491edo
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Prime factorization
491 (prime)
Step size
2.44399¢
Fifth
287\491 (701.426¢)
Semitones (A1:m2)
45:38 (110¢ : 92.87¢)
Consistency limit
9
Distinct consistency limit
9
| ← 490edo | 491edo | 492edo → |
491 equal divisions of the octave (abbreviated 491edo or 491ed2), also called 491-tone equal temperament (491tet) or 491 equal temperament (491et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 491 equal parts of about 2.44 ¢ each. Each step represents a frequency ratio of 21/491, or the 491st root of 2.
In the 5-limit the equal temperament tempers out the parakleisma, [8 14 -13⟩; in the 7-limit 65625/65536 and 420175/419904; in the 11-limit 441/440 and 8019/8000; in the 13-limit 729/728 and 4225/4224, and provides the optimal patent val for 11-limit history, tempering out 441/440 and 4000/3993.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.53 | -0.16 | -1.01 | -1.06 | +1.02 | +0.21 | -0.69 | +0.14 | +0.65 | +0.91 | -0.17 |
| Relative (%) | -21.7 | -6.7 | -41.1 | -43.3 | +41.9 | +8.4 | -28.3 | +5.6 | +26.8 | +37.2 | -6.9 | |
| Steps (reduced) |
778 (287) |
1140 (158) |
1378 (396) |
1556 (83) |
1699 (226) |
1817 (344) |
1918 (445) |
2007 (43) |
2086 (122) |
2157 (193) |
2221 (257) | |
Subsets and supersets
491edo is the 94th prime edo.