131edt: Difference between revisions

(9 intermediate revisions by 3 users not shown)

Line 1:

'''~~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).

== Intervals ==

== Theory ==

131edt is strong in the 3.5.7.11.13.17.19.23 [[subgroup]], [[tempering out]] 1377/1375, [[1575/1573]], 3591/3575, [[4459/4455]], 1617/1615 and 6561/6545. Additionally, 131edt tempers out [[3213/3211]] in the 3.7.13.17.19 subgroup and [[2205/2197]] in the 3.5.7.13 subgroup. It [[support]]s [[procyon]], [[erigone]], [[hemigone]] and [[mebsuta]].

=== Intervals ===

== Harmonics ==

=== Harmonics ===

{{Harmonics in equal|131|3|1|start = 12|collapsed = 1|intervals = odd|columns = 16}}

{{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

@@ Line 1: / Line 1: @@
 {{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).
-== Intervals ==
+== Theory ==
+edt is strong in the 3.5.7.11.13.17.19.23 [[subgroup]], [[tempering out]] 1377/1375, [[1575/1573]], 3591/3575, [[4459/4455]], 1617/1615 and 6561/6545. Additionally, 131edt tempers out [[3213/3211]] in the 3.7.13.17.19 subgroup and [[2205/2197]] in the 3.5.7.13 subgroup. It [[support]]s [[procyon]], [[erigone]], [[hemigone]] and [[mebsuta]].
+=== Intervals ===
 {{Interval table}}
-== Harmonics ==
+=== Harmonics ===
 {{Harmonics in equal|131|3|1|intervals = prime|columns = 9}}
-{{Harmonics in equal|131|3|1|start = 12|collapsed = 1|intervals = odd|columns = 16}}
+{{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