# 563edo

 ← 562edo 563edo 564edo →
Prime factorization 563 (prime)
Step size 2.13144¢
Fifth 329\563 (701.243¢)
Semitones (A1:m2) 51:44 (108.7¢ : 93.78¢)
Dual sharp fifth 330\563 (703.375¢)
Dual flat fifth 329\563 (701.243¢)
Dual major 2nd 96\563 (204.618¢)
Consistency limit 5
Distinct consistency limit 5

563 equal divisions of the octave (abbreviated 563edo or 563ed2), also called 563-tone equal temperament (563tet) or 563 equal temperament (563et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 563 equal parts of about 2.13 ¢ each. Each step represents a frequency ratio of 21/563, or the 563rd root of 2.

## Theory

563edo is only consistent to the 5-odd-limit and the error of harmonic 3 is quite large. It is suitable for the 2.9.7.11.19.23 subgroup, tempering out 1863/1862, 3971/3969, 3449952/3447493, 7901568/7891499 and 4333568/4322241.

### Odd harmonics

Approximation of odd harmonics in 563edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -0.712 -0.523 +0.979 +0.708 +0.725 -0.741 +0.896 -0.515 +0.888 +0.267 +0.500
Relative (%) -33.4 -24.6 +45.9 +33.2 +34.0 -34.8 +42.1 -24.2 +41.7 +12.5 +23.5
Steps
(reduced)
892
(329)
1307
(181)
1581
(455)
1785
(96)
1948
(259)
2083
(394)
2200
(511)
2301
(49)
2392
(140)
2473
(221)
2547
(295)

### Subsets and supersets

563edo is the 103rd prime edo. 1689edo, which triples it, gives a good correction to the harmonic 3.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.9 [1785 -563 [563 1785]] -0.1117 0.1117 5.24

### Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 263\563 560.57 864/625 Whoosh

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

Francium