69420edo

69420 equal divisions of the octave (abbreviated as 69420edo or 69420ed2), also called 69420-tone equal temperament (69420tet) or 69420 equal temperament (69420et) is a tuning system that divides each octave into 69420 equal parts of about 0.0173¢ (0.0144μoct). Each step represents a frequency ratio of 2^1/69420, or the 69420th root of 2.

← 69419edo

69420edo

69421edo →

Prime factorization	22 × 3 × 5 × 13 × 89
Step size	0.0172861 ¢
Fifth	40608\69420 (701.953 ¢) (→ 3384\5785)
Semitones (A1:m2)	6576:5220 (113.7 ¢ : 90.23 ¢)
Consistency limit	5
Distinct consistency limit	5

69420edo has an incredibly precise approximation of 3/2, with an error of only 0.002¢, as well as accurate approximations of prime harmonics, with the largest error up to the 31st prime harmonic being +0.00728¢.

Prime Harmonics

Approximation of prime harmonics in 69420edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00000	-0.00167	-0.00429	+0.00728	+0.00444	+0.00821	+0.00570	-0.00221	+0.00569	-0.00070	-0.00532
	Relative (%)	+0.0	-9.7	-24.8	+42.1	+25.7	+47.5	+33.0	-12.8	+32.9	-4.1	-30.8
Steps (reduced)		69420 (0)	110028 (40608)	161188 (22348)	194887 (56047)	240154 (31894)	256885 (48625)	283752 (6072)	294891 (17211)	314026 (36346)	337241 (59561)	343920 (66240)