58973edo

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58973edo

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Prime factorization	17 × 3469
Step size	0.0203483 ¢
Fifth	34497\58973 (701.955 ¢)
Semitones (A1:m2)	5587:4434 (113.7 ¢ : 90.22 ¢)
Consistency limit	47
Distinct consistency limit	47
Special properties	Zeta peak Zeta peak integer Zeta integral Zeta gap

58973 equal divisions of the octave (abbreviated 58973edo or 58973ed2), also called 58973-tone equal temperament (58973tet) or 58973 equal temperament (58973et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 58973 equal parts of about 0.0203 ¢ each. Each step represents a frequency ratio of 2^1/58973, or the 58973rd root of 2.

58973edo is a zeta peak, integral, and gap edo. It is distinctly consistent in the 47-odd-limit, and has lower relative errors than any smaller equal temperaments in the 37-limit and way beyond.

Prime harmonics

Approximation of prime harmonics in 58973edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31	37	41	43	47
Error	Absolute (¢)	+0.00000	+0.00013	-0.00133	-0.00289	-0.00124	-0.00064	+0.00110	-0.00060	-0.00039	+0.00584	+0.00368	-0.00190	+0.00174	-0.00227	+0.00471
	Relative (%)	+0.0	+0.6	-6.6	-14.2	-6.1	-3.1	+5.4	-2.9	-1.9	+28.7	+18.1	-9.3	+8.6	-11.1	+23.2
Steps (reduced)		58973 (0)	93470 (34497)	136931 (18985)	165558 (47612)	204013 (27094)	218226 (41307)	241050 (5158)	250513 (14621)	266768 (30876)	286490 (50598)	292164 (56272)	307217 (12352)	315951 (21086)	320003 (25138)	327571 (32706)