8269edo: Difference between revisions

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8269edo is both a [[The Riemann zeta function and tuning #Zeta EDO lists|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 [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any smaller division, a lower 19-limit [[Tenney-Euclidean temperament measures #TE simple badness|TE logflat badness]] than any smaller division, and a lower 23-limit logflat badness than any excepting 311, 581, 1578 and 2460. While [[8539edo|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'''.

8269edo is both a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak and zeta integral edo]], which has to do with the fact that it is a very strong [[19-limit|19-]] and [[23-limit]] system. It has a lower 19-limit and a lower 23-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any smaller division, a lower 19-limit [[Tenney-Euclidean temperament measures #TE simple badness|TE logflat badness]] than any smaller division, and a lower 23-limit logflat badness than any excepting [[311edo|311]], [[581edo|581]], [[1578edo|1578]] and [[2460edo|2460]]. While [[8539edo|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'''.

Some of the simpler commas it [[tempering out|tempers out]] include [[123201/123200]] in the 13-limit; [[194481/194480]], [[336141/336140]] in the 17-limit; 23409/23408, 28900/28899, 43681/43680, 89376/89375 in the 19-limit; and 21505/21504 among others in the 23-limit.

=== Prime harmonics ===

=== Subsets and supersets ===

8269edo is the 1037th [[prime edo]].

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 {{EDO intro|8269}}
-edo is both a [[The Riemann zeta function and tuning #Zeta EDO lists|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 [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any smaller division, a lower 19-limit [[Tenney-Euclidean temperament measures #TE simple badness|TE logflat badness]] than any smaller division, and a lower 23-limit logflat badness than any excepting 311, 581, 1578 and 2460. While [[8539edo|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'''.
+edo is both a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak and zeta integral edo]], which has to do with the fact that it is a very strong [[19-limit|19-]] and [[23-limit]] system. It has a lower 19-limit and a lower 23-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any smaller division, a lower 19-limit [[Tenney-Euclidean temperament measures #TE simple badness|TE logflat badness]] than any smaller division, and a lower 23-limit logflat badness than any excepting [[311edo|311]], [[581edo|581]], [[1578edo|1578]] and [[2460edo|2460]]. While [[8539edo|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'''.
+Some of the simpler commas it [[tempering out|tempers out]] include [[123201/123200]] in the 13-limit; [[194481/194480]], [[336141/336140]] in the 17-limit; 23409/23408, 28900/28899, 43681/43680, 89376/89375 in the 19-limit; and 21505/21504 among others in the 23-limit.
 === Prime harmonics ===
-{{Harmonics in equal|8269}}
+{{Harmonics in equal|8269|columns=12}}
 === Subsets and supersets ===
 edo is the 1037th [[prime edo]].