90edo: Difference between revisions

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Since 90 factors into primes as 2 x 3<sup>2</sup> × 5, 90 has subset edos {{EDOs| 2, 3, 5, 6, 9, 10, 15, 18, 30, 45 }}.

As a composite edo, the smallest subsets it lacks are subsets of [[4edo|4]], [[7edo|7]] and [[8edo|8]], but 13\90 = 173.333{{cent}} offers a good approximation to 1\7 = 171.428{{c}}, and instead of 1\8 = 150{{cent}}, it has 27\80 = 146.667{{cent}}, serving a similar function.

As a composite edo, the smallest subsets it lacks are subsets of [[4edo|4]], [[7edo|7]] and [[8edo|8]], but 13\90 = 173.333{{cent}} offers a good approximation to 1\7 = 171.428{{c}}, and instead of 1\8 = 150{{cent}}, it has 27\90 = 146.667{{cent}}, serving a similar function.

Like [[80edo]], this may offer a relatively unexplored strategy of "tempered [[detempering]]", a sort of middle path between complete detempering to JI (which lacks the simplifications and unique comma pumping and structural opportunities of tempering) and not detempering the small edo at all (which can lead to challenging interpretation of harmony if one's goal is approximation to JI).

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 Since 90 factors into primes as 2 x 3<sup>2</sup> × 5, 90 has subset edos {{EDOs| 2, 3, 5, 6, 9, 10, 15, 18, 30, 45 }}.
-As a composite edo, the smallest subsets it lacks are subsets of [[4edo|4]], [[7edo|7]] and [[8edo|8]], but 13\90 = 173.333{{cent}} offers a good approximation to 1\7 = 171.428{{c}}, and instead of 1\8 = 150{{cent}}, it has 27\80 = 146.667{{cent}}, serving a similar function.
+As a composite edo, the smallest subsets it lacks are subsets of [[4edo|4]], [[7edo|7]] and [[8edo|8]], but 13\90 = 173.333{{cent}} offers a good approximation to 1\7 = 171.428{{c}}, and instead of 1\8 = 150{{cent}}, it has 27\90 = 146.667{{cent}}, serving a similar function.
 Like [[80edo]], this may offer a relatively unexplored strategy of "tempered [[detempering]]", a sort of middle path between complete detempering to JI (which lacks the simplifications and unique comma pumping and structural opportunities of tempering) and not detempering the small edo at all (which can lead to challenging interpretation of harmony if one's goal is approximation to JI).