323edo: Difference between revisions

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323edo is a strong [[5-limit]] system and an excellent tuning when considered in the no-11 [[subgroup]], with errors of 25% or less all the way into the [[31-limit]].

As an equal temperament, 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]].

As an equal temperament, 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]], [[support]]ing 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. It provides the [[optimal patent val]] for the rank-5 temperament tempering out [[1573/1568]], the lambeth comma, as well as 13-limit [[stockhausenic]], and [[deuteromere]], the 2.3.5.11 subgroup temperament tempering out 14641/14580.

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. It provides the [[optimal patent val]] for the rank-5 temperament tempering out [[1573/1568]], the lambeth comma, as well as 13-limit [[stockhausenic]], and [[deuteromere]], the [[2.3.5.11 subgroup|2.3.5.11-subgroup]] temperament tempering out 14641/14580.

=== Prime harmonics ===

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 edo is a strong [[5-limit]] system and an excellent tuning when considered in the no-11 [[subgroup]], with errors of 25% or less all the way into the [[31-limit]].
-As an equal temperament, 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]].
+As an equal temperament, 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]], [[support]]ing 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. It provides the [[optimal patent val]] for the rank-5 temperament tempering out [[1573/1568]], the lambeth comma, as well as 13-limit [[stockhausenic]], and [[deuteromere]], the 2.3.5.11 subgroup temperament tempering out 14641/14580.
+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. It provides the [[optimal patent val]] for the rank-5 temperament tempering out [[1573/1568]], the lambeth comma, as well as 13-limit [[stockhausenic]], and [[deuteromere]], the [[2.3.5.11 subgroup|2.3.5.11-subgroup]] temperament tempering out 14641/14580.
 === Prime harmonics ===