Porcupine family: Difference between revisions
Jump to navigation
Jump to search
Wikispaces>genewardsmith **Imported revision 187288527 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 203540390 - 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>2011-02-20 18:38:20 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>203540390</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 17: | Line 17: | ||
The second comma of the [[Normal lists|normal comma list]] defines which 7-limit family member we are looking at. That means 64/63, the Archytas comma, for porcupine, 36/35, the septimal quarter tone, for hystrix, 50/49, the jubilisma, for hedgehog, and 49/48, the slendro diesis, for nautilus. | The second comma of the [[Normal lists|normal comma list]] defines which 7-limit family member we are looking at. That means 64/63, the Archytas comma, for porcupine, 36/35, the septimal quarter tone, for hystrix, 50/49, the jubilisma, for hedgehog, and 49/48, the slendro diesis, for nautilus. | ||
==Porcupine== | |||
Porcupine, with wedgie <<3 5 -6 1 -18 -28||, uses six of its minor tone generator steps to get to 7/4. For this to work you need a small minor tone such as [[22edo]] provides, and once again 3/22 is a good tuning choice, though we might pick in preference 8/59, 11/81, or 19/140 for our generator. | Porcupine, with wedgie <<3 5 -6 1 -18 -28||, uses six of its minor tone generator steps to get to 7/4. For this to work you need a small minor tone such as [[22edo]] provides, and once again 3/22 is a good tuning choice, though we might pick in preference 8/59, 11/81, or 19/140 for our generator. | ||
Commas: 250/243, 64/63 | Commas: 250/243, 64/63 | ||
[[POTE tuning|POTE generator]]: 162.880 | [[POTE tuning|POTE generator]]: ~10/9 = 162.880 | ||
Map: [<1 2 3 2|, <0 -3 -5 6|] | Map: [<1 2 3 2|, <0 -3 -5 6|] | ||
EDOs: 22, 59, 81, 140 | |||
===11-limit=== | |||
Commas: 55/54, 64/63, 100/99 | |||
POTE generator: ~10/9 = 162.747 | |||
EDOs: 22, 59 | Map: [<1 2 3 2 4|, <0 -3 -5 6 -4|] | ||
EDOs: 7, 15, 22, 37, 59 | |||
Badness: 0.0217 | |||
==Hystrix== | |||
Hystrix, with wedgie <<3 5 1 1 -7 -12||, provides a less complex avenue to the 7-limit. Unfortunately in temperaments as in life you get what you pay for, and hystrix, for which a generator of 2/15 or 9/68 can be used, is a temperament for the adventurous souls who have probably already tried [[15edo]]. They can try the even sharper fifth of hystrix in [[68edo]] and see how that suits. | Hystrix, with wedgie <<3 5 1 1 -7 -12||, provides a less complex avenue to the 7-limit. Unfortunately in temperaments as in life you get what you pay for, and hystrix, for which a generator of 2/15 or 9/68 can be used, is a temperament for the adventurous souls who have probably already tried [[15edo]]. They can try the even sharper fifth of hystrix in [[68edo]] and see how that suits. | ||
| Line 39: | Line 47: | ||
EDOs: 15, 68 | EDOs: 15, 68 | ||
==Hedgehog== | |||
Hedgehog, with wedgie <<6 10 10 2 -1 -5||, has a period 1/2 octave and a generator which can be taken to be 9/7 instead of 10/9. It also tempers out 245/243, the sensamagic comma. 22et provides the obvious tuning, but if you are looking for an alternative, you could try the <146 232 338 411| val with generator 10/73, or you could try 164 cents if you are fond of round numbers. The 14 note MOS gives scope for harmony while stopping well short of 22. | Hedgehog, with wedgie <<6 10 10 2 -1 -5||, has a period 1/2 octave and a generator which can be taken to be 9/7 instead of 10/9. It also tempers out 245/243, the sensamagic comma. 22et provides the obvious tuning, but if you are looking for an alternative, you could try the <146 232 338 411| val with generator 10/73, or you could try 164 cents if you are fond of round numbers. The 14 note MOS gives scope for harmony while stopping well short of 22. | ||
| Line 61: | Line 69: | ||
The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which 7-limit family member we are looking at. That means 64/63, the Archytas comma, for porcupine, 36/35, the septimal quarter tone, for hystrix, 50/49, the jubilisma, for hedgehog, and 49/48, the slendro diesis, for nautilus.<br /> | The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which 7-limit family member we are looking at. That means 64/63, the Archytas comma, for porcupine, 36/35, the septimal quarter tone, for hystrix, 50/49, the jubilisma, for hedgehog, and 49/48, the slendro diesis, for nautilus.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt; | <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-Porcupine"></a><!-- ws:end:WikiTextHeadingRule:2 -->Porcupine</h2> | ||
Porcupine, with wedgie &lt;&lt;3 5 -6 1 -18 -28||, uses six of its minor tone generator steps to get to 7/4. For this to work you need a small minor tone such as <a class="wiki_link" href="/22edo">22edo</a> provides, and once again 3/22 is a good tuning choice, though we might pick in preference 8/59, 11/81, or 19/140 for our generator.<br /> | Porcupine, with wedgie &lt;&lt;3 5 -6 1 -18 -28||, uses six of its minor tone generator steps to get to 7/4. For this to work you need a small minor tone such as <a class="wiki_link" href="/22edo">22edo</a> provides, and once again 3/22 is a good tuning choice, though we might pick in preference 8/59, 11/81, or 19/140 for our generator.<br /> | ||
<br /> | <br /> | ||
Commas: 250/243, 64/63<br /> | Commas: 250/243, 64/63<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 162.880<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~10/9 = 162.880<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 2 3 2|, &lt;0 -3 -5 6|]<br /> | Map: [&lt;1 2 3 2|, &lt;0 -3 -5 6|]<br /> | ||
EDOs: 22, 59, 81, 140<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x-Porcupine-11-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->11-limit</h3> | |||
Commas: 55/54, 64/63, 100/99<br /> | |||
<br /> | |||
POTE generator: ~10/9 = 162.747<br /> | |||
<br /> | <br /> | ||
EDOs: 22, 59 | Map: [&lt;1 2 3 2 4|, &lt;0 -3 -5 6 -4|]<br /> | ||
EDOs: 7, 15, 22, 37, 59<br /> | |||
Badness: 0.0217<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x-Hystrix"></a><!-- ws:end:WikiTextHeadingRule:6 -->Hystrix</h2> | ||
Hystrix, with wedgie &lt;&lt;3 5 1 1 -7 -12||, provides a less complex avenue to the 7-limit. Unfortunately in temperaments as in life you get what you pay for, and hystrix, for which a generator of 2/15 or 9/68 can be used, is a temperament for the adventurous souls who have probably already tried <a class="wiki_link" href="/15edo">15edo</a>. They can try the even sharper fifth of hystrix in <a class="wiki_link" href="/68edo">68edo</a> and see how that suits.<br /> | Hystrix, with wedgie &lt;&lt;3 5 1 1 -7 -12||, provides a less complex avenue to the 7-limit. Unfortunately in temperaments as in life you get what you pay for, and hystrix, for which a generator of 2/15 or 9/68 can be used, is a temperament for the adventurous souls who have probably already tried <a class="wiki_link" href="/15edo">15edo</a>. They can try the even sharper fifth of hystrix in <a class="wiki_link" href="/68edo">68edo</a> and see how that suits.<br /> | ||
<br /> | <br /> | ||
| Line 83: | Line 99: | ||
EDOs: 15, 68<br /> | EDOs: 15, 68<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="x-Hedgehog"></a><!-- ws:end:WikiTextHeadingRule:8 -->Hedgehog</h2> | ||
Hedgehog, with wedgie &lt;&lt;6 10 10 2 -1 -5||, has a period 1/2 octave and a generator which can be taken to be 9/7 instead of 10/9. It also tempers out 245/243, the sensamagic comma. 22et provides the obvious tuning, but if you are looking for an alternative, you could try the &lt;146 232 338 411| val with generator 10/73, or you could try 164 cents if you are fond of round numbers. The 14 note MOS gives scope for harmony while stopping well short of 22.<br /> | Hedgehog, with wedgie &lt;&lt;6 10 10 2 -1 -5||, has a period 1/2 octave and a generator which can be taken to be 9/7 instead of 10/9. It also tempers out 245/243, the sensamagic comma. 22et provides the obvious tuning, but if you are looking for an alternative, you could try the &lt;146 232 338 411| val with generator 10/73, or you could try 164 cents if you are fond of round numbers. The 14 note MOS gives scope for harmony while stopping well short of 22.<br /> | ||
<br /> | <br /> | ||
Revision as of 18:38, 20 February 2011
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author genewardsmith and made on 2011-02-20 18:38:20 UTC.
- The original revision id was 203540390.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
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 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. [[POTE tuning|POTE generator]]: 163.950 Map: [<1 2 3|, <0 -3 -5|] EDOs: 22, 161, 183 ==Seven limit children== The second comma of the [[Normal lists|normal comma list]] defines which 7-limit family member we are looking at. That means 64/63, the Archytas comma, for porcupine, 36/35, the septimal quarter tone, for hystrix, 50/49, the jubilisma, for hedgehog, and 49/48, the slendro diesis, for nautilus. ==Porcupine== Porcupine, with wedgie <<3 5 -6 1 -18 -28||, uses six of its minor tone generator steps to get to 7/4. For this to work you need a small minor tone such as [[22edo]] provides, and once again 3/22 is a good tuning choice, though we might pick in preference 8/59, 11/81, or 19/140 for our generator. Commas: 250/243, 64/63 [[POTE tuning|POTE generator]]: ~10/9 = 162.880 Map: [<1 2 3 2|, <0 -3 -5 6|] EDOs: 22, 59, 81, 140 ===11-limit=== Commas: 55/54, 64/63, 100/99 POTE generator: ~10/9 = 162.747 Map: [<1 2 3 2 4|, <0 -3 -5 6 -4|] EDOs: 7, 15, 22, 37, 59 Badness: 0.0217 ==Hystrix== Hystrix, with wedgie <<3 5 1 1 -7 -12||, provides a less complex avenue to the 7-limit. Unfortunately in temperaments as in life you get what you pay for, and hystrix, for which a generator of 2/15 or 9/68 can be used, is a temperament for the adventurous souls who have probably already tried [[15edo]]. They can try the even sharper fifth of hystrix in [[68edo]] and see how that suits. Commas: 36/35, 160/147 [[POTE tuning|POTE generator]]: 158.868 Map: [<1 2 3 3|, <0 -3 -5 -1|] EDOs: 15, 68 ==Hedgehog== Hedgehog, with wedgie <<6 10 10 2 -1 -5||, has a period 1/2 octave and a generator which can be taken to be 9/7 instead of 10/9. It also tempers out 245/243, the sensamagic comma. 22et provides the obvious tuning, but if you are looking for an alternative, you could try the <146 232 338 411| val with generator 10/73, or you could try 164 cents if you are fond of round numbers. The 14 note MOS gives scope for harmony while stopping well short of 22. Commas: 50/49, 245/243 [[POTE tuning|POTE generator]]: 164.352 Map: [<2 1 1 2|, <0 3 5 5|] EDOs: 22, 146
Original HTML content:
<html><head><title>Porcupine family</title></head><body>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>, and flipping that yields <<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 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.<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 163.950<br /> <br /> Map: [<1 2 3|, <0 -3 -5|]<br /> <br /> EDOs: 22, 161, 183<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-Seven limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->Seven limit children</h2> The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which 7-limit family member we are looking at. That means 64/63, the Archytas comma, for porcupine, 36/35, the septimal quarter tone, for hystrix, 50/49, the jubilisma, for hedgehog, and 49/48, the slendro diesis, for nautilus.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="x-Porcupine"></a><!-- ws:end:WikiTextHeadingRule:2 -->Porcupine</h2> Porcupine, with wedgie <<3 5 -6 1 -18 -28||, uses six of its minor tone generator steps to get to 7/4. For this to work you need a small minor tone such as <a class="wiki_link" href="/22edo">22edo</a> provides, and once again 3/22 is a good tuning choice, though we might pick in preference 8/59, 11/81, or 19/140 for our generator.<br /> <br /> Commas: 250/243, 64/63<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~10/9 = 162.880<br /> <br /> Map: [<1 2 3 2|, <0 -3 -5 6|]<br /> EDOs: 22, 59, 81, 140<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h3> --><h3 id="toc2"><a name="x-Porcupine-11-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->11-limit</h3> Commas: 55/54, 64/63, 100/99<br /> <br /> POTE generator: ~10/9 = 162.747<br /> <br /> Map: [<1 2 3 2 4|, <0 -3 -5 6 -4|]<br /> EDOs: 7, 15, 22, 37, 59<br /> Badness: 0.0217<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="x-Hystrix"></a><!-- ws:end:WikiTextHeadingRule:6 -->Hystrix</h2> Hystrix, with wedgie <<3 5 1 1 -7 -12||, provides a less complex avenue to the 7-limit. Unfortunately in temperaments as in life you get what you pay for, and hystrix, for which a generator of 2/15 or 9/68 can be used, is a temperament for the adventurous souls who have probably already tried <a class="wiki_link" href="/15edo">15edo</a>. They can try the even sharper fifth of hystrix in <a class="wiki_link" href="/68edo">68edo</a> and see how that suits.<br /> <br /> Commas: 36/35, 160/147<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 158.868<br /> <br /> Map: [<1 2 3 3|, <0 -3 -5 -1|]<br /> <br /> EDOs: 15, 68<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h2> --><h2 id="toc4"><a name="x-Hedgehog"></a><!-- ws:end:WikiTextHeadingRule:8 -->Hedgehog</h2> Hedgehog, with wedgie <<6 10 10 2 -1 -5||, has a period 1/2 octave and a generator which can be taken to be 9/7 instead of 10/9. It also tempers out 245/243, the sensamagic comma. 22et provides the obvious tuning, but if you are looking for an alternative, you could try the <146 232 338 411| val with generator 10/73, or you could try 164 cents if you are fond of round numbers. The 14 note MOS gives scope for harmony while stopping well short of 22.<br /> <br /> Commas: 50/49, 245/243<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 164.352<br /> <br /> Map: [<2 1 1 2|, <0 3 5 5|]<br /> <br /> EDOs: 22, 146</body></html>