279edo: Difference between revisions

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~~'''279edo''' is the [[EDO|equal division of the octave]] into 279 parts of 4.3011 cents each.~~

== ~~Theory~~ ==

279edo is closely related to [[31edo]], but the [[patent val]]s differ on the mapping for [[3/1|3]]. It [[tempering out|tempers out]] 78732/78125 ([[sensipent comma]]) and {{monzo| -64 36 3 }} in the 5-limit, as well as {{monzo| -68 18 17 }} (vavoom comma); [[3136/3125]], [[19683/19600]], and [[823543/819200]] in the 7-limit. Using the [[patent val]], it tempers out [[441/440]], [[5632/5625]], 24057/24010, and 35937/35840 in the 11-limit; [[351/350]], [[676/675]], [[1716/1715]], [[4225/4224]], and [[6656/6655]] in the 13-limit.

5 steps of 279edo is close to the syntonic comma, [[81/80]]. Unfortunately, it is not compatible with the patent val, but the 279c val.

=== Prime harmonics ===

~~[[Category:Equal divisions of the octave|###]]~~

It is closely related to [[31edo]], but the patent vals differ on the mapping for 3. It tempers out 78732/78125 (sensipent comma) and |-64 36 3> in the 5-limit, as well as |-68 18 17> (vavoom comma); 3136/3125, 19683/19600, and 823543/819200 in the 7-limit. Using the patent val, it tempers out 441/440, 5632/5625, 24057/24010, and 35937/35840 in the 11-limit; 351/350, 676/675, 1716/1715, 4225/4224, and 6656/6655 in the 13-limit.

~~5 steps of~~ 279edo ~~closely represent the syntonic comma~~, [[~~81/80~~]].~~~~

=== Subsets and supersets ===

Since 279 factors into {{factorization|279}}, 279edo has subset edos {{EDOs| 3, 9, 31, and 93 }}. [[1395edo]], which divides its step into five, makes for a strong higher-limit system.

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 {{Infobox ET}}
-'''279edo''' is the [[EDO|equal division of the octave]] into 279 parts of 4.3011 cents each.
+{{ED intro}}
-== Theory ==
+edo is closely related to [[31edo]], but the [[patent val]]s differ on the mapping for [[3/1|3]]. It [[tempering out|tempers out]] 78732/78125 ([[sensipent comma]]) and {{monzo| -64 36 3 }} in the 5-limit, as well as {{monzo| -68 18 17 }} (vavoom comma); [[3136/3125]], [[19683/19600]], and [[823543/819200]] in the 7-limit. Using the [[patent val]], it tempers out [[441/440]], [[5632/5625]], 24057/24010, and 35937/35840 in the 11-limit; [[351/350]], [[676/675]], [[1716/1715]], [[4225/4224]], and [[6656/6655]] in the 13-limit.
+steps of 279edo is close to the syntonic comma, [[81/80]]. Unfortunately, it is not compatible with the patent val, but the 279c val.
+=== Prime harmonics ===
 {{Harmonics in equal|279}}
-[[Category:Equal divisions of the octave|###]]
-It is closely related to [[31edo]], but the patent vals differ on the mapping for 3. It tempers out 78732/78125 (sensipent comma) and |-64 36 3&gt; in the 5-limit, as well as |-68 18 17&gt; (vavoom comma); 3136/3125, 19683/19600, and 823543/819200 in the 7-limit. Using the patent val, it tempers out 441/440, 5632/5625, 24057/24010, and 35937/35840 in the 11-limit; 351/350, 676/675, 1716/1715, 4225/4224, and 6656/6655 in the 13-limit.
-steps of 279edo closely represent the syntonic comma, [[81/80]].<!-- 3-digit number -->
+=== Subsets and supersets ===
+Since 279 factors into {{factorization|279}}, 279edo has subset edos {{EDOs| 3, 9, 31, and 93 }}. [[1395edo]], which divides its step into five, makes for a strong higher-limit system.