Minimal consistent EDOs: Difference between revisions

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m Removing from Category:Theory using Cat-a-lot
Cleanup, and explain odd limits beyond 135 in plain text
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An [[EDO]] N is [[consistent]] with respect to the 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. Below is a table of the smallest consistent, and the smallest distinctly consistent, edo for every odd number up to 135.
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. Below is a table of the smallest consistent, and the smallest distinctly consistent, edo for every odd number up to 135.


{| class="wikitable"
{| class="wikitable right-all"
|-
|-
! Odd limit
! Odd<br>Limit
! Smallest consistent edo
! Smallest<br>Consistent Edo
! Smallest distinctly consistent edo
! Smallest<br>Distinctly Consistent Edo
|-
|-
| 1
| 1
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| 70910024
| 70910024
| 70910024
| 70910024
|-
| 137
| 5407372813
| 5407372813
|-
| 139
| 5407372813
| 5407372813
|-
| 141
| 5407372813
| 5407372813
|-
| 143
| 5407372813
| 5407372813
|-
| 145
| 5407372813
| 5407372813
|-
| 147
| 5407372813
| 5407372813
|-
| 149
| 5407372813
| 5407372813
|-
| 151
| 5407372813
| 5407372813
|-
| 153
| 5407372813
| 5407372813
|-
| 155
| 5407372813
| 5407372813
|}
|}
The last entry, 70910024edo, is consistent up to the 135-odd-limit. The next edo is 5407372813, reported to be consistent to the 155-odd-limit.


== OEIS integer sequences links ==
== OEIS integer sequences links ==