323edo: Difference between revisions

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'''323edo''' is the [[EDO|equal division of the octave]] into 323 parts of 3.7152 [[cent]]s each. It [[~~tempering_out~~|tempers out]] ~~10485760000/10460353203~~ and ~~274877906944/274658203125~~ in the [[5-limit]]; 4375/4374, 589824/588245 and 703125/702464 in the [[7-limit]], supporting 7-limit [[~~Vulture family|~~vulture]], [[~~Luna family|~~lunatic]], [[~~Ragismic microtemperaments|~~enneadecal]], and [[~~Ragismic microtemperaments|~~gamera]]. 11-limit ~~commas~~ 1375/1372, 5632/5625, 14641/14580, and 19712/19683 are tempered out in the patent val; 540/539, 6250/6237, 12005/11979, and 16384/16335 are tempered out in the 323e val.

The '''323 equal divisions of the octave''' ('''323edo''') is the [[EDO|equal division of the octave]] into 323 parts of 3.7152 [[cent]]s each.

== Theory ==

It [[tempering out|tempers out]] the [[vulture comma]], {{monzo| 24 -21 4 }} and the [[luna comma]], {{monzo| 38 -2 -15 }}, in the [[5-limit]]; [[4375/4374]], 589824/588245 and [[703125/702464]] in the [[7-limit]], supporting 7-limit [[vulture]], [[lunatic]], [[enneadecal]], and [[gamera]]. In the 11-limit, the 323e val and the [[patent val]] are comparable in errors. 1375/1372, 5632/5625, [[14641/14580]], and [[19712/19683]] are tempered out in the patent val; [[540/539]], [[6250/6237]], 12005/11979, and [[16384/16335]] are tempered out in the 323e val.

323 = 17 × 19, and shares the excellent approximations of [[25/24]] in [[17edo]] and of the [[28/27]] and the [[6/5]] in [[19edo]].

=== Prime harmonics ===

[[Category:Equal divisions of the octave]]

[[Category:Theory]]

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-'''323edo''' is the [[EDO|equal division of the octave]] into 323 parts of 3.7152 [[cent]]s each. It [[tempering_out|tempers out]] 10485760000/10460353203 and 274877906944/274658203125 in the [[5-limit]]; 4375/4374, 589824/588245 and 703125/702464 in the [[7-limit]], supporting 7-limit [[Vulture family|vulture]], [[Luna family|lunatic]], [[Ragismic microtemperaments|enneadecal]], and [[Ragismic microtemperaments|gamera]]. 11-limit commas 1375/1372, 5632/5625, 14641/14580, and 19712/19683 are tempered out in the patent val; 540/539, 6250/6237, 12005/11979, and 16384/16335 are tempered out in the 323e val.
+The '''323 equal divisions of the octave''' ('''323edo''') is the [[EDO|equal division of the octave]] into 323 parts of 3.7152 [[cent]]s each.
+== Theory ==
+It [[tempering out|tempers out]] the [[vulture comma]], {{monzo| 24 -21 4 }} and the [[luna comma]], {{monzo| 38 -2 -15 }}, in the [[5-limit]]; [[4375/4374]], 589824/588245 and [[703125/702464]] in the [[7-limit]], supporting 7-limit [[vulture]], [[lunatic]], [[enneadecal]], and [[gamera]]. In the 11-limit, the 323e val and the [[patent val]] are comparable in errors. 1375/1372, 5632/5625, [[14641/14580]], and [[19712/19683]] are tempered out in the patent val; [[540/539]], [[6250/6237]], 12005/11979, and [[16384/16335]] are tempered out in the 323e val.
+= 17 × 19, and shares the excellent approximations of [[25/24]] in [[17edo]] and of the [[28/27]] and the [[6/5]] in [[19edo]].
+=== Prime harmonics ===
+{{Primes in edo|323}}
 [[Category:Equal divisions of the octave]]
 [[Category:Theory]]