14348edo

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14348edo

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Prime factorization	22 × 17 × 211
Step size	0.0836353¢
Fifth	8393\14348 (701.951¢)
Semitones (A1:m2)	1359:1079 (113.7¢ : 90.24¢)
Consistency limit	29
Distinct consistency limit	29
Special properties	Zeta peak Zeta peak integer Zeta integral Zeta gap

14348 equal divisions of the octave (abbreviated 14348edo or 14348ed2), also called 14348-tone equal temperament (14348tet) or 14348 equal temperament (14348et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 14348 equal parts of about 0.0836 ¢ each. Each step represents a frequency ratio of 2^1/14348, or the 14348th root of 2.

14348edo is a strong 17-limit system, with a lower 17-limit relative error than any smaller edo aside from 7033. It is also distinctly consistent in the 29-odd-limit, and has a lower 23-limit relative error than any lower equal temperaments aside from 2460, 8269, 8539 and 11664. Besides all that, it is a zeta peak, integral and gap edo, which has to do with its higher limit capability—it has lower relative errors than any smaller equal temperaments in the 41-limit and way beyond.

Prime harmonics

Approximation of prime harmonics in 14348edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31	37
Error	Absolute (¢)	+0.0000	-0.0035	-0.0020	+0.0060	+0.0063	+0.0076	+0.0070	-0.0221	-0.0056	-0.0260	+0.0160	-0.0198
	Relative (%)	+0.0	-4.2	-2.4	+7.2	+7.5	+9.1	+8.3	-26.4	-6.7	-31.1	+19.1	-23.7
Steps (reduced)		14348 (0)	22741 (8393)	33315 (4619)	40280 (11584)	49636 (6592)	53094 (10050)	58647 (1255)	60949 (3557)	64904 (7512)	69702 (12310)	71083 (13691)	74745 (3005)

Approximation of prime harmonics in 14348edo (continued)

Harmonic		41	43	47	53	59	61	67	71	73	79	83	89
Error	Absolute (¢)	-0.0131	-0.0039	-0.0201	-0.0170	-0.0136	-0.0183	-0.0207	+0.0358	+0.0332	+0.0296	-0.0055	+0.0148
	Relative (%)	-15.6	-4.7	-24.1	-20.3	-16.2	-21.9	-24.8	+42.8	+39.7	+35.4	-6.6	+17.7
Steps (reduced)		76870 (5130)	77856 (6116)	79697 (7957)	82184 (10444)	84404 (12664)	85094 (13354)	87036 (948)	88237 (2149)	88812 (2724)	90447 (4359)	91469 (5381)	92914 (6826)

Subsets and supersets

It factors as 2² × 17 × 211, so 17, 34, 68 and 422 are all divisors.