270edo: Difference between revisions

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* 270et has lower [[Tenney-Euclidean temperament measures #TE simple badness|relative errors]] than any previous equal temperaments in the 11- and 13-limit. It is the first to beat [[72edo|72]] in the 11-limit ~~and~~ [[224edo|224]] in the 13-limit. The next equal temperament that does better in terms of either absolute or relative error in the 11-limit is [[342edo|342]], ~~and~~ in the 13-limit, [[494edo|494]].

* 270et has lower [[Tenney-Euclidean temperament measures #TE simple badness|relative errors]] than any previous equal temperaments in the 11-, 13-, and 19-limit. It is the first to beat [[72edo|72]] in the 11-limit, [[224edo|224]] in the 13-limit, and [[217edo|217]] in the 19-limit. The next equal temperament that does better in terms of either absolute or relative error in the 11-limit is [[342edo|342]], in the 13-limit [[494edo|494]], and in the 19-limit, [[311edo|311]] for absolute error and [[581edo|581]] for relative error.

* It is even more prominent in the 2.3.5.7.11.13.19 subgroup. Not until [[552edo|552]] do we reach a better equal temperament in terms of absolute error, and not until [[2190edo|2190]] do we reach one in terms of relative error.

* It is also prominent in the 17-~~, 19-,~~ and 23-limit, ~~where it has~~ lower absolute errors than any previous equal temperaments, despite inconsistency in the corresponding odd limits.

* It is also prominent in the 17- and 23-limit, with lower absolute errors than any previous equal temperaments, despite inconsistency in the corresponding odd limits.

=== Rank-2 temperaments ===

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-* 270et has lower [[Tenney-Euclidean temperament measures #TE simple badness|relative errors]] than any previous equal temperaments in the 11- and 13-limit. It is the first to beat [[72edo|72]] in the 11-limit and [[224edo|224]] in the 13-limit. The next equal temperament that does better in terms of either absolute or relative error in the 11-limit is [[342edo|342]], and in the 13-limit, [[494edo|494]].
+* 270et has lower [[Tenney-Euclidean temperament measures #TE simple badness|relative errors]] than any previous equal temperaments in the 11-, 13-, and 19-limit. It is the first to beat [[72edo|72]] in the 11-limit, [[224edo|224]] in the 13-limit, and [[217edo|217]] in the 19-limit. The next equal temperament that does better in terms of either absolute or relative error in the 11-limit is [[342edo|342]], in the 13-limit [[494edo|494]], and in the 19-limit, [[311edo|311]] for absolute error and [[581edo|581]] for relative error.
 * It is even more prominent in the 2.3.5.7.11.13.19 subgroup. Not until [[552edo|552]] do we reach a better equal temperament in terms of absolute error, and not until [[2190edo|2190]] do we reach one in terms of relative error.
-* It is also prominent in the 17-, 19-, and 23-limit, where it has lower absolute errors than any previous equal temperaments, despite inconsistency in the corresponding odd limits.
+* It is also prominent in the 17- and 23-limit, with lower absolute errors than any previous equal temperaments, despite inconsistency in the corresponding odd limits.
 === Rank-2 temperaments ===