32edo: Difference between revisions

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It also tempers out 2048/2025 in the 5-limit, and [[50/49|50/49]] with [[64/63|64/63]] in the [[7-limit|7-limit]], which means it supports [[Diaschismic_family|pajara temperament]], with a very sharp fifth of 712.5 cents which could be experimented with by those with a penchant for fifths even sharper than the fifth of [[27edo|27edo]]; this fifth is in fact very close to the minimax tuning of the pajara extension [[Diaschismic_family#Pajara-Pajaro|pajaro]], using the 32f val. In the 11-limit it provides the optimal patent val for the 15&32 temperament, tempering out 55/54, 64/63 and 245/242.

Since 32edo is poor at approximating primes and it is a high power of 2, both traditional RTT-based and temperament agnostic MOS theory are of limited usefulness in the system (though it has [[ultrasoft]] [[smitonic]] with L/s = 5/4 and [[supersoft]] [[semiquartal]]). 32edo's 5:2:1 [[blackdye]] scale (1525152515) is notable for having neogothic major thirds, and naiadics in place of the traditional 5-limit and Pythagorean major thirds in 5-limit blackdye, and the 75¢ semitone in place of 16/15.

== Intervals ==

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 It also tempers out 2048/2025 in the 5-limit, and [[50/49|50/49]] with [[64/63|64/63]] in the [[7-limit|7-limit]], which means it supports [[Diaschismic_family|pajara temperament]], with a very sharp fifth of 712.5 cents which could be experimented with by those with a penchant for fifths even sharper than the fifth of [[27edo|27edo]]; this fifth is in fact very close to the minimax tuning of the pajara extension [[Diaschismic_family#Pajara-Pajaro|pajaro]], using the 32f val. In the 11-limit it provides the optimal patent val for the 15&amp;32 temperament, tempering out 55/54, 64/63 and 245/242.
+Since 32edo is poor at approximating primes and it is a high power of 2, both traditional RTT-based and temperament agnostic MOS theory are of limited usefulness in the system (though it has [[ultrasoft]] [[smitonic]] with L/s = 5/4 and [[supersoft]] [[semiquartal]]). 32edo's 5:2:1 [[blackdye]] scale (1525152515) is notable for having neogothic major thirds, and naiadics in place of the traditional 5-limit and Pythagorean major thirds in 5-limit blackdye, and the 75¢ semitone in place of 16/15.
 == Intervals ==