Minimal consistent EDOs: Difference between revisions

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<noinclude>{{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%. It is ''accurately consistent''{{idiosyncratic}} if the edo is consistent to [[Consistency #Generalization|distance 2]], or alternatively put, every ''q''-odd-limit interval in the edo has at most 25% relative error. 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%. It is ''accurately consistent''{{idiosyncratic}} if the edo is consistent to [[Consistency #Generalization|distance 2]], or alternatively put, every ''q''-odd-limit interval in the edo has at most 25% relative error. 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'''.</noinclude>

~~<onlyinclude>~~

{| class="wikitable center-all"

|+ style="font-size: 105%;" | Smallest consistent EDOs per odd limit

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|-

| 135 || 70910024 || 70910024 || 93678217813 || ||

~~{{table notes|cols=6~~

~~| Apart from 0edo~~

~~| Purely consistent to the 137-odd-limit~~

}}

|}

</~~onlyinclude~~>

<nowiki />* Apart from 0edo

<nowiki />** Purely consistent to the 137-odd-limit<noinclude>

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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[[Category:Consistency]]

[[Category:Odd limit]]

</noinclude>

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-{{Idiosyncratic terms}}
+<noinclude>{{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%. It is ''accurately consistent''{{idiosyncratic}} if the edo is consistent to [[Consistency #Generalization|distance 2]], or alternatively put, every ''q''-odd-limit interval in the edo has at most 25% relative error. 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> &minus; 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%. It is ''accurately consistent''{{idiosyncratic}} if the edo is consistent to [[Consistency #Generalization|distance 2]], or alternatively put, every ''q''-odd-limit interval in the edo has at most 25% relative error. 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> &minus; 1}} are '''highlighted'''.</noinclude>
-<onlyinclude>
 {| class="wikitable center-all"
 |+ style="font-size: 105%;" | Smallest consistent EDOs per odd limit
@@ Line 150: / Line 149: @@
 |-
 | 135 || 70910024 || 70910024 || 93678217813 ||  ||
-{{table notes|cols=6
-| Apart from 0edo
-| Purely consistent to the 137-odd-limit
-}}
 |}
-</onlyinclude>
+<nowiki />* Apart from 0edo
+<nowiki />** Purely consistent to the 137-odd-limit<noinclude>
 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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 [[Category:Consistency]]
 [[Category:Odd limit]]
+</noinclude>