267edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
'''267edo''' is the [[EDO|equal division of the octave]] into 267 parts of 4.494382 [[cent]]s each. | '''267edo''' is the [[EDO|equal division of the octave]] into 267 parts of 4.494382 [[cent]]s each. | ||
In the 5-limit, it tempers out both [[Graviton|129140163/128000000]] and 274877906944/274658203125, enabling it to support both [[Gravity_family|gravity]] and [[Luna_family|luna]] temperaments. In the 7-limit, it tempers out 1029/1024, 3136/3125, 50421/50000, 65625/65536, 9882516/9765625 and 28824005/28697814, enabling it to support [[Gamelismic_clan|gamelismic]], [[Hemimean_family|hemimean]] and [[Trimyna_family|trimyna]] temperaments among others. In the 11-limit, it tempers out 243/242, 1375/1372, 4000/3993, 6144/6125, 8019/8000, 16896/16807, 30375/30184, 43923/43904 and [[Quartisma|117440512/117406179]]. In the 13-limit, it tempers out 351/350, 1375/1372, 1575/1573, 2080/2079, [[4096/4095]], 4225/4224 and 59535/59488. | |||
{{Harmonics in equal|267}} | |||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||
[[Category:Gravity]] | [[Category:Gravity]] | ||
[[Category:Luna]] | [[Category:Luna]] | ||
[[Category:Quartismic]] | [[Category:Quartismic]] | ||
Revision as of 03:26, 24 June 2023
| ← 266edo | 267edo | 268edo → |
267edo is the equal division of the octave into 267 parts of 4.494382 cents each.
In the 5-limit, it tempers out both 129140163/128000000 and 274877906944/274658203125, enabling it to support both gravity and luna temperaments. In the 7-limit, it tempers out 1029/1024, 3136/3125, 50421/50000, 65625/65536, 9882516/9765625 and 28824005/28697814, enabling it to support gamelismic, hemimean and trimyna temperaments among others. In the 11-limit, it tempers out 243/242, 1375/1372, 4000/3993, 6144/6125, 8019/8000, 16896/16807, 30375/30184, 43923/43904 and 117440512/117406179. In the 13-limit, it tempers out 351/350, 1375/1372, 1575/1573, 2080/2079, 4096/4095, 4225/4224 and 59535/59488.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.83 | +0.20 | +1.96 | +1.49 | -0.08 | -1.58 | -0.88 | +0.94 | -0.36 | +1.03 |
| Relative (%) | +0.0 | -18.5 | +4.5 | +43.6 | +33.2 | -1.7 | -35.3 | -19.7 | +20.9 | -8.1 | +23.0 | |
| Steps (reduced) |
267 (0) |
423 (156) |
620 (86) |
750 (216) |
924 (123) |
988 (187) |
1091 (23) |
1134 (66) |
1208 (140) |
1297 (229) |
1323 (255) | |