462edo: Difference between revisions
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== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
|- | |||
! rowspan="2" | [[Subgroup]] | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" | [[Comma list | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br>8ve | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
! colspan="2" | Tuning | ! colspan="2" | Tuning error | ||
|- | |- | ||
! [[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
! [[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
|} | |} | ||
--> | --> | ||
Latest revision as of 12:52, 21 February 2025
| ← 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 (%) | -25.3 | +26.9 | +0.2 | +49.5 | -25.7 | +39.7 | +1.7 | -40.8 | +45.7 | -25.1 | +11.4 | |
| 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.