161edo: Difference between revisions
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The ''161 equal division'' divides the octave into 161 equal parts of 7.453 cents each. It tempers out the Würschmidt comma, 393216/390625, in the 5-limit; 3136/3125, 6144/6125 and 2401/2400 in the 7-limit; 243/242, 441/440, 540/539 and 5632/5625 in the 11-limit; and 1188/1183, 351/350, 847/845, 1575/1573, 1001/1000 and 1716/1715 in the 13-limit. It serves as the optimal patent val for [[ | The '''161 equal division''' divides the octave into 161 equal parts of 7.453 cents each. It tempers out the [[Würschmidt comma]], 393216/390625, in the 5-limit; [[3136/3125]], [[6144/6125]] and [[2401/2400]] in the 7-limit; [[243/242]], [[441/440]], [[540/539]] and 5632/5625 in the 11-limit; and [[1188/1183]], [[351/350]], [[847/845]], [[1575/1573]], [[1001/1000]] and [[1716/1715]] in the 13-limit. It serves as the [[optimal patent val]] for the [[mintone]] temperament in the 5-, 7-, 11- and 13-limits. | ||
== | == Prime harmonics == | ||
161edo is notable as being low in [[29-limit]] relative error in the 100 to 200 range. | 161edo is notable as being low in [[29-limit]] relative error in the 100 to 200 range. | ||
{{ | |||
{{Harmonics in equal|161}} | |||
[[Category:Equal divisions of the octave]] | |||
[[Category:Mintone]] | |||
Revision as of 13:33, 6 March 2022
The 161 equal division divides the octave into 161 equal parts of 7.453 cents each. It tempers out the Würschmidt comma, 393216/390625, in the 5-limit; 3136/3125, 6144/6125 and 2401/2400 in the 7-limit; 243/242, 441/440, 540/539 and 5632/5625 in the 11-limit; and 1188/1183, 351/350, 847/845, 1575/1573, 1001/1000 and 1716/1715 in the 13-limit. It serves as the optimal patent val for the mintone temperament in the 5-, 7-, 11- and 13-limits.
Prime harmonics
161edo is notable as being low in 29-limit relative error in the 100 to 200 range.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -1.33 | +1.26 | +0.12 | +0.23 | +1.71 | -0.61 | +0.62 | -2.19 | -1.01 | +2.79 |
| Relative (%) | +0.0 | -17.9 | +17.0 | +1.6 | +3.2 | +22.9 | -8.2 | +8.4 | -29.3 | -13.5 | +37.4 | |
| Steps (reduced) |
161 (0) |
255 (94) |
374 (52) |
452 (130) |
557 (74) |
596 (113) |
658 (14) |
684 (40) |
728 (84) |
782 (138) |
798 (154) | |