631edo: Difference between revisions

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== Theory ==

631edo is [[consistent]] to the [[9-odd-limit]], with all of the odd harmonics having a flat tendency. Using the [[patent val]], it [[tempers out]] [[~~4375~~/~~4374~~]], [[~~41503~~/~~41472~~]], [[~~32805~~/~~32768~~]] and [[~~12005~~/~~11979~~]] in the [[11-limit]]; [[1575/1573]]~~, 4375/4374~~, [[~~4459~~/~~4455~~]], [[~~4225~~/~~4224~~]], and 83349/83200 in the [[13-limit]].

631edo is [[consistent]] to the [[9-odd-limit]], with all of the odd harmonics having a flat tendency. Using the [[patent val]], it [[tempering out|tempers out]] [[32805/32768]] in the 5-limit; [[4375/4374]] in the 7-limit; [[12005/11979]] and [[41503/41472]] in the [[11-limit]]; [[1575/1573]], [[4225/4224]], [[4459/4455]], and 83349/83200 in the [[13-limit]].

=== Odd harmonics ===

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=== Subsets and supersets ===

631edo is the 115th [[prime ~~EDO~~]].

631edo is the 115th [[prime edo]].

== Intervals ==

== Regular temperament properties ==

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| 498.257

| 4/3

| [[Helmholtz]] / [[Pontiac]]

| [[Helmholtz (temperament)|Helmholtz]] / [[Pontiac]]

|}

<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct

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; [[Francium]]

* "DUMPSTER FIRE" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/7noSmEcwOfZpnFsiQ6vYNv Spotify] | [https://francium223.bandcamp.com/track/dumpster-fire Bandcamp] | [https://www.youtube.com/watch?v=PWP2o71Kqes YouTube]

* "Remember To Forget It." from ''Random Sentences'' (2025) – [https://open.spotify.com/track/7h0mRNT7iS8L722566rzlJ Spotify] | [https://francium223.bandcamp.com/track/remember-to-forget-it Bandcamp] | [https://www.youtube.com/watch?v=Jwuqj4BJHwY YouTube]

* "Don't Have a Problem With You" from ''Don't'' (2025) – [https://open.spotify.com/track/2dBYarUaS8dxuHx91zGVEt Spotify] | [https://francium223.bandcamp.com/track/dont-have-a-problem-with-you Bandcamp] | [https://www.youtube.com/watch?v=bxuOZQwOO30 YouTube]

[[Category:Listen]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro}}
+{{ED intro}}
 == Theory ==
-edo is [[consistent]] to the [[9-odd-limit]], with all of the odd harmonics having a flat tendency. Using the [[patent val]], it [[tempers out]] [[4375/4374]], [[41503/41472]], [[32805/32768]] and [[12005/11979]] in the [[11-limit]]; [[1575/1573]], 4375/4374, [[4459/4455]], [[4225/4224]], and 83349/83200 in the [[13-limit]].
+edo is [[consistent]] to the [[9-odd-limit]], with all of the odd harmonics having a flat tendency. Using the [[patent val]], it [[tempering out|tempers out]] [[32805/32768]] in the 5-limit; [[4375/4374]] in the 7-limit; [[12005/11979]] and [[41503/41472]] in the [[11-limit]]; [[1575/1573]], [[4225/4224]], [[4459/4455]], and 83349/83200 in the [[13-limit]].
 === Odd harmonics ===
@@ Line 9: / Line 9: @@
 === Subsets and supersets ===
-edo is the 115th [[prime EDO]].
+edo is the 115th [[prime edo]].
+== Intervals ==
+{{Main|Table of 631edo intervals}}
 == Regular temperament properties ==
@@ Line 80: / Line 83: @@
 | 498.257
 | 4/3
-| [[Helmholtz]] / [[Pontiac]]
+| [[Helmholtz (temperament)|Helmholtz]] / [[Pontiac]]
 |}
 <nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
@@ Line 87: / Line 90: @@
 ; [[Francium]]
 * "DUMPSTER FIRE" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/7noSmEcwOfZpnFsiQ6vYNv Spotify] | [https://francium223.bandcamp.com/track/dumpster-fire Bandcamp] | [https://www.youtube.com/watch?v=PWP2o71Kqes YouTube]
+* "Remember To Forget It." from ''Random Sentences'' (2025) – [https://open.spotify.com/track/7h0mRNT7iS8L722566rzlJ Spotify] | [https://francium223.bandcamp.com/track/remember-to-forget-it Bandcamp] | [https://www.youtube.com/watch?v=Jwuqj4BJHwY YouTube]
+* "Don't Have a Problem With You" from ''Don't'' (2025) – [https://open.spotify.com/track/2dBYarUaS8dxuHx91zGVEt Spotify] | [https://francium223.bandcamp.com/track/dont-have-a-problem-with-you Bandcamp] | [https://www.youtube.com/watch?v=bxuOZQwOO30 YouTube]
 [[Category:Listen]]