382edo

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← 381edo382edo383edo →
Prime factorization 2 × 191
Step size 3.14136¢
Fifth 223\382 (700.524¢)
Semitones (A1:m2) 33:31 (103.7¢ : 97.38¢)
Dual sharp fifth 224\382 (703.665¢) (→112\191)
Dual flat fifth 223\382 (700.524¢)
Dual major 2nd 65\382 (204.188¢)
Consistency limit 7
Distinct consistency limit 7

382 equal divisions of the octave (abbreviated 382edo), or 382-tone equal temperament (382tet), 382 equal temperament (382et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 382 equal parts of about 3.14 ¢ each. Each step of 382edo represents a frequency ratio of 21/382, or the 382nd root of 2.

Theory

382edo is consistent to the 7-odd-limit, but harmonics 3 and 7 are about halfway between its steps. It is also bad at approximating 11, 13, 15, and 17, though its 5, 9, 19, 21, and 23 are good, making it suitable for a 2.9.5.21.19.23 subgroup interpretation.

Using the patent val nonetheless, the equal temperament tempers out 65625/65536 in the 7-limit; 540/539, 4000/3993, and 9801/9800 in the 11-limit. It supports bastille.

Odd harmonics

Approximation of odd harmonics in 382edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error absolute (¢) -1.43 +0.07 -1.29 +0.28 +1.56 +1.36 -1.36 -1.29 +0.92 +0.42 -0.00
relative (%) -46 +2 -41 +9 +50 +43 -43 -41 +29 +13 -0
Steps
(reduced)
605
(223)
887
(123)
1072
(308)
1211
(65)
1322
(176)
1414
(268)
1492
(346)
1561
(33)
1623
(95)
1678
(150)
1728
(200)

Subsets and supersets

382 factors into 2 × 191 with 2edo and 191edo as its subset edos. 764edo, which doubles it, gives a good correction to the harmonics 3, 7, 11, 13, and 17.

Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.9 [1211 -382 [382 1211]] -0.0439 0.0439 1.40
2.9.5 [38 -1 -15, [25 -24 22 [382 1211 887]] -0.0399 0.0363 1.16
2.9.5.21 4375/4374, 52734375/52706752, [31 0 -2 -6 [382 1211 887 1678]] -0.0552 0.0412 1.31