List of 47-odd-limit intervals
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author Andrew_Heathwaite and made on 2013-10-25 13:25:32 UTC.
- The original revision id was 463113976.
- The revision comment was:
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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:<h2> --><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:<h2> --><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:<h2> --><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:<h2> --><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:<h3> --><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:<h3> --><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:<h3> --><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:<h2> --><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:<h3> --><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:<h3> --><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:<h3> --><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:<h2> --><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>