5941edo

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5941edo

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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 5941ed2), also called 5941-tone equal temperament (5941tet) or 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 represents a frequency ratio of 2^1/5941, 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 (%)	-26.2	+42.5	-49.6	+47.6	-48.3	-31.2	+16.3	+38.3	+6.3	+24.2	-48.2	-15.0
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 (%)	+21.3	-26.5	+12.0	+25.5	-7.0	-36.2	+42.5	-21.6	-43.9	-9.9	+18.8	+0.9
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)