == | ||
; [[Bryan Deister]] | ; [[Bryan Deister]] | ||
* [https://www.youtube.com/watch?v=4NZvSgS3ryY ''57edo improv''] (2025) | * [https://www.youtube.com/watch?v=4NZvSgS3ryY ''57edo improv''] (2025-05-12) | ||
* ''Prelude in 57edo'' (2025) ( | * ''Prelude in 57edo'' (2025) (Uses different temperaments in different sections) | ||
** [https://www.youtube.com/shorts/FylRB5MGBz4 ''Part 1 (short clip)''] | ** [https://www.youtube.com/shorts/FylRB5MGBz4 ''Part 1 (short clip)''] (Lumatone view using [[5L 2s|diatonic]] sharp fifth + [[mothra]] flat fifth mapping) | ||
** [https://www.youtube.com/shorts/yVv0s8t--pg ''Part 2 (short clip)''] | ** [https://www.youtube.com/shorts/yVv0s8t--pg ''Part 2 (short clip)''] (Lumatone view using [[lithium]] mapping) | ||
** [https://www.youtube.com/watch?v=RH2QkHqVb2c ''Whole composition''] (but no view of Lumatone) | ** [https://www.youtube.com/watch?v=RH2QkHqVb2c ''Whole composition''] (but no view of Lumatone) | ||
* [https://www.youtube.com/shorts/MTMRlRxRbjQ ''57edo groove''] (2025) | * [https://www.youtube.com/shorts/MTMRlRxRbjQ ''57edo groove''] (2025) | ||
* [https://www.youtube.com/shorts/TrgdgDduDIk ''57edo improv''] (2026-09-27) | |||