20203edo: Difference between revisions
Expand and simplify the comma basis |
Insatinismic endgame |
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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]]. | 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, | 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]], [[5767168/5767125]] and [[1990656/1990625]] supporting [[insanismic]]; in the [[17-limit]] [[194481/194480]] and [[336141/336140]]; in the [[19-limit]] 89376/89375, 104976/104975, and 165376/165375, supporting [[insatinismic]] and providing not the optimal patent val, but an extremely efficient tuning; in the [[23-limit]] 43264/43263 and 52326/52325, in the 31-limit 176176/176175 and 178126/178125 among others. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|20203|columns=11}} | {{Harmonics in equal|20203|columns=11}} | ||
{{Harmonics in equal|20203|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 20203edo (continued)}} | {{Harmonics in equal|20203|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 20203edo (continued)}} | ||