51edo: Difference between revisions

Line 1:

== Theory ==

Using the [[patent val]], 51et [[tempering out|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 [[sonic]], the rank-3 temperament tempering out 55/54, 100/99, and 250/243, and also for the rank-4 temperament tempering out 55/54. It provides an alternative tuning to [[22edo]] for [[porcupine]], with a nice fifth but a rather flat major third, and the optimal patent val for the 7- and 11-limit [[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.

~~{{harmonics in equal|51}}~~

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.

~~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.~~

=== Odd harmonics ===

== Intervals ==

{| class="wikitable center-all right-2 left-3"

|-

! Degrees

! [[~~Cents|Cents~~]]

! [[Cent]]s

! colspan="3" | [[Ups and Downs Notation]]

|-

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
 {{EDO intro|51}}
 == Theory ==
+Using the [[patent val]], 51et [[tempering out|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 [[sonic]], the rank-3 temperament tempering out 55/54, 100/99, and 250/243, and also for the rank-4 temperament tempering out 55/54. It provides an alternative tuning to [[22edo]] for [[porcupine]], with a nice fifth but a rather flat major third, and the optimal patent val for the 7- and 11-limit [[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.
-{{harmonics in equal|51}}
+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.
-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.
+=== Odd harmonics ===
+{{Harmonics in equal|51}}
 == Intervals ==
 {| class="wikitable center-all right-2 left-3"
 |-
 ! Degrees
-! [[Cents|Cents]]
+! [[Cent]]s
 ! colspan="3" | [[Ups and Downs Notation]]
 |-