Consistency limits of small EDOs: Difference between revisions

Revision as of 16:55, 12 January 2017

IMPORTED REVISION FROM WIKISPACES

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This revision was by author TallKite and made on 2017-01-12 16:55:36 UTC.

The original revision id was 603954448.

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The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

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 the least consistent, and least uniquely consistent, edo for every odd number up to 135.

In the table below, "Consistent" gives the consistency level, and "Distinct" the distinct consistency level.

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

Original HTML content:

<html><head><title>Consistency levels of small EDOs</title></head><body>An <a class="wiki_link" href="/edo">edo</a> N is <a class="wiki_link" href="/consistent">consistent</a> with respect to a set of rational numbers s if the <a class="wiki_link" href="/patent%20val">patent val</a> mapping of every element of s is the nearest N-edo approximation. It is <em>uniquely consistent</em> if every element of s is mapped to a unique value. If the set s is the q <a class="wiki_link" href="/odd%20limit">odd limit</a>, we say N is q-limit consistent and q-limit uniquely consistent, respectively. Below is a table of the least consistent, and least uniquely consistent, edo for every odd number up to 135.<br />
<br />
In the table below, &quot;Consistent&quot; gives the consistency level, and &quot;Distinct&quot; the distinct consistency level.<br />
<br />


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

</body></html>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2017-01-11 11:42:13 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-01-12 16:55:36 UTC</tt>.<br>
-: The original revision id was <tt>603818020</tt>.<br>
+: The original revision id was <tt>603954448</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 the least consistent,  and least uniquely consistent, edo for every odd number up to 135.
+<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 the least consistent, and least uniquely consistent, edo for every odd number up to 135.
 In the table below, "Consistent" gives the consistency level, and "Distinct" the distinct consistency level.
@@ Line 109: / Line 109: @@
 || 97 || 5 || 5 ||
 || 98 || 3 || 3 ||
-|| 99 || 9 || 9 ||
+|| 99 || 9 || 9 ||</pre></div>
-</pre></div>
 <h4>Original HTML 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;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;em&gt;consistent&lt;/em&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 the least consistent,  and least uniquely consistent, edo for every odd number up to 135.&lt;br /&gt;
+<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 the least consistent, and least uniquely consistent, edo for every odd number up to 135.&lt;br /&gt;
 &lt;br /&gt;
 In the table below, &amp;quot;Consistent&amp;quot; gives the consistency level, and &amp;quot;Distinct&amp;quot; the distinct consistency level.&lt;br /&gt;

Consistency limits of small EDOs: Difference between revisions

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