User:Tristanbay/My favorite EDOs: Difference between revisions

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[[41edo]]: Highlights the distinction between Pythagorean, syntonic, and septimal intervals by exaggerating both 81/80 and 64/63. It also works quite well (skip-fretted) on guitar and is consistent in the 15-odd-limit.

[[46edo]]: Good, although simplistic, representation of the 13-limit. The only interval in the entire 15-odd-limit it represents inconsistently is 15/13, and only by a little bit. It works great for 13-limit neogothic tunings.

[[46edo]]: Good, although simplistic, representation of the 13-limit. The only interval in the entire 15-odd-limit it represents inconsistently is 15/13, and only by a little bit, and it tempers out the smallest superparticular intervals with all primes up to 7, all primes up to 11, all primes up to 13, all primes up to 17, and all primes up to 19 (known as [[PIFE comma|SPIFEs]]). It works great for 13-limit neogothic tunings.

[[53edo]]: Takes advantage of the fact that the intervals found just beyond a traditional Pythagorean pentatonic scale are very close to common syntonic intervals by tempering out 32805/32768 (41edo also does this, but 53edo really focuses in on the 5-limit). Generally a good stand-in for syntonic just intonation and also approximates the 13th harmonic well.

@@ Line 11: / Line 11: @@
 [[41edo]]: Highlights the distinction between Pythagorean, syntonic, and septimal intervals by exaggerating both 81/80 and 64/63. It also works quite well (skip-fretted) on guitar and is consistent in the 15-odd-limit.
-[[46edo]]: Good, although simplistic, representation of the 13-limit. The only interval in the entire 15-odd-limit it represents inconsistently is 15/13, and only by a little bit. It works great for 13-limit neogothic tunings.
+[[46edo]]: Good, although simplistic, representation of the 13-limit. The only interval in the entire 15-odd-limit it represents inconsistently is 15/13, and only by a little bit, and it tempers out the smallest superparticular intervals with all primes up to 7, all primes up to 11, all primes up to 13, all primes up to 17, and all primes up to 19 (known as [[PIFE comma|SPIFEs]]). It works great for 13-limit neogothic tunings.
 [[53edo]]: Takes advantage of the fact that the intervals found just beyond a traditional Pythagorean pentatonic scale are very close to common syntonic intervals by tempering out 32805/32768 (41edo also does this, but 53edo really focuses in on the 5-limit). Generally a good stand-in for syntonic just intonation and also approximates the 13th harmonic well.