Consistency limits of small EDOs
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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, "Consistent" gives the consistency level, and "Distinct" 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>