300edo: Difference between revisions

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'''300edo''' is the [[EDO|equal division of the octave]] into 300 parts of exact 4 cents each. It is the largest number EDO which tempers out the [[pythagorean comma]], 531441/524288. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <300 475 697| (patent val), <300 476 697| (300b), and <300 475 696| (300c). Using the patent val, it tempers out 531441/524288 and |47 7 -25> in the 5-limit; 6144/6125, 50421/50000, and 1594323/1568000 in the 7-limit. Using the 300b val, it tempers out 393216/390625 and |51 -38 4> in the 5-limit; 153664/151875, 179200/177147, and 823543/819200 in the 7-limit. Using the 300bd val, it tempers out 10976/10935, 65536/64827, and 390625/388962 in the 7-limit. Using the 300c val, it tempers out 531441/524288 and |-58 0 25> in the 5-limit; 225/224, 250047/250000, and 69206436005/68719476736 in the 7-limit.

[[~~Category~~:~~Edo~~]]

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).

Using the patent val, it tempers out 531441/524288 and {{monzo| 47 7 -25 }} in the 5-limit; [[6144/6125]], [[50421/50000]], and 1594323/1568000 in the 7-limit.

Using the 300b val, it tempers out [[393216/390625]] and {{monzo| 51 -38 4 }} in the 5-limit; 153664/151875, 179200/177147, and [[823543/819200]] in the 7-limit. Using the 300bd val, it tempers out [[10976/10935]], 65536/64827, and [[390625/388962]] in the 7-limit.

Using the 300c val, it tempers out 531441/524288 and {{monzo| -58 0 25 }} in the 5-limit; [[225/224]], [[250047/250000]], and 69206436005/68719476736 in the 7-limit.

=== Odd harmonics ===

=== Subsets and supersets ===

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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-'''300edo''' is the [[EDO|equal division of the octave]] into 300 parts of exact 4 cents each. It is the largest number EDO which tempers out the [[pythagorean comma]], 531441/524288. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: &lt;300 475 697| (patent val), &lt;300 476 697| (300b), and &lt;300 475 696| (300c). Using the patent val, it tempers out 531441/524288 and |47 7 -25&gt; in the 5-limit; 6144/6125, 50421/50000, and 1594323/1568000 in the 7-limit. Using the 300b val, it tempers out 393216/390625 and |51 -38 4&gt; in the 5-limit; 153664/151875, 179200/177147, and 823543/819200 in the 7-limit. Using the 300bd val, it tempers out 10976/10935, 65536/64827, and 390625/388962 in the 7-limit. Using the 300c val, it tempers out 531441/524288 and |-58 0 25&gt; in the 5-limit; 225/224, 250047/250000, and 69206436005/68719476736 in the 7-limit.
+{{Infobox ET}}
+{{ED intro}}
-[[Category:Edo]]
+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).
+Using the patent val, it tempers out 531441/524288 and {{monzo| 47 7 -25 }} in the 5-limit; [[6144/6125]], [[50421/50000]], and 1594323/1568000 in the 7-limit.
+Using the 300b val, it tempers out [[393216/390625]] and {{monzo| 51 -38 4 }} in the 5-limit; 153664/151875, 179200/177147, and [[823543/819200]] in the 7-limit. Using the 300bd val, it tempers out [[10976/10935]], 65536/64827, and [[390625/388962]] in the 7-limit.
+Using the 300c val, it tempers out 531441/524288 and {{monzo| -58 0 25 }} in the 5-limit; [[225/224]], [[250047/250000]], and 69206436005/68719476736 in the 7-limit.
+=== Odd harmonics ===
+{{Harmonics in equal|300}}
+=== Subsets and supersets ===
+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]]