730edo: Difference between revisions

Line 3:

== Theory ==

730edo is a very strong 5-limit system, but is also [[consistency|distinctly consistent]] up to the [[15-odd-limit]]. The equal temperament [[tempering out|tempers out]] the {{monzo| -69 45 -1 }} ([[counterschisma]]), {{monzo| -16 35 -17 }} (minortone comma), {{monzo| -53 10 16 }} (kwazy comma), {{monzo| 37 25 -33 }} (whoosh comma), and {{monzo| -90 -15 49 }} (pirate comma). 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.

730edo is a very strong 5-limit system, but is also [[consistency|distinctly consistent]] up to the [[15-odd-limit]]. The equal temperament [[tempering out|tempers out]] the {{monzo| -69 45 -1 }} ([[counterschisma]]), {{monzo| -16 35 -17 }} (minortone comma), {{monzo| -53 10 16 }} ([[kwazy comma]]), {{monzo| 37 25 -33 }} (whoosh comma), and {{monzo| -90 -15 49 }} (pirate comma). 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 as a [[interval size measure|logarithmic measure of interval size]]<ref name="summary">[https://www.webcitation.org/5zxZzQ3eS A summary of W. S. B. Woolhouse's Essay on musical intervals], 1999 by [[Joseph Monzo]]</ref>, 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.

{{W|W. S. B. Woolhouse}} proposed 730edo as a [[interval size measure|logarithmic measure of interval size]]<ref name="summary">[https://www.webcitation.org/5zxZzQ3eS A summary of W. S. B. Woolhouse's Essay on musical intervals], 1999 by [[Joseph Monzo]]</ref>, 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 ===

Line 93:

! Generator*

! Cents*

! Associated<br>Ratio

! Associated<br>Ratio*

! Temperaments

|-

@@ Line 3: / Line 3: @@
 == Theory ==
-edo is a very strong 5-limit system, but is also [[consistency|distinctly consistent]] up to the [[15-odd-limit]]. The equal temperament [[tempering out|tempers out]] the {{monzo| -69 45 -1 }} ([[counterschisma]]), {{monzo| -16 35 -17 }} (minortone comma), {{monzo| -53 10 16 }} (kwazy comma), {{monzo| 37 25 -33 }} (whoosh comma), and {{monzo| -90 -15 49 }} (pirate comma). 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.
+edo is a very strong 5-limit system, but is also [[consistency|distinctly consistent]] up to the [[15-odd-limit]]. The equal temperament [[tempering out|tempers out]] the {{monzo| -69 45 -1 }} ([[counterschisma]]), {{monzo| -16 35 -17 }} (minortone comma), {{monzo| -53 10 16 }} ([[kwazy comma]]), {{monzo| 37 25 -33 }} (whoosh comma), and {{monzo| -90 -15 49 }} (pirate comma). 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 as a [[interval size measure|logarithmic measure of interval size]]<ref name="summary">[https://www.webcitation.org/5zxZzQ3eS A summary of W. S. B. Woolhouse's Essay on musical intervals], 1999 by [[Joseph Monzo]]</ref>, 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.
+{{W|W. S. B. Woolhouse}} proposed 730edo as a [[interval size measure|logarithmic measure of interval size]]<ref name="summary">[https://www.webcitation.org/5zxZzQ3eS A summary of W. S. B. Woolhouse's Essay on musical intervals], 1999 by [[Joseph Monzo]]</ref>, 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 ===
@@ Line 93: / Line 93: @@
 ! Generator*
 ! Cents*
-! Associated<br>Ratio
+! Associated<br>Ratio*
 ! Temperaments
 |-