267edo
| ← 266edo | 267edo | 268edo → |
267 equal divisions of the octave (abbreviated 267edo or 267ed2), also called 267-tone equal temperament (267tet) or 267 equal temperament (267et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 267 equal parts of about 4.49 ¢ each. Each step represents a frequency ratio of 21/267, or the 267th root of 2.
267edo is a fairly good 5-limit tuning, but inconsistent in the 7-odd-limit. In the 5-limit, the equal temperament tempers out both 129140163/128000000 (graviton) and 274877906944/274658203125 (luna comma), enabling it to support gravity and luna temperaments.
The 267d val being the best, tempers out 1029/1024, 3136/3125, 50421/50000, 65625/65536, 9882516/9765625 and 28824005/28697814, supporting gamelismic, hemimean and trimyna temperaments among others; in the 11-limit, 243/242, 1375/1372, 4000/3993, 6144/6125, 8019/8000; in the 13-limit, 351/350, 1375/1372, 1575/1573, 2080/2079, 4096/4095, 4225/4224 and 59535/59488.
Prime harmonics
| 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 | -18 | +5 | +44 | +33 | -2 | -35 | -20 | +21 | -8 | +23 | |
| Steps (reduced) |
267 (0) |
423 (156) |
620 (86) |
750 (216) |
924 (123) |
988 (187) |
1091 (23) |
1134 (66) |
1208 (140) |
1297 (229) |
1323 (255) | |