Porcupine intervals
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Original Wikitext content:
This is one possible naming and organization system for intervals of [[porcupine]] temperament. It's based on the porcupine[7] scale, or equivalently on the [[val]] <7 11 16|. In [[22edo]], all the neighboring intervals on this chart that are shown as about 20 cents apart are actually the same. For example, the augmented third (9/7) and the diminished fourth (14/11) are both the same interval (8\22) in 22edo. This corresponds to 99/98 being tempered out in 22edo. In [[15edo]], on the other hand, the intervals that are shown as about 40 cents apart are actually the same. For example, the augmented third (9/7), is now the same as a **minor** fourth (4/3) rather than a diminished one. That is because 28/27 is tempered out in 15edo. ||~ Name ||~ Size* ||~ Ratios ||~ Comments || ||||||||~ Unisons || || Perfect unison (P1) || 0 || 1/1 || || || Augmented unison (A1) || 61.1 || 81/80~36/35~33/32~25/24 || And other ratios, of course || ||||||||~ Seconds || || Diminished second (d2) || 101.6 || 21/20~16/15 || || || Minor second (m2) || 162.7 || 12/11~11/10~10/9 || || || Major second (M2) || 223.8 || 9/8~8/7 || || || Augmented second (A2) || 284.9 || Close to 13/11 || || ||||||||~ Thirds || || Diminished third (d3) || 264.3 || 7/6 || || || Minor third (m3) || 325.4 || 6/5~11/9 || Coincidentally familiar || || Major third (M3) || 386.5 || 5/4 || Coincidentally familiar || || Augmented third (A3) || 447.6 || 9/7 || || ||||||||~ Fourths || || Diminished fourth (d4) || 427.0 || 14/11 || || || Minor fourth (m4) || 488.1 || 4/3 || Rather than "perfect fourth" || || Major fourth (M4) || 549.2 || 11/8 || || || Augmented fourth (A4) || 610.3 || 10/7 || || ||||||||~ Fifths || || Diminished fifth (d5) || 589.7 || 7/5 || || || Minor fifth (m5) || 650.8 || 16/11 || || || Major fifth (M5) || 711.9 || 3/2 || Rather than "perfect fifth" || || Augmented fifth (A5) || 773.0 || 11/7 || || ||||||||~ Sixths || || Diminished sixth (d6) || 752.4 || 14/9 || || || Minor sixth (m6) || 813.5 || 8/5 || Coincidentally familiar || || Major sixth (M6) || 874.6 || 5/3 || Coincidentally familiar || || Augmented sixth (A6) || 935.7 || 12/7 || || ||||||||~ Sevenths || || Diminished seventh (d7) || 915.1 || Close to 22/13 || || || Minor seventh (m7) || 976.2 || 7/4~16/9 || || || Major seventh (M7) || 1037.3 || 9/5~11/6 || || || Augmented seventh (A7) || 1098.4 || 15/8 || || ||||||||~ Octaves || || Diminished octave (d8) || 1138.9 || 21/11~35/18~160/81 || || || Perfect octave (P8) || 1200 || 2/1 || || || Augmented octave (A8) || 1061.1 || 81/40~45/22~33/16~25/12 || || ``*`` In POTE 11-limit porcupine
Original HTML content:
<html><head><title>Porcupine intervals</title></head><body>This is one possible naming and organization system for intervals of <a class="wiki_link" href="/porcupine">porcupine</a> temperament. It's based on the porcupine[7] scale, or equivalently on the <a class="wiki_link" href="/val">val</a> <7 11 16|.<br />
<br />
In <a class="wiki_link" href="/22edo">22edo</a>, all the neighboring intervals on this chart that are shown as about 20 cents apart are actually the same. For example, the augmented third (9/7) and the diminished fourth (14/11) are both the same interval (8\22) in 22edo. This corresponds to 99/98 being tempered out in 22edo.<br />
<br />
In <a class="wiki_link" href="/15edo">15edo</a>, on the other hand, the intervals that are shown as about 40 cents apart are actually the same. For example, the augmented third (9/7), is now the same as a <strong>minor</strong> fourth (4/3) rather than a diminished one. That is because 28/27 is tempered out in 15edo.<br />
<br />
<table class="wiki_table">
<tr>
<th>Name<br />
</th>
<th>Size*<br />
</th>
<th>Ratios<br />
</th>
<th>Comments<br />
</th>
</tr>
<tr>
<th colspan="4">Unisons<br />
</th>
</tr>
<tr>
<td>Perfect unison (P1)<br />
</td>
<td>0<br />
</td>
<td>1/1<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>Augmented unison (A1)<br />
</td>
<td>61.1<br />
</td>
<td>81/80~36/35~33/32~25/24<br />
</td>
<td>And other ratios, of course<br />
</td>
</tr>
<tr>
<th colspan="4">Seconds<br />
</th>
</tr>
<tr>
<td>Diminished second (d2)<br />
</td>
<td>101.6<br />
</td>
<td>21/20~16/15<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>Minor second (m2)<br />
</td>
<td>162.7<br />
</td>
<td>12/11~11/10~10/9<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>Major second (M2)<br />
</td>
<td>223.8<br />
</td>
<td>9/8~8/7<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>Augmented second (A2)<br />
</td>
<td>284.9<br />
</td>
<td>Close to 13/11<br />
</td>
<td><br />
</td>
</tr>
<tr>
<th colspan="4">Thirds<br />
</th>
</tr>
<tr>
<td>Diminished third (d3)<br />
</td>
<td>264.3<br />
</td>
<td>7/6<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>Minor third (m3)<br />
</td>
<td>325.4<br />
</td>
<td>6/5~11/9<br />
</td>
<td>Coincidentally familiar<br />
</td>
</tr>
<tr>
<td>Major third (M3)<br />
</td>
<td>386.5<br />
</td>
<td>5/4<br />
</td>
<td>Coincidentally familiar<br />
</td>
</tr>
<tr>
<td>Augmented third (A3)<br />
</td>
<td>447.6<br />
</td>
<td>9/7<br />
</td>
<td><br />
</td>
</tr>
<tr>
<th colspan="4">Fourths<br />
</th>
</tr>
<tr>
<td>Diminished fourth (d4)<br />
</td>
<td>427.0<br />
</td>
<td>14/11<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>Minor fourth (m4)<br />
</td>
<td>488.1<br />
</td>
<td>4/3<br />
</td>
<td>Rather than "perfect fourth"<br />
</td>
</tr>
<tr>
<td>Major fourth (M4)<br />
</td>
<td>549.2<br />
</td>
<td>11/8<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>Augmented fourth (A4)<br />
</td>
<td>610.3<br />
</td>
<td>10/7<br />
</td>
<td><br />
</td>
</tr>
<tr>
<th colspan="4">Fifths<br />
</th>
</tr>
<tr>
<td>Diminished fifth (d5)<br />
</td>
<td>589.7<br />
</td>
<td>7/5<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>Minor fifth (m5)<br />
</td>
<td>650.8<br />
</td>
<td>16/11<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>Major fifth (M5)<br />
</td>
<td>711.9<br />
</td>
<td>3/2<br />
</td>
<td>Rather than "perfect fifth"<br />
</td>
</tr>
<tr>
<td>Augmented fifth (A5)<br />
</td>
<td>773.0<br />
</td>
<td>11/7<br />
</td>
<td><br />
</td>
</tr>
<tr>
<th colspan="4">Sixths<br />
</th>
</tr>
<tr>
<td>Diminished sixth (d6)<br />
</td>
<td>752.4<br />
</td>
<td>14/9<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>Minor sixth (m6)<br />
</td>
<td>813.5<br />
</td>
<td>8/5<br />
</td>
<td>Coincidentally familiar<br />
</td>
</tr>
<tr>
<td>Major sixth (M6)<br />
</td>
<td>874.6<br />
</td>
<td>5/3<br />
</td>
<td>Coincidentally familiar<br />
</td>
</tr>
<tr>
<td>Augmented sixth (A6)<br />
</td>
<td>935.7<br />
</td>
<td>12/7<br />
</td>
<td><br />
</td>
</tr>
<tr>
<th colspan="4">Sevenths<br />
</th>
</tr>
<tr>
<td>Diminished seventh (d7)<br />
</td>
<td>915.1<br />
</td>
<td>Close to 22/13<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>Minor seventh (m7)<br />
</td>
<td>976.2<br />
</td>
<td>7/4~16/9<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>Major seventh (M7)<br />
</td>
<td>1037.3<br />
</td>
<td>9/5~11/6<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>Augmented seventh (A7)<br />
</td>
<td>1098.4<br />
</td>
<td>15/8<br />
</td>
<td><br />
</td>
</tr>
<tr>
<th colspan="4">Octaves<br />
</th>
</tr>
<tr>
<td>Diminished octave (d8)<br />
</td>
<td>1138.9<br />
</td>
<td>21/11~35/18~160/81<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>Perfect octave (P8)<br />
</td>
<td>1200<br />
</td>
<td>2/1<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>Augmented octave (A8)<br />
</td>
<td>1061.1<br />
</td>
<td>81/40~45/22~33/16~25/12<br />
</td>
<td><br />
</td>
</tr>
</table>
<!-- ws:start:WikiTextRawRule:00:``*`` -->*<!-- ws:end:WikiTextRawRule:00 --> In POTE 11-limit porcupine</body></html>