300edo: Difference between revisions

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300edo is the largest-number edo which [[tempering out|tempers out]] the [[~~pythagorean~~ comma]], 531441/524288, in the [[patent val]].

300edo's step size is called a '''savart''' when used as an [[interval size unit]].

== Theory ==

300edo is the largest-number edo which [[tempering out|tempers out]] the [[Pythagorean comma]], 531441/524288, in the [[patent val]].

It is in[[consistent]] to the [[5-odd-limit]] and higher, with three mappings possible for the 5-limit: {{val| 300 475 697 }} (patent val), {{val| 300 '''476''' 697 }} (300b), and {{val| 300 475 '''696''' }} (300c).

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=== Subsets and supersets ===

Since 300 factors into ~~{{factorization|300}}~~, 300edo has subset edos {{EDOs| 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, and 150 }}. [[600edo]], which doubles it, gives a good correction to its approximation of the 5-limit.

Since 300 factors into 2<sup>2</sup> × 3 × 5<sup>2</sup>, 300edo has subset edos {{EDOs| 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, and 150 }}. [[600edo]], which doubles it, gives a good correction to its approximation of the 5-limit.

== External links ==

* [http://tonalsoft.com/enc/s/savart.aspx savart] on [[Tonalsoft Encyclopedia]]

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 {{Infobox ET}}
-{{EDO intro}}
+{{ED intro}}
-edo is the largest-number edo which [[tempering out|tempers out]] the [[pythagorean comma]], 531441/524288, in the [[patent val]].
+edo's step size is called a '''savart''' when used as an [[interval size unit]].
+== Theory ==
+edo is the largest-number edo which [[tempering out|tempers out]] the [[Pythagorean comma]], 531441/524288, in the [[patent val]].
 It is in[[consistent]] to the [[5-odd-limit]] and higher, with three mappings possible for the 5-limit: {{val| 300 475 697 }} (patent val), {{val| 300 '''476''' 697 }} (300b), and {{val| 300 475 '''696''' }} (300c).
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 === Subsets and supersets ===
-Since 300 factors into {{factorization|300}}, 300edo has subset edos {{EDOs| 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, and 150 }}. [[600edo]], which doubles it, gives a good correction to its approximation of the 5-limit.
+Since 300 factors into 2<sup>2</sup> × 3 × 5<sup>2</sup>, 300edo has subset edos {{EDOs| 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, and 150 }}. [[600edo]], which doubles it, gives a good correction to its approximation of the 5-limit.
+== External links ==
+* [http://tonalsoft.com/enc/s/savart.aspx savart] on [[Tonalsoft Encyclopedia]]