1000edo

← 999edo

1000edo

1001edo →

Prime factorization	23 × 53
Step size	1.2 ¢
Fifth	585\1000 (702 ¢) (→ 117\200)
Semitones (A1:m2)	95:75 (114 ¢ : 90 ¢)
Consistency limit	9
Distinct consistency limit	9

1000edo is notable mostly because it is the equal division corresponding to millioctaves.

Theory

1000edo is related to 200edo, but the patent vals differ on the mapping for 5 and 7. In the 5-limit, it tempers out [38 -2 -15⟩ (luna comma) and [-17 62 -35⟩ (senior comma). In the 7-limit, it tempers out 4375/4374, 201768035/201326592, and 165288374272/164794921875, leading to the lunatic temperament and seniority temperament. It also tempers out 3025/3024, 9801/9800, and 391314/390625 in the 11-limit; 1001/1000, 4225/4224, 4459/4455, and 10648/10647 in the 13-limit, leading to the deca temperament and donar temperament.

Prime harmonics

Approximation of prime harmonics in 1000edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.045	+0.086	-0.426	-0.518	-0.528	-0.555	+0.087	+0.526	+0.023	-0.236
	Relative (%)	+0.0	+3.7	+7.2	-35.5	-43.2	-44.0	-46.3	+7.2	+43.8	+1.9	-19.6
Steps (reduced)		1000 (0)	1585 (585)	2322 (322)	2807 (807)	3459 (459)	3700 (700)	4087 (87)	4248 (248)	4524 (524)	4858 (858)	4954 (954)

Subsets and supersets

1000edo carries the interval size measure millioctave. Since 1000 factors into 2³ × 5³, 1000edo has subset edos 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, and 500.

2000edo, which doubles 1000edo, is consistent in the 29-odd-limit and thus provides good corrections for harmonics 7, 11, 13, 17, and 23.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[317 -200⟩	[⟨1000 1585]]	-0.0142	0.0142	1.18
2.3.5	[38 -2 -15⟩, [55 -64 20⟩	[⟨1000 1585 2322]]	-0.0219	0.0159	1.33
2.3.5.7	4375/4374, 201768035/201326592, [12 -3 -14 9⟩	[⟨1000 1585 2322 2807]]	+0.0215	0.0764	6.37
2.3.5.7.11	3025/3024, 4375/4374, 391314/390625, [-32 13 1 2 1⟩	[⟨1000 1585 2322 2807 3459]]	+0.0472	0.0854	7.12
2.3.5.7.11.13	1001/1000, 3025/3024, 4225/4224, 4375/4374, 708883245/708837376	[⟨1000 1585 2322 2807 3459 3700]]	+0.0631	0.0857	7.14

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated Ratio*	Temperaments
1	161\1000	193.200	262144/234375	Lunatic (7-limit)
1	269\1000	322.800	3087/2560	Seniority
4	317\1000 (67\1000)	380.400 (80.400)	5103/4096 (22/21)	Quasithird
10	263\1000 (37\1000)	315.600 (44.400)	6/5 (15/14)	Deca
25	301\1000 (21\1000)	361.200 (25.200)	[54 13 -32⟩ (?)	Manganese

* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct

Music

Xotla

• "Moongazing" from Lessor Groove (2020) Bandcamp | YouTube – atmospheric-electro, luna[25] in 1000edo