20203edo: Difference between revisions

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~~The 20203 division divides the octave into 20203 equal parts of cents each. It~~ is a very strong ~~higher~~ 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 limit, and has a lower relative error than any smaller ~~distinctly consistent 41~~-limit ~~patent val except 17461~~.

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)}}

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-The 20203 division divides the octave into 20203 equal parts of  cents each. It is a very strong higher 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 limit, and has a lower relative error than any smaller distinctly consistent 41-limit patent val except 17461.
+{{Infobox ET|Consistency=45|Distinct consistency=45}}
+{{ED intro}}
+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)}}