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Consistency limits of small EDOs

Revision as of 11:42, 11 January 2017 by Wikispaces>genewardsmith (**Imported revision 603818020 - Original comment: **)
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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 <em>consistent</em> 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>
Retrieved from "https://en.xen.wiki/index.php?title=Consistency_limits_of_small_EDOs&oldid=13698"