221edo: Difference between revisions
m Infobox ET added |
m Added "harmonics in equal" table |
||
| Line 1: | Line 1: | ||
{{Infobox ET}} | {{Infobox ET}} | ||
'''221edo''' is the [[EDO|equal division of the octave]] into 221 parts of 5.4299 [[cent]]s each | '''221edo''' is the [[EDO|equal division of the octave]] into 221 parts of 5.4299 [[cent]]s each. | ||
It tempers out 2109375/2097152 (semicomma) and 2541865828329/2500000000000 in the 5-limit; 1029/1024, 19683/19600, and 235298/234375 in the 7-limit, so that it provides the [[optimal patent val]] for the 7-limit [[Gamelismic clan|hemiseven temperament]]. | |||
Using the patent val, it tempers out 540/539, 2835/2816, 4375/4356, and 33614/33275 in the 11-limit; 364/363, 625/624, 1701/1690, and 2200/2197 in the 13-limit. | |||
Using the 221ef val, it tempers out 385/384, 441/440, 24057/24010, and 43923/43750 in the 11-limit; 351/350, 676/675, 1287/1280, 1573/1568, and 14641/14625 in the 13-limit; 273/272, 561/560, 715/714, 833/832, 2187/2176, and 10648/10625 in the 17-limit, supporting the 17-limit hemiseven and the 11-limit [[Semicomma family|triwell]]. | |||
{{Harmonics in equal|221}} | |||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||
Revision as of 03:39, 24 June 2023
| ← 220edo | 221edo | 222edo → |
221edo is the equal division of the octave into 221 parts of 5.4299 cents each.
It tempers out 2109375/2097152 (semicomma) and 2541865828329/2500000000000 in the 5-limit; 1029/1024, 19683/19600, and 235298/234375 in the 7-limit, so that it provides the optimal patent val for the 7-limit hemiseven temperament.
Using the patent val, it tempers out 540/539, 2835/2816, 4375/4356, and 33614/33275 in the 11-limit; 364/363, 625/624, 1701/1690, and 2200/2197 in the 13-limit.
Using the 221ef val, it tempers out 385/384, 441/440, 24057/24010, and 43923/43750 in the 11-limit; 351/350, 676/675, 1287/1280, 1573/1568, and 14641/14625 in the 13-limit; 273/272, 561/560, 715/714, 833/832, 2187/2176, and 10648/10625 in the 17-limit, supporting the 17-limit hemiseven and the 11-limit triwell.
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.50 | -0.79 | -2.31 | +2.42 | +2.53 | +1.10 | -2.30 | -1.79 | +1.13 | +1.62 | +1.59 |
| Relative (%) | -27.7 | -14.6 | -42.5 | +44.7 | +46.6 | +20.3 | -42.3 | -32.9 | +20.8 | +29.8 | +29.3 | |
| Steps (reduced) |
350 (129) |
513 (71) |
620 (178) |
701 (38) |
765 (102) |
818 (155) |
863 (200) |
903 (19) |
939 (55) |
971 (87) |
1000 (116) | |