1583edo

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1583edo

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Prime factorization	1583 (prime)
Step size	0.758054 ¢
Fifth	926\1583 (701.958 ¢)
Semitones (A1:m2)	150:119 (113.7 ¢ : 90.21 ¢)
Consistency limit	9
Distinct consistency limit	9

Theory

1583edo is consistent to the 9-odd-limit. Using the patent val, it tempers out 2401/2400, [36 -16 -7 2⟩ and [9 21 -17 -1⟩ in the 7-limit; 2401/2400, 172032/171875, 766656/765625 and 387420489/387200000 in the 11-limit. It supports empress and vili.

Prime harmonics

Approximation of prime harmonics in 1583edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.003	+0.294	-0.032	-0.212	+0.155	-0.344	-0.356	+0.153	-0.139	-0.374
	Relative (%)	+0.0	+0.4	+38.8	-4.3	-28.0	+20.4	-45.4	-46.9	+20.1	-18.4	-49.3
Steps (reduced)		1583 (0)	2509 (926)	3676 (510)	4444 (1278)	5476 (727)	5858 (1109)	6470 (138)	6724 (392)	7161 (829)	7690 (1358)	7842 (1510)

Subsets and supersets

1583edo is the 250th prime EDO.

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.3	[2509 -1583⟩	[⟨1583 2509]]	-0.0010	0.0010	0.13
2.3.5	[77 -31 -12⟩, [-23 57 -29⟩	[⟨1583 2509 3676]]	-0.0429	0.0592	7.81
2.3.5.7	2401/2400, 3367254360064/3363025078125, 5355700839936/5340576171875	[⟨1583 2509 3676 4444]]	-0.0293	0.0564	7.44

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated ratio*	Temperaments
1	341\1583	258.497	[-32 13 5⟩	Lafa

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

Music

Francium

• "BEEFY!" from CAPSLOCK (2024) – Spotify | Bandcamp | YouTube – vili in 1583edo tuning