51edo: Difference between revisions
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''51 | ''<b>51-EDO</b>'' 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. | ||
[[Category:51edo]] | [[Category:51edo]] | ||
[[Category:edo]] | [[Category:edo]] | ||
[[Category:theory]] | [[Category:theory]] | ||
Revision as of 05:27, 1 January 2019
51-EDO divides the octave into 51 equal parts of 23.529 cents each, which is about the size of the Pythagorean comma (even though this comma itself is mapped to a different interval). It 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 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 temperament, with a nice fifth but a rather flat major third, and the optimal patent val for 7- and 11-limit porky temperament, which is sonic plus 225/224.