14842edo

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14842edo

14843edo →

Prime factorization	2 × 41 × 181
Step size	0.0808516¢
Fifth	8682\14842 (701.954¢) (→4341\7421)
Semitones (A1:m2)	1406:1116 (113.7¢ : 90.23¢)
Consistency limit	41
Distinct consistency limit	41

14842 equal divisions of the octave (abbreviated 14842edo or 14842ed2), also called 14842-tone equal temperament (14842tet) or 14842 equal temperament (14842et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 14842 equal parts of about 0.0809 ¢ each. Each step represents a frequency ratio of 2^1/14842, or the 14842nd root of 2.

14842edo is a remarkable very high-limit system, consistent through the 41-odd-limit distinctly, tempering out 17918/17917, 45696/45695, 53505/53504, 55056/55055, 57970/57967, 60516/60515, 64125/64124, 76875/76874, 81549/81548, 101270/101269, 250976/250971, and 444000/443989.

In light of being a multiple of 41, it tempers out the niobium comma and is a tuning for the associated rank-2 temperament.

Prime harmonics

Approximation of prime harmonics in 14842edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.0000	-0.0011	-0.0046	+0.0193	+0.0094	+0.0060	-0.0100	+0.0210	+0.0237	-0.0124	-0.0147
	Relative (%)	+0.0	-1.3	-5.7	+23.8	+11.6	+7.4	-12.3	+26.0	+29.3	-15.4	-18.2
Steps (reduced)		14842 (0)	23524 (8682)	34462 (4778)	41667 (11983)	51345 (6819)	54922 (10396)	60666 (1298)	63048 (3680)	67139 (7771)	72102 (12734)	73530 (14162)