8269edo: Difference between revisions
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== Theory == | |||
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'''. | 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'''. | ||