136edo: Difference between revisions
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{{Infobox ET}} | |||
'''136edo''' is the [[EDO|equal division of the octave]] into 136 parts of 8.8235 cents each. It is closely related to [[68edo]], but the patent vals differ on the mapping for 13. It is [[contorted]] in the 11-limit, tempering out 121/120, 176/175, 245/243, and 1375/1372. Using the patent val, it tempers out 169/168 and 847/845 in the 13-limit; 136/135, 154/153, 256/255, 561/560, and 1089/1088 in the 17-limit; 190/189, 343/342, 361/360, 363/361, and 400/399 in the 19-limit. Using the 136b val, it tempers out 81/80, 99/98, 126/125, and 136410197/134217728 in the 11-limit; 847/845, 2704/2695, 3042/3025, 5445/5408, and 15379/15360 in the 13-limit, making it close to optimal as an 11-limit meantone tuning [http://www.tonalsoft.com/enc/m/meantone-error.aspx | by some metrics]. Using the 136bcd val, it tempers out 540/539, 1375/1372, 2079/2048, and 3125/3072 in the 11-limit; 105/104, 847/845, 1188/1183, 1287/1280, and 6561/6500 in the 13-limit. Using the 136e val, it tempers out 245/243, 2048/2025, 2401/2400, and 2560/2541 in the 11-limit; 169/168, 352/351, 832/825, 1001/1000, and 1716/1715 in the 13-limit. Using the 136ef val, it tempers out 196/195, 325/324, 364/363, 512/507, and 625/624 in the 13-limit. | '''136edo''' is the [[EDO|equal division of the octave]] into 136 parts of 8.8235 cents each. It is closely related to [[68edo]], but the patent vals differ on the mapping for 13. It is [[contorted]] in the 11-limit, tempering out 121/120, 176/175, 245/243, and 1375/1372. Using the patent val, it tempers out 169/168 and 847/845 in the 13-limit; 136/135, 154/153, 256/255, 561/560, and 1089/1088 in the 17-limit; 190/189, 343/342, 361/360, 363/361, and 400/399 in the 19-limit. Using the 136b val, it tempers out 81/80, 99/98, 126/125, and 136410197/134217728 in the 11-limit; 847/845, 2704/2695, 3042/3025, 5445/5408, and 15379/15360 in the 13-limit, making it close to optimal as an 11-limit meantone tuning [http://www.tonalsoft.com/enc/m/meantone-error.aspx | by some metrics]. Using the 136bcd val, it tempers out 540/539, 1375/1372, 2079/2048, and 3125/3072 in the 11-limit; 105/104, 847/845, 1188/1183, 1287/1280, and 6561/6500 in the 13-limit. Using the 136e val, it tempers out 245/243, 2048/2025, 2401/2400, and 2560/2541 in the 11-limit; 169/168, 352/351, 832/825, 1001/1000, and 1716/1715 in the 13-limit. Using the 136ef val, it tempers out 196/195, 325/324, 364/363, 512/507, and 625/624 in the 13-limit. | ||
{{Harmonics in equal|136}} | {{Harmonics in equal|136}} | ||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||
Revision as of 19:04, 4 October 2022
| ← 135edo | 136edo | 137edo → |
136edo is the equal division of the octave into 136 parts of 8.8235 cents each. It is closely related to 68edo, but the patent vals differ on the mapping for 13. It is contorted in the 11-limit, tempering out 121/120, 176/175, 245/243, and 1375/1372. Using the patent val, it tempers out 169/168 and 847/845 in the 13-limit; 136/135, 154/153, 256/255, 561/560, and 1089/1088 in the 17-limit; 190/189, 343/342, 361/360, 363/361, and 400/399 in the 19-limit. Using the 136b val, it tempers out 81/80, 99/98, 126/125, and 136410197/134217728 in the 11-limit; 847/845, 2704/2695, 3042/3025, 5445/5408, and 15379/15360 in the 13-limit, making it close to optimal as an 11-limit meantone tuning | by some metrics. Using the 136bcd val, it tempers out 540/539, 1375/1372, 2079/2048, and 3125/3072 in the 11-limit; 105/104, 847/845, 1188/1183, 1287/1280, and 6561/6500 in the 13-limit. Using the 136e val, it tempers out 245/243, 2048/2025, 2401/2400, and 2560/2541 in the 11-limit; 169/168, 352/351, 832/825, 1001/1000, and 1716/1715 in the 13-limit. Using the 136ef val, it tempers out 196/195, 325/324, 364/363, 512/507, and 625/624 in the 13-limit.
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +3.93 | +1.92 | +1.76 | -0.97 | -4.26 | -2.29 | -2.97 | +0.93 | +2.49 | -3.13 | -1.80 |
| Relative (%) | +44.5 | +21.8 | +20.0 | -11.0 | -48.3 | -26.0 | -33.7 | +10.5 | +28.2 | -35.5 | -20.4 | |
| Steps (reduced) |
216 (80) |
316 (44) |
382 (110) |
431 (23) |
470 (62) |
503 (95) |
531 (123) |
556 (12) |
578 (34) |
597 (53) |
615 (71) | |