1905370edo

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← 1905369edo1905370edo1905371edo →
Prime factorization 2 × 5 × 190537
Step size 0.000629799¢
Fifth 1114570\1905370 (701.955¢) (→111457\190537)
Semitones (A1:m2) 180510:143260 (113.7¢ : 90.22¢)
Consistency limit 17
Distinct consistency limit 17

1905370 equal divisions of the octave (abbreviated 1905370edo), or 1905370-tone equal temperament (1905370tet), 1905370 equal temperament (1905370et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1905370 equal parts of about 0.00063 ¢ each. Each step of 1905370edo represents a frequency ratio of 21/1905370, or the 1905370th root of 2.

Theory

This EDO has a consistency limit of 17, but seems to be at its best in the 2.3.5.7.13.17 subgroup. It tempers out the Archangelic comma in the 3-limit.


Approximation of prime harmonics in 1905370edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error absolute (¢) +0.000000 +0.000000 -0.000084 +0.000096 -0.000141 +0.000110 -0.000047 +0.000223 -0.000154 -0.000157 -0.000015
relative (%) +0 +0 -13 +15 -22 +17 -7 +35 -24 -25 -2
Steps
(reduced)
1905370
(0)
3019940
(1114570)
4424132
(613392)
5349050
(1538310)
6591497
(875387)
7050707
(1334597)
7788129
(166649)
8093874
(472394)
8619059
(997579)
9256251
(1634771)
9439577
(1818097)