563edo

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← 562edo563edo564edo →
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 563-tone equal temperament (563tet), 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 of 563edo 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 -25 +46 +33 +34 -35 +42 -24 +42 +13 +23
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