Porcupine family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 468004376 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 519361368 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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:genewardsmith|genewardsmith]] and made on <tt> | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-08-22 21:51:50 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>519361368</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 9: | Line 9: | ||
---- | ---- | ||
The 5-limit parent comma for the porcupine family is 250/243, the maximal [[diesis]] or porcupine comma. Its [[monzo]] is |1 -5 3>, and flipping that yields <<3 5 1|| for the [[wedgie]]. This tells us the [[generator]] is a minor whole tone, the [[10_9|10/9]] interval, and that three of these add up to a fourth, with two more giving the minor sixth. In fact, (10/9)^3 = 4/3 * 250/243, and (10/9)^5 = 8/5 * (250/243)^2. 3/22 is a very recommendable generator, and MOS of 7, 8 and 15 notes make for some nice scale possibilities. | The 5-limit parent comma for the porcupine family is 250/243, the maximal [[diesis]] or porcupine comma. Its [[monzo]] is |1 -5 3>, and flipping that yields <<3 5 1|| for the [[wedgie]]. This tells us the [[generator]] is a minor whole tone, the [[10_9|10/9]] interval, and that three of these add up to a fourth, with two more giving the minor sixth. In fact, (10/9)^3 = 4/3 * 250/243, and (10/9)^5 = 8/5 * (250/243)^2. 3/22 is a very recommendable generator, and MOS of 7, 8 and 15 notes make for some nice scale possibilities. | ||
valid range: [150.000, 171.429] (8 to 7) | |||
nice range: [157.821, 166.015] | |||
strict range: [157.821, 166.015] | |||
[[POTE tuning|POTE generator]]: 163.950 | [[POTE tuning|POTE generator]]: 163.950 | ||
| Line 24: | Line 28: | ||
Commas: 250/243, 64/63 | Commas: 250/243, 64/63 | ||
valid range: [160.000, 163.636] (15 to 22) | |||
nice range: [157.821, 166.015] | |||
strict range: [160.000, 163.636] | |||
[[POTE tuning|POTE generator]]: ~10/9 = 162.880 | [[POTE tuning|POTE generator]]: ~10/9 = 162.880 | ||
| Line 34: | Line 42: | ||
==11-limit== | ==11-limit== | ||
Commas: 55/54, 64/63, 100/99 | Commas: 55/54, 64/63, 100/99 | ||
valid range: [160.000, 163.636] (15 to 22) | |||
nice range: [150.637, 182.404] | |||
strict range: [160.000, 163.636] | |||
POTE generator: ~10/9 = 162.747 | POTE generator: ~10/9 = 162.747 | ||
| Line 44: | Line 56: | ||
==13-limit== | ==13-limit== | ||
Commas: 40/39, 55/54, 64/63, 66/65 | Commas: 40/39, 55/54, 64/63, 66/65 | ||
valid range: [160.000, 163.636] (15 to 22f) | |||
nice range: [138.573, 182.404] | |||
strict range: [160.000, 163.636] | |||
POTE generator: ~10/9 = 162.708 | POTE generator: ~10/9 = 162.708 | ||
| Line 55: | Line 71: | ||
See also: [[The Biosphere]] | See also: [[The Biosphere]] | ||
Commas: 55/54, 64/63, 91/90, 100/99 | Commas: 55/54, 64/63, 91/90, 100/99 | ||
valid range: [160.000, 162.162] (15 to 37) | |||
nice range: [150.637, 182.404] | |||
strict range: [160.000, 162.162] | |||
POTE generator: ~10/9 = 162.277 | POTE generator: ~10/9 = 162.277 | ||
| Line 304: | Line 324: | ||
<!-- ws:end:WikiTextTocRule:91 --><hr /> | <!-- ws:end:WikiTextTocRule:91 --><hr /> | ||
The 5-limit parent comma for the porcupine family is 250/243, the maximal <a class="wiki_link" href="/diesis">diesis</a> or porcupine comma. Its <a class="wiki_link" href="/monzo">monzo</a> is |1 -5 3&gt;, and flipping that yields &lt;&lt;3 5 1|| for the <a class="wiki_link" href="/wedgie">wedgie</a>. This tells us the <a class="wiki_link" href="/generator">generator</a> is a minor whole tone, the <a class="wiki_link" href="/10_9">10/9</a> interval, and that three of these add up to a fourth, with two more giving the minor sixth. In fact, (10/9)^3 = 4/3 * 250/243, and (10/9)^5 = 8/5 * (250/243)^2. 3/22 is a very recommendable generator, and MOS of 7, 8 and 15 notes make for some nice scale possibilities.<br /> | The 5-limit parent comma for the porcupine family is 250/243, the maximal <a class="wiki_link" href="/diesis">diesis</a> or porcupine comma. Its <a class="wiki_link" href="/monzo">monzo</a> is |1 -5 3&gt;, and flipping that yields &lt;&lt;3 5 1|| for the <a class="wiki_link" href="/wedgie">wedgie</a>. This tells us the <a class="wiki_link" href="/generator">generator</a> is a minor whole tone, the <a class="wiki_link" href="/10_9">10/9</a> interval, and that three of these add up to a fourth, with two more giving the minor sixth. In fact, (10/9)^3 = 4/3 * 250/243, and (10/9)^5 = 8/5 * (250/243)^2. 3/22 is a very recommendable generator, and MOS of 7, 8 and 15 notes make for some nice scale possibilities.<br /> | ||
<br /> | |||
valid range: [150.000, 171.429] (8 to 7)<br /> | |||
nice range: [157.821, 166.015]<br /> | |||
strict range: [157.821, 166.015]<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 163.950<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 163.950<br /> | ||
| Line 319: | Line 343: | ||
<br /> | <br /> | ||
Commas: 250/243, 64/63<br /> | Commas: 250/243, 64/63<br /> | ||
<br /> | |||
valid range: [160.000, 163.636] (15 to 22)<br /> | |||
nice range: [157.821, 166.015]<br /> | |||
strict range: [160.000, 163.636]<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~10/9 = 162.880<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~10/9 = 162.880<br /> | ||
| Line 329: | Line 357: | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Porcupine-11-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->11-limit</h2> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Porcupine-11-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->11-limit</h2> | ||
Commas: 55/54, 64/63, 100/99<br /> | Commas: 55/54, 64/63, 100/99<br /> | ||
<br /> | |||
valid range: [160.000, 163.636] (15 to 22)<br /> | |||
nice range: [150.637, 182.404]<br /> | |||
strict range: [160.000, 163.636]<br /> | |||
<br /> | <br /> | ||
POTE generator: ~10/9 = 162.747<br /> | POTE generator: ~10/9 = 162.747<br /> | ||
| Line 339: | Line 371: | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Porcupine-13-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Porcupine-13-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-limit</h2> | ||
Commas: 40/39, 55/54, 64/63, 66/65<br /> | Commas: 40/39, 55/54, 64/63, 66/65<br /> | ||
<br /> | |||
valid range: [160.000, 163.636] (15 to 22f)<br /> | |||
nice range: [138.573, 182.404]<br /> | |||
strict range: [160.000, 163.636]<br /> | |||
<br /> | <br /> | ||
POTE generator: ~10/9 = 162.708<br /> | POTE generator: ~10/9 = 162.708<br /> | ||
| Line 350: | Line 386: | ||
See also: <a class="wiki_link" href="/The%20Biosphere">The Biosphere</a><br /> | See also: <a class="wiki_link" href="/The%20Biosphere">The Biosphere</a><br /> | ||
Commas: 55/54, 64/63, 91/90, 100/99<br /> | Commas: 55/54, 64/63, 91/90, 100/99<br /> | ||
<br /> | |||
valid range: [160.000, 162.162] (15 to 37)<br /> | |||
nice range: [150.637, 182.404]<br /> | |||
strict range: [160.000, 162.162]<br /> | |||
<br /> | <br /> | ||
POTE generator: ~10/9 = 162.277<br /> | POTE generator: ~10/9 = 162.277<br /> | ||