131edt: Difference between revisions

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'''131edt''' is the [[EDT|equal division of the third harmonic]] into 131 parts of 14.5187 [[cent|cents]] each, corresponding to 82.6520 [[edo]] (similar to every third step of [[248edo]]). It is notable for consistency to the no-evens 25-[[odd limit#Nonoctave equaves|throdd limit]]. Furthermore, several higher primes, including 29, 31, 37, 43, and 53, lie at close to halfway between 131edt's steps; therefore [[262edt]], which doubles it, improves representation of a large spectrum of primes, though it loses consistency of a few intervals of 19.

'''131edt''' is the [[EDT|equal division of the third harmonic]] into 131 parts of 14.5187 [[cent|cents]] each, corresponding to 82.6520 [[edo]] (similar to every third step of [[248edo]]). It is notable for consistency to the no-evens 27-[[odd limit#Nonoctave equaves|throdd limit]]. Furthermore, several higher primes, including 29, 31, 37, 43, and 53, lie at close to halfway between 131edt's steps; therefore [[262edt]], which doubles it, improves representation of a large spectrum of primes, though it loses consistency of a few intervals of 19.

131edt is the 16th [[The_Riemann_Zeta_Function_and_Tuning#Removing primes|no-twos zeta peak EDT]].

131edt is the 16th [[The_Riemann_Zeta_Function_and_Tuning#Removing primes|no-twos zeta peak EDT]], and is the smallest EDT to be [[purely consistent]]{{idio}} in the 27-odd-limit (i.e. maintains no greater than 25% relative error on all odd harmonocs up to and including 27).

== Theory ==

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 {{Infobox ET}}
-'''131edt''' is the [[EDT|equal division of the third harmonic]] into 131 parts of 14.5187 [[cent|cents]] each, corresponding to 82.6520 [[edo]] (similar to every third step of [[248edo]]). It is notable for consistency to the no-evens 25-[[odd limit#Nonoctave equaves|throdd limit]]. Furthermore, several higher primes, including 29, 31, 37, 43, and 53, lie at close to halfway between 131edt's steps; therefore [[262edt]], which doubles it, improves representation of a large spectrum of primes, though it loses consistency of a few intervals of 19.
+'''131edt''' is the [[EDT|equal division of the third harmonic]] into 131 parts of 14.5187 [[cent|cents]] each, corresponding to 82.6520 [[edo]] (similar to every third step of [[248edo]]). It is notable for consistency to the no-evens 27-[[odd limit#Nonoctave equaves|throdd limit]]. Furthermore, several higher primes, including 29, 31, 37, 43, and 53, lie at close to halfway between 131edt's steps; therefore [[262edt]], which doubles it, improves representation of a large spectrum of primes, though it loses consistency of a few intervals of 19.
-edt is the 16th [[The_Riemann_Zeta_Function_and_Tuning#Removing primes|no-twos zeta peak EDT]].
+edt is the 16th [[The_Riemann_Zeta_Function_and_Tuning#Removing primes|no-twos zeta peak EDT]], and is the smallest EDT to be [[purely consistent]]{{idio}} in the 27-odd-limit (i.e. maintains no greater than 25% relative error on all odd harmonocs up to and including 27).
 == Theory ==