180edo: Difference between revisions

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'''180edo''' is the [[EDO|equal division of the octave]] into 180 parts of 6.6667 cents each. It tempers out 531441/524288 (pythagorean comma) and 30958682112/30517578125 (trisedodge comma) in the 5-limit, as well as 31381059609/30517578125 (mowgli) and 274877906944/274658203125 (hemithirds comma); 1029/1024, 3136/3125, and 118098/117649 in the 7-limit. Using the patent val, it tempers out 540/539, 2835/2816, 4000/3993, and 6912/6875 in the 11-limit; 351/350, 364/363, 1001/1000, and 1701/1690 in the 13-limit. Using the 180e val, it tempers out 385/384, 441/440, 3388/3375, and 216513/214375 in the 11-limit; 351/350, 1188/1183, 1287/1280, 1573/1568, and 3146/3125 in the 13-limit.

~~180edo is~~ the ~~11th~~ [[~~superabundant EDO~~]].

The equal temperament [[tempering out|tempers out]] 531441/524288 ([[pythagorean comma]]) and 30958682112/30517578125 (trisedodge comma) in the 5-limit, as well as 31381059609/30517578125 (mowgli comma) and 274877906944/274658203125 (hemithirds comma); [[1029/1024]], [[3136/3125]], and 118098/117649 in the 7-limit.

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

Using the [[patent val]], it tempers out [[540/539]], 2835/2816, [[4000/3993]], and 6912/6875 in the 11-limit; [[351/350]], [[364/363]], [[1001/1000]], and 1701/1690 in the 13-limit. Using the 180e val, it tempers out [[385/384]], [[441/440]], [[3388/3375]], and 216513/214375 in the 11-limit; 351/350, [[1188/1183]], [[1287/1280]], [[1573/1568]], and 3146/3125 in the 13-limit.

[[~~Category:Highly~~ composite]]

=== Odd harmonics ===

=== Subsets and supersets ===

180edo is the 11th [[highly composite edo]]; its nontrivial subsets are: {{EDOs| 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, and 90 }}.

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 {{Infobox ET}}
-'''180edo''' is the [[EDO|equal division of the octave]] into 180 parts of 6.6667 cents each. It tempers out 531441/524288 (pythagorean comma) and 30958682112/30517578125 (trisedodge comma) in the 5-limit, as well as 31381059609/30517578125 (mowgli) and 274877906944/274658203125 (hemithirds comma); 1029/1024, 3136/3125, and 118098/117649 in the 7-limit. Using the patent val, it tempers out 540/539, 2835/2816, 4000/3993, and 6912/6875 in the 11-limit; 351/350, 364/363, 1001/1000, and 1701/1690 in the 13-limit. Using the 180e val, it tempers out 385/384, 441/440, 3388/3375, and 216513/214375 in the 11-limit; 351/350, 1188/1183, 1287/1280, 1573/1568, and 3146/3125 in the 13-limit.
+{{ED intro}}
-edo is the 11th [[superabundant EDO]].
+The equal temperament [[tempering out|tempers out]] 531441/524288 ([[pythagorean comma]]) and 30958682112/30517578125 (trisedodge comma) in the 5-limit, as well as 31381059609/30517578125 (mowgli comma) and 274877906944/274658203125 (hemithirds comma); [[1029/1024]], [[3136/3125]], and 118098/117649 in the 7-limit.
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+Using the [[patent val]], it tempers out [[540/539]], 2835/2816, [[4000/3993]], and 6912/6875 in the 11-limit; [[351/350]], [[364/363]], [[1001/1000]], and 1701/1690 in the 13-limit. Using the 180e val, it tempers out [[385/384]], [[441/440]], [[3388/3375]], and 216513/214375 in the 11-limit; 351/350, [[1188/1183]], [[1287/1280]], [[1573/1568]], and 3146/3125 in the 13-limit.
-[[Category:Highly composite]]
+=== Odd harmonics ===
+{{harmonics in equal|180}}
+=== Subsets and supersets ===
+edo is the 11th [[highly composite edo]]; its nontrivial subsets are: {{EDOs| 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, and 90 }}.