34691edo

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34691edo

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Prime factorization	113 × 307
Step size	0.0345911 ¢
Fifth	20293\34691 (701.957 ¢)
Semitones (A1:m2)	3287:2608 (113.7 ¢ : 90.21 ¢)
Consistency limit	41
Distinct consistency limit	41

34691 equal divisions of the octave (abbreviated 34691edo or 34691ed2), also called 34691-tone equal temperament (34691tet) or 34691 equal temperament (34691et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 34691 equal parts of about 0.0346 ¢ each. Each step represents a frequency ratio of 2^1/34691, or the 34691st root of 2.

34691edo is a zeta peak edo and zeta peak integer edo, consistent in the 41-odd-limit with a lower relative error than any previous equal temperaments in the 41-limit.

Prime harmonics

Approximation of prime harmonics in 34691edo

Harmonic		2	3	5	7	11	13	17	19	23
Error	Absolute (¢)	+0.0000	+0.0023	-0.0003	+0.0017	-0.0049	+0.0016	-0.0060	+0.0051	+0.0039
	Relative (%)	+0.0	+6.6	-0.8	+5.0	-14.2	+4.6	-17.3	+14.7	+11.2
Steps (reduced)		34691 (0)	54984 (20293)	80550 (11168)	97390 (28008)	120011 (15938)	128372 (24299)	141798 (3034)	147365 (8601)	156927 (18163)

Approximation of prime harmonics in 34691edo (continued)

Harmonic		29	31	37	41	43	47	53	59	61
Error	Absolute (¢)	-0.0076	-0.0008	-0.0051	+0.0057	+0.0155	-0.0084	-0.0100	+0.0080	-0.0072
	Relative (%)	-21.9	-2.4	-14.7	+16.3	+44.9	-24.2	-28.8	+23.0	-20.9
Steps (reduced)		168528 (29764)	171866 (33102)	180721 (7266)	185859 (12404)	188243 (14788)	192694 (19239)	198707 (25252)	204075 (30620)	205743 (32288)

Approximation of prime harmonics in 34691edo (continued)

Harmonic		67	71	73	79	83	89	97	101	103
Error	Absolute (¢)	+0.0104	+0.0042	-0.0070	-0.0158	-0.0171	+0.0115	+0.0147	-0.0005	-0.0135
	Relative (%)	+30.0	+12.3	-20.4	-45.8	-49.3	+33.2	+42.4	-1.5	-39.0
Steps (reduced)		210439 (2293)	213341 (5195)	214731 (6585)	218684 (10538)	221156 (13010)	224650 (16504)	228958 (20812)	230980 (22834)	231961 (23815)