Consistency limits of small EDOs: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
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 every edo up to 99. "Consistent" gives its consistency limit, i.e. the highest odd limit to which the edo is consistent, and "Distinct" gives the distinct consistency limit, i.e. the highest odd limit to which the edo is distinctly consistent. The remaining columns give the [[Consistent #Consistency to distance d|consistency distance]] (also called ''consistency level''<ref group="note">This term was coined by [[Paul Hahn]] in 1996. See [https://yahootuninggroupsultimatebackup.github.io/mills-tuning-list/topicId_884.html Yahoo! Tuning Group | ''Consistency generalized'']. </ref>) for every odd limit from 3 to 23.
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-01-12 16:57:24 UTC</tt>.<br>
: The original revision id was <tt>603954526</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">An [[edo]] N is [[consistent]] with respect to a set of rational numbers s if the [[patent val]] mapping of every element of s is the nearest N-edo approximation. It is //uniquely consistent// if every element of s is mapped to a unique value. If the set s is the q [[odd limit]], we say N is q-limit consistent and q-limit uniquely consistent, respectively. Below is a table of every edo up to 99. "Consistent" gives the consistency level, and "Distinct" the distinct consistency level.


|| EDO || Consistent || Distinct ||
{| class="wikitable sortable mw-collapsible right-all"
|| 1 || 3 || 1 ||
|-
|| 2 || 3 || 1 ||
! rowspan="2" | Edo
|| 3 || 5 || 3 ||
! colspan="2" | Consistency limit
|| 4 || 7 || 1 ||
! colspan="11" | Consistency distance
|| 5 || 9 || 3 ||
|-
|| 6 || 7 || 3 ||
! Consistent
|| 7 || 5 || 3 ||
! Distinct
|| 8 || 5 || 3 ||
! 3-limit
|| 9 || 7 || 5 ||
! 5-limit
|| 10 || 7 || 3 ||
! 7-limit
|| 11 || 3 || 3 ||
! 9-limit
|| 12 || 9 || 5 ||
! 11-limit
|| 13 || 3 || 3 ||
! 13-limit
|| 14 || 3 || 3 ||
! 15-limit
|| 15 || 7 || 5 ||
! 17-limit
|| 16 || 7 || 5 ||
! 19-limit
|| 17 || 3 || 3 ||
! 21-limit
|| 18 || 7 || 5 ||
! 23-limit
|| 19 || 9 || 5 ||
|-
|| 20 || 3 || 3 ||
| 1 || style="background-color: #fefefe;"| 3 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|| 21 || 3 || 3 ||
|-
|| 22 || 11 || 5 ||
| 2 || style="background-color: #fefefe;"| 3 || 1 || style="background-color: #fefefe;"| 2 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|| 23 || 5 || 5 ||
|-
|| 24 || 5 || 5 ||
| 3 || style="background-color: #fefefe;"| 5 || 3 || 2 || style="background-color: #fefefe;"| 2 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|| 25 || 5 || 5 ||
|-
|| 26 || 13 || 5 ||
| 4 || style="background-color: #fefefe;"| 7 || 1 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|| 27 || 9 || 7 ||
|-
|| 28 || 5 || 5 ||
| 5 || style="background-color: #fefefe;"| 9 || 3 || 6 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|| 29 || 15 || 5 ||
|-
|| 30 || 5 || 5 ||
| 6 || style="background-color: #fefefe;"| 7 || 3 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|| 31 || 11 || 7 ||
|-
|| 32 || 3 || 3 ||
| 7 || style="background-color: #fefefe;"| 5 || 3 || 5 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|| 33 || 3 || 3 ||
|-
|| 34 || 5 || 5 ||
| 8 || style="background-color: #fefefe;"| 5 || 3 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|| 35 || 7 || 7 ||
|-
|| 36 || 7 || 7 ||
| 9 || style="background-color: #fefefe;"| 7 || 5 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|| 37 || 7 || 7 ||
|-
|| 38 || 5 || 5 ||
| 10 || style="background-color: #fefefe;"| 7 || 3 || 3 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|| 39 || 5 || 5 ||
|-
|| 40 || 3 || 3 ||
| 11 || style="background-color: #fefefe;"| 3 || 3 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|| 41 || 15 || 9 ||
|-
|| 42 || 7 || 7 ||
| 12 || style="background-color: #fefefe;"| 9 || 5 || 25 || 3 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|| 43 || 7 || 7 ||
|-
|| 44 || 5 || 5 ||
| 13 || style="background-color: #fefefe;"| 3 || 3 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|| 45 || 7 || 7 ||
|-
|| 46 || 13 || 9 ||
| 14 || style="background-color: #fefefe;"| 3 || 3 || style="background-color: #fefefe;"| 2 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|| 47 || 5 || 5 ||
|-
|| 48 || 5 || 5 ||
| 15 || style="background-color: #fefefe;"| 7 || 5 || 2 || 2 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|| 49 || 7 || 7 ||
|-
|| 50 || 9 || 7 ||
| 16 || style="background-color: #fefefe;"| 7 || 5 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|| 51 || 3 || 3 ||
|-
|| 52 || 3 || 3 ||
| 17 || style="background-color: #fefefe;"| 3 || 3 || style="background-color: #fefefe;"| 8 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|| 53 || 9 || 9 ||
|-
|| 54 || 3 || 3 ||
| 18 || style="background-color: #fefefe;"| 7 || 5 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|| 55 || 5 || 5 ||
|-
|| 56 || 7 || 7 ||
| 19 || style="background-color: #fefefe;"| 9 || 5 || 4 || 4 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|| 57 || 7 || 7 ||
|-
|| 58 || 17 || 11 ||
| 20 || style="background-color: #fefefe;"| 3 || 3 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|| 59 || 7 || 7 ||
|-
|| 60 || 9 || 9 ||
| 21 || style="background-color: #fefefe;"| 3 || 3 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|| 61 || 5 || 5 ||
|-
|| 62 || 7 || 7 ||
| 22 || style="background-color: #fefefe;"| 11 || 5 || 3 || 2 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0
|| 63 || 7 || 7 ||
|-
|| 64 || 3 || 3 ||
| 23 || style="background-color: #fefefe;"| 5 || 5 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|| 65 || 5 || 5 ||
|-
|| 66 || 3 || 3 ||
| 24 || style="background-color: #fefefe;"| 5 || 5 || 12 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|| 67 || 3 || 3 ||
|-
|| 68 || 9 || 9 ||
| 25 || style="background-color: #fefefe;"| 5 || 5 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|| 69 || 5 || 5 ||
|-
|| 70 || 9 || 9 ||
| 26 || style="background-color: #fefefe;"| 13 || 5 || 2 || 1 || 1 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0
|| 71 || 5 || 5 ||
|-
|| 72 || 17 || 11 ||
| 27 || style="background-color: #fefefe;"| 9 || 7 || 2 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|| 73 || 7 || 7 ||
|-
|| 74 || 5 || 5 ||
| 28 || style="background-color: #fefefe;"| 5 || 5 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|| 75 || 5 || 5 ||
|-
|| 76 || 7 || 7 ||
| 29 || style="background-color: #fefefe;"| 15 || 5 || 13 || 1 || 1 || 1 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0
|| 77 || 9 || 9 ||
|-
|| 78 || 7 || 7 ||
| 30 || style="background-color: #fefefe;"| 5 || 5 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|| 79 || 5 || 5 ||
|-
|| 80 || 19 || 11 ||
| 31 || style="background-color: #fefefe;"| 11 || 7 || 3 || 3 || 3 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0
|| 81 || 7 || 7 ||
|-
|| 82 || 9 || 9 ||
| 32 || style="background-color: #fefefe;"| 3 || 3 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|| 83 || 7 || 7 ||
|-
|| 84 || 9 || 9 ||
| 33 || style="background-color: #fefefe;"| 3 || 3 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|| 85 || 3 || 3 ||
|-
|| 86 || 3 || 3 ||
| 34 || style="background-color: #fefefe;"| 5 || 5 || 4 || style="background-color: #fefefe;"| 4 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|| 87 || 15 || 13 ||
|-
|| 88 || 7 || 7 ||
| 35 || style="background-color: #fefefe;"| 7 || 7 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|| 89 || 11 || 11 ||
|-
|| 90 || 7 || 7 ||
| 36 || style="background-color: #fefefe;"| 7 || 7 || 8 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|| 91 || 9 || 9 ||
|-
|| 92 || 5 || 5 ||
| 37 || style="background-color: #fefefe;"| 7 || 7 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|| 93 || 7 || 7 ||
|-
|| 94 || 23 || 13 ||
| 38 || style="background-color: #fefefe;"| 5 || 5 || 2 || style="background-color: #fefefe;"| 2 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|| 95 || 7 || 7 ||
|-
|| 96 || 5 || 5 ||
| 39 || style="background-color: #fefefe;"| 5 || 5 || 2 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|| 97 || 5 || 5 ||
|-
|| 98 || 3 || 3 ||
| 40 || style="background-color: #fefefe;"| 3 || 3 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|| 99 || 9 || 9 ||</pre></div>
|-
<h4>Original HTML content:</h4>
| 41 || style="background-color: #fefefe;"| 15 || 9 || 30 || 2 || 2 || 2 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Consistency levels of small EDOs&lt;/title&gt;&lt;/head&gt;&lt;body&gt;An &lt;a class="wiki_link" href="/edo"&gt;edo&lt;/a&gt; N is &lt;a class="wiki_link" href="/consistent"&gt;consistent&lt;/a&gt; with respect to a set of rational numbers s if the &lt;a class="wiki_link" href="/patent%20val"&gt;patent val&lt;/a&gt; mapping of every element of s is the nearest N-edo approximation. It is &lt;em&gt;uniquely consistent&lt;/em&gt; if every element of s is mapped to a unique value. If the set s is the q &lt;a class="wiki_link" href="/odd%20limit"&gt;odd limit&lt;/a&gt;, we say N is q-limit consistent and q-limit uniquely consistent, respectively. Below is a table of every edo up to 99. &amp;quot;Consistent&amp;quot; gives the consistency level, and &amp;quot;Distinct&amp;quot; the distinct consistency level.&lt;br /&gt;
|-
&lt;br /&gt;
| 42 || style="background-color: #fefefe;"| 7 || 7 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 43 || style="background-color: #fefefe;"| 7 || 7 || 3 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 44 || style="background-color: #fefefe;"| 5 || 5 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 45 || style="background-color: #fefefe;"| 7 || 7 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 46 || style="background-color: #fefefe;"| 13 || 9 || 5 || 2 || 1 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0
|-
| 47 || style="background-color: #fefefe;"| 5 || 5 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 48 || style="background-color: #fefefe;"| 5 || 5 || 6 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 49 || style="background-color: #fefefe;"| 7 || 7 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 50 || style="background-color: #fefefe;"| 9 || 7 || 2 || 2 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 51 || style="background-color: #fefefe;"| 3 || 3 || style="background-color: #fefefe;"| 2 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 52 || style="background-color: #fefefe;"| 3 || 3 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 53 || style="background-color: #fefefe;"| 9 || 9 || 165 || 8 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 54 || style="background-color: #fefefe;"| 3 || 3 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 55 || style="background-color: #fefefe;"| 5 || 5 || 2 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 56 || style="background-color: #fefefe;"| 7 || 7 || 2 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 57 || style="background-color: #fefefe;"| 7 || 7 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 58 || style="background-color: #fefefe;"| 17 || 11 || 6 || 1 || 1 || 1 || 1 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0
|-
| 59 || style="background-color: #fefefe;"| 7 || 7 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 60 || style="background-color: #fefefe;"| 9 || 9 || 5 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 61 || style="background-color: #fefefe;"| 5 || 5 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 62 || style="background-color: #fefefe;"| 7 || 7 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 63 || style="background-color: #fefefe;"| 7 || 7 || 3 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 64 || style="background-color: #fefefe;"| 3 || 3 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 65 || style="background-color: #fefefe;"| 5 || 5 || 22 || style="background-color: #fefefe;"| 5 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 66 || style="background-color: #fefefe;"| 3 || 3 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 67 || style="background-color: #fefefe;"| 3 || 3 || style="background-color: #fefefe;"| 2 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 68 || style="background-color: #fefefe;"| 9 || 9 || 2 || 2 || 2 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 69 || style="background-color: #fefefe;"| 5 || 5 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 70 || style="background-color: #fefefe;"| 9 || 9 || 9 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 71 || style="background-color: #fefefe;"| 5 || 5 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 72 || style="background-color: #fefefe;"| 17 || 11 || 4 || 2 || 2 || 2 || 2 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0
|-
| 73 || style="background-color: #fefefe;"| 7 || 7 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 74 || style="background-color: #fefefe;"| 5 || 5 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 75 || style="background-color: #fefefe;"| 5 || 5 || 3 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 76 || style="background-color: #fefefe;"| 7 || 7 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 77 || style="background-color: #fefefe;"| 9 || 9 || 11 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 78 || style="background-color: #fefefe;"| 7 || 7 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 79 || style="background-color: #fefefe;"| 5 || 5 || 2 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 80 || style="background-color: #fefefe;"| 19 || 11 || 2 || 2 || 1 || 1 || 1 || 1 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0
|-
| 81 || style="background-color: #fefefe;"| 7 || 7 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 82 || style="background-color: #fefefe;"| 9 || 9 || 15 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 83 || style="background-color: #fefefe;"| 7 || 7 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 84 || style="background-color: #fefefe;"| 9 || 9 || 3 || 3 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 85 || style="background-color: #fefefe;"| 3 || 3 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 86 || style="background-color: #fefefe;"| 3 || 3 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 87 || style="background-color: #fefefe;"| 15 || 13 || 4 || 4 || 1 || 1 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0
|-
| 88 || style="background-color: #fefefe;"| 7 || 7 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 89 || style="background-color: #fefefe;"| 11 || 11 || 8 || 1 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 90 || style="background-color: #fefefe;"| 7 || 7 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 91 || style="background-color: #fefefe;"| 9 || 9 || 2 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 92 || style="background-color: #fefefe;"| 5 || 5 || 2 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 93 || style="background-color: #fefefe;"| 7 || 7 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 94 || style="background-color: #fefefe;"| 23 || 13 || 36 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || style="background-color: #fefefe;"| 1
|-
| 95 || style="background-color: #fefefe;"| 7 || 7 || 1 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 96 || style="background-color: #fefefe;"| 5 || 5 || 3 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 97 || style="background-color: #fefefe;"| 5 || 5 || 1 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 98 || style="background-color: #fefefe;"| 3 || 3 || style="background-color: #fefefe;"| 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|-
| 99 || style="background-color: #fefefe;"| 9 || 9 || 5 || 3 || 3 || style="background-color: #fefefe;"| 2 || 0 || 0 || 0 || 0 || 0 || 0 || 0
|}


== Notes ==
<references group="note"/>


&lt;table class="wiki_table"&gt;
[[Category:Mapping]]
    &lt;tr&gt;
[[Category:Consistency]]
        &lt;td&gt;EDO&lt;br /&gt;
[[Category:Odd limit]]
&lt;/td&gt;
        &lt;td&gt;Consistent&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Distinct&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
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        &lt;td&gt;8&lt;br /&gt;
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        &lt;td&gt;9&lt;br /&gt;
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        &lt;td&gt;10&lt;br /&gt;
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        &lt;td&gt;11&lt;br /&gt;
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        &lt;td&gt;12&lt;br /&gt;
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        &lt;td&gt;13&lt;br /&gt;
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        &lt;td&gt;14&lt;br /&gt;
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        &lt;td&gt;15&lt;br /&gt;
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        &lt;td&gt;16&lt;br /&gt;
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        &lt;td&gt;17&lt;br /&gt;
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        &lt;td&gt;18&lt;br /&gt;
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        &lt;td&gt;19&lt;br /&gt;
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        &lt;td&gt;20&lt;br /&gt;
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        &lt;td&gt;21&lt;br /&gt;
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        &lt;td&gt;22&lt;br /&gt;
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        &lt;td&gt;11&lt;br /&gt;
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        &lt;td&gt;23&lt;br /&gt;
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        &lt;td&gt;24&lt;br /&gt;
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        &lt;td&gt;25&lt;br /&gt;
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        &lt;td&gt;26&lt;br /&gt;
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        &lt;td&gt;27&lt;br /&gt;
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        &lt;td&gt;28&lt;br /&gt;
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        &lt;td&gt;29&lt;br /&gt;
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        &lt;td&gt;15&lt;br /&gt;
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        &lt;td&gt;30&lt;br /&gt;
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        &lt;td&gt;31&lt;br /&gt;
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        &lt;td&gt;11&lt;br /&gt;
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        &lt;td&gt;32&lt;br /&gt;
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        &lt;td&gt;33&lt;br /&gt;
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        &lt;td&gt;34&lt;br /&gt;
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        &lt;td&gt;35&lt;br /&gt;
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        &lt;td&gt;36&lt;br /&gt;
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        &lt;td&gt;37&lt;br /&gt;
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        &lt;td&gt;38&lt;br /&gt;
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        &lt;td&gt;39&lt;br /&gt;
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        &lt;td&gt;40&lt;br /&gt;
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        &lt;td&gt;41&lt;br /&gt;
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        &lt;td&gt;15&lt;br /&gt;
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        &lt;td&gt;42&lt;br /&gt;
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        &lt;td&gt;43&lt;br /&gt;
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        &lt;td&gt;44&lt;br /&gt;
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        &lt;td&gt;45&lt;br /&gt;
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        &lt;td&gt;46&lt;br /&gt;
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        &lt;td&gt;47&lt;br /&gt;
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        &lt;td&gt;48&lt;br /&gt;
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        &lt;td&gt;49&lt;br /&gt;
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        &lt;td&gt;50&lt;br /&gt;
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        &lt;td&gt;51&lt;br /&gt;
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        &lt;td&gt;52&lt;br /&gt;
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        &lt;td&gt;53&lt;br /&gt;
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        &lt;td&gt;54&lt;br /&gt;
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        &lt;td&gt;55&lt;br /&gt;
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        &lt;td&gt;56&lt;br /&gt;
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        &lt;td&gt;57&lt;br /&gt;
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        &lt;td&gt;58&lt;br /&gt;
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        &lt;td&gt;59&lt;br /&gt;
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        &lt;td&gt;60&lt;br /&gt;
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        &lt;td&gt;61&lt;br /&gt;
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        &lt;td&gt;62&lt;br /&gt;
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        &lt;td&gt;63&lt;br /&gt;
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        &lt;td&gt;64&lt;br /&gt;
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        &lt;td&gt;65&lt;br /&gt;
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        &lt;td&gt;66&lt;br /&gt;
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        &lt;td&gt;67&lt;br /&gt;
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        &lt;td&gt;68&lt;br /&gt;
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        &lt;td&gt;69&lt;br /&gt;
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        &lt;td&gt;70&lt;br /&gt;
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        &lt;td&gt;71&lt;br /&gt;
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        &lt;td&gt;72&lt;br /&gt;
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        &lt;td&gt;73&lt;br /&gt;
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        &lt;td&gt;74&lt;br /&gt;
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        &lt;td&gt;75&lt;br /&gt;
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        &lt;td&gt;76&lt;br /&gt;
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        &lt;td&gt;7&lt;br /&gt;
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&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;77&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;78&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;79&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;80&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;81&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;82&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;83&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;84&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;85&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;86&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;87&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;88&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;89&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;90&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;91&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;92&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;93&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;94&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;95&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;96&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;97&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;98&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;99&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/body&gt;&lt;/html&gt;</pre></div>

Latest revision as of 11:49, 7 August 2025

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 every edo up to 99. "Consistent" gives its consistency limit, i.e. the highest odd limit to which the edo is consistent, and "Distinct" gives the distinct consistency limit, i.e. the highest odd limit to which the edo is distinctly consistent. The remaining columns give the consistency distance (also called consistency level[note 1]) for every odd limit from 3 to 23.

Edo Consistency limit Consistency distance
Consistent Distinct 3-limit 5-limit 7-limit 9-limit 11-limit 13-limit 15-limit 17-limit 19-limit 21-limit 23-limit
1 3 1 1 0 0 0 0 0 0 0 0 0 0
2 3 1 2 0 0 0 0 0 0 0 0 0 0
3 5 3 2 2 0 0 0 0 0 0 0 0 0
4 7 1 1 1 1 0 0 0 0 0 0 0 0
5 9 3 6 1 1 1 0 0 0 0 0 0 0
6 7 3 1 1 1 0 0 0 0 0 0 0 0
7 5 3 5 1 0 0 0 0 0 0 0 0 0
8 5 3 1 1 0 0 0 0 0 0 0 0 0
9 7 5 1 1 1 0 0 0 0 0 0 0 0
10 7 3 3 1 1 0 0 0 0 0 0 0 0
11 3 3 1 0 0 0 0 0 0 0 0 0 0
12 9 5 25 3 1 1 0 0 0 0 0 0 0
13 3 3 1 0 0 0 0 0 0 0 0 0 0
14 3 3 2 0 0 0 0 0 0 0 0 0 0
15 7 5 2 2 1 0 0 0 0 0 0 0 0
16 7 5 1 1 1 0 0 0 0 0 0 0 0
17 3 3 8 0 0 0 0 0 0 0 0 0 0
18 7 5 1 1 1 0 0 0 0 0 0 0 0
19 9 5 4 4 1 1 0 0 0 0 0 0 0
20 3 3 1 0 0 0 0 0 0 0 0 0 0
21 3 3 1 0 0 0 0 0 0 0 0 0 0
22 11 5 3 2 1 1 1 0 0 0 0 0 0
23 5 5 1 1 0 0 0 0 0 0 0 0 0
24 5 5 12 1 0 0 0 0 0 0 0 0 0
25 5 5 1 1 0 0 0 0 0 0 0 0 0
26 13 5 2 1 1 1 1 1 0 0 0 0 0
27 9 7 2 1 1 1 0 0 0 0 0 0 0
28 5 5 1 1 0 0 0 0 0 0 0 0 0
29 15 5 13 1 1 1 1 1 1 0 0 0 0
30 5 5 1 1 0 0 0 0 0 0 0 0 0
31 11 7 3 3 3 1 1 0 0 0 0 0 0
32 3 3 1 0 0 0 0 0 0 0 0 0 0
33 3 3 1 0 0 0 0 0 0 0 0 0 0
34 5 5 4 4 0 0 0 0 0 0 0 0 0
35 7 7 1 1 1 0 0 0 0 0 0 0 0
36 7 7 8 1 1 0 0 0 0 0 0 0 0
37 7 7 1 1 1 0 0 0 0 0 0 0 0
38 5 5 2 2 0 0 0 0 0 0 0 0 0
39 5 5 2 1 0 0 0 0 0 0 0 0 0
40 3 3 1 0 0 0 0 0 0 0 0 0 0
41 15 9 30 2 2 2 1 1 1 0 0 0 0
42 7 7 1 1 1 0 0 0 0 0 0 0 0
43 7 7 3 1 1 0 0 0 0 0 0 0 0
44 5 5 1 1 0 0 0 0 0 0 0 0 0
45 7 7 1 1 1 0 0 0 0 0 0 0 0
46 13 9 5 2 1 1 1 1 0 0 0 0 0
47 5 5 1 1 0 0 0 0 0 0 0 0 0
48 5 5 6 1 0 0 0 0 0 0 0 0 0
49 7 7 1 1 1 0 0 0 0 0 0 0 0
50 9 7 2 2 1 1 0 0 0 0 0 0 0
51 3 3 2 0 0 0 0 0 0 0 0 0 0
52 3 3 1 0 0 0 0 0 0 0 0 0 0
53 9 9 165 8 1 1 0 0 0 0 0 0 0
54 3 3 1 0 0 0 0 0 0 0 0 0 0
55 5 5 2 1 0 0 0 0 0 0 0 0 0
56 7 7 2 1 1 0 0 0 0 0 0 0 0
57 7 7 1 1 1 0 0 0 0 0 0 0 0
58 17 11 6 1 1 1 1 1 1 1 0 0 0
59 7 7 1 1 1 0 0 0 0 0 0 0 0
60 9 9 5 1 1 1 0 0 0 0 0 0 0
61 5 5 1 1 0 0 0 0 0 0 0 0 0
62 7 7 1 1 1 0 0 0 0 0 0 0 0
63 7 7 3 1 1 0 0 0 0 0 0 0 0
64 3 3 1 0 0 0 0 0 0 0 0 0 0
65 5 5 22 5 0 0 0 0 0 0 0 0 0
66 3 3 1 0 0 0 0 0 0 0 0 0 0
67 3 3 2 0 0 0 0 0 0 0 0 0 0
68 9 9 2 2 2 1 0 0 0 0 0 0 0
69 5 5 1 1 0 0 0 0 0 0 0 0 0
70 9 9 9 1 1 1 0 0 0 0 0 0 0
71 5 5 1 1 0 0 0 0 0 0 0 0 0
72 17 11 4 2 2 2 2 1 1 1 0 0 0
73 7 7 1 1 1 0 0 0 0 0 0 0 0
74 5 5 1 1 0 0 0 0 0 0 0 0 0
75 5 5 3 1 0 0 0 0 0 0 0 0 0
76 7 7 1 1 1 0 0 0 0 0 0 0 0
77 9 9 11 1 1 1 0 0 0 0 0 0 0
78 7 7 1 1 1 0 0 0 0 0 0 0 0
79 5 5 2 1 0 0 0 0 0 0 0 0 0
80 19 11 2 2 1 1 1 1 1 1 1 0 0
81 7 7 1 1 1 0 0 0 0 0 0 0 0
82 9 9 15 1 1 1 0 0 0 0 0 0 0
83 7 7 1 1 1 0 0 0 0 0 0 0 0
84 9 9 3 3 1 1 0 0 0 0 0 0 0
85 3 3 1 0 0 0 0 0 0 0 0 0 0
86 3 3 1 0 0 0 0 0 0 0 0 0 0
87 15 13 4 4 1 1 1 1 1 0 0 0 0
88 7 7 1 1 1 0 0 0 0 0 0 0 0
89 11 11 8 1 1 1 1 0 0 0 0 0 0
90 7 7 1 1 1 0 0 0 0 0 0 0 0
91 9 9 2 1 1 1 0 0 0 0 0 0 0
92 5 5 2 1 0 0 0 0 0 0 0 0 0
93 7 7 1 1 1 0 0 0 0 0 0 0 0
94 23 13 36 1 1 1 1 1 1 1 1 1 1
95 7 7 1 1 1 0 0 0 0 0 0 0 0
96 5 5 3 1 0 0 0 0 0 0 0 0 0
97 5 5 1 1 0 0 0 0 0 0 0 0 0
98 3 3 1 0 0 0 0 0 0 0 0 0 0
99 9 9 5 3 3 2 0 0 0 0 0 0 0

Notes

  1. ↑ This term was coined by Paul Hahn in 1996. See Yahoo! Tuning Group | Consistency generalized.
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