20567edo: Difference between revisions

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20567edo is a remarkable very high-limit system, distinctly (and almost purely, as all odd harmonics 57 and below, except 49, are within 25% relative error) [[consistent]] through the [[57-odd-limit]], with a lower [[relative error]] than any previous equal temperaments in the 43-limit. It tempers out 33814/33813, 35344/35343, 37180/37179, 42484/42483, 42688/42687, 47125/47124, 48504/48503, 67915/67914, 70500/70499, 91885/91884, 126225/126224, 156520/156519, 194580/194579, 206800/206793, and 561925/561924 in the 53-limit.

Although [[prime interval|prime]] [[61/1|61]] is poorly approximated, the next four primes are fairly accurate, so it can be used all the way to the no-61 [[79-limit]], with the only inconsistent intervals in the no-61 81-odd-limit being 81/47, 81/55, 81/59, 81/67, 63/47, 63/55, 63/59, 67/63, 67/49, 59/41, 59/42, 59/49, 59/51, 59/54, and their [[octave complement]]s.

=== Prime harmonics ===

{{Harmonics in equal|20567|columns=12|start=13|collapsed=1|title=Approximation of prime harmonics in 20567edo (continued)}}

{{Harmonics in equal|20567|columns=11|start=12|collapsed=1|title=Approximation of prime harmonics in 20567edo (continued)}}

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 edo is a remarkable very high-limit system, distinctly (and almost purely, as all odd harmonics 57 and below, except 49, are within 25% relative error) [[consistent]] through the [[57-odd-limit]], with a lower [[relative error]] than any previous equal temperaments in the 43-limit. It tempers out 33814/33813, 35344/35343, 37180/37179, 42484/42483, 42688/42687, 47125/47124, 48504/48503, 67915/67914, 70500/70499, 91885/91884, 126225/126224, 156520/156519, 194580/194579, 206800/206793, and 561925/561924 in the 53-limit.
+Although [[prime interval|prime]] [[61/1|61]] is poorly approximated, the next four primes are fairly accurate, so it can be used all the way to the no-61 [[79-limit]], with the only inconsistent intervals in the no-61 81-odd-limit being 81/47, 81/55, 81/59, 81/67, 63/47, 63/55, 63/59, 67/63, 67/49, 59/41, 59/42, 59/49, 59/51, 59/54, and their [[octave complement]]s.
 === Prime harmonics ===
-{{Harmonics in equal|20567|columns=12}}
+{{Harmonics in equal|20567|columns=11}}
-{{Harmonics in equal|20567|columns=12|start=13|collapsed=1|title=Approximation of prime harmonics in 20567edo (continued)}}
+{{Harmonics in equal|20567|columns=11|start=12|collapsed=1|title=Approximation of prime harmonics in 20567edo (continued)}}