571edo

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← 570edo

571edo

572edo →

Prime factorization	571 (prime)
Step size	2.10158 ¢
Fifth	334\571 (701.926 ¢)
Semitones (A1:m2)	54:43 (113.5 ¢ : 90.37 ¢)
Consistency limit	9
Distinct consistency limit	9

Theory

571edo tempers out the parakleisma, [8 14 -13⟩, and the counterschisma, [-69 45 -1⟩, in the 5-limit, as well as the lafa comma, [77 -31 -12⟩; 2401/2400, 14348907/14336000, and 29360128/29296875 in the 7-limit; 3025/3024, 5632/5625, 41503/41472, and 17537553/17500000 in the 11-limit; 1001/1000, 1716/1715, 4096/4095, 17303/17280, and 107811/107653 in the 13-limit, supporting the 13-limit quasiorwell temperament; 1089/1088, 1701/1700, 2431/2430, 2601/2600, 5832/5831 and 7744/7735 in the 17-limit. The 7th harmonic is only 0.0007135 cents sharp in 571edo, as the denominator of a convergent to log₂7, after 109 and before 2393.

571edo is the 105th prime edo.

Prime harmonics

Approximation of prime harmonics in 571edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	-0.029	+0.376	+0.001	-0.705	+0.103	+0.123	+0.911	+0.097	+0.195	+0.323
	Relative (%)	+0.0	-1.4	+17.9	+0.0	-33.5	+4.9	+5.9	+43.3	+4.6	+9.3	+15.4
Steps (reduced)		571 (0)	905 (334)	1326 (184)	1603 (461)	1975 (262)	2113 (400)	2334 (50)	2426 (142)	2583 (299)	2774 (490)	2829 (545)

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[-905 571⟩	[⟨571 905]]	+0.0090	0.0090	0.43
2.3.5	[8 14 -13⟩, [-69 45 -1⟩	[⟨571 905 1326]]	-0.0480	0.0810	3.85
2.3.5.7	2401/2400, 14348907/14336000, 29360128/29296875	[⟨571 905 1326 1603]]	-0.0361	0.0731	3.48
2.3.5.7.11	2401/2400, 3025/3024, 5632/5625, 14348907/14336000	[⟨571 905 1326 1603 1975]]	+0.0119	0.1161	5.53
2.3.5.7.11.13	1001/1000, 1716/1715, 3025/3024, 4096/4095, 107811/107653	[⟨571 905 1326 1603 1975 2113]]	+0.0053	0.1070	5.09
2.3.5.7.11.13.17	1001/1000, 1089/1088, 1716/1715, 2601/2600, 3025/3024, 4096/4095	[⟨571 905 1326 1603 1975 2113 2334]]	+0.0002	0.0999	4.75

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per Octave	Generator (Reduced)	Cents (Reduced)	Associated Ratio	Temperaments
1	123\571	258.49	[-32 13 5⟩	Lafa
1	129\571	271.10	90/77	Quasiorwell
1	147\571	315.24	6/5	Parakleismic (5-limit)
1	237\571	498.07	4/3	Counterschismic
1	248\571	521.19	875/648	Maviloid