Magic family: Difference between revisions
Jump to navigation
Jump to search
Wikispaces>xenwolf **Imported revision 179391683 - Original comment: links added** |
Wikispaces>genewardsmith **Imported revision 187194121 - 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: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-12-10 14:35:25 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>187194121</tt>.<br> | ||
: The revision comment was: <tt> | : 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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
| Line 35: | Line 35: | ||
[|1 0 0 0>, |0 1 0 0>, |2 1/5 0 0>, |-1 12/5 0 0>] | [|1 0 0 0>, |0 1 0 0>, |2 1/5 0 0>, |-1 12/5 0 0>] | ||
[[Eigenmonzo|Eigenmonzos]]: 2, 3 | [[Eigenmonzo|Eigenmonzos]]: 2, 3 | ||
[[POTE tuning|POTE generator]]: 380.352 | |||
Algebraic generators: Tirzbirat or Septimage, the real root of 5x^5+4x-20, 380.7604 cents. | Algebraic generators: Tirzbirat or Septimage, the real root of 5x^5+4x-20, 380.7604 cents. | ||
| Line 40: | Line 42: | ||
Map: [<1 0 2 -1|, <0 5 1 12|] | Map: [<1 0 2 -1|, <0 5 1 12|] | ||
[[Generator|Generators]]: 2, 5/4 | [[Generator|Generators]]: 2, 5/4 | ||
EDOs: 41, 183, 224 | |||
===Muggles=== | ===Muggles=== | ||
Aside from 3125/3072 and 525/512 muggles also tempers out 126/125 and 1323/1280. A good muggles tuning is [[19edo]], in which tuning it's the same thing as magic. Muggles works better for small scales than magic in the sense that 7 or 10 note MOS are reasonable choices. The muggles wedgie is <<5 1 -7 -10 -25 -19||.</pre></div> | Aside from 3125/3072 and 525/512 muggles also tempers out 126/125 and 1323/1280. A good muggles tuning is [[19edo]], in which tuning it's the same thing as magic. Muggles works better for small scales than magic in the sense that 7 or 10 note MOS are reasonable choices. The muggles wedgie is <<5 1 -7 -10 -25 -19||. | ||
Commas: 126/125, 525/512 | |||
[[POTE tuning|POTE generator]]: 378.479 | |||
Map: [<1 0 2 5|, <0 5 1 -7|] | |||
EDOs: 19, 130</pre></div> | |||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Magic family</title></head><body>The 5-limit parent comma for the magic family is 3125/3072, the small diesis or magic comma. Its monzo is |-10 -1 5&gt;, and flipping that yields &lt;&lt;5 1 -10|| for the wedgie. This tells us the generator is a major third, and that to get to the interval class of fifths will require five of these. In fact, (5/4)^5 = 3 * 3125/3072. 13/41 is a highly recommendable generator, though 19/60 also makes sense and using <a class="wiki_link" href="/19edo">19edo</a> or <a class="wiki_link" href="/22edo">22edo</a> is always possible.<br /> | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Magic family</title></head><body>The 5-limit parent comma for the magic family is 3125/3072, the small diesis or magic comma. Its monzo is |-10 -1 5&gt;, and flipping that yields &lt;&lt;5 1 -10|| for the wedgie. This tells us the generator is a major third, and that to get to the interval class of fifths will require five of these. In fact, (5/4)^5 = 3 * 3125/3072. 13/41 is a highly recommendable generator, though 19/60 also makes sense and using <a class="wiki_link" href="/19edo">19edo</a> or <a class="wiki_link" href="/22edo">22edo</a> is always possible.<br /> | ||
| Line 73: | Line 85: | ||
[|1 0 0 0&gt;, |0 1 0 0&gt;, |2 1/5 0 0&gt;, |-1 12/5 0 0&gt;]<br /> | [|1 0 0 0&gt;, |0 1 0 0&gt;, |2 1/5 0 0&gt;, |-1 12/5 0 0&gt;]<br /> | ||
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 3<br /> | <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 3<br /> | ||
<br /> | |||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 380.352<br /> | |||
<br /> | <br /> | ||
Algebraic generators: Tirzbirat or Septimage, the real root of 5x^5+4x-20, 380.7604 cents.<br /> | Algebraic generators: Tirzbirat or Septimage, the real root of 5x^5+4x-20, 380.7604 cents.<br /> | ||
| Line 78: | Line 92: | ||
Map: [&lt;1 0 2 -1|, &lt;0 5 1 12|]<br /> | Map: [&lt;1 0 2 -1|, &lt;0 5 1 12|]<br /> | ||
<a class="wiki_link" href="/Generator">Generators</a>: 2, 5/4<br /> | <a class="wiki_link" href="/Generator">Generators</a>: 2, 5/4<br /> | ||
<br /> | |||
EDOs: 41, 183, 224<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x-Seven limit children-Muggles"></a><!-- ws:end:WikiTextHeadingRule:4 -->Muggles</h3> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x-Seven limit children-Muggles"></a><!-- ws:end:WikiTextHeadingRule:4 -->Muggles</h3> | ||
Aside from 3125/3072 and 525/512 muggles also tempers out 126/125 and 1323/1280. A good muggles tuning is <a class="wiki_link" href="/19edo">19edo</a>, in which tuning it's the same thing as magic. Muggles works better for small scales than magic in the sense that 7 or 10 note MOS are reasonable choices. The muggles wedgie is &lt;&lt;5 1 -7 -10 -25 -19||.</body></html></pre></div> | Aside from 3125/3072 and 525/512 muggles also tempers out 126/125 and 1323/1280. A good muggles tuning is <a class="wiki_link" href="/19edo">19edo</a>, in which tuning it's the same thing as magic. Muggles works better for small scales than magic in the sense that 7 or 10 note MOS are reasonable choices. The muggles wedgie is &lt;&lt;5 1 -7 -10 -25 -19||.<br /> | ||
<br /> | |||
Commas: 126/125, 525/512<br /> | |||
<br /> | |||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 378.479<br /> | |||
<br /> | |||
Map: [&lt;1 0 2 5|, &lt;0 5 1 -7|]<br /> | |||
<br /> | |||
EDOs: 19, 130</body></html></pre></div> | |||
Revision as of 14:35, 10 December 2010
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 2010-12-10 14:35:25 UTC.
- The original revision id was 187194121.
- 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 magic family is 3125/3072, the small diesis or magic comma. Its monzo is |-10 -1 5>, and flipping that yields <<5 1 -10|| for the wedgie. This tells us the generator is a major third, and that to get to the interval class of fifths will require five of these. In fact, (5/4)^5 = 3 * 3125/3072. 13/41 is a highly recommendable generator, though 19/60 also makes sense and using [[19edo]] or [[22edo]] is always possible. [[Comma]]: 3125/3072 5-limit minimax [<1 0 0|, <0 1 0|, <2 1/5 0|] [[Eigenmonzo|Eigenmonzos]]: 2, 3 Algebraic generator: Terzbirat, the positive root of 9x^2-8x-4 = (4+2*sqrt(13))/9; approximately 380.3175 [[Cent|cents]]. Map: [<1 0 2|, <0 5 1|] [[Generator|Generators]]: 2, 5/4 [[Edo|Edos]]: [[6edo|6]], [[16edo|16]], [[19edo|19]], [[22edo|22]], [[41edo|41]], [[60edo|60]] ==Seven limit children== The second comma of the [[Normal lists|normal comma list]] defines which 7-limit family member we are looking at. 875/864, the keemic comma, gives magic, and 525/512, Avicenna's enharmonic diesis, gives his annoying brother muggles. Both use the major third as a generator. ===Magic=== Magic tempers out not only 3125/3072 and 875/864, but also 225/224, 245/243, and 10976/10935. [[41edo]] is a good magic tuning, and 19 or 22 note MOS are possible scales. Five major thirds approximate 3/1. Twelve major thirds, less an octave, approximate 7/1. Magic, with its accurate fifths, works well with 9-limit harmony. It's more accurate than meantone and simpler than garibaldi. It's a little tricky to work with because in it fifths are a relatively complex interval and it doesn't naturally work with scales of around seven notes to the octave. Its wedgie is <<5 1 12 -10 5 25||. By adding 100/99 to the list of commas, magic can be extended to an 11-limit version, <<5 1 12 -8 ... ||. For this, [[104edo]] provides an excellent tuning, as it does also for the rank three temperaments tempering out 100/99 with 225/224, 245/243 or 875/864. Septimage (see below) is also an excellent 11-limit magic tuning. Commas: 225/224, 245/243 7 and 9 limit minimax [|1 0 0 0>, |0 1 0 0>, |2 1/5 0 0>, |-1 12/5 0 0>] [[Eigenmonzo|Eigenmonzos]]: 2, 3 [[POTE tuning|POTE generator]]: 380.352 Algebraic generators: Tirzbirat or Septimage, the real root of 5x^5+4x-20, 380.7604 cents. Map: [<1 0 2 -1|, <0 5 1 12|] [[Generator|Generators]]: 2, 5/4 EDOs: 41, 183, 224 ===Muggles=== Aside from 3125/3072 and 525/512 muggles also tempers out 126/125 and 1323/1280. A good muggles tuning is [[19edo]], in which tuning it's the same thing as magic. Muggles works better for small scales than magic in the sense that 7 or 10 note MOS are reasonable choices. The muggles wedgie is <<5 1 -7 -10 -25 -19||. Commas: 126/125, 525/512 [[POTE tuning|POTE generator]]: 378.479 Map: [<1 0 2 5|, <0 5 1 -7|] EDOs: 19, 130
Original HTML content:
<html><head><title>Magic family</title></head><body>The 5-limit parent comma for the magic family is 3125/3072, the small diesis or magic comma. Its monzo is |-10 -1 5>, and flipping that yields <<5 1 -10|| for the wedgie. This tells us the generator is a major third, and that to get to the interval class of fifths will require five of these. In fact, (5/4)^5 = 3 * 3125/3072. 13/41 is a highly recommendable generator, though 19/60 also makes sense and using <a class="wiki_link" href="/19edo">19edo</a> or <a class="wiki_link" href="/22edo">22edo</a> is always possible.<br /> <br /> <a class="wiki_link" href="/Comma">Comma</a>: 3125/3072<br /> <br /> 5-limit minimax<br /> [<1 0 0|, <0 1 0|, <2 1/5 0|]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 3<br /> <br /> Algebraic generator: Terzbirat, the positive root of 9x^2-8x-4 = (4+2*sqrt(13))/9; approximately 380.3175 <a class="wiki_link" href="/Cent">cents</a>.<br /> <br /> Map: [<1 0 2|, <0 5 1|]<br /> <a class="wiki_link" href="/Generator">Generators</a>: 2, 5/4<br /> <a class="wiki_link" href="/Edo">Edos</a>: <a class="wiki_link" href="/6edo">6</a>, <a class="wiki_link" href="/16edo">16</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/22edo">22</a>, <a class="wiki_link" href="/41edo">41</a>, <a class="wiki_link" href="/60edo">60</a><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. 875/864, the keemic comma, gives magic, and 525/512, Avicenna's enharmonic diesis, gives his annoying brother muggles. Both use the major third as a generator.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h3> --><h3 id="toc1"><a name="x-Seven limit children-Magic"></a><!-- ws:end:WikiTextHeadingRule:2 -->Magic</h3> Magic tempers out not only 3125/3072 and 875/864, but also 225/224, 245/243, and 10976/10935. <a class="wiki_link" href="/41edo">41edo</a> is a good magic tuning, and 19 or 22 note MOS are possible scales. Five major thirds approximate 3/1. Twelve major thirds, less an octave, approximate 7/1.<br /> <br /> Magic, with its accurate fifths, works well with 9-limit harmony. It's more accurate than meantone and simpler than garibaldi. It's a little tricky to work with because in it fifths are a relatively complex interval and it doesn't naturally work with scales of around seven notes to the octave. Its wedgie is <<5 1 12 -10 5 25||.<br /> <br /> By adding 100/99 to the list of commas, magic can be extended to an 11-limit version, <<5 1 12 -8 ... ||. For this, <a class="wiki_link" href="/104edo">104edo</a> provides an excellent tuning, as it does also for the rank three temperaments tempering out 100/99 with 225/224, 245/243 or 875/864. Septimage (see below) is also an excellent 11-limit magic tuning.<br /> <br /> Commas: 225/224, 245/243<br /> <br /> 7 and 9 limit minimax<br /> [|1 0 0 0>, |0 1 0 0>, |2 1/5 0 0>, |-1 12/5 0 0>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 3<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 380.352<br /> <br /> Algebraic generators: Tirzbirat or Septimage, the real root of 5x^5+4x-20, 380.7604 cents.<br /> <br /> Map: [<1 0 2 -1|, <0 5 1 12|]<br /> <a class="wiki_link" href="/Generator">Generators</a>: 2, 5/4<br /> <br /> EDOs: 41, 183, 224<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h3> --><h3 id="toc2"><a name="x-Seven limit children-Muggles"></a><!-- ws:end:WikiTextHeadingRule:4 -->Muggles</h3> Aside from 3125/3072 and 525/512 muggles also tempers out 126/125 and 1323/1280. A good muggles tuning is <a class="wiki_link" href="/19edo">19edo</a>, in which tuning it's the same thing as magic. Muggles works better for small scales than magic in the sense that 7 or 10 note MOS are reasonable choices. The muggles wedgie is <<5 1 -7 -10 -25 -19||.<br /> <br /> Commas: 126/125, 525/512<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 378.479<br /> <br /> Map: [<1 0 2 5|, <0 5 1 -7|]<br /> <br /> EDOs: 19, 130</body></html>