Minimal consistent EDOs: Difference between revisions
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{{Idiosyncratic terms}} | |||
An [[edo]] ''N'' is ''[[consistent]]'' with respect to the [[Odd limit|''q''-odd-limit]] if the closest approximations of the odd harmonics of the q-odd-limit in that edo also give the closest approximations of all the differences between these odd harmonics. It is ''[[distinctly consistent]]'' if every one of those closest approximations is a distinct value, and ''purely consistent''{{idiosyncratic}} if its [[relative interval error|relative errors]] on odd harmonics up to and including ''q'' never exceed 25%. Below is a table of the smallest consistent, and the smallest distinctly consistent, edo for every odd number up to 135. Odd limits of {{nowrap|2<sup>''n''</sup> − 1}} are '''highlighted'''. | An [[edo]] ''N'' is ''[[consistent]]'' with respect to the [[Odd limit|''q''-odd-limit]] if the closest approximations of the odd harmonics of the q-odd-limit in that edo also give the closest approximations of all the differences between these odd harmonics. It is ''[[distinctly consistent]]'' if every one of those closest approximations is a distinct value, and ''purely consistent''{{idiosyncratic}} if its [[relative interval error|relative errors]] on odd harmonics up to and including ''q'' never exceed 25%. Below is a table of the smallest consistent, and the smallest distinctly consistent, edo for every odd number up to 135. Odd limits of {{nowrap|2<sup>''n''</sup> − 1}} are '''highlighted'''. | ||
< | |||
{| class="wikitable center-all" | <onlyinclude>{| class="wikitable center-all" | ||
|+ style="font-size: 105%;" | Smallest consistent EDOs per odd limit | |+ style="font-size: 105%;" | Smallest consistent EDOs per odd limit | ||
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<nowiki />* Apart from 0edo | <nowiki />* Apart from 0edo | ||
<nowiki />** Purely consistent to the 137-odd-limit< | <nowiki />** Purely consistent to the 137-odd-limit</onlyinclude> | ||
The last entry, 70910024edo, is consistent up to the 135-odd-limit. The next edo is [[5407372813edo|5407372813]], reported to be consistent to the 155-odd-limit. | The last entry, 70910024edo, is consistent up to the 135-odd-limit. The next edo is [[5407372813edo|5407372813]], reported to be consistent to the 155-odd-limit. | ||
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== See also == | == See also == | ||
* [[Consistency limits of small EDOs]] | * [[Consistency limits of small EDOs]] | ||
* | * {{u|ArrowHead294|First 50 purely consistent EDOs by odd limit}} | ||
[[Category:Mapping]] | [[Category:Mapping]] | ||