List of 47-odd-limit intervals: Difference between revisions
Wikispaces>Andrew_Heathwaite **Imported revision 463187734 - Original comment: ** |
Wikispaces>Andrew_Heathwaite **Imported revision 463335936 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2013-10- | : This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2013-10-26 13:40:17 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>463335936</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
Line 224: | Line 224: | ||
|| 39/31 || 397.447 || 31 || | || 39/31 || 397.447 || 31 || | ||
|| 34/27 || 399.090 || 17 || | || 34/27 || 399.090 || 17 || | ||
===Middle Major Thirds (400-423 cents)=== | |||
||~ ratio ||~ cents value ||~ prime limit || | |||
|| 29/23 || 401.303 || 29 || | |||
|| 24/19 || 404.442 || 19 || | |||
|| 43/34 || 406.562 || 43 || | |||
|| 19/15 || 409.244 || 19 || | |||
|| 52/41 || 411.465 || 41 || | |||
|| 33/26 || 412.745 || 13 || | |||
|| 47/37 || 414.163 || 47 || | |||
|| 14/11 = 42/33 || 417.508 || 11 || | |||
|| 37/29 || 421.767 || 37 || | |||
|| 60/47 || 422.762 || 47 || | |||
===Large Major Thirds (423-440 cents)=== | |||
||~ ratio ||~ cents value ||~ prime limit || | |||
|| 23/18 || 424.364 || 23 || | |||
|| 32/25 || 427.373 || 5 || | |||
|| 41/32 || 429.062 || 41 || | |||
|| 50/39 || 430.145 || 13 || | |||
|| 9/7 = 27/21 = 45/35 || 435.084 || 7 || | |||
|| 58/45 || 439.353 || 29 || | |||
==Interseptimal Region (M3-4) (440-468 cents)== | |||
||~ ratio ||~ cents value ||~ prime limit || | |||
|| 40/31 || 441.278 || 31 || | |||
|| 31/24 || 443.081 || 31 || | |||
|| 22/17 || 446.363 || 17 || | |||
|| 35/27 || 449.275 || 7 || | |||
|| 48/37 || 450.611 || 37 || | |||
|| 13/10 = 39/30 || 454.214 || 13 || | |||
|| 56/43 || 457.308 || 43 || | |||
|| 43/33 || 458.245 || 43 || | |||
|| 30/23 || 459.994 || 23 || | |||
|| 47/36 || 461.597 || 47 || | |||
|| 17/13 || 464.428 || 17 || | |||
|| 38/29 || 467.936 || 29 || | |||
==Perfect Fourths (468-528 cents)== | |||
===Small Perfect Fourths (468-491 cents)=== | |||
||~ ratio ||~ cents value ||~ prime limit || | |||
|| 21/16 || 470.781 || 7 || | |||
|| 46/35 || 473.135 || 23 || | |||
|| 25/19 || 475.114 || 19 || | |||
|| 54/41 || 476.803 || 41 || | |||
|| 29/22 || 478.259 || 29 || | |||
|| 62/47 || 479.529 || 47 || | |||
|| 33/25 || 480.646 || 11 || | |||
|| 37/28 || 482.518 || 37 || | |||
|| 41/31 || 484.027 || 41 || | |||
|| 45/34 || 485.268 || 17 || | |||
===Middle Perfect Fourths (491-505 cents)=== | |||
||~ ratio ||~ cents value ||~ prime limit || | |||
|| 4/3 = 12/9 = 20/15 = 36/27 = 36/27 = 44/33 = 52/39 = 60/45 || 498.045 || 3 || | |||
===Large Perfect Fourths (505-528 cents)=== | |||
||~ ratio ||~ cents value ||~ prime limit || | |||
|| 47/35 || 510.367 || 47 || | |||
|| 43/32 || 511.518 || 43 || | |||
|| 39/29 || 512.905 || 29 || | |||
|| 35/26 || 514.612 || 13 || | |||
|| 31/23 || 516.761 || 31 || | |||
|| 58/43 || 518.059 || 43 || | |||
|| 27/20 || 519.551 || 5 || | |||
|| 50/37 || 521.283 || 37 || | |||
|| 23/17 || 523.319 || 23 || | |||
|| 42/31 || 525.745 || 31 || | |||
==Superfourths (528-560 cents)== | |||
||~ ratio ||~ cents value ||~ prime limit || | |||
|| 19/14 || 528.687 || 19 || | |||
|| 34/25 || 532.328 || 17 || | |||
|| 64/47 || 534.493 || 47 || | |||
|| 15/11 = 45/33 || 536.951 || 11 || | |||
|| 56/41 || 539.764 || 41 || | |||
|| 41/30 || 540.794 || 41 || | |||
|| 26/19 || 543.015 || 19 || | |||
|| 37/27 || 545.479 || 37 || | |||
|| 48/35 || 546.815 || 7 || | |||
|| 11/8 = 33/24 || 551.318 || 11 || | |||
|| 62/45 || 554.812 || 31 || | |||
|| 40/29 || 556.737 || 29 || | |||
|| 29/21 || 558.796 || 29 || | |||
|| 47/34 || 560.551 || 47 || | |||
...to be continued...</pre></div> | ...to be continued...</pre></div> | ||
Line 1,773: | Line 1,855: | ||
</table> | </table> | ||
<!-- ws:start:WikiTextHeadingRule:62:&lt;h3&gt; --><h3 id="toc31"><a name="x-Major Thirds (372-440 cents)-Middle Major Thirds (400-423 cents)"></a><!-- ws:end:WikiTextHeadingRule:62 -->Middle Major Thirds (400-423 cents)</h3> | |||
<table class="wiki_table"> | |||
<tr> | |||
<th>ratio<br /> | |||
</th> | |||
<th>cents value<br /> | |||
</th> | |||
<th>prime limit<br /> | |||
</th> | |||
</tr> | |||
<tr> | |||
<td>29/23<br /> | |||
</td> | |||
<td>401.303<br /> | |||
</td> | |||
<td>29<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>24/19<br /> | |||
</td> | |||
<td>404.442<br /> | |||
</td> | |||
<td>19<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>43/34<br /> | |||
</td> | |||
<td>406.562<br /> | |||
</td> | |||
<td>43<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>19/15<br /> | |||
</td> | |||
<td>409.244<br /> | |||
</td> | |||
<td>19<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>52/41<br /> | |||
</td> | |||
<td>411.465<br /> | |||
</td> | |||
<td>41<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>33/26<br /> | |||
</td> | |||
<td>412.745<br /> | |||
</td> | |||
<td>13<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>47/37<br /> | |||
</td> | |||
<td>414.163<br /> | |||
</td> | |||
<td>47<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>14/11 = 42/33<br /> | |||
</td> | |||
<td>417.508<br /> | |||
</td> | |||
<td>11<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>37/29<br /> | |||
</td> | |||
<td>421.767<br /> | |||
</td> | |||
<td>37<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>60/47<br /> | |||
</td> | |||
<td>422.762<br /> | |||
</td> | |||
<td>47<br /> | |||
</td> | |||
</tr> | |||
</table> | |||
<!-- ws:start:WikiTextHeadingRule:64:&lt;h3&gt; --><h3 id="toc32"><a name="x-Major Thirds (372-440 cents)-Large Major Thirds (423-440 cents)"></a><!-- ws:end:WikiTextHeadingRule:64 -->Large Major Thirds (423-440 cents)</h3> | |||
<table class="wiki_table"> | |||
<tr> | |||
<th>ratio<br /> | |||
</th> | |||
<th>cents value<br /> | |||
</th> | |||
<th>prime limit<br /> | |||
</th> | |||
</tr> | |||
<tr> | |||
<td>23/18<br /> | |||
</td> | |||
<td>424.364<br /> | |||
</td> | |||
<td>23<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>32/25<br /> | |||
</td> | |||
<td>427.373<br /> | |||
</td> | |||
<td>5<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>41/32<br /> | |||
</td> | |||
<td>429.062<br /> | |||
</td> | |||
<td>41<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>50/39<br /> | |||
</td> | |||
<td>430.145<br /> | |||
</td> | |||
<td>13<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>9/7 = 27/21 = 45/35<br /> | |||
</td> | |||
<td>435.084<br /> | |||
</td> | |||
<td>7<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>58/45<br /> | |||
</td> | |||
<td>439.353<br /> | |||
</td> | |||
<td>29<br /> | |||
</td> | |||
</tr> | |||
</table> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:66:&lt;h2&gt; --><h2 id="toc33"><a name="x-Interseptimal Region (M3-4) (440-468 cents)"></a><!-- ws:end:WikiTextHeadingRule:66 -->Interseptimal Region (M3-4) (440-468 cents)</h2> | |||
<table class="wiki_table"> | |||
<tr> | |||
<th>ratio<br /> | |||
</th> | |||
<th>cents value<br /> | |||
</th> | |||
<th>prime limit<br /> | |||
</th> | |||
</tr> | |||
<tr> | |||
<td>40/31<br /> | |||
</td> | |||
<td>441.278<br /> | |||
</td> | |||
<td>31<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>31/24<br /> | |||
</td> | |||
<td>443.081<br /> | |||
</td> | |||
<td>31<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>22/17<br /> | |||
</td> | |||
<td>446.363<br /> | |||
</td> | |||
<td>17<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>35/27<br /> | |||
</td> | |||
<td>449.275<br /> | |||
</td> | |||
<td>7<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>48/37<br /> | |||
</td> | |||
<td>450.611<br /> | |||
</td> | |||
<td>37<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>13/10 = 39/30<br /> | |||
</td> | |||
<td>454.214<br /> | |||
</td> | |||
<td>13<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>56/43<br /> | |||
</td> | |||
<td>457.308<br /> | |||
</td> | |||
<td>43<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>43/33<br /> | |||
</td> | |||
<td>458.245<br /> | |||
</td> | |||
<td>43<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>30/23<br /> | |||
</td> | |||
<td>459.994<br /> | |||
</td> | |||
<td>23<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>47/36<br /> | |||
</td> | |||
<td>461.597<br /> | |||
</td> | |||
<td>47<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>17/13<br /> | |||
</td> | |||
<td>464.428<br /> | |||
</td> | |||
<td>17<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>38/29<br /> | |||
</td> | |||
<td>467.936<br /> | |||
</td> | |||
<td>29<br /> | |||
</td> | |||
</tr> | |||
</table> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:68:&lt;h2&gt; --><h2 id="toc34"><a name="x-Perfect Fourths (468-528 cents)"></a><!-- ws:end:WikiTextHeadingRule:68 -->Perfect Fourths (468-528 cents)</h2> | |||
<!-- ws:start:WikiTextHeadingRule:70:&lt;h3&gt; --><h3 id="toc35"><a name="x-Perfect Fourths (468-528 cents)-Small Perfect Fourths (468-491 cents)"></a><!-- ws:end:WikiTextHeadingRule:70 -->Small Perfect Fourths (468-491 cents)</h3> | |||
<table class="wiki_table"> | |||
<tr> | |||
<th>ratio<br /> | |||
</th> | |||
<th>cents value<br /> | |||
</th> | |||
<th>prime limit<br /> | |||
</th> | |||
</tr> | |||
<tr> | |||
<td>21/16<br /> | |||
</td> | |||
<td>470.781<br /> | |||
</td> | |||
<td>7<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>46/35<br /> | |||
</td> | |||
<td>473.135<br /> | |||
</td> | |||
<td>23<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>25/19<br /> | |||
</td> | |||
<td>475.114<br /> | |||
</td> | |||
<td>19<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>54/41<br /> | |||
</td> | |||
<td>476.803<br /> | |||
</td> | |||
<td>41<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>29/22<br /> | |||
</td> | |||
<td>478.259<br /> | |||
</td> | |||
<td>29<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>62/47<br /> | |||
</td> | |||
<td>479.529<br /> | |||
</td> | |||
<td>47<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>33/25<br /> | |||
</td> | |||
<td>480.646<br /> | |||
</td> | |||
<td>11<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>37/28<br /> | |||
</td> | |||
<td>482.518<br /> | |||
</td> | |||
<td>37<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>41/31<br /> | |||
</td> | |||
<td>484.027<br /> | |||
</td> | |||
<td>41<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>45/34<br /> | |||
</td> | |||
<td>485.268<br /> | |||
</td> | |||
<td>17<br /> | |||
</td> | |||
</tr> | |||
</table> | |||
<!-- ws:start:WikiTextHeadingRule:72:&lt;h3&gt; --><h3 id="toc36"><a name="x-Perfect Fourths (468-528 cents)-Middle Perfect Fourths (491-505 cents)"></a><!-- ws:end:WikiTextHeadingRule:72 -->Middle Perfect Fourths (491-505 cents)</h3> | |||
<table class="wiki_table"> | |||
<tr> | |||
<th>ratio<br /> | |||
</th> | |||
<th>cents value<br /> | |||
</th> | |||
<th>prime limit<br /> | |||
</th> | |||
</tr> | |||
<tr> | |||
<td>4/3 = 12/9 = 20/15 = 36/27 = 36/27 = 44/33 = 52/39 = 60/45<br /> | |||
</td> | |||
<td>498.045<br /> | |||
</td> | |||
<td>3<br /> | |||
</td> | |||
</tr> | |||
</table> | |||
<!-- ws:start:WikiTextHeadingRule:74:&lt;h3&gt; --><h3 id="toc37"><a name="x-Perfect Fourths (468-528 cents)-Large Perfect Fourths (505-528 cents)"></a><!-- ws:end:WikiTextHeadingRule:74 -->Large Perfect Fourths (505-528 cents)</h3> | |||
<table class="wiki_table"> | |||
<tr> | |||
<th>ratio<br /> | |||
</th> | |||
<th>cents value<br /> | |||
</th> | |||
<th>prime limit<br /> | |||
</th> | |||
</tr> | |||
<tr> | |||
<td>47/35<br /> | |||
</td> | |||
<td>510.367<br /> | |||
</td> | |||
<td>47<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>43/32<br /> | |||
</td> | |||
<td>511.518<br /> | |||
</td> | |||
<td>43<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>39/29<br /> | |||
</td> | |||
<td>512.905<br /> | |||
</td> | |||
<td>29<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>35/26<br /> | |||
</td> | |||
<td>514.612<br /> | |||
</td> | |||
<td>13<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>31/23<br /> | |||
</td> | |||
<td>516.761<br /> | |||
</td> | |||
<td>31<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>58/43<br /> | |||
</td> | |||
<td>518.059<br /> | |||
</td> | |||
<td>43<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>27/20<br /> | |||
</td> | |||
<td>519.551<br /> | |||
</td> | |||
<td>5<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>50/37<br /> | |||
</td> | |||
<td>521.283<br /> | |||
</td> | |||
<td>37<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>23/17<br /> | |||
</td> | |||
<td>523.319<br /> | |||
</td> | |||
<td>23<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>42/31<br /> | |||
</td> | |||
<td>525.745<br /> | |||
</td> | |||
<td>31<br /> | |||
</td> | |||
</tr> | |||
</table> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:76:&lt;h2&gt; --><h2 id="toc38"><a name="x-Superfourths (528-560 cents)"></a><!-- ws:end:WikiTextHeadingRule:76 -->Superfourths (528-560 cents)</h2> | |||
<table class="wiki_table"> | |||
<tr> | |||
<th>ratio<br /> | |||
</th> | |||
<th>cents value<br /> | |||
</th> | |||
<th>prime limit<br /> | |||
</th> | |||
</tr> | |||
<tr> | |||
<td>19/14<br /> | |||
</td> | |||
<td>528.687<br /> | |||
</td> | |||
<td>19<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>34/25<br /> | |||
</td> | |||
<td>532.328<br /> | |||
</td> | |||
<td>17<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>64/47<br /> | |||
</td> | |||
<td>534.493<br /> | |||
</td> | |||
<td>47<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>15/11 = 45/33<br /> | |||
</td> | |||
<td>536.951<br /> | |||
</td> | |||
<td>11<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>56/41<br /> | |||
</td> | |||
<td>539.764<br /> | |||
</td> | |||
<td>41<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>41/30<br /> | |||
</td> | |||
<td>540.794<br /> | |||
</td> | |||
<td>41<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>26/19<br /> | |||
</td> | |||
<td>543.015<br /> | |||
</td> | |||
<td>19<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>37/27<br /> | |||
</td> | |||
<td>545.479<br /> | |||
</td> | |||
<td>37<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>48/35<br /> | |||
</td> | |||
<td>546.815<br /> | |||
</td> | |||
<td>7<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>11/8 = 33/24<br /> | |||
</td> | |||
<td>551.318<br /> | |||
</td> | |||
<td>11<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>62/45<br /> | |||
</td> | |||
<td>554.812<br /> | |||
</td> | |||
<td>31<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>40/29<br /> | |||
</td> | |||
<td>556.737<br /> | |||
</td> | |||
<td>29<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>29/21<br /> | |||
</td> | |||
<td>558.796<br /> | |||
</td> | |||
<td>29<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>47/34<br /> | |||
</td> | |||
<td>560.551<br /> | |||
</td> | |||
<td>47<br /> | |||
</td> | |||
</tr> | |||
</table> | |||
<br /> | |||
<br /> | <br /> | ||
...to be continued...</body></html></pre></div> | ...to be continued...</body></html></pre></div> |