730edo: Difference between revisions

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The '''730 equal divisions of the octave''' ('''730edo'''), or the '''730(-tone) equal temperament''' ('''730tet''', '''730et''') divides the [[octave]] into 730 [[equal]] parts of 1.644 [[cent]]s each. It is a very strong five-limit system, but is also distinctly consistent up to the [[15-odd-limit]]. It tempers out 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 supports 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.

The '''730 equal divisions of the octave''' ('''730edo'''), or the '''730(-tone) equal temperament''' ('''730tet''', '''730et''') divides the [[octave]] into 730 [[equal]] parts of 1.644 [[cent]]s each. It is a very strong five-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 supports 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.

Revision as of 10:44, 23 October 2021 view source FloraC (talk \| contribs) autopatrolled, Bureaucrats, Interface administrators, Sysops 23,813 edits Cleanup and +prime error table ← Older edit		Revision as of 10:46, 23 October 2021 view source FloraC (talk \| contribs) autopatrolled, Bureaucrats, Interface administrators, Sysops 23,813 edits Mention counterschisma Newer edit →
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	The '''730 equal divisions of the octave''' ('''730edo'''), or the '''730(-tone) equal temperament''' ('''730tet''', '''730et''') divides the [[octave]] into 730 [[equal]] parts of 1.644 [[cent]]s each. It is a very strong five-limit system, but is also distinctly consistent up to the [[15-odd-limit]]. It tempers out 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 supports 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.		The '''730 equal divisions of the octave''' ('''730edo'''), or the '''730(-tone) equal temperament''' ('''730tet''', '''730et''') divides the [[octave]] into 730 [[equal]] parts of 1.644 [[cent]]s each. It is a very strong five-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 supports 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">[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.