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]] and temperament-agnostic [[MOS]] theory are of limited usefulness in the system (though it has [[ultrasoft]] [[smitonic]] with L/s = 5/4). 32edo's 5:2:1 [[blackdye]] scale (1525152515), which is melodically comparable to [[31edo]]'s 5:2:1 [[diasem]], is notable for having 412.5¢ neogothic major thirds and 450¢ 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. The 712.5¢ sharp fifth and the 675¢ flat fifth correspond to the 3/2 and 40/27 in 5-limit blackdye~~; hence 32edo's~~ 5:2:1 blackdye is a dual-fifth scale.

Since 32edo is poor at approximating primes and it is a high power of 2, both traditional [[RTT]] and temperament-agnostic [[MOS]] theory are of limited usefulness in the system (though it has [[ultrasoft]] [[smitonic]] with L/s = 5/4). 32edo's 5:2:1 [[blackdye]] scale (1525152515), which is melodically comparable to [[31edo]]'s 5:2:1 [[diasem]], is notable for having 412.5¢ neogothic major thirds and 450¢ 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. The 712.5¢ sharp fifth and the 675¢ flat fifth correspond to the 3/2 and 40/27 in 5-limit blackdye, making 5:2:1 blackdye a [[dual-fifth]] scale.

== 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]] and temperament-agnostic [[MOS]] theory are of limited usefulness in the system (though it has [[ultrasoft]] [[smitonic]] with L/s = 5/4). 32edo's 5:2:1 [[blackdye]] scale (1525152515), which is melodically comparable to [[31edo]]'s 5:2:1 [[diasem]], is notable for having 412.5¢ neogothic major thirds and 450¢ 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. The 712.5¢ sharp fifth and the 675¢ flat fifth correspond to the 3/2 and 40/27 in 5-limit blackdye; hence 32edo's 5:2:1 blackdye is a dual-fifth scale.
+Since 32edo is poor at approximating primes and it is a high power of 2, both traditional [[RTT]] and temperament-agnostic [[MOS]] theory are of limited usefulness in the system (though it has [[ultrasoft]] [[smitonic]] with L/s = 5/4). 32edo's 5:2:1 [[blackdye]] scale (1525152515), which is melodically comparable to [[31edo]]'s 5:2:1 [[diasem]], is notable for having 412.5¢ neogothic major thirds and 450¢ 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. The 712.5¢ sharp fifth and the 675¢ flat fifth correspond to the 3/2 and 40/27 in 5-limit blackdye, making 5:2:1 blackdye a [[dual-fifth]] scale.
 == Intervals ==