57edo: Difference between revisions
→Music: Add Bryan Deister's ''57edo improv'' (2026-09-27) and add a more specific date to the previous one; also improve description of ''Prelude in 57edo'' (2025) videos |
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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 === | ||