8269edo

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8269edo

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Prime factorization	8269 (prime)
Step size	0.14512 ¢
Fifth	4837\8269 (701.947 ¢)
Semitones (A1:m2)	783:622 (113.6 ¢ : 90.26 ¢)
Consistency limit	27
Distinct consistency limit	27

8269edo is both a zeta peak and zeta integral edo, which has to do with the fact that it is a very strong 19- and 23-limit division. It has a lower 19-limit and a lower 23-limit relative error than any smaller division, a lower 19-limit TE loglfat badness than any smaller division, and a lower 23-limit logflat badness than any excepting 311, 581, 1578 and 2460. While 8539 has received most of the attention in this size range, 8269 is actually a bit better in the 23-limit and nearly as good in the 19-limit. They are rather like twins, including the fact both are primes. A step of 8269edo has also been similarly proposed as an interval size measure, the major tina.

Prime harmonics

Approximation of prime harmonics in 8269edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.0000	-0.0080	-0.0034	-0.0026	-0.0058	+0.0093	-0.0334	-0.0163	-0.0484	+0.0515	-0.0362
	Relative (%)	+0.0	-5.5	-2.3	-1.8	-4.0	+6.4	-23.0	-11.3	-33.4	+35.5	-24.9
Steps (reduced)		8269 (0)	13106 (4837)	19200 (2662)	23214 (6676)	28606 (3799)	30599 (5792)	33799 (723)	35126 (2050)	37405 (4329)	40171 (7095)	40966 (7890)

Subsets and supersets

8269edo is the 1037th prime edo.