584edo

From Xenharmonic Wiki
Jump to navigation Jump to search
← 583edo584edo585edo →
Prime factorization 23 × 73
Step size 2.05479¢
Fifth 342\584 (702.74¢) (→171\292)
Semitones (A1:m2) 58:42 (119.2¢ : 86.3¢)
Dual sharp fifth 342\584 (702.74¢) (→171\292)
Dual flat fifth 341\584 (700.685¢)
Dual major 2nd 99\584 (203.425¢)
Consistency limit 5
Distinct consistency limit 5

584 equal divisions of the octave (584edo), or 584-tone equal temperament (584tet), 584 equal temperament (584et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 584 equal parts of about 2.05 ¢ each.

Theory

584et tempers out 48828125/48771072 and 67108864/66976875 in the 7-limit (hemiluna temperament), and 12005/11979, 131072/130977, 5632/5625, 537109375/536870912, 9453125/9437184, 160083/160000 and 391314/390625 in the 11-limit.

Approximation of odd harmonics in 584edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error absolute (¢) +0.785 -0.012 -1.018 -0.485 -0.633 -0.117 +0.772 -0.161 +0.432 -0.233 +0.493
relative (%) +38 -1 -50 -24 -31 -6 +38 -8 +21 -11 +24
Steps
(reduced)
926
(342)
1356
(188)
1639
(471)
1851
(99)
2020
(268)
2161
(409)
2282
(530)
2387
(51)
2481
(145)
2565
(229)
2642
(306)

Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [463 -292 584 926] -0.2476 0.2475 12.05
2.3.5 [3 -18 11, [21 -20 4 584 926 1356] -0.1633 0.2346 11.42
2.3.5.7 1500625/1492992, 1605632/1594323, 235298/234375 584​ 926 ​1356 ​1639] -0.0319 0.3052 14.85
2.3.5.7.11 5632/5625, 160083/160000, 26411/26244, 968000/964467 584​ 926 ​1356 ​1639​ 2020​] +0.0111 0.2862 13.93
2.3.5.7.11.13 2080/2079, 1001/1000, 4096/4095, 85750/85293, 983125/979776 584​ 926 ​1356​ 1639 ​2020 ​2161] +0.0145 0.2613 12.72

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator
(reduced)
Cents
(reduced)
Associated
ratio
Temperaments
1 47\584 96.58 200/189 Hemiluna

Scales

Music