563edo

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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

Theory

563et is only consistent to the 5-odd-limit and the harmonic 3 is about halfway its steps. 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. 1126edo, which doubles 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