1600edo

The 1600 equal divisions of the octave (1600edo), or the 1600-tone equal temperament (1600tet), 1600 equal temperament (1600et) when viewed from a regular temperament perspective, divides the octave into 1600 equal parts of exactly 750 millicents each.

Theory

Approximation of prime harmonics in 1600edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.045	-0.064	+0.174	-0.068	+0.222	+0.045	+0.237	+0.226	+0.173	+0.214
	Relative (%)	+0.0	+6.0	-8.5	+23.2	-9.1	+29.6	+5.9	+31.6	+30.1	+23.0	+28.6
Steps (reduced)		1600 (0)	2536 (936)	3715 (515)	4492 (1292)	5535 (735)	5921 (1121)	6540 (140)	6797 (397)	7238 (838)	7773 (1373)	7927 (1527)

1600edo is a very strong 37-limit system, being distinctly consistent in the 37-limit with a smaller relative error than anything else with this property until 4501. It is also the first division past 311 with a lower 43-limit relative error. One step of it is the relative cent for 16.

1600's divisors are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 320, 400, 800.

In the 5-limit, it supports kwazy.

In the 7-limit, it tempers out the ragisma, 4375/4374.

In the 11-limit, it supports the rank-3 temperament thor.

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.3.5	[-53, 10, 16⟩, [26, -75, 40⟩	[⟨1600 2536 3715]]	-0.000318	0.022794
2.3.5.7	4375/4374, [36, -5, 0, -10⟩, [-17, 5, 16, -10⟩	[⟨1600 2536 3715 4492]]	-0.015742	0.033217
2.3.5.7.11.13.17	2500/2499, 3025/3024, 4375/4374, 14875/14872, 154880/154791, 1724800/1724463	[⟨1600 2536 3715 4492 5535 5921 6540]]	-0.016332