# 541edo

 ← 540edo 541edo 542edo →
Prime factorization 541 (prime)
Step size 2.21811¢
Fifth 316\541 (700.924¢)
Semitones (A1:m2) 48:43 (106.5¢ : 95.38¢)
Dual sharp fifth 317\541 (703.142¢)
Dual flat fifth 316\541 (700.924¢)
Dual major 2nd 92\541 (204.067¢)
Consistency limit 5
Distinct consistency limit 5

541 equal divisions of the octave (abbreviated 541edo or 541ed2), also called 541-tone equal temperament (541tet) or 541 equal temperament (541et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 541 equal parts of about 2.22 ¢ each. Each step represents a frequency ratio of 21/541, or the 541st root of 2.

## Theory

541et is only consistent to the 5-odd-limit and the harmonic 3 is about halfway between its steps. It has a reasonable approximation to the 2.9.5.7.13 subgroup.

### Odd harmonics

Approximation of odd harmonics in 541edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -1.031 -0.362 +0.490 +0.157 +0.993 +0.138 +0.826 -0.704 -0.286 -0.541 -0.548
Relative (%) -46.5 -16.3 +22.1 +7.1 +44.7 +6.2 +37.2 -31.7 -12.9 -24.4 -24.7
Steps
(reduced)
857
(316)
1256
(174)
1519
(437)
1715
(92)
1872
(249)
2002
(379)
2114
(491)
2211
(47)
2298
(134)
2376
(212)
2447
(283)

### Subsets and supersets

541edo is the 100th prime edo. 1082edo, 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 [1715 -541 [541 1715]] -0.0247 0.0247 1.11
2.9.5 [-20 -12 25, [63 -25 7 [541 1715 1256]] +0.0355 0.0874 3.94
2.9.5.7 40500000/40353607, 43046721/43025920, 95703125/95551488 [541 1715 1256 1519]] -0.0171 0.1184 5.34
2.9.5.7.13 4096/4095, 10985/10976, 2734375/2729376, 11390625/11361532 [541 1715 1256 1519 2002]] -0.0211 0.1062 4.79