# 566edo

 ← 565edo 566edo 567edo →
Prime factorization 2 × 283
Step size 2.12014¢
Fifth 331\566 (701.767¢)
Semitones (A1:m2) 53:43 (112.4¢ : 91.17¢)
Consistency limit 15
Distinct consistency limit 15

566 equal divisions of the octave (abbreviated 566edo or 566ed2), also called 566-tone equal temperament (566tet) or 566 equal temperament (566et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 566 equal parts of about 2.12 ¢ each. Each step represents a frequency ratio of 21/566, or the 566th root of 2.

## Theory

566edo is distinctly consistent in the 15-odd-limit. The equal temperament tempers out the schisma in the 5-limit; 4375/4374 (ragisma), 65625/65536 (horwell comma), and 14348907/14336000 (skeetsma) in the 7-limit; 3025/3024 in the 11-limit; 1716/1715 and 2080/2079 in the 13-limit. It notably supports pontiac and orga.

The 566g val is interesting in the higher limits, and in the 23-limit in particular it has a great rating in terms of absolute error. It tempers out 1156/1155, 1275/1274, 2431/2430, 2500/2499 and 2601/2600 in the 17-limit; 1445/1444, 1521/1520 and 1729/1728 in the 19-limit; 1105/1104 and 2025/2024 in the 23-limit.

### Prime harmonics

Approximation of prime harmonics in 566edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 -0.188 -0.448 +0.079 -0.081 -0.952 +1.052 -0.693 -0.713 +0.811 -0.159
Relative (%) +0.0 -8.9 -21.1 +3.7 -3.8 -44.9 +49.6 -32.7 -33.6 +38.3 -7.5
Steps
(reduced)
566
(0)
897
(331)
1314
(182)
1589
(457)
1958
(260)
2094
(396)
2314
(50)
2404
(140)
2560
(296)
2750
(486)
2804
(540)

### Subsets and supersets

Since 566 factors into 2 × 283, 566edo contains 2edo and 283edo as subsets.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [-897 566 [566 897]] +0.0594 0.0594 2.80
2.3.5 32805/32768, [-3 -86 60 [566 897 1314]] +0.1039 0.0795 3.75
2.3.5.7 4375/4374, 32805/32768, [10 5 8 -13 [566 897 1314 1589]] +0.0709 0.0894 4.22
2.3.5.7.11 3025/3024, 4375/4374, 32805/32768, 825000/823543 [566 897 1314 1589 1958]] +0.0614 0.0822 3.88
2.3.5.7.11.13 1716/1715, 2080/2079, 3025/3024, 15379/15360, 31250/31213 [566 897 1314 1589 1958 2094]] +0.0941 0.1047 4.94
• 566et (566g val) has a lower absolute error in the 23-limit than any previous equal temperaments, past 525 and followed by 581.

### Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 235\566 498.23 4/3 Pontiac
2 109\566 231.10 8/7 Orga

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