1905370edo

This page presents a topic of primarily mathematical interest. While it is derived from sound mathematical principles, its applications in terms of utility for actual music may be limited, highly contrived, or as yet unknown.

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1905370edo

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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 1905370ed2), also called 1905370-tone equal temperament (1905370tet) or 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 represents a frequency ratio of 2^1/1905370, or the 1905370th root of 2.

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.

Prime harmonics

Approximation of prime harmonics in 1905370edo

Harmonic		2	3	5	7	11	13	17	19	23
Error	Absolute (¢)	+0.000000	+0.000000	-0.000084	+0.000096	-0.000141	+0.000110	-0.000047	+0.000223	-0.000154
	Relative (%)	+0.0	+0.0	-13.4	+15.2	-22.3	+17.4	-7.4	+35.4	-24.4
Steps (reduced)		1905370 (0)	3019940 (1114570)	4424132 (613392)	5349050 (1538310)	6591497 (875387)	7050707 (1334597)	7788129 (166649)	8093874 (472394)	8619059 (997579)

Approximation of prime harmonics in 1905370edo (continued)

Harmonic		29	31	37	41	43	47	53	59	61
Error	Absolute (¢)	-0.000157	-0.000015	-0.000100	+0.000086	-0.000048	+0.000025	+0.000128	+0.000260	-0.000001
	Relative (%)	-24.9	-2.4	-15.9	+13.7	-7.6	+4.0	+20.3	+41.3	-0.1
Steps (reduced)		9256251 (1634771)	9439577 (1818097)	9925936 (399086)	10208119 (681269)	10339042 (812192)	10583547 (1056697)	10913808 (1386958)	11208612 (1681762)	11300249 (1773399)