482edo

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The 482 equal divisions of the octave (482edo), or the 482-tone equal temperament (482tet), 482 equal temperament (482et) when viewed from a regular temperament perspective, divides the octave into 482 equal parts of about 2.49 cents each.

Theory

Prime harmonics with less than 17% (1 standard deviation error) in 482edo are 3, 5, 7, 17, 31, 37. 11 and 13 have rather large errors, but they are reasonable to work with.

In the 7-limit, 482edo provides excellent tuning for the tertiaseptal temperament.

Prime harmonics

Approximation of prime harmonics in 482edo
Harmonic 2 3 5 7 11 13 17 19 23 29
Error absolute (¢) +0.00 +0.12 -0.42 -0.36 -1.11 +0.97 -0.39 +1.24 -0.89 +1.13
relative (%) +0 +5 -17 -15 -45 +39 -16 +50 -36 +45
Steps
(reduced)
482
(0)
764
(282)
1119
(155)
1353
(389)
1667
(221)
1784
(338)
1970
(42)
2048
(120)
2180
(252)
2342
(414)

Regular temperament properties

Subgroup Comma list Mapping Optimal
8ve stretch (¢)
Tuning error
Absolute (¢) Relative (%)
2.3.5 [24 -21 4, [-59 5 22 [482 764 1119]] +0.0353 0.0587 4.33
2.3.5.7 2401/2400, 65625/65536, [8 -20 9 1 [482 764 1119 1353]] +0.0587 0.1018 4.09
2.3.5.7.11 2401/2400, 9801/9800, 19712/19683, 65625/65536 [482 764 1119 1353 1667]] +0.1111 0.1389 5.58
2.3.5.7.11.13 676/675, 1001/1000, 1716/1715, 10648/10647, 65625/65536 [482 764 1119 1353 1667 1783]] (482f) +0.1612 0.1692 6.80
2.3.5.7.11.13 625/624, 847/845, 2401/2400, 9801/9800, 35750/35721 [482 764 1119 1353 1667 1784]] (482) +0.0491 0.1880 7.55