2190edo: Difference between revisions

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{{EDO intro|2190}} It is is a very strong 13-limit system; no smaller division has a smaller 13-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]], and nothing beats it until [[2684edo|2684]]. A basis for the 13-limit commas is {9801/9800, 10648/10647, 105644/105625, 140625/140608, 196625/196608}; also tempered out are 123201/123200 and 151263/151250. It is not as impressive beyond the 13-limit, though it does well in the 2.3.5.7.11.13.19.29 subgroup.

2190edo is is a very strong 13-limit system; no smaller division has a smaller 13-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]], and nothing beats it until [[2684edo|2684]]. A basis for the 13-limit commas is {[[9801/9800]], [[10648/10647]], 105644/105625, 140625/140608, 196625/196608}; also [[tempering out|tempered out]] are 123201/123200 and 151263/151250. It is not as impressive beyond the 13-limit, though it does well in the 2.3.5.7.11.13.19.29 [[subgroup]].

=== Prime harmonics ===

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=== Subsets and supersets ===

2190 factors ~~as 2 × 3 × 5 × 73~~; among its divisors is the Woolhouse unit system, [[730edo|730]].

2190 factors into {{factorization|2190}}; among its divisors is the Woolhouse unit system, [[730edo|730]].

[[4380edo]], which doubles 2190edo, provides a good correction to the harmonics 17 and 23.

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 {{Infobox ET}}
-{{EDO intro|2190}} It is is a very strong 13-limit system; no smaller division has a smaller 13-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]], and nothing beats it until [[2684edo|2684]]. A basis for the 13-limit commas is {9801/9800, 10648/10647, 105644/105625, 140625/140608, 196625/196608}; also tempered out are 123201/123200 and 151263/151250. It is not as impressive beyond the 13-limit, though it does well in the 2.3.5.7.11.13.19.29 subgroup.
+{{EDO intro|2190}}
+edo is is a very strong 13-limit system; no smaller division has a smaller 13-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]], and nothing beats it until [[2684edo|2684]]. A basis for the 13-limit commas is {[[9801/9800]], [[10648/10647]], 105644/105625, 140625/140608, 196625/196608}; also [[tempering out|tempered out]] are 123201/123200 and 151263/151250. It is not as impressive beyond the 13-limit, though it does well in the 2.3.5.7.11.13.19.29 [[subgroup]].
 === Prime harmonics ===
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 === Subsets and supersets ===
-factors as 2 × 3 × 5 × 73; among its divisors is the Woolhouse unit system, [[730edo|730]].
+factors into {{factorization|2190}}; among its divisors is the Woolhouse unit system, [[730edo|730]].
 [[4380edo]], which doubles 2190edo, provides a good correction to the harmonics 17 and 23.