5941edo

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← 5940edo5941edo5942edo →
Prime factorization 13 × 457
Step size 0.201986¢
Fifth 3475\5941 (701.902¢)
Semitones (A1:m2) 561:448 (113.3¢ : 90.49¢)
Consistency limit 3
Distinct consistency limit 3

5941 equal divisions of the octave (abbreviated 5941edo), or 5941-tone equal temperament (5941tet), 5941 equal temperament (5941et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 5941 equal parts of about 0.202 ¢ each. Each step of 5941edo represents a frequency ratio of 21/5941, or the 5941st root of 2.

As the zeta valley edo after 79edo, it approximates prime harmonics with very high errors. In particular, the 7th, 9th, 11th and 23rd harmonics are off by nearly half a step. In light of this, 5941edo can be seen as excelling in the 2.92.72.112.232 subgroup. Otherwise, it is strong in the 2.45.35.49.19.(31.51) subgroup.

Rather fittingly, it has a consistency limit of 3.

Odd harmonics

Approximation of odd harmonics in 5941edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25
Error absolute (¢) -0.0530 +0.0859 -0.1001 +0.0961 -0.0976 -0.0631 +0.0329 +0.0774 +0.0127 +0.0489 -0.0973 -0.0302
relative (%) -26 +43 -50 +48 -48 -31 +16 +38 +6 +24 -48 -15
Steps
(reduced)
9416
(3475)
13795
(1913)
16678
(4796)
18833
(1010)
20552
(2729)
21984
(4161)
23211
(5388)
24284
(520)
25237
(1473)
26095
(2331)
26874
(3110)
27589
(3825)
Approximation of odd harmonics in 5941edo (continued)
Harmonic 27 29 31 33 35 37 39 41 43 45 47 49
Error absolute (¢) +0.0431 -0.0535 +0.0242 +0.0514 -0.0142 -0.0732 +0.0859 -0.0437 -0.0887 -0.0200 +0.0379 +0.0018
relative (%) +21 -27 +12 +25 -7 -36 +43 -22 -44 -10 +19 +1
Steps
(reduced)
28249
(4485)
28861
(5097)
29433
(5669)
29969
(264)
30473
(768)
30949
(1244)
31401
(1696)
31829
(2124)
32237
(2532)
32627
(2922)
33000
(3295)
33357
(3652)