462edo
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Prime factorization
2 × 3 × 7 × 11
Step size
2.5974¢
Fifth
270\462 (701.299¢) (→45\77)
Semitones (A1:m2)
42:36 (109.1¢ : 93.51¢)
Consistency limit
3
Distinct consistency limit
3
| ← 461edo | 462edo | 463edo → |
462 equal divisions of the octave (abbreviated 462edo or 462ed2), also called 462-tone equal temperament (462tet) or 462 equal temperament (462et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 462 equal parts of about 2.6 ¢ each. Each step represents a frequency ratio of 21/462, or the 462nd root of 2.
462edo is enfactored in the 3-limit and inconsistent to the 5-odd-limit. It can be considered for the 2.3.7.11.17 subgroup, tempering out 1089/1088, 34992/34969, 944163/941192 and 10323369/10307264.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | -0.66 | +0.70 | +0.01 | +1.28 | -0.67 | +1.03 | +0.04 | -1.06 | +1.19 | -0.65 | +0.30 |
| relative (%) | -25 | +27 | +0 | +49 | -26 | +40 | +2 | -41 | +46 | -25 | +11 | |
| Steps (reduced) |
732 (270) |
1073 (149) |
1297 (373) |
1465 (79) |
1598 (212) |
1710 (324) |
1805 (419) |
1888 (40) |
1963 (115) |
2029 (181) |
2090 (242) | |
Subsets and supersets
462 factors into 2 × 3 × 7 × 11, with subset edos 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, and 231. 1386edo, which triples it, gives a good correction to the harmonics 3 and 5.