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

Theory

487et 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 (Reduced)	Cents (Reduced)	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)

Scales

• Silver7
• Silver10
• Silver17