A-team: Difference between revisions

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In general sharper subfourths are better if you don't care about approximating 5/4 and only care about optimizing the 4:9:21 triad. Apart from that, there's no common JI interpretation shared by these sharper tunings. One tradeoff is that small steps in the oneirotonic scale get smaller than 1/3-tones (as in 18edo) and become quarter-tones (as in 23edo) and thus become less melodically recognizable.

[[23edo]] is a special beast with its own JI identifications, for example two tones represent 14/11 and 33/26, rather than 5/4, and J-O# becomes a 5/3 rather than a 13/8. Best to treat it as its own thing, 23edo being the weird but special temperament that it is?

[[23edo]] (469.57 cents) is a special beast with its own JI identifications, for example two tones represent 14/11 and 33/26, rather than 5/4, and J-O# becomes a 5/3 rather than a 13/8. Best to treat it as its own thing, 23edo being the weird but special temperament that it is?

[[41edo]] is similar, I guess.

[[18edo]] (466.67 cents) is an edge case, as it tempers out 81/80 but fails to approximate more diverse intervals with the same identifications used by 13edo, 44edo or 23edo. 18edo's oneirotonic is analogous to 17edo's diatonic scale in that L/s = 3, while 13edo is analogous to 12edo.

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 In general sharper subfourths are better if you don't care about approximating 5/4 and only care about optimizing the 4:9:21 triad.  Apart from that, there's no common JI interpretation shared by these sharper tunings. One tradeoff is that small steps in the oneirotonic scale get smaller than 1/3-tones (as in 18edo) and become quarter-tones (as in 23edo) and thus become less melodically recognizable.
-[[23edo]] is a special beast with its own JI identifications, for example two tones represent 14/11 and 33/26, rather than 5/4, and J-O# becomes a 5/3 rather than a 13/8. Best to treat it as its own thing, 23edo being the weird but special temperament that it is?
+[[23edo]] (469.57 cents) is a special beast with its own JI identifications, for example two tones represent 14/11 and 33/26, rather than 5/4, and J-O# becomes a 5/3 rather than a 13/8. Best to treat it as its own thing, 23edo being the weird but special temperament that it is?
 [[41edo]] is similar, I guess.
 [[18edo]] (466.67 cents) is an edge case, as it tempers out 81/80 but fails to approximate more diverse intervals with the same identifications used by 13edo, 44edo or 23edo. 18edo's oneirotonic is analogous to 17edo's diatonic scale in that L/s = 3, while 13edo is analogous to 12edo.