# 571edo

 ← 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

571 equal divisions of the octave (abbreviated 571edo or 571ed2), also called 571-tone equal temperament (571tet) or 571 equal temperament (571et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 571 equal parts of about 2.1 ¢ each. Each step represents a frequency ratio of 21/571, or the 571st root of 2.

## Theory

The equal temperament 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.

### 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)

### Subsets and supersets

571edo is the 105th prime edo.

## 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 8ve
Generator* Cents* 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

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

Francium