User:Aura/2667518edo

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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2667518edo

2667519edo →

Prime factorization	2 × 7 × 190537
Step size	0.000449856 ¢
Fifth	1560398\2667518 (701.955 ¢) (→ 111457\190537)
Semitones (A1:m2)	252714:200564 (113.7 ¢ : 90.22 ¢)
Consistency limit	11
Distinct consistency limit	11

2667518 equal divisions of the octave (abbreviated 2667518edo or 2667518ed2), also called 2667518-tone equal temperament (2667518tet) or 2667518 equal temperament (2667518et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2667518 equal parts of about 0.00045 ¢ each. Each step represents a frequency ratio of 2^1/2667518, or the 2667518th root of 2.

Theory

This EDO inherits its fifth from 190537edo and seems to be at its best in the 2.3.5.11.19.23 subgroup.

Approximation of prime harmonics in 2667518edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000000	+0.000000	+0.000005	+0.000096	-0.000051	+0.000200	+0.000133	-0.000047	+0.000026	+0.000113	+0.000075
	Relative (%)	+0.0	+0.0	+1.2	+21.3	-11.2	+44.4	+29.7	-10.5	+5.8	+25.2	+16.7
Steps (reduced)		2667518 (0)	4227916 (1560398)	6193785 (858749)	7488670 (2153634)	9228096 (1225542)	9870990 (1868436)	10903381 (233309)	11331423 (661351)	12066683 (1396611)	12958752 (2288680)	13215408 (2545336)