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]]s 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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{{Harmonics in equal|131|3|1|start = 12|collapsed = 1|intervals = odd|columns = 15}}

== Music ==

; [[Francium]]

* "cocoon" from ''wiloliquy'' (2025) – [https://open.spotify.com/track/1XnR14gAGjVIe6SKf7bWfv Spotify] | [https://francium223.bandcamp.com/track/cocoon Bandcamp] | [https://www.youtube.com/watch?v=rVn0fcY0RBI YouTube] – in Cobaltomenite, 131edt tuning

* "Boing Going Up?" from ''Questions, Vol. 2'' (2025) – [https://open.spotify.com/track/3kbXkD9GRC1qeENsMZtFmO Spotify] | [https://francium223.bandcamp.com/track/boing-going-up Bandcamp] | [https://www.youtube.com/watch?v=rsW7_utEdbc YouTube] – in Gordaite, 131edt tuning

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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]]s 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 ==
@@ Line 13: / Line 13: @@
 {{Harmonics in equal|131|3|1|intervals = prime|columns = 9}}
 {{Harmonics in equal|131|3|1|start = 12|collapsed = 1|intervals = odd|columns = 15}}
+== Music ==
+; [[Francium]]
+* "cocoon" from ''wiloliquy'' (2025) – [https://open.spotify.com/track/1XnR14gAGjVIe6SKf7bWfv Spotify] | [https://francium223.bandcamp.com/track/cocoon Bandcamp] | [https://www.youtube.com/watch?v=rVn0fcY0RBI YouTube] – in Cobaltomenite, 131edt tuning
+* "Boing Going Up?" from ''Questions, Vol. 2'' (2025) – [https://open.spotify.com/track/3kbXkD9GRC1qeENsMZtFmO Spotify] | [https://francium223.bandcamp.com/track/boing-going-up Bandcamp] | [https://www.youtube.com/watch?v=rsW7_utEdbc YouTube] – in Gordaite, 131edt tuning