165edo: Difference between revisions
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[[{{PAGENAME}}]] is the [[EDO|equal division of the octave]] into 165 parts of {{#expr: 1200/165}} [[cent]]s each. That's the triple of [[55edo]]!!! It is inconsistent to the 5-limit and higher limit, with | [[{{PAGENAME}}]] is the [[EDO|equal division of the octave]] into 165 parts of {{#expr: 1200/165}} [[cent]]s each. That's the triple of [[55edo]]!!! It is inconsistent to the 5-limit and higher limit, with, like in any [[Equal-step Tuning]] (ET), infinitely many mappings possible for the 5-limit, including, but not limited to: <165 262 383| (patent val) and <165 261 383| (165b) and <165 261 384| ([[K/N|165/3]] generic meantone val). Using the patent val (with a sharp fifth), it tempers out 1638400/1594323 (immunity comma) and 1220703125/1207959552 (ditonma) in the 5-limit; 4000/3969, 65625/65536, and 84035/82944 in the 7-limit; 385/384, 2401/2376, 3388/3375, and 6655/6561 in the 11-limit; 196/195, 364/363, 676/675, 3185/3168, and 3200/3159 in the 13-limit. Using the 165b val (with a flat fifth), it tempers out 34171875/33554432 (Ampersand's comma) and 129140163/125000000 in the 5-limit; 225/224, 1029/1024, and 100442349/97656250 in the 7-limit; 1944/1925, 2187/2156, 4000/3993, and 12005/11979 in the 11-limit; 144/143, 351/350, 625/624, 847/845, and 9261/9152 in the 13-limit. Using the 165bf val, it tempers out 364/363, 975/968, 1001/1000, 1701/1690, and 1716/1715 in the 13-limit. | ||
[[Category:Edo]] | [[Category:Edo]] | ||
Revision as of 18:04, 17 July 2020
165edo is the equal division of the octave into 165 parts of 7.2727272727273 cents each. That's the triple of 55edo!!! It is inconsistent to the 5-limit and higher limit, with, like in any Equal-step Tuning (ET), infinitely many mappings possible for the 5-limit, including, but not limited to: <165 262 383| (patent val) and <165 261 383| (165b) and <165 261 384| (165/3 generic meantone val). Using the patent val (with a sharp fifth), it tempers out 1638400/1594323 (immunity comma) and 1220703125/1207959552 (ditonma) in the 5-limit; 4000/3969, 65625/65536, and 84035/82944 in the 7-limit; 385/384, 2401/2376, 3388/3375, and 6655/6561 in the 11-limit; 196/195, 364/363, 676/675, 3185/3168, and 3200/3159 in the 13-limit. Using the 165b val (with a flat fifth), it tempers out 34171875/33554432 (Ampersand's comma) and 129140163/125000000 in the 5-limit; 225/224, 1029/1024, and 100442349/97656250 in the 7-limit; 1944/1925, 2187/2156, 4000/3993, and 12005/11979 in the 11-limit; 144/143, 351/350, 625/624, 847/845, and 9261/9152 in the 13-limit. Using the 165bf val, it tempers out 364/363, 975/968, 1001/1000, 1701/1690, and 1716/1715 in the 13-limit.