1147edo: Difference between revisions

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1147edo can be defined as the unique ET in the [[2.3.7 subgroup]] that tempers out the [[Don Page comma]]s among the intervals [[9/8]], [[8/7]], and [[7/6]], and therefore contains [[28ed4/3]] and [[32ed9/7]] within it. This edo notably also tempers out the [[quartisma]], by virtue of 28ed4/3 mapping 7/6 to a number of steps divisible by 5. Therefore, the representation of [[33/32]] is accurate and the edo overall excels in the [[2.3.7.11 subgroup]], with an additional very good prime 43.

In [[regular temperament]] terms, in addition to the quartisma, 1147edo also tempers out the [[elysia]] (117649/117612), and the comma {{monzo|18 -31 0 0 9}}, which sets [[44/27]] equal to [[9edt|4\9edt]] (alternatively the difference between the [[gothic comma]] and nine [[~~rastmas~~]]), in the 2.3.7.11 subgroup.

In [[regular temperament]] terms, in addition to the quartisma, 1147edo also tempers out the [[elysia]] (117649/117612), and the comma {{monzo|18 -31 0 0 9}}, which sets [[44/27]] equal to [[9edt|4\9edt]] (alternatively the difference between the [[gothic comma]] and nine [[rastma]]s), in the 2.3.7.11 subgroup.

=== Odd harmonics ===

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 edo can be defined as the unique ET in the [[2.3.7 subgroup]] that tempers out the [[Don Page comma]]s among the intervals [[9/8]], [[8/7]], and [[7/6]], and therefore contains [[28ed4/3]] and [[32ed9/7]] within it. This edo notably also tempers out the [[quartisma]], by virtue of 28ed4/3 mapping 7/6 to a number of steps divisible by 5. Therefore, the representation of [[33/32]] is accurate and the edo overall excels in the [[2.3.7.11 subgroup]], with an additional very good prime 43.
-In [[regular temperament]] terms, in addition to the quartisma, 1147edo also tempers out the [[elysia]] (117649/117612), and the comma {{monzo|18 -31 0 0 9}}, which sets [[44/27]] equal to [[9edt|4\9edt]] (alternatively the difference between the [[gothic comma]] and nine [[rastmas]]), in the 2.3.7.11 subgroup.
+In [[regular temperament]] terms, in addition to the quartisma, 1147edo also tempers out the [[elysia]] (117649/117612), and the comma {{monzo|18 -31 0 0 9}}, which sets [[44/27]] equal to [[9edt|4\9edt]] (alternatively the difference between the [[gothic comma]] and nine [[rastma]]s), in the 2.3.7.11 subgroup.
 === Odd harmonics ===