730edo: Difference between revisions

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730edo is a very strong 5-limit system, but is also distinctly consistent up to the [[15-odd-limit]]. It tempers out the [[counterschisma]], {{monzo| -69 45 -1 }}, the minortone comma, {{monzo| -16 35 -17 }}, the kwazy comma, {{monzo| -53 10 16 }}, the whoosh comma, {{monzo| 37 25 -33 }}, and the pirate comma, {{monzo| -90 -15 49 }}. In the 7-limit it tempers out [[4375/4374]] and {{monzo| -21 0 3 5 }}, so that it [[support]]s the [[mitonic]] temperament. In the 11-limit, [[3025/3024]] and {{monzo| 4 -3 -6 4 1 }}, so that it supports the [[deca]] temperament. In the 13-limit, [[1001/1000]] and [[4225/4224]], supporting 13-limit deca.

[[W. S. B. Woolhouse]] proposed 730edo<ref name="summary">[~~http~~://www.webcitation.org/5zxZzQ3eS A summary of W. S. B. Woolhouse's Essay on musical intervals], 1999 by [[Joe Monzo]]</ref> as a [[Interval size measure|logarithmic measure of interval size]], sometimes called the '''Woolhouse unit'''. While 730 is divisible by 2, 5, 10, 73, 146 and 365, it is not divisible by 12, which ~~can be regarded~~ as ~~either a good thing or a bad one~~.

[[W. S. B. Woolhouse]] proposed 730edo<ref name="summary">[https://www.webcitation.org/5zxZzQ3eS A summary of W. S. B. Woolhouse's Essay on musical intervals], 1999 by [[Joe Monzo]]</ref> as a [[Interval size measure|logarithmic measure of interval size]], sometimes called the '''Woolhouse unit'''. While 730 is divisible by 2, 5, 10, 73, 146 and 365, it is not divisible by 12 and it is also deficient, with [[abundancy index]] of 0.82, which limits its application as an interval size measure.

=== Prime harmonics ===

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 edo is a very strong 5-limit system, but is also distinctly consistent up to the [[15-odd-limit]]. It tempers out the [[counterschisma]], {{monzo| -69 45 -1 }}, the minortone comma, {{monzo| -16 35 -17 }}, the kwazy comma, {{monzo| -53 10 16 }}, the whoosh comma, {{monzo| 37 25 -33 }}, and the pirate comma, {{monzo| -90 -15 49 }}. In the 7-limit it tempers out [[4375/4374]] and {{monzo| -21 0 3 5 }}, so that it [[support]]s the [[mitonic]] temperament. In the 11-limit, [[3025/3024]] and {{monzo| 4 -3 -6 4 1 }}, so that it supports the [[deca]] temperament. In the 13-limit, [[1001/1000]] and [[4225/4224]], supporting 13-limit deca.
-[[W. S. B. Woolhouse]] proposed 730edo<ref name="summary">[http://www.webcitation.org/5zxZzQ3eS A summary of W. S. B. Woolhouse's Essay on musical intervals], 1999 by [[Joe Monzo]]</ref> as a [[Interval size measure|logarithmic measure of interval size]], sometimes called the '''Woolhouse unit'''. While 730 is divisible by 2, 5, 10, 73, 146 and 365, it is not divisible by 12, which can be regarded as either a good thing or a bad one.
+[[W. S. B. Woolhouse]] proposed 730edo<ref name="summary">[https://www.webcitation.org/5zxZzQ3eS A summary of W. S. B. Woolhouse's Essay on musical intervals], 1999 by [[Joe Monzo]]</ref> as a [[Interval size measure|logarithmic measure of interval size]], sometimes called the '''Woolhouse unit'''. While 730 is divisible by 2, 5, 10, 73, 146 and 365, it is not divisible by 12 and it is also deficient, with [[abundancy index]] of 0.82, which limits its application as an interval size measure.
 === Prime harmonics ===