267edo: Difference between revisions
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{{Infobox ET}} | |||
{{ED intro}} | |||
267edo is a fairly good [[5-limit]] tuning, but in[[consistent]] in the [[7-odd-limit]]. In the 5-limit, the equal temperament [[tempering out|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 === | |||
{{Harmonics in equal|267}} | |||
[[Category:Gravity]] | [[Category:Gravity]] | ||
[[Category:Luna]] | [[Category:Luna]] | ||
Latest revision as of 22:48, 20 February 2025
| ← 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 (%) | +0.0 | -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) | |