Xenharmonic Wiki

List of 47-odd-limit intervals

Revision as of 13:25, 25 October 2013 by Wikispaces>Andrew_Heathwaite (**Imported revision 463113976 - Original comment: **)

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Original Wikitext content:

The 47-limit. Whoa.

Here is a list of the intervals within the octave belonging to the 47-odd limit -- that is, intervals between 1/1 and 2/1 which contain no odd numbers greater than 47. It is organized by [[interval category]] according to the Schulter System outlined in [[http://www.bestii.com/~mschulter/IntervalSpectrumRegions.txt|Regions of the Interval Spectrum]].

==Pure Unison (0 cents)== 
||~ ratio ||~ cents value ||
|| 1/1 || 0 ||

==Commas (0-30 cents)== 
None within the 47-odd limit.

==Dieses (30-60 cents)== 
||~ ratio ||~ cents value ||~ prime limit ||
|| 48/47 || 36.448 || 47 ||
|| 47/46 || 37.232 || 47 ||
|| 46/45 || 38.051 || 23 ||
|| 45/44 || 38.906 || 11 ||
|| 44/43 || 39.800 || 43 ||
|| 43/42 || 40.737 || 43 ||
|| 42/41 || 41.719 || 41 ||
|| 41/40 || 42.749 || 41 ||
|| 40/39 || 43.831 || 13 ||
|| 39/38 || 44.970 || 19 ||
|| 38/37 || 46/169 || 37 ||
|| 37/36 || 47.434 || 37 ||
|| 36/35 || 48.770 || 7 ||
|| 35/34 || 50.184 || 17 ||
|| 34/33 || 51.682 || 17 ||
|| 33/32 || 53.273 || 11 ||
|| 32/31 || 54.964 || 31 ||
|| 31/30 || 56.767 || 31 ||
|| 30/29 || 58.692 || 29 ||

==Minor Seconds (60-125 cents)== 
===Small Minor Seconds (60-80 cents)=== 
||~ ratio ||~ cents value ||~ prime limit ||
|| 29/28 || 60.751 || 29 ||
|| 28/27 || 62.961 || 7 ||
|| 27/26 || 65.337 || 13 ||
|| 26/25 || 67.900 || 13 ||
|| 25/24 || 70.672 || 5 ||
|| 24/23 || 73.681 || 23 ||
|| 47/45 || 75.283 || 47 ||
|| 23/22 || 76.956 || 23 ||
|| 45/43 || 78.706 || 43 ||
===Middle Minor Seconds (80-100 cents)=== 
||~ ratio ||~ cents value ||~ prime limit ||
|| 22/21 || 80.537 || 11 ||
|| 43/41 || 82.455 || 43 ||
|| 21/20 || 84.467 || 7 ||
|| 41/39 || 86.580 || 41 ||
|| 20/19 || 88.801 || 19 ||
|| 39/37 || 91.139 || 37 ||
|| 19/18 || 93.603 || 19 ||
|| 37/35 || 96.204 || 37 ||
|| 18/17 || 98.955 || 17 ||
===Large Minor Seconds (100-125 cents)=== 
||~ ratio ||~ cents value ||~ prime limit ||
|| 35/33 || 101.867 || 11 ||
|| 17/16 || 104.955 || 17 ||
|| 50/47 || 107.121 || 47 ||
|| 33/31 || 108.237 || 31 ||
|| 16/15 = 48/45 || 111.731 || 5 ||
|| 47/44 || 114.189 || 47 ||
|| 31/29 || 115.458 || 31 ||
|| 46/43 || 116.757 || 43 ||
|| 15/14 = 45/42 || 119.443 || 7 ||
|| 44/41 || 122.256 || 41 ||
|| 29/27 || 123.712 || 29 ||

==Central or Zalzalian Seconds (formerly Neutral Seconds) (125-170 cents)== 
===Small Central Seconds (125-170 cents)=== 
||~ ratio ||~ cents value ||~ prime limit ||
|| 43/40 || 125.204 || 43 ||
|| 14/13 = 42/39 || 128.298 || 13 ||
|| 41/38 || 131.549 || 41 ||
|| 27/25 || 133.238 || 5 ||
|| 40/37 || 134.970 || 37 ||
===Middle Central Seconds (135-160 cents)=== 
||~ ratio ||~ cents value ||~ prime limit ||
|| 13/12 = 39/36 || 138.573 || 13 ||
|| 38/35 || 142.373 || 19 ||
|| 25/23 || 144.353 || 23 ||
|| 37/34 || 146.389 || 37 ||
|| 12/11 = 36/33 || 150.637 || 11 ||
|| 47/43 || 153.989 || 47 ||
|| 35/32 || 155.140 || 7 ||
|| 23/21 || 157.493 || 23 ||
|| 34/31 || 159.920 || 31 ||
===Large Central Seconds (160-170 cents)=== 
Beginning of Equable Heptatonic Region (160-182 cents)
||~ ratio ||~ cents value ||~ prime limit ||
|| 45/41 || 161.161 || 41 ||
|| 11/10 = 33/30 || 165.004 || 11 ||
|| 43/39 || 169.035 || 43 ||
End of Large Central Seconds Region, continuation of Equable Heptatonic Region
||~ ratio ||~ cents value ||~ prime limit ||
|| 32/29 || 170.423 || 29 ||
|| 21/19 || 173.268 || 19 ||
|| 52/47 || 175.021 || 47 ||
|| 31/28 || 176.210 || 31 ||
|| 41/37 || 177.718 || 41 ||
End of Equable Heptatonic Region.

==Major Seconds (180-240 cents)== 
TO BE CONTINUED

Original HTML content:

<html><head><title>47-limit</title></head><body>The 47-limit. Whoa.<br />
<br />
Here is a list of the intervals within the octave belonging to the 47-odd limit -- that is, intervals between 1/1 and 2/1 which contain no odd numbers greater than 47. It is organized by <a class="wiki_link" href="/interval%20category">interval category</a> according to the Schulter System outlined in <a class="wiki_link_ext" href="http://www.bestii.com/~mschulter/IntervalSpectrumRegions.txt" rel="nofollow">Regions of the Interval Spectrum</a>.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Pure Unison (0 cents)"></a><!-- ws:end:WikiTextHeadingRule:0 -->Pure Unison (0 cents)</h2>
 

<table class="wiki_table">
    <tr>
        <th>ratio<br />
</th>
        <th>cents value<br />
</th>
    </tr>
    <tr>
        <td>1/1<br />
</td>
        <td>0<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-Commas (0-30 cents)"></a><!-- ws:end:WikiTextHeadingRule:2 -->Commas (0-30 cents)</h2>
 None within the 47-odd limit.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x-Dieses (30-60 cents)"></a><!-- ws:end:WikiTextHeadingRule:4 -->Dieses (30-60 cents)</h2>
 

<table class="wiki_table">
    <tr>
        <th>ratio<br />
</th>
        <th>cents value<br />
</th>
        <th>prime limit<br />
</th>
    </tr>
    <tr>
        <td>48/47<br />
</td>
        <td>36.448<br />
</td>
        <td>47<br />
</td>
    </tr>
    <tr>
        <td>47/46<br />
</td>
        <td>37.232<br />
</td>
        <td>47<br />
</td>
    </tr>
    <tr>
        <td>46/45<br />
</td>
        <td>38.051<br />
</td>
        <td>23<br />
</td>
    </tr>
    <tr>
        <td>45/44<br />
</td>
        <td>38.906<br />
</td>
        <td>11<br />
</td>
    </tr>
    <tr>
        <td>44/43<br />
</td>
        <td>39.800<br />
</td>
        <td>43<br />
</td>
    </tr>
    <tr>
        <td>43/42<br />
</td>
        <td>40.737<br />
</td>
        <td>43<br />
</td>
    </tr>
    <tr>
        <td>42/41<br />
</td>
        <td>41.719<br />
</td>
        <td>41<br />
</td>
    </tr>
    <tr>
        <td>41/40<br />
</td>
        <td>42.749<br />
</td>
        <td>41<br />
</td>
    </tr>
    <tr>
        <td>40/39<br />
</td>
        <td>43.831<br />
</td>
        <td>13<br />
</td>
    </tr>
    <tr>
        <td>39/38<br />
</td>
        <td>44.970<br />
</td>
        <td>19<br />
</td>
    </tr>
    <tr>
        <td>38/37<br />
</td>
        <td>46/169<br />
</td>
        <td>37<br />
</td>
    </tr>
    <tr>
        <td>37/36<br />
</td>
        <td>47.434<br />
</td>
        <td>37<br />
</td>
    </tr>
    <tr>
        <td>36/35<br />
</td>
        <td>48.770<br />
</td>
        <td>7<br />
</td>
    </tr>
    <tr>
        <td>35/34<br />
</td>
        <td>50.184<br />
</td>
        <td>17<br />
</td>
    </tr>
    <tr>
        <td>34/33<br />
</td>
        <td>51.682<br />
</td>
        <td>17<br />
</td>
    </tr>
    <tr>
        <td>33/32<br />
</td>
        <td>53.273<br />
</td>
        <td>11<br />
</td>
    </tr>
    <tr>
        <td>32/31<br />
</td>
        <td>54.964<br />
</td>
        <td>31<br />
</td>
    </tr>
    <tr>
        <td>31/30<br />
</td>
        <td>56.767<br />
</td>
        <td>31<br />
</td>
    </tr>
    <tr>
        <td>30/29<br />
</td>
        <td>58.692<br />
</td>
        <td>29<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x-Minor Seconds (60-125 cents)"></a><!-- ws:end:WikiTextHeadingRule:6 -->Minor Seconds (60-125 cents)</h2>
 <!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="x-Minor Seconds (60-125 cents)-Small Minor Seconds (60-80 cents)"></a><!-- ws:end:WikiTextHeadingRule:8 -->Small Minor Seconds (60-80 cents)</h3>
 

<table class="wiki_table">
    <tr>
        <th>ratio<br />
</th>
        <th>cents value<br />
</th>
        <th>prime limit<br />
</th>
    </tr>
    <tr>
        <td>29/28<br />
</td>
        <td>60.751<br />
</td>
        <td>29<br />
</td>
    </tr>
    <tr>
        <td>28/27<br />
</td>
        <td>62.961<br />
</td>
        <td>7<br />
</td>
    </tr>
    <tr>
        <td>27/26<br />
</td>
        <td>65.337<br />
</td>
        <td>13<br />
</td>
    </tr>
    <tr>
        <td>26/25<br />
</td>
        <td>67.900<br />
</td>
        <td>13<br />
</td>
    </tr>
    <tr>
        <td>25/24<br />
</td>
        <td>70.672<br />
</td>
        <td>5<br />
</td>
    </tr>
    <tr>
        <td>24/23<br />
</td>
        <td>73.681<br />
</td>
        <td>23<br />
</td>
    </tr>
    <tr>
        <td>47/45<br />
</td>
        <td>75.283<br />
</td>
        <td>47<br />
</td>
    </tr>
    <tr>
        <td>23/22<br />
</td>
        <td>76.956<br />
</td>
        <td>23<br />
</td>
    </tr>
    <tr>
        <td>45/43<br />
</td>
        <td>78.706<br />
</td>
        <td>43<br />
</td>
    </tr>
</table>

<!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="x-Minor Seconds (60-125 cents)-Middle Minor Seconds (80-100 cents)"></a><!-- ws:end:WikiTextHeadingRule:10 -->Middle Minor Seconds (80-100 cents)</h3>
 

<table class="wiki_table">
    <tr>
        <th>ratio<br />
</th>
        <th>cents value<br />
</th>
        <th>prime limit<br />
</th>
    </tr>
    <tr>
        <td>22/21<br />
</td>
        <td>80.537<br />
</td>
        <td>11<br />
</td>
    </tr>
    <tr>
        <td>43/41<br />
</td>
        <td>82.455<br />
</td>
        <td>43<br />
</td>
    </tr>
    <tr>
        <td>21/20<br />
</td>
        <td>84.467<br />
</td>
        <td>7<br />
</td>
    </tr>
    <tr>
        <td>41/39<br />
</td>
        <td>86.580<br />
</td>
        <td>41<br />
</td>
    </tr>
    <tr>
        <td>20/19<br />
</td>
        <td>88.801<br />
</td>
        <td>19<br />
</td>
    </tr>
    <tr>
        <td>39/37<br />
</td>
        <td>91.139<br />
</td>
        <td>37<br />
</td>
    </tr>
    <tr>
        <td>19/18<br />
</td>
        <td>93.603<br />
</td>
        <td>19<br />
</td>
    </tr>
    <tr>
        <td>37/35<br />
</td>
        <td>96.204<br />
</td>
        <td>37<br />
</td>
    </tr>
    <tr>
        <td>18/17<br />
</td>
        <td>98.955<br />
</td>
        <td>17<br />
</td>
    </tr>
</table>

<!-- ws:start:WikiTextHeadingRule:12:&lt;h3&gt; --><h3 id="toc6"><a name="x-Minor Seconds (60-125 cents)-Large Minor Seconds (100-125 cents)"></a><!-- ws:end:WikiTextHeadingRule:12 -->Large Minor Seconds (100-125 cents)</h3>
 

<table class="wiki_table">
    <tr>
        <th>ratio<br />
</th>
        <th>cents value<br />
</th>
        <th>prime limit<br />
</th>
    </tr>
    <tr>
        <td>35/33<br />
</td>
        <td>101.867<br />
</td>
        <td>11<br />
</td>
    </tr>
    <tr>
        <td>17/16<br />
</td>
        <td>104.955<br />
</td>
        <td>17<br />
</td>
    </tr>
    <tr>
        <td>50/47<br />
</td>
        <td>107.121<br />
</td>
        <td>47<br />
</td>
    </tr>
    <tr>
        <td>33/31<br />
</td>
        <td>108.237<br />
</td>
        <td>31<br />
</td>
    </tr>
    <tr>
        <td>16/15 = 48/45<br />
</td>
        <td>111.731<br />
</td>
        <td>5<br />
</td>
    </tr>
    <tr>
        <td>47/44<br />
</td>
        <td>114.189<br />
</td>
        <td>47<br />
</td>
    </tr>
    <tr>
        <td>31/29<br />
</td>
        <td>115.458<br />
</td>
        <td>31<br />
</td>
    </tr>
    <tr>
        <td>46/43<br />
</td>
        <td>116.757<br />
</td>
        <td>43<br />
</td>
    </tr>
    <tr>
        <td>15/14 = 45/42<br />
</td>
        <td>119.443<br />
</td>
        <td>7<br />
</td>
    </tr>
    <tr>
        <td>44/41<br />
</td>
        <td>122.256<br />
</td>
        <td>41<br />
</td>
    </tr>
    <tr>
        <td>29/27<br />
</td>
        <td>123.712<br />
</td>
        <td>29<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="x-Central or Zalzalian Seconds (formerly Neutral Seconds) (125-170 cents)"></a><!-- ws:end:WikiTextHeadingRule:14 -->Central or Zalzalian Seconds (formerly Neutral Seconds) (125-170 cents)</h2>
 <!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><h3 id="toc8"><a name="x-Central or Zalzalian Seconds (formerly Neutral Seconds) (125-170 cents)-Small Central Seconds (125-170 cents)"></a><!-- ws:end:WikiTextHeadingRule:16 -->Small Central Seconds (125-170 cents)</h3>
 

<table class="wiki_table">
    <tr>
        <th>ratio<br />
</th>
        <th>cents value<br />
</th>
        <th>prime limit<br />
</th>
    </tr>
    <tr>
        <td>43/40<br />
</td>
        <td>125.204<br />
</td>
        <td>43<br />
</td>
    </tr>
    <tr>
        <td>14/13 = 42/39<br />
</td>
        <td>128.298<br />
</td>
        <td>13<br />
</td>
    </tr>
    <tr>
        <td>41/38<br />
</td>
        <td>131.549<br />
</td>
        <td>41<br />
</td>
    </tr>
    <tr>
        <td>27/25<br />
</td>
        <td>133.238<br />
</td>
        <td>5<br />
</td>
    </tr>
    <tr>
        <td>40/37<br />
</td>
        <td>134.970<br />
</td>
        <td>37<br />
</td>
    </tr>
</table>

<!-- ws:start:WikiTextHeadingRule:18:&lt;h3&gt; --><h3 id="toc9"><a name="x-Central or Zalzalian Seconds (formerly Neutral Seconds) (125-170 cents)-Middle Central Seconds (135-160 cents)"></a><!-- ws:end:WikiTextHeadingRule:18 -->Middle Central Seconds (135-160 cents)</h3>
 

<table class="wiki_table">
    <tr>
        <th>ratio<br />
</th>
        <th>cents value<br />
</th>
        <th>prime limit<br />
</th>
    </tr>
    <tr>
        <td>13/12 = 39/36<br />
</td>
        <td>138.573<br />
</td>
        <td>13<br />
</td>
    </tr>
    <tr>
        <td>38/35<br />
</td>
        <td>142.373<br />
</td>
        <td>19<br />
</td>
    </tr>
    <tr>
        <td>25/23<br />
</td>
        <td>144.353<br />
</td>
        <td>23<br />
</td>
    </tr>
    <tr>
        <td>37/34<br />
</td>
        <td>146.389<br />
</td>
        <td>37<br />
</td>
    </tr>
    <tr>
        <td>12/11 = 36/33<br />
</td>
        <td>150.637<br />
</td>
        <td>11<br />
</td>
    </tr>
    <tr>
        <td>47/43<br />
</td>
        <td>153.989<br />
</td>
        <td>47<br />
</td>
    </tr>
    <tr>
        <td>35/32<br />
</td>
        <td>155.140<br />
</td>
        <td>7<br />
</td>
    </tr>
    <tr>
        <td>23/21<br />
</td>
        <td>157.493<br />
</td>
        <td>23<br />
</td>
    </tr>
    <tr>
        <td>34/31<br />
</td>
        <td>159.920<br />
</td>
        <td>31<br />
</td>
    </tr>
</table>

<!-- ws:start:WikiTextHeadingRule:20:&lt;h3&gt; --><h3 id="toc10"><a name="x-Central or Zalzalian Seconds (formerly Neutral Seconds) (125-170 cents)-Large Central Seconds (160-170 cents)"></a><!-- ws:end:WikiTextHeadingRule:20 -->Large Central Seconds (160-170 cents)</h3>
 Beginning of Equable Heptatonic Region (160-182 cents)<br />


<table class="wiki_table">
    <tr>
        <th>ratio<br />
</th>
        <th>cents value<br />
</th>
        <th>prime limit<br />
</th>
    </tr>
    <tr>
        <td>45/41<br />
</td>
        <td>161.161<br />
</td>
        <td>41<br />
</td>
    </tr>
    <tr>
        <td>11/10 = 33/30<br />
</td>
        <td>165.004<br />
</td>
        <td>11<br />
</td>
    </tr>
    <tr>
        <td>43/39<br />
</td>
        <td>169.035<br />
</td>
        <td>43<br />
</td>
    </tr>
</table>

End of Large Central Seconds Region, continuation of Equable Heptatonic Region<br />


<table class="wiki_table">
    <tr>
        <th>ratio<br />
</th>
        <th>cents value<br />
</th>
        <th>prime limit<br />
</th>
    </tr>
    <tr>
        <td>32/29<br />
</td>
        <td>170.423<br />
</td>
        <td>29<br />
</td>
    </tr>
    <tr>
        <td>21/19<br />
</td>
        <td>173.268<br />
</td>
        <td>19<br />
</td>
    </tr>
    <tr>
        <td>52/47<br />
</td>
        <td>175.021<br />
</td>
        <td>47<br />
</td>
    </tr>
    <tr>
        <td>31/28<br />
</td>
        <td>176.210<br />
</td>
        <td>31<br />
</td>
    </tr>
    <tr>
        <td>41/37<br />
</td>
        <td>177.718<br />
</td>
        <td>41<br />
</td>
    </tr>
</table>

End of Equable Heptatonic Region.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="x-Major Seconds (180-240 cents)"></a><!-- ws:end:WikiTextHeadingRule:22 -->Major Seconds (180-240 cents)</h2>
 TO BE CONTINUED</body></html>
Retrieved from "https://en.xen.wiki/index.php?title=List_of_47-odd-limit_intervals&oldid=8958"