8269edo: Difference between revisions

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The 8269 division divides the octave into 8269 equal parts of 0.14512 cents each. It 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_metrics#Logflat TE badness| TE loglfat 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.

The '''8269 division''' divides the octave into 8269 equal parts of 0.14512 cents each. It 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_metrics#Logflat TE badness| TE loglfat 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.

[[Category:Equal divisions of the octave|####]]

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	The 8269 division divides the octave into 8269 equal parts of 0.14512 cents each. It 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_metrics#Logflat TE badness\| TE loglfat 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.		The '''8269 division''' divides the octave into 8269 equal parts of 0.14512 cents each. It 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_metrics#Logflat TE badness\| TE loglfat 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.

			[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->