541edo

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← 540edo541edo542edo →
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