1583edo

 ← 1582edo 1583edo 1584edo →
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

1583 equal divisions of the octave (abbreviated 1583edo or 1583ed2), also called 1583-tone equal temperament (1583tet) or 1583 equal temperament (1583et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1583 equal parts of about 0.758 ¢ each. Each step represents a frequency ratio of 21/1583, or the 1583rd root of 2.

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