462edo

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← 461edo462edo463edo →
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

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 2.597 ¢ 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

Approximation of odd harmonics in 462edo
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.