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]].

180edo 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. It is a strong 2.5.13 subgroup system.

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.

=== Odd harmonics ===

=== Subsets and supersets ===

180edo is the 11th [[highly composite EDO]].

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

[[Category:Highly composite]]

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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.
+{{EDO intro|180}}
-edo is the 11th [[superabundant EDO]].
+edo 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. It is a strong 2.5.13 subgroup system.
+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.
+=== Odd harmonics ===
+{{harmonics in equal|180}}
+=== Subsets and supersets ===
+edo is the 11th [[highly composite EDO]].
 [[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
 [[Category:Highly composite]]