List of 47-odd-limit intervals

Revision as of 14:03, 25 October 2013 by Wikispaces>Andrew_Heathwaite (**Imported revision 463126730 - Original comment: **)

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This revision was by author Andrew_Heathwaite and made on 2013-10-25 14:03:54 UTC.
The original revision id was 463126730.
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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)== 
===Small Major Seconds (180-200 cents)=== 
||~ ratio ||~ cents value ||~ prime limit ||
|| 10/9 = 30/27 = 50/45 || 182.404 || 5 ||
|| 39/35 || 187.343 || 13 ||
|| 29/26 || 189.050 || 29 ||
|| 19/17 || 192.558 || 19 ||
|| 47/42 || 194.726 || 47 ||
|| 28/25 || 196.198 || 7 ||
|| 37/33 || 198.071 || 37 ||
|| 46/41 || 199.212 || 41 ||
===Middle Major Seconds (200-220 cents)=== 
||~ ratio ||~ cents value ||~ prime limit ||
|| 9/8 = 27/24 = 45/40 || 203.910 || 3 ||
|| 44/39 || 208.835 || 13 ||
|| 35/31 || 210.104 || 31 ||
|| 26/23 || 212.253 || 23 ||
|| 43/38 || 214.005 || 43 ||
|| 17/15 || 216.687 || 17 ||
|| 42/37 || 219.437 || 37 ||
===Large Major Seconds (220-240 cents)=== 
||~ ratio ||~ cents value ||~ prime limit ||
|| 25/22 || 221.309 || 11 ||
|| 33/29 || 223.696 || 29 ||
|| 41/36 || 225.152 || 41 ||
|| 8/7 = 24/21 = 40/35 || 231.174 || 7 ||
|| 47/41 || 236.444 || 47 ||
|| 39/34 || 237.527 || 17 ||
|| 31/27 || 239.171 || 31 ||
==Interseptimal Region (M2-m3) (240-260 cents)== 
||~ ratio ||~ cents value ||~ prime limit ||
|| 54/47 || 240.358 || 47 ||
|| 23/20 || 241.961 || 23 ||
|| 38/33 || 244.240 || 19 ||
|| 15/13 = 45/39 || 247.741 || 13 ||
|| 52/45 || 250.304 || 13 ||
|| 37/32 || 251.344 || 37 ||
|| 22/19 || 253.805 || 19 ||
|| 29/25 || 256.950 || 29 ||
|| 36/31 || 258.874 || 31 ||
== == 
==Minor Thirds (260-330 cents)== 
===Small Minor Thirds (260-280 cents)=== 
||~ ratio ||~ cents value ||~ prime limit ||
|| 43/37 || 260.174 || 43 ||
|| 50/43 || 261.110 || 43 ||
|| 7/6 = 21/18 = 35/30 || 266.871 || 7 ||
|| 48/41 || 272.893 || 41 ||
|| 41/35 || 273.923 || 41 ||
|| 34/29 || 275.378 || 29 ||
|| 27/23 || 277.591 || 23 ||
|| 47/40 || 279.193 || 47 ||
===Middle Minor Thirds (280-300 cents)=== 
||~ ratio ||~ cents value ||~ prime limit ||
|| 20/17 || 281.358 || 17 ||
|| 33/28 || 284.447 || 11 ||
|| 46/39 || 285.792 || 23 ||
|| 13/11 = 39/33 || 289.210 || 13 ||
|| 45/38 || 292.711 || 19 ||
|| 32/27 || 294.135 || 3 ||
|| 19/16 || 297.513 || 19 ||
|| 44/37 || 299.974 || 37 ||
===Large Minor Thirds (300-330 cents)=== 
||~ ratio ||~ cents value ||~ prime limit ||
|| 25/21 || 301.847 || 7 ||
|| 56/47 || 303.319 || 47 ||
|| 31/26 || 304.508 || 31 ||
|| 37/31 || 306.308 || 37 ||
|| 43/36 || 307.608 || 43 ||
|| 6/5 = 18/15 = 30/25 = 42/35 = 54/45 || 315.641 || 5 ||
|| 47/39 || 323.024 || 47 ||
|| 41/34 || 324.107 || 41 ||
|| 35/29 || 325.562 || 29 ||
|| 29/24 || 327.622 || 29 ||
|| 52/43 || 329.010 || 43 ||
== == 
==Central or Zalzalian Thirds (formerly Neutral Thirds) (330-372 cents)== 
===Small Central Thirds (330-342 cents)=== 
||~ ratio ||~ cents value ||~ prime limit ||
|| 23/19 || 330.761 || 23 ||
|| 40/33 || 333.041 || 11 ||
|| 17/14 || 336.130 || 17 ||
|| 45/37 || 338.880 || 37 ||
|| 28/23 || 340.552 || 23 ||
===Middle Central Thirds (342-360 cents)=== 
||~ ratio ||~ cents value ||~ prime limit ||
|| 39/32 || 342.483 || 13 ||
|| 50/41 || 343.565 || 41 ||
|| 11/9 = 33/27 || 347.408 || 11 ||
|| 38/31 || 352.477 || 31 ||
|| 27/22 || 354.547 || 11 ||
|| 43/35 || 356.378 || 43 ||
|| 16/13 = 48/39 || 359.472 || 13 ||
===Large Central Thirds (360-372 cents)=== 
||~ ratio ||~ cents value ||~ prime limit ||
|| 37/30 || 363.075 || 37 ||
|| 58/47 || 364.071 || 47 ||
|| 21/17 || 365.825 || 17 ||
|| 47/38 || 367.994 || 47 ||
|| 26/21 || 369.747 || 13 ||

==Major Thirds (372-440 cents)== 
===Small Major Thirds (372-400 cents)=== 
||~ ratio ||~ cents value ||~ prime limit ||
|| 31/25 || 372.408 || 31 ||
|| 36/29 || 374.333 || 29 ||
||   ||   ||   ||
||   ||   ||   ||
||   ||   ||   ||
||   ||   ||   ||
||   ||   ||   ||
||   ||   ||   ||
||   ||   ||   ||
||   ||   ||   ||

...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>
 <!-- ws:start:WikiTextHeadingRule:22:&lt;h4&gt; --><h4 id="toc11"><a name="x-Central or Zalzalian Seconds (formerly Neutral Seconds) (125-170 cents)-Large Central Seconds (160-170 cents)-Beginning of Equable Heptatonic Region (160-182 cents)"></a><!-- ws:end:WikiTextHeadingRule:22 -->Beginning of Equable Heptatonic Region (160-182 cents)</h4>
 

<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>

<!-- ws:start:WikiTextHeadingRule:24:&lt;h4&gt; --><h4 id="toc12"><a name="x-Central or Zalzalian Seconds (formerly Neutral Seconds) (125-170 cents)-Large Central Seconds (160-170 cents)-End of Large Central Seconds Region, continuation of Equable Heptatonic Region"></a><!-- ws:end:WikiTextHeadingRule:24 -->End of Large Central Seconds Region, continuation of Equable Heptatonic Region</h4>
 

<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>

<!-- ws:start:WikiTextHeadingRule:26:&lt;h4&gt; --><h4 id="toc13"><a name="x-Central or Zalzalian Seconds (formerly Neutral Seconds) (125-170 cents)-Large Central Seconds (160-170 cents)-End of Equable Heptatonic Region."></a><!-- ws:end:WikiTextHeadingRule:26 -->End of Equable Heptatonic Region.</h4>
 <br />
<!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="x-Major Seconds (180-240 cents)"></a><!-- ws:end:WikiTextHeadingRule:28 -->Major Seconds (180-240 cents)</h2>
 <!-- ws:start:WikiTextHeadingRule:30:&lt;h3&gt; --><h3 id="toc15"><a name="x-Major Seconds (180-240 cents)-Small Major Seconds (180-200 cents)"></a><!-- ws:end:WikiTextHeadingRule:30 -->Small Major Seconds (180-200 cents)</h3>
 

<table class="wiki_table">
    <tr>
        <th>ratio<br />
</th>
        <th>cents value<br />
</th>
        <th>prime limit<br />
</th>
    </tr>
    <tr>
        <td>10/9 = 30/27 = 50/45<br />
</td>
        <td>182.404<br />
</td>
        <td>5<br />
</td>
    </tr>
    <tr>
        <td>39/35<br />
</td>
        <td>187.343<br />
</td>
        <td>13<br />
</td>
    </tr>
    <tr>
        <td>29/26<br />
</td>
        <td>189.050<br />
</td>
        <td>29<br />
</td>
    </tr>
    <tr>
        <td>19/17<br />
</td>
        <td>192.558<br />
</td>
        <td>19<br />
</td>
    </tr>
    <tr>
        <td>47/42<br />
</td>
        <td>194.726<br />
</td>
        <td>47<br />
</td>
    </tr>
    <tr>
        <td>28/25<br />
</td>
        <td>196.198<br />
</td>
        <td>7<br />
</td>
    </tr>
    <tr>
        <td>37/33<br />
</td>
        <td>198.071<br />
</td>
        <td>37<br />
</td>
    </tr>
    <tr>
        <td>46/41<br />
</td>
        <td>199.212<br />
</td>
        <td>41<br />
</td>
    </tr>
</table>

<!-- ws:start:WikiTextHeadingRule:32:&lt;h3&gt; --><h3 id="toc16"><a name="x-Major Seconds (180-240 cents)-Middle Major Seconds (200-220 cents)"></a><!-- ws:end:WikiTextHeadingRule:32 -->Middle Major Seconds (200-220 cents)</h3>
 

<table class="wiki_table">
    <tr>
        <th>ratio<br />
</th>
        <th>cents value<br />
</th>
        <th>prime limit<br />
</th>
    </tr>
    <tr>
        <td>9/8 = 27/24 = 45/40<br />
</td>
        <td>203.910<br />
</td>
        <td>3<br />
</td>
    </tr>
    <tr>
        <td>44/39<br />
</td>
        <td>208.835<br />
</td>
        <td>13<br />
</td>
    </tr>
    <tr>
        <td>35/31<br />
</td>
        <td>210.104<br />
</td>
        <td>31<br />
</td>
    </tr>
    <tr>
        <td>26/23<br />
</td>
        <td>212.253<br />
</td>
        <td>23<br />
</td>
    </tr>
    <tr>
        <td>43/38<br />
</td>
        <td>214.005<br />
</td>
        <td>43<br />
</td>
    </tr>
    <tr>
        <td>17/15<br />
</td>
        <td>216.687<br />
</td>
        <td>17<br />
</td>
    </tr>
    <tr>
        <td>42/37<br />
</td>
        <td>219.437<br />
</td>
        <td>37<br />
</td>
    </tr>
</table>

<!-- ws:start:WikiTextHeadingRule:34:&lt;h3&gt; --><h3 id="toc17"><a name="x-Major Seconds (180-240 cents)-Large Major Seconds (220-240 cents)"></a><!-- ws:end:WikiTextHeadingRule:34 -->Large Major Seconds (220-240 cents)</h3>
 

<table class="wiki_table">
    <tr>
        <th>ratio<br />
</th>
        <th>cents value<br />
</th>
        <th>prime limit<br />
</th>
    </tr>
    <tr>
        <td>25/22<br />
</td>
        <td>221.309<br />
</td>
        <td>11<br />
</td>
    </tr>
    <tr>
        <td>33/29<br />
</td>
        <td>223.696<br />
</td>
        <td>29<br />
</td>
    </tr>
    <tr>
        <td>41/36<br />
</td>
        <td>225.152<br />
</td>
        <td>41<br />
</td>
    </tr>
    <tr>
        <td>8/7 = 24/21 = 40/35<br />
</td>
        <td>231.174<br />
</td>
        <td>7<br />
</td>
    </tr>
    <tr>
        <td>47/41<br />
</td>
        <td>236.444<br />
</td>
        <td>47<br />
</td>
    </tr>
    <tr>
        <td>39/34<br />
</td>
        <td>237.527<br />
</td>
        <td>17<br />
</td>
    </tr>
    <tr>
        <td>31/27<br />
</td>
        <td>239.171<br />
</td>
        <td>31<br />
</td>
    </tr>
</table>

<!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="x-Interseptimal Region (M2-m3) (240-260 cents)"></a><!-- ws:end:WikiTextHeadingRule:36 -->Interseptimal Region (M2-m3) (240-260 cents)</h2>
 

<table class="wiki_table">
    <tr>
        <th>ratio<br />
</th>
        <th>cents value<br />
</th>
        <th>prime limit<br />
</th>
    </tr>
    <tr>
        <td>54/47<br />
</td>
        <td>240.358<br />
</td>
        <td>47<br />
</td>
    </tr>
    <tr>
        <td>23/20<br />
</td>
        <td>241.961<br />
</td>
        <td>23<br />
</td>
    </tr>
    <tr>
        <td>38/33<br />
</td>
        <td>244.240<br />
</td>
        <td>19<br />
</td>
    </tr>
    <tr>
        <td>15/13 = 45/39<br />
</td>
        <td>247.741<br />
</td>
        <td>13<br />
</td>
    </tr>
    <tr>
        <td>52/45<br />
</td>
        <td>250.304<br />
</td>
        <td>13<br />
</td>
    </tr>
    <tr>
        <td>37/32<br />
</td>
        <td>251.344<br />
</td>
        <td>37<br />
</td>
    </tr>
    <tr>
        <td>22/19<br />
</td>
        <td>253.805<br />
</td>
        <td>19<br />
</td>
    </tr>
    <tr>
        <td>29/25<br />
</td>
        <td>256.950<br />
</td>
        <td>29<br />
</td>
    </tr>
    <tr>
        <td>36/31<br />
</td>
        <td>258.874<br />
</td>
        <td>31<br />
</td>
    </tr>
</table>

<!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><!-- ws:end:WikiTextHeadingRule:38 --> </h2>
 <!-- ws:start:WikiTextHeadingRule:40:&lt;h2&gt; --><h2 id="toc20"><a name="x-Minor Thirds (260-330 cents)"></a><!-- ws:end:WikiTextHeadingRule:40 -->Minor Thirds (260-330 cents)</h2>
 <!-- ws:start:WikiTextHeadingRule:42:&lt;h3&gt; --><h3 id="toc21"><a name="x-Minor Thirds (260-330 cents)-Small Minor Thirds (260-280 cents)"></a><!-- ws:end:WikiTextHeadingRule:42 -->Small Minor Thirds (260-280 cents)</h3>
 

<table class="wiki_table">
    <tr>
        <th>ratio<br />
</th>
        <th>cents value<br />
</th>
        <th>prime limit<br />
</th>
    </tr>
    <tr>
        <td>43/37<br />
</td>
        <td>260.174<br />
</td>
        <td>43<br />
</td>
    </tr>
    <tr>
        <td>50/43<br />
</td>
        <td>261.110<br />
</td>
        <td>43<br />
</td>
    </tr>
    <tr>
        <td>7/6 = 21/18 = 35/30<br />
</td>
        <td>266.871<br />
</td>
        <td>7<br />
</td>
    </tr>
    <tr>
        <td>48/41<br />
</td>
        <td>272.893<br />
</td>
        <td>41<br />
</td>
    </tr>
    <tr>
        <td>41/35<br />
</td>
        <td>273.923<br />
</td>
        <td>41<br />
</td>
    </tr>
    <tr>
        <td>34/29<br />
</td>
        <td>275.378<br />
</td>
        <td>29<br />
</td>
    </tr>
    <tr>
        <td>27/23<br />
</td>
        <td>277.591<br />
</td>
        <td>23<br />
</td>
    </tr>
    <tr>
        <td>47/40<br />
</td>
        <td>279.193<br />
</td>
        <td>47<br />
</td>
    </tr>
</table>

<!-- ws:start:WikiTextHeadingRule:44:&lt;h3&gt; --><h3 id="toc22"><a name="x-Minor Thirds (260-330 cents)-Middle Minor Thirds (280-300 cents)"></a><!-- ws:end:WikiTextHeadingRule:44 -->Middle Minor Thirds (280-300 cents)</h3>
 

<table class="wiki_table">
    <tr>
        <th>ratio<br />
</th>
        <th>cents value<br />
</th>
        <th>prime limit<br />
</th>
    </tr>
    <tr>
        <td>20/17<br />
</td>
        <td>281.358<br />
</td>
        <td>17<br />
</td>
    </tr>
    <tr>
        <td>33/28<br />
</td>
        <td>284.447<br />
</td>
        <td>11<br />
</td>
    </tr>
    <tr>
        <td>46/39<br />
</td>
        <td>285.792<br />
</td>
        <td>23<br />
</td>
    </tr>
    <tr>
        <td>13/11 = 39/33<br />
</td>
        <td>289.210<br />
</td>
        <td>13<br />
</td>
    </tr>
    <tr>
        <td>45/38<br />
</td>
        <td>292.711<br />
</td>
        <td>19<br />
</td>
    </tr>
    <tr>
        <td>32/27<br />
</td>
        <td>294.135<br />
</td>
        <td>3<br />
</td>
    </tr>
    <tr>
        <td>19/16<br />
</td>
        <td>297.513<br />
</td>
        <td>19<br />
</td>
    </tr>
    <tr>
        <td>44/37<br />
</td>
        <td>299.974<br />
</td>
        <td>37<br />
</td>
    </tr>
</table>

<!-- ws:start:WikiTextHeadingRule:46:&lt;h3&gt; --><h3 id="toc23"><a name="x-Minor Thirds (260-330 cents)-Large Minor Thirds (300-330 cents)"></a><!-- ws:end:WikiTextHeadingRule:46 -->Large Minor Thirds (300-330 cents)</h3>
 

<table class="wiki_table">
    <tr>
        <th>ratio<br />
</th>
        <th>cents value<br />
</th>
        <th>prime limit<br />
</th>
    </tr>
    <tr>
        <td>25/21<br />
</td>
        <td>301.847<br />
</td>
        <td>7<br />
</td>
    </tr>
    <tr>
        <td>56/47<br />
</td>
        <td>303.319<br />
</td>
        <td>47<br />
</td>
    </tr>
    <tr>
        <td>31/26<br />
</td>
        <td>304.508<br />
</td>
        <td>31<br />
</td>
    </tr>
    <tr>
        <td>37/31<br />
</td>
        <td>306.308<br />
</td>
        <td>37<br />
</td>
    </tr>
    <tr>
        <td>43/36<br />
</td>
        <td>307.608<br />
</td>
        <td>43<br />
</td>
    </tr>
    <tr>
        <td>6/5 = 18/15 = 30/25 = 42/35 = 54/45<br />
</td>
        <td>315.641<br />
</td>
        <td>5<br />
</td>
    </tr>
    <tr>
        <td>47/39<br />
</td>
        <td>323.024<br />
</td>
        <td>47<br />
</td>
    </tr>
    <tr>
        <td>41/34<br />
</td>
        <td>324.107<br />
</td>
        <td>41<br />
</td>
    </tr>
    <tr>
        <td>35/29<br />
</td>
        <td>325.562<br />
</td>
        <td>29<br />
</td>
    </tr>
    <tr>
        <td>29/24<br />
</td>
        <td>327.622<br />
</td>
        <td>29<br />
</td>
    </tr>
    <tr>
        <td>52/43<br />
</td>
        <td>329.010<br />
</td>
        <td>43<br />
</td>
    </tr>
</table>

<!-- ws:start:WikiTextHeadingRule:48:&lt;h2&gt; --><h2 id="toc24"><!-- ws:end:WikiTextHeadingRule:48 --> </h2>
 <!-- ws:start:WikiTextHeadingRule:50:&lt;h2&gt; --><h2 id="toc25"><a name="x-Central or Zalzalian Thirds (formerly Neutral Thirds) (330-372 cents)"></a><!-- ws:end:WikiTextHeadingRule:50 -->Central or Zalzalian Thirds (formerly Neutral Thirds) (330-372 cents)</h2>
 <!-- ws:start:WikiTextHeadingRule:52:&lt;h3&gt; --><h3 id="toc26"><a name="x-Central or Zalzalian Thirds (formerly Neutral Thirds) (330-372 cents)-Small Central Thirds (330-342 cents)"></a><!-- ws:end:WikiTextHeadingRule:52 -->Small Central Thirds (330-342 cents)</h3>
 

<table class="wiki_table">
    <tr>
        <th>ratio<br />
</th>
        <th>cents value<br />
</th>
        <th>prime limit<br />
</th>
    </tr>
    <tr>
        <td>23/19<br />
</td>
        <td>330.761<br />
</td>
        <td>23<br />
</td>
    </tr>
    <tr>
        <td>40/33<br />
</td>
        <td>333.041<br />
</td>
        <td>11<br />
</td>
    </tr>
    <tr>
        <td>17/14<br />
</td>
        <td>336.130<br />
</td>
        <td>17<br />
</td>
    </tr>
    <tr>
        <td>45/37<br />
</td>
        <td>338.880<br />
</td>
        <td>37<br />
</td>
    </tr>
    <tr>
        <td>28/23<br />
</td>
        <td>340.552<br />
</td>
        <td>23<br />
</td>
    </tr>
</table>

<!-- ws:start:WikiTextHeadingRule:54:&lt;h3&gt; --><h3 id="toc27"><a name="x-Central or Zalzalian Thirds (formerly Neutral Thirds) (330-372 cents)-Middle Central Thirds (342-360 cents)"></a><!-- ws:end:WikiTextHeadingRule:54 -->Middle Central Thirds (342-360 cents)</h3>
 

<table class="wiki_table">
    <tr>
        <th>ratio<br />
</th>
        <th>cents value<br />
</th>
        <th>prime limit<br />
</th>
    </tr>
    <tr>
        <td>39/32<br />
</td>
        <td>342.483<br />
</td>
        <td>13<br />
</td>
    </tr>
    <tr>
        <td>50/41<br />
</td>
        <td>343.565<br />
</td>
        <td>41<br />
</td>
    </tr>
    <tr>
        <td>11/9 = 33/27<br />
</td>
        <td>347.408<br />
</td>
        <td>11<br />
</td>
    </tr>
    <tr>
        <td>38/31<br />
</td>
        <td>352.477<br />
</td>
        <td>31<br />
</td>
    </tr>
    <tr>
        <td>27/22<br />
</td>
        <td>354.547<br />
</td>
        <td>11<br />
</td>
    </tr>
    <tr>
        <td>43/35<br />
</td>
        <td>356.378<br />
</td>
        <td>43<br />
</td>
    </tr>
    <tr>
        <td>16/13 = 48/39<br />
</td>
        <td>359.472<br />
</td>
        <td>13<br />
</td>
    </tr>
</table>

<!-- ws:start:WikiTextHeadingRule:56:&lt;h3&gt; --><h3 id="toc28"><a name="x-Central or Zalzalian Thirds (formerly Neutral Thirds) (330-372 cents)-Large Central Thirds (360-372 cents)"></a><!-- ws:end:WikiTextHeadingRule:56 -->Large Central Thirds (360-372 cents)</h3>
 

<table class="wiki_table">
    <tr>
        <th>ratio<br />
</th>
        <th>cents value<br />
</th>
        <th>prime limit<br />
</th>
    </tr>
    <tr>
        <td>37/30<br />
</td>
        <td>363.075<br />
</td>
        <td>37<br />
</td>
    </tr>
    <tr>
        <td>58/47<br />
</td>
        <td>364.071<br />
</td>
        <td>47<br />
</td>
    </tr>
    <tr>
        <td>21/17<br />
</td>
        <td>365.825<br />
</td>
        <td>17<br />
</td>
    </tr>
    <tr>
        <td>47/38<br />
</td>
        <td>367.994<br />
</td>
        <td>47<br />
</td>
    </tr>
    <tr>
        <td>26/21<br />
</td>
        <td>369.747<br />
</td>
        <td>13<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:58:&lt;h2&gt; --><h2 id="toc29"><a name="x-Major Thirds (372-440 cents)"></a><!-- ws:end:WikiTextHeadingRule:58 -->Major Thirds (372-440 cents)</h2>
 <!-- ws:start:WikiTextHeadingRule:60:&lt;h3&gt; --><h3 id="toc30"><a name="x-Major Thirds (372-440 cents)-Small Major Thirds (372-400 cents)"></a><!-- ws:end:WikiTextHeadingRule:60 -->Small Major Thirds (372-400 cents)</h3>
 

<table class="wiki_table">
    <tr>
        <th>ratio<br />
</th>
        <th>cents value<br />
</th>
        <th>prime limit<br />
</th>
    </tr>
    <tr>
        <td>31/25<br />
</td>
        <td>372.408<br />
</td>
        <td>31<br />
</td>
    </tr>
    <tr>
        <td>36/29<br />
</td>
        <td>374.333<br />
</td>
        <td>29<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
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        <td><br />
</td>
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</td>
        <td><br />
</td>
    </tr>
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        <td><br />
</td>
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</td>
        <td><br />
</td>
    </tr>
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        <td><br />
</td>
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</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
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</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
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</td>
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</td>
    </tr>
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        <td><br />
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</td>
    </tr>
    <tr>
        <td><br />
</td>
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</td>
        <td><br />
</td>
    </tr>
</table>

<br />
...to be continued...</body></html>