# 487edo

 ← 486edo 487edo 488edo →
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 2.46 ¢ 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 (%) +0.0 +12.3 +22.1 -18.2 +25.7 -11.4 +40.6 +25.9 +2.5 +16.3 +30.6
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