20203edo: Difference between revisions

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{{~~EDO~~ intro~~|20203}}~~

~~==Theory==~~

2023edo is a very strong high limit edo, with a lower 19-limit [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]] than any edo until 128125. It is also distinctly consistent through the [[45-odd-limit|45-limit]], and has a lower relative error than any smaller distinctly consistent 41-limit patent val except 17461. It tempers out 47151/47150, 52326/52325, 69875/69874, 81796/81795, 111112/111111, 127281/127280, 156520/156519, 315495/315491, 395200/395199, 728365/728364, 1324323/1324300, 1518804/1518803, and 3845961/3845920 in the 43-limit.

~~===Prime harmonics===~~

~~{{harmonics in equal|20203~~}}

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

20203edo is a very strong high-limit system, and specializes in the [[17-limit|17-]] and [[19-limit]], with lower 17- and 19-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative errors]] than any smaller edo until [[102557edo|102557]] and 128215, respectively. It is also distinctly [[consistent]] through the [[45-odd-limit]], and has a lower [[43-limit]] relative error than any smaller edo except for [[7361edo|7361]], [[14348edo|14348]] and [[17461edo|17461]].

A 43-limit [[comma basis]] for this temperament is {29792/29791, 32799/32798, 43264/43263, 45696/45695, 47151/47150, 52326/52325, 53361/53360, 69875/69874, 81796/81795, 83521/83520, 87465/87464, 96876/96875, 111112/111111}. In the [[13-limit]] it tempers out [[123201/123200]] and [[1990656/1990625]]; in the [[17-limit]] [[194481/194480]] and [[336141/336140]]; in the [[19-limit]] 89376/89375, 104976/104975, and 165376/165375; in the [[23-limit]] 43264/43263 and 52326/52325 among others.

=== Prime harmonics ===

{{Harmonics in equal|20203|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 20203edo (continued)}}

@@ Line 1: / Line 1: @@
 {{Infobox ET|Consistency=45|Distinct consistency=45}}
-{{EDO intro|20203}}
+{{ED intro}}
-==Theory==
-edo is a very strong high limit edo, with a lower 19-limit [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]] than any edo until 128125. It is also distinctly consistent through the [[45-odd-limit|45-limit]], and has a lower relative error than any smaller distinctly consistent 41-limit patent val except 17461. It tempers out 47151/47150, 52326/52325, 69875/69874, 81796/81795, 111112/111111, 127281/127280, 156520/156519, 315495/315491, 395200/395199, 728365/728364, 1324323/1324300, 1518804/1518803, and 3845961/3845920 in the 43-limit.
-===Prime harmonics===
-{{harmonics in equal|20203}}
-[[Category:Equal divisions of the octave|#####]] <!-- 5-digit number -->
+edo is a very strong high-limit system, and specializes in the [[17-limit|17-]] and [[19-limit]], with lower 17- and 19-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative errors]] than any smaller edo until [[102557edo|102557]] and 128215, respectively. It is also distinctly [[consistent]] through the [[45-odd-limit]], and has a lower [[43-limit]] relative error than any smaller edo except for [[7361edo|7361]], [[14348edo|14348]] and [[17461edo|17461]].
+A 43-limit [[comma basis]] for this temperament is {29792/29791, 32799/32798, 43264/43263, 45696/45695, 47151/47150, 52326/52325, 53361/53360, 69875/69874, 81796/81795, 83521/83520, 87465/87464, 96876/96875, 111112/111111}. In the [[13-limit]] it tempers out [[123201/123200]] and [[1990656/1990625]]; in the [[17-limit]] [[194481/194480]] and [[336141/336140]]; in the [[19-limit]] 89376/89375,  104976/104975, and 165376/165375; in the [[23-limit]] 43264/43263 and 52326/52325 among others.
+=== Prime harmonics ===
+{{Harmonics in equal|20203|columns=11}}
+{{Harmonics in equal|20203|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 20203edo (continued)}}