8269 equal divisions of the octave (8269edo), or 8269-tone equal temperament (8269tet), 8269 equal temperament (8269et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 8269 equal parts of about 0.145 ¢ each.
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.
Subsets and supersets
8269edo is the 1037th prime edo.