179edo: Difference between revisions

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~~'''~~179edo'~~'' is the~~ [[~~EDO|equal division of the octave~~]] ~~into 179 parts~~ of 6.~~7039 cents each. It~~ tempers out the parakleisma, 1224440064/1220703125 in the 5-limit, and [[support]]s parakleismic and its extensions, providing the optimal patent val for 11- and 13-limit [[Ragismic_microtemperaments|parkleismic temperament]]. In the 7-limit it tempers out 3136/3125, 4375/4374 and 10976/10935, in the 11-limit 176/175 and 1375/1372 and in the 13-limit 169/168, 325/324, 351/350 and 352/351, providing the optimal patent val for 11- and 13-limit [[Valinorismic_temperaments#Ulmo|ulmo temperament]]. 179 is the 41st [[~~prime_numbers|~~prime ~~number~~]]~~, with all of the advantages and disadvantages that brings~~.

179edo doesn't approximate any odd harmonic up to 23 with less than 22% error on [[21/16]]. Nonetheless, it is consistent in the 7-limit and there are anumber of temperaments to be considered.

179edo tempers out the parakleisma, 1224440064/1220703125 in the 5-limit, and [[support]]s parakleismic and its extensions, providing the optimal patent val for 11- and 13-limit [[Ragismic_microtemperaments|parkleismic temperament]]. In the 7-limit it tempers out 3136/3125, 4375/4374 and 10976/10935, in the 11-limit 176/175 and 1375/1372 and in the 13-limit 169/168, 325/324, 351/350 and 352/351, providing the optimal patent val for 11- and 13-limit [[Valinorismic_temperaments#Ulmo|ulmo temperament]].

=== Odd harmonics ===

=== Subsets and supersets ===

179edo is the 41st [[prime edo]].

[[Category:Equal divisions of the octave|###]]

[[Category:Prime EDO]]

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 {{Infobox ET}}
-'''179edo''' is the [[EDO|equal division of the octave]] into 179 parts of 6.7039 cents each. It tempers out the parakleisma, 1224440064/1220703125 in the 5-limit, and [[support]]s parakleismic and its extensions, providing the optimal patent val for 11- and 13-limit [[Ragismic_microtemperaments|parkleismic temperament]]. In the 7-limit it tempers out 3136/3125, 4375/4374 and 10976/10935, in the 11-limit 176/175 and 1375/1372 and in the 13-limit 169/168, 325/324, 351/350 and 352/351, providing the optimal patent val for 11- and 13-limit [[Valinorismic_temperaments#Ulmo|ulmo temperament]]. 179 is the 41st [[prime_numbers|prime number]], with all of the advantages and disadvantages that brings.
+{{EDO intro|179}}
+edo doesn't approximate any odd harmonic up to 23 with less than 22% error on [[21/16]]. Nonetheless, it is consistent in the 7-limit and there are anumber of temperaments to be considered.
+edo tempers out the parakleisma, 1224440064/1220703125 in the 5-limit, and [[support]]s parakleismic and its extensions, providing the optimal patent val for 11- and 13-limit [[Ragismic_microtemperaments|parkleismic temperament]]. In the 7-limit it tempers out 3136/3125, 4375/4374 and 10976/10935, in the 11-limit 176/175 and 1375/1372 and in the 13-limit 169/168, 325/324, 351/350 and 352/351, providing the optimal patent val for 11- and 13-limit [[Valinorismic_temperaments#Ulmo|ulmo temperament]].
+=== Odd harmonics ===
+{{Harmonics in equal|179}}
+=== Subsets and supersets ===
+edo is the 41st [[prime edo]].
 [[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
 [[Category:Prime EDO]]