Hemimean family: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 247439609 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 247450555 - 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:genewardsmith|genewardsmith]] and made on <tt>2011-08-21 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-08-21 17:04:00 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>247450555</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> | ||
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Badness: 0.000160 | Badness: 0.000160 | ||
[[Projection pairs]]: 5 3136/625 7 68841472/9765625 to 2. | [[Projection pairs]]: 5 3136/625 7 68841472/9765625 to 2.3.25/7 | ||
==Belobog== | ==Belobog== | ||
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Badness: 0.000160<br /> | Badness: 0.000160<br /> | ||
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<a class="wiki_link" href="/Projection%20pairs">Projection pairs</a>: 5 3136/625 7 68841472/9765625 to 2. | <a class="wiki_link" href="/Projection%20pairs">Projection pairs</a>: 5 3136/625 7 68841472/9765625 to 2.3.25/7<br /> | ||
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Revision as of 17:04, 21 August 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 2011-08-21 17:04:00 UTC.
- The original revision id was 247450555.
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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 hemimean comma, 3136/3125, is the ratio between the diesis and the tritonic diesis, or jubilisma; that is, (128/125)/(50/49). This is a no-threes comma, with [[Spectrum of a temperament|spectrum]] 5/4, 7/5, 4/3, 6/5, 8/7, 7/6, 9/8, 10/9, 9/7. [[Comma]]: 3136/3125, hemimean 7 and 9 limit minimax [|1 0 0 0>, |0 1 0 0>, |6/5 0 0 2/5>, |0 0 0 1>] [[Eigenmonzo|Eigenmonzos]]: 2, 7/6, 4/3 Lattice basis: 28/25 length 0.5055 3/2 length 1.5849 Angle(28/25, 3/2) = 90 degrees Map to lattice: [<0 0 2 5|, <0 1 0 0|] Map: [<1 0 0 -3|, <0 1 0 0|, <0 0 2 5|] [[Generator|Generators]]: 2, 3, 56/25 [[edo|Edos]]: [[217edo|217]], [[229edo|229]], [[328edo|328]], [[359edo|359]], [[446edo|446]] Badness: 0.000160 [[Projection pairs]]: 5 3136/625 7 68841472/9765625 to 2.3.25/7 ==Belobog== [[Comma|Commas]]: 3136/3125, 441/440 11 limit minimax [|1 0 0 0 0>, |27/22 6/11 -5/22 -3/11 5/22>, |24/11 -4/11 -2/11 2/11 2/11>, |27/11 -10/11 -5/11 5/11 5/11>, |24/11 -4/11 -13/11 2/11 13/11>] [[Eigenmonzo|Eigenmonzos]]: 2, 11/10, 9/7 Lattice basis: 28/25 0.3829 16/15 1.1705 Angle(28/25, 16/15) = 93.2696 Map to lattice: [<0 -2 2 5 4|, <0 -1 0 0 -2|] Map: [<1 0 0 -3 -9|, <0 1 0 0 2|, [0 0 2 5 8|] [[Generator|Generators]]: 2, 3, 56/25 [[edo|Edos]]: 12, 31, 87, 118, 130, 217, [[248edo|248]], [[378edo|378]], [[626edo|626]] Badness: 0.000609 Scales: [[belobog31]] ===13-limit=== Commas: 441/440, 1001/1000, 3136/3125 Map: [<1 0 0 -3 -9 15|, <0 1 0 0 2 -2|, <0 0 2 5 8 -7|] EDOs: 12, 31, 43, 56, 74, 87, 118, 130, 217, 248, 378, 465 Badness: 0.00111 ===Bellowblog=== Commas: 196/195, 352/351, 625/624 Map: [<1 0 0 -3 -9 -4|, <0 1 0 0 2 -1|, <0 0 2 5 8 8|] EDOs: 31, 56, 87, 118 Badness: 0.00126 ==Siebog== [[Comma|Commas]]: 3136/3125, 540/539 11 limit minimax [|1 0 0 0 0>, |0 1 0 0 0>, |8/5 3/5 1/5 0 -1/5>, |1 3/2 1/2 0 -1/2>, |8/5 3/5 -4/5 0 4/5>] [[Eigenmonzo|Eigenmonzos]]: 2, 11/10, 4/3 Map: [<1 0 0 -3 8|, <0 1 0 0 3|, <0 0 2 5 -8|] [[Generator|Generators]]: 2, 3, 768/343 [[edo|Edos]]: 19, 31, 80, 111, [[130edo|130]], [[241edo|241]] Badness: 0.000870
Original HTML content:
<html><head><title>Hemimean family</title></head><body>The hemimean comma, 3136/3125, is the ratio between the diesis and the tritonic diesis, or jubilisma; that is, (128/125)/(50/49). This is a no-threes comma, with <a class="wiki_link" href="/Spectrum%20of%20a%20temperament">spectrum</a> 5/4, 7/5, 4/3, 6/5, 8/7, 7/6, 9/8, 10/9, 9/7.<br /> <br /> <br /> <a class="wiki_link" href="/Comma">Comma</a>: 3136/3125, hemimean<br /> <br /> 7 and 9 limit minimax<br /> [|1 0 0 0>, |0 1 0 0>, |6/5 0 0 2/5>, |0 0 0 1>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 7/6, 4/3<br /> <br /> Lattice basis: 28/25 length 0.5055 3/2 length 1.5849<br /> Angle(28/25, 3/2) = 90 degrees<br /> Map to lattice: [<0 0 2 5|, <0 1 0 0|]<br /> <br /> Map: [<1 0 0 -3|, <0 1 0 0|, <0 0 2 5|] <br /> <a class="wiki_link" href="/Generator">Generators</a>: 2, 3, 56/25<br /> <a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/217edo">217</a>, <a class="wiki_link" href="/229edo">229</a>, <a class="wiki_link" href="/328edo">328</a>, <a class="wiki_link" href="/359edo">359</a>, <a class="wiki_link" href="/446edo">446</a><br /> Badness: 0.000160<br /> <br /> <a class="wiki_link" href="/Projection%20pairs">Projection pairs</a>: 5 3136/625 7 68841472/9765625 to 2.3.25/7<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-Belobog"></a><!-- ws:end:WikiTextHeadingRule:0 -->Belobog</h2> <a class="wiki_link" href="/Comma">Commas</a>: 3136/3125, 441/440<br /> <br /> 11 limit minimax<br /> [|1 0 0 0 0>, |27/22 6/11 -5/22 -3/11 5/22>, <br /> |24/11 -4/11 -2/11 2/11 2/11>, <br /> |27/11 -10/11 -5/11 5/11 5/11>, <br /> |24/11 -4/11 -13/11 2/11 13/11>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 11/10, 9/7<br /> <br /> Lattice basis: 28/25 0.3829 16/15 1.1705<br /> Angle(28/25, 16/15) = 93.2696<br /> Map to lattice: [<0 -2 2 5 4|, <0 -1 0 0 -2|]<br /> <br /> Map: [<1 0 0 -3 -9|, <0 1 0 0 2|, [0 0 2 5 8|]<br /> <a class="wiki_link" href="/Generator">Generators</a>: 2, 3, 56/25<br /> <a class="wiki_link" href="/edo">Edos</a>: 12, 31, 87, 118, 130, 217, <a class="wiki_link" href="/248edo">248</a>, <a class="wiki_link" href="/378edo">378</a>, <a class="wiki_link" href="/626edo">626</a><br /> Badness: 0.000609<br /> <br /> Scales: <a class="wiki_link" href="/belobog31">belobog31</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h3> --><h3 id="toc1"><a name="x-Belobog-13-limit"></a><!-- ws:end:WikiTextHeadingRule:2 -->13-limit</h3> Commas: 441/440, 1001/1000, 3136/3125<br /> <br /> Map: [<1 0 0 -3 -9 15|, <0 1 0 0 2 -2|, <0 0 2 5 8 -7|]<br /> EDOs: 12, 31, 43, 56, 74, 87, 118, 130, 217, 248, 378, 465<br /> Badness: 0.00111<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h3> --><h3 id="toc2"><a name="x-Belobog-Bellowblog"></a><!-- ws:end:WikiTextHeadingRule:4 -->Bellowblog</h3> Commas: 196/195, 352/351, 625/624<br /> <br /> Map: [<1 0 0 -3 -9 -4|, <0 1 0 0 2 -1|, <0 0 2 5 8 8|]<br /> EDOs: 31, 56, 87, 118<br /> Badness: 0.00126<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="x-Siebog"></a><!-- ws:end:WikiTextHeadingRule:6 -->Siebog</h2> <a class="wiki_link" href="/Comma">Commas</a>: 3136/3125, 540/539<br /> <br /> 11 limit minimax<br /> [|1 0 0 0 0>, |0 1 0 0 0>, |8/5 3/5 1/5 0 -1/5>, <br /> |1 3/2 1/2 0 -1/2>, |8/5 3/5 -4/5 0 4/5>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 11/10, 4/3<br /> <br /> Map: [<1 0 0 -3 8|, <0 1 0 0 3|, <0 0 2 5 -8|]<br /> <a class="wiki_link" href="/Generator">Generators</a>: 2, 3, 768/343<br /> <a class="wiki_link" href="/edo">Edos</a>: 19, 31, 80, 111, <a class="wiki_link" href="/130edo">130</a>, <a class="wiki_link" href="/241edo">241</a><br /> Badness: 0.000870</body></html>