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 (abbreviated 487edo or 487ed2), also called 487-tone equal temperament (487tet) or 487 equal temperament (487et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 487 equal parts of about 2.464 ¢ each. Each step represents a frequency ratio of 21/487, or the 487th root of 2.

Theory

487edo is distinctly consistent to the 13-odd-limit. The equal temperament tempers out [24 -21 4 (vulture comma) and [55 -1 -23 (counterwürschmidt comma) 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)

Subsets and supersets

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* Cents* Associated
Ratio*
Temperaments
1 131\487 322.79 3087/2560 Seniority
1 157\487 386.86 5/4 Counterwürschmidt
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)

* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct

Scales