587edo

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587edo

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Prime factorization	587 (prime)
Step size	2.04429¢
Fifth	343\587 (701.193¢)
Semitones (A1:m2)	53:46 (108.3¢ : 94.04¢)
Dual sharp fifth	344\587 (703.237¢)
Dual flat fifth	343\587 (701.193¢)
Dual major 2nd	100\587 (204.429¢)
Consistency limit	7
Distinct consistency limit	7

587 equal divisions of the octave (abbreviated 587edo or 587ed2), also called 587-tone equal temperament (587tet) or 587 equal temperament (587et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 587 equal parts of about 2.04 ¢ each. Each step represents a frequency ratio of 2^1/587, or the 587th root of 2.

587edo is consistent to the 7-odd-limit, but the error of harmonic 3 is quite large. With good approximations to harmonics 5, 7, 9, 11, and 13, it commends itself as a 2.9.5.7.11.13 subgroup tuning.

Using the patent val, however, the equal temperament tempers out 19683/19600 and 703125/702464 in the 7-limit, providing the optimal patent val for the 19 & 183 temperament and the planar temperament cataharry tempering out 19683/19600.

Odd harmonics

Approximation of odd harmonics in 587edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-0.762	+0.058	+0.169	+0.519	+0.641	-0.323	-0.705	-0.696	+0.954	-0.594	-0.676
	Relative (%)	-37.3	+2.8	+8.3	+25.4	+31.4	-15.8	-34.5	-34.1	+46.7	-29.0	-33.1
Steps (reduced)		930 (343)	1363 (189)	1648 (474)	1861 (100)	2031 (270)	2172 (411)	2293 (532)	2399 (51)	2494 (146)	2578 (230)	2655 (307)

Subsets and supersets

587edo is the 107th prime edo.