2901533edo: Difference between revisions

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2901533edo is the smallest edo to be [[consistent]] ~~in the 79-~~odd-limit, and is consistent ~~up to~~ the ~~131~~-odd-limit. Because of its unusual consistency at its size range, it could be a candidate for "miracle edo" (not [[miracle]], the temperament) after [[311edo]].

As noted in the page on [[minimal consistent EDOs]], 2901533edo is the smallest edo to be [[consistent]] to every odd-limit from 79 to 131. Due to its extremely small step size, distinct consistency is a given, and its tuning properties are in fact a lot more exceptional: Except for 8 barely in[[consistent]] interval pairs, 2901533edo is consistent in the 137-prime-limited no-247's 255-odd-limit (a total of 4067 interval pairs), with primes 151, 157, 163, 173, 181, 197 and 211 being includable to that odd limit for a tiny penalty of only 3 more barely-inconsistent interval pairs (and for a total of 4830). Including odd 247 adds 8 more inconsistent interval pairs and 90 more consistent interval pairs for a total of 4928 interval pairs (of which 19 interval pairs are inconsistent). Because of its unusual [[consistency]] at its size range, it could be a candidate for "miracle edo" (not [[miracle]], the temperament) after [[311edo]], although this is not entirely certain or clear because a deep exhaustive search of comprehensive odd-limit performance has not been done up until this point, but it is at least significant that it holds a significant amount of records for [[odd limit]] [[consistency]] as detailed on the page for [[minimal consistent edos]]. Furthermore, it is consistent up to the [[odd prime sum limit|25-OPSL]], and is [[Consistency #Consistency to distance d|consistent to distance 4]] in the 16-OPSL.

=== Prime harmonics ===

{{Harmonics in equal|2901533|columns=9|start=10|collapsed=true|title=Approximation of prime harmonics in 2901533edo (continued)}}

{{Harmonics in equal|2901533|columns=12|start=13|collapsed=true|title=Approximation of prime harmonics in 2901533edo (continued)}}

{{Harmonics in equal|2901533|columns=9|start=19|collapsed=true|title=Approximation of prime harmonics in 2901533edo (continued)}}

{{Harmonics in equal|2901533|columns=12|start=25|collapsed=true|title=Approximation of prime harmonics in 2901533edo (continued)}}

{{Harmonics in equal|2901533|columns=9|start=28|collapsed=true|title=Approximation of prime harmonics in 2901533edo (continued)}}

{{Harmonics in equal|2901533|columns=12|start=37|collapsed=true|title=Approximation of prime harmonics in 2901533edo (continued)}}

=== Subsets and supersets ===

~~Since~~ 2901533 ~~factors into primes as~~ {{~~nowrap|~~ 433 × 6701 }}, so 2901533edo contains [[433edo]] and [[6701edo]] as subsets.

{{Nowrap|2901533 {{=}} 433 × 6701}}, so 2901533edo contains [[433edo]] and [[6701edo]] as subsets.

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 {{ED intro}}
-2901533edo is the smallest edo to be [[consistent]] in the 79-odd-limit, and is consistent up to the 131-odd-limit. Because of its unusual consistency at its size range, it could be a candidate for "miracle edo" (not [[miracle]], the temperament) after [[311edo]].
+As noted in the page on [[minimal consistent EDOs]], 2901533edo is the smallest edo to be [[consistent]] to every odd-limit from 79 to 131. Due to its extremely small step size, distinct consistency is a given, and its tuning properties are in fact a lot more exceptional: Except for 8 barely in[[consistent]] interval pairs, 2901533edo is consistent in the 137-prime-limited no-247's 255-odd-limit (a total of 4067 interval pairs), with primes 151, 157, 163, 173, 181, 197 and 211 being includable to that odd limit for a tiny penalty of only 3 more barely-inconsistent interval pairs (and for a total of 4830). Including odd 247 adds 8 more inconsistent interval pairs and 90 more consistent interval pairs for a total of 4928 interval pairs (of which 19 interval pairs are inconsistent). Because of its unusual [[consistency]] at its size range, it could be a candidate for "miracle edo" (not [[miracle]], the temperament) after [[311edo]], although this is not entirely certain or clear because a deep exhaustive search of comprehensive odd-limit performance has not been done up until this point, but it is at least significant that it holds a significant amount of records for [[odd limit]] [[consistency]] as detailed on the page for [[minimal consistent edos]]. Furthermore, it is consistent up to the [[odd prime sum limit|25-OPSL]], and is [[Consistency #Consistency to distance d|consistent to distance 4]] in the 16-OPSL.
 === Prime harmonics ===
-{{Harmonics in equal|2901533|columns=9}}
+{{Harmonics in equal|2901533|columns=12}}
-{{Harmonics in equal|2901533|columns=9|start=10|collapsed=true|title=Approximation of prime harmonics in 2901533edo (continued)}}
+{{Harmonics in equal|2901533|columns=12|start=13|collapsed=true|title=Approximation of prime harmonics in 2901533edo (continued)}}
-{{Harmonics in equal|2901533|columns=9|start=19|collapsed=true|title=Approximation of prime harmonics in 2901533edo (continued)}}
+{{Harmonics in equal|2901533|columns=12|start=25|collapsed=true|title=Approximation of prime harmonics in 2901533edo (continued)}}
-{{Harmonics in equal|2901533|columns=9|start=28|collapsed=true|title=Approximation of prime harmonics in 2901533edo (continued)}}
+{{Harmonics in equal|2901533|columns=12|start=37|collapsed=true|title=Approximation of prime harmonics in 2901533edo (continued)}}
 === Subsets and supersets ===
-Since 2901533 factors into primes as {{nowrap| 433 × 6701 }}, so 2901533edo contains [[433edo]] and [[6701edo]] as subsets.
+{{Nowrap|2901533 {{=}} 433 × 6701}}, so 2901533edo contains [[433edo]] and [[6701edo]] as subsets.