51edo: Difference between revisions

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| Augmented 1sn = 6\51 ≈ 141¢

}}

'''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 ==

~~'''~~51-EDO''' divides the [[Octave|octave]] into 51 equal parts of 23.529 [[cent|cent]]s each, which is about the size of the [http://en.wikipedia.org/wiki/Pythagorean_comma Pythagorean comma] (even though this comma itself is mapped to a different interval). It tempers out [[~~250/243|~~250/243]] in the [[~~5-limit|~~5-limit]], [[~~225/224|~~225/224]] and [[~~2401/2400|~~2401/2400]] in the [[~~7-limit|~~7-limit]], and [[~~55/54|~~55/54]] and [[~~100/99|~~100/99]] in the [[~~11-limit|~~11-limit]]. It is the [[~~Optimal_patent_val|~~optimal patent val]] for [[~~Porcupine_rank_three_family~~|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|~~22edo]] for [[~~Porcupine_family~~|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 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.

== Intervals ==

@@ Line 7: / Line 7: @@
 | Augmented 1sn = 6\51 ≈ 141¢
 }}
+'''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 ==
 {{primes in edo|51}}
-'''51-EDO''' divides the [[Octave|octave]] into 51 equal parts of 23.529 [[cent|cent]]s each, which is about the size of the [http://en.wikipedia.org/wiki/Pythagorean_comma Pythagorean comma] (even though this comma itself is mapped to a different interval). It tempers out [[250/243|250/243]] in the [[5-limit|5-limit]], [[225/224|225/224]] and [[2401/2400|2401/2400]] in the [[7-limit|7-limit]], and [[55/54|55/54]] and [[100/99|100/99]] in the [[11-limit|11-limit]]. It is the [[Optimal_patent_val|optimal patent val]] for [[Porcupine_rank_three_family|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|22edo]] for [[Porcupine_family|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.
+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.
 == Intervals ==