51edo: Difference between revisions

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~~'''51~~ EDO~~''' divides the [[octave]] into~~ 51 ~~equal parts of 23.5 [[cent]]s each, which is about the size of the [[Pythagorean comma]] (even though this comma itself is mapped to a different interval).~~

== Theory ==

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51 EDO tempers out [[250/243]] in the [[5-limit]], [[225/224]] and [[2401/2400]] in the [[7-limit]], and [[55/54]] and [[100/99]] in the [[11-limit]]. It is the [[optimal patent val]] for [[Porcupine rank three family #Sonic|sonic]], the rank three temperament tempering out 250/243, 55/54 and 100/99, and also for the rank four temperament tempering out 55/54. It provides an alternative tuning to [[22edo]] for [[Porcupine family #Porcupine|porcupine temperament]], with a nice fifth but a rather flat major third, and the optimal patent val for 7 and 11-limit [[Porcupine family #Porky|porky temperament]], which is sonic plus 225/224. 51 contains an [[6L 1s|Archeotonic]] scale based on repetitions of 8\51, creating a scale with a whole tone-like drive towards the tonic through the 17edo semitone at the top.

51edo's step is the closest direct approximation to the [[Pythagorean comma]] by edo steps, though that comma itself is mapped to a different interval.

== Intervals ==

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''51 EDO''' divides the [[octave]] into 51 equal parts of 23.5 [[cent]]s each, which is about the size of the [[Pythagorean comma]] (even though this comma itself is mapped to a different interval).
+{{EDO intro|51}}
 == Theory ==
@@ Line 7: / Line 7: @@
 {{primes in edo|51}}
 EDO tempers out [[250/243]] in the [[5-limit]], [[225/224]] and [[2401/2400]] in the [[7-limit]], and [[55/54]] and [[100/99]] in the [[11-limit]]. It is the [[optimal patent val]] for [[Porcupine rank three family #Sonic|sonic]], the rank three temperament tempering out 250/243, 55/54 and 100/99, and also for the rank four temperament tempering out 55/54. It provides an alternative tuning to [[22edo]] for [[Porcupine family #Porcupine|porcupine temperament]], with a nice fifth but a rather flat major third, and the optimal patent val for 7 and 11-limit [[Porcupine family #Porky|porky temperament]], which is sonic plus 225/224. 51 contains an [[6L 1s|Archeotonic]] scale based on repetitions of 8\51, creating a scale with a whole tone-like drive towards the tonic through the 17edo semitone at the top.
+edo's step is the closest direct approximation to the [[Pythagorean comma]] by edo steps, though that comma itself is mapped to a different interval.
 == Intervals ==