2000edo

← 1999edo

2000edo

2001edo →

Prime factorization	24 × 53
Step size	0.6 ¢
Fifth	1170\2000 (702 ¢) (→ 117\200)
Semitones (A1:m2)	190:150 (114 ¢ : 90 ¢)
Consistency limit	29
Distinct consistency limit	29

Theory

It is distinctly consistent through the 29-odd-limit and a strong no-31's 41-limit system; the only smaller edo with a smaller 29-limit relative error being 1578edo. The only ones superior to it in the 23-limit are 1578 and 1889edo.

2000 = 2⁴ × 5³ , and its divisors are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000. From these, 1000edo is notable because it carries the interval size measure millioctave. It is argued that cutting millioctaves in half makes for a better interval measuring system, in light of 2000edo's high consistency limit, which introduces just interval approximations not present in 1000edo. In addition, 2000edo inherits its fifth from 200edo, where it is semiconvergent.

Prime harmonics

Approximation of prime harmonics in 2000edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31	37	41
Error	Absolute (¢)	+0.000	+0.045	+0.086	+0.174	+0.082	+0.072	+0.045	+0.087	-0.074	+0.023	-0.236	+0.056	-0.062
	Relative (%)	+0.0	+7.5	+14.4	+29.0	+13.7	+12.1	+7.4	+14.5	-12.4	+3.8	-39.3	+9.3	-10.4
Steps (reduced)		2000 (0)	3170 (1170)	4644 (644)	5615 (1615)	6919 (919)	7401 (1401)	8175 (175)	8496 (496)	9047 (1047)	9716 (1716)	9908 (1908)	10419 (419)	10715 (715)

Regular temperament properties

2000edo has the smallest relative error than any previous temperament in the 19-limit. It is only bettered by 2460edo.

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per octave	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
20	287\2000 (87\2000)	172.2 (52.2)	169/153 (?)	Calcium
80	619\2000 (19\2000)	371.4 (11.4)	2275/1836 (?)	Mercury