487edo

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← 486edo487edo488edo →
Prime factorization 487 (prime)
Step size 2.46407¢
Fifth 285\487 (702.259¢)
Semitones (A1:m2) 47:36 (115.8¢ : 88.71¢)
Consistency limit 13
Distinct consistency limit 13

487 equal divisions of the octave (487edo), or 487-tone equal temperament (487tet), 487 equal temperament (487et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 487 equal parts of about 2.46 ¢ each.

Theory

487et tempers out [24 -21 4 (vulture comma) and [55 -1 -23 in the 5-limit, 4375/4374 (ragisma), 235298/234375 (triwellisma), and 33554432/33480783 (garischisma) in the 7-limit, 5632/5625, 12005/11979, 19712/19683, 41503/41472 in the 11-limit, 676/675, 1001/1000, 2080/2079, 4096/4095, and 4225/4224 in the 13-limit. It supports semidimfourth, seniority, and vulture.

Prime harmonics

Approximation of prime harmonics in 487edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error absolute (¢) +0.00 +0.30 +0.54 -0.45 +0.63 -0.28 +1.00 +0.64 +0.06 +0.40 +0.75
relative (%) +0 +12 +22 -18 +26 -11 +41 +26 +3 +16 +31
Steps
(reduced)
487
(0)
772
(285)
1131
(157)
1367
(393)
1685
(224)
1802
(341)
1991
(43)
2069
(121)
2203
(255)
2366
(418)
2413
(465)

Miscellaneous properties

487edo is the 93rd prime edo.

Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [772 -487 [487 772]] -0.0958 0.0958 3.89
2.3.5 [24 -21 4, [55 -1 -23 [487 772 1131]] -0.1421 0.1020 4.14
2.3.5.7 4375/4374, 235298/234375, 33554432/33480783 [487 772 1131 1367]] -0.0667 0.1577 6.40
2.3.5.7.11 4375/4374, 5632/5625, 12005/11979, 41503/41472 [487 772 1131 1367 1685]] -0.0899 0.1485 6.03
2.3.5.7.11.13 676/675, 1001/1000, 4096/4095, 4375/4374, 12005/11979 [487 772 1131 1367 1685 1802]] -0.0623 0.1490 6.05

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator
(Reduced)
Cents
(Reduced)
Associated
Ratio
Temperaments
1 131\487 322.79 3087/2560 Seniority
1 182\487 448.46 35/27 Semidimfourth
1 193\487 475.56 320/243 Vulture
1 202\487 497.74 4/3 Gary
1 227\487 559.34 864/625 Tritriple (5-limit)

Scales