14842edo

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← 14841edo14842edo14843edo →
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 21/14842, 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)