Chromatic pairs: Difference between revisions
Wikispaces>genewardsmith **Imported revision 351349780 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 351442572 - 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>2012-07- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-07-08 13:25:07 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>351442572</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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Map: [<1 0 -4 -13|, <0 1 4 10|] | Map: [<1 0 -4 -13|, <0 1 4 10|] | ||
EDOs: 5, 7, 12, 19, 31, 81, 112b, 143b | EDOs: 5, 7, 12, 19, 31, 81, 112b, 143b | ||
[[Lp tuning#L2 tuning|L2 error]]: 2.763 cents | |||
[[image:meantone_31edo.jpg]] | [[image:meantone_31edo.jpg]] | ||
Line 552: | Line 552: | ||
Svalname: 4&15 | Svalname: 4&15 | ||
Related temperaments: starling; becomes myna | Related temperaments: starling; becomes myna | ||
[[Lp tuning|POL2 generator]]: ~6/5 = 311.154 | |||
[[Gencom]]: | [[Gencom]]: [2 6/5; 126/125] | ||
Gencom map: | Gencom map: [<1 -1 0 1|, <0 4/3 1/3 -5/3|] | ||
Map: [<1 0 -1|, <0 1 3|] | Map: [<1 0 -1|, <0 1 3|] | ||
EDOs: 15, 19, 23, 27, 239b, 266b, 293b, 320b, 347b, 374b, 401b | EDOs: 15, 19, 23, 27, 239b, 266b, 293b, 320b, 347b, 374b, 401b | ||
[[Lp tuning#L2 tuning|L2 error]]: 1.680 cents | |||
[[xenharmonic/starlingtet4|Four note haplotonic scale]] | [[xenharmonic/starlingtet4|Four note haplotonic scale]] | ||
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Sval name: 8&33 | Sval name: 8&33 | ||
[[Lp tuning|POL2 generator]]: ~12/11 = 147.010 | |||
[[Gencom]]: | [[Gencom]]: [2 12/11; 3025/3024 3125/3087] | ||
Gencom map: | Gencom map: [<1 -1/2 -1/2 -1/2 3/2|, <0 -15/4 9/4 25/4 -19/4|] | ||
Map: [<1 0 0 2|, <0 6 10 -1|] | Map: [<1 0 0 2|, <0 6 10 -1|] | ||
EDOs: 33, 41, 49, 57, 106, 204, 253 | EDOs: 33, 41, 49, 57, 106, 204, 253 | ||
[[Lp tuning#L2 tuning|L2 error]]: 1.741 cents | |||
[[image:indium_253edo.png]] | [[image:indium_253edo.png]] | ||
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Val name: 19&22 | Val name: 19&22 | ||
[[Lp tuning|POL2 generator]]: ~5/4 = 380.696 | |||
[[Gencom]]: | [[Gencom]]: [2 5/4; 100/99 225/224 245/243] | ||
Gencom map: | Gencom map: [<1 0 2 -1 6|, <0 5 1 12 -8|] | ||
Map: [<1 0 2 -1 6|, <0 5 1 12 -8|] | Map: [<1 0 2 -1 6|, <0 5 1 12 -8|] | ||
EDOs: 19, 22, 41, 104, 145 | EDOs: 19, 22, 41, 104, 145 | ||
[[Lp tuning#L2 tuning|L2 error]]: 2.741 cents | |||
[[image:xenharmonic/magic_145edo.jpg]] | [[image:xenharmonic/magic_145edo.jpg]] | ||
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Svalname: 4&29 | Svalname: 4&29 | ||
[[Lp tuning|POL2 generator]]: ~13/11 = 293.679 | |||
[[Gencom]]: | [[Gencom]]: [2 13/11; 275/273 847/845] | ||
Gencom map: | Gencom map: [<1 0 0 0 0 0|, <0 -8/3 1/3 7/3 -1/2 1/2|] | ||
Map: [<1 0 0 0|, <0 3 5 1|] | Map: [<1 0 0 0|, <0 3 5 1|] | ||
EDOs: 29, 33, 37, 41, 78 | EDOs: 29, 33, 37, 41, 45, 49, 78, 94, 143d, 237bd, 380bd | ||
[[Lp tuning#L2 tuning|L2 error]]: 1.694 cents | |||
[[xenharmonic/gariberttet5|Five note haplotonic scale]] | [[xenharmonic/gariberttet5|Five note haplotonic scale]] | ||
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Related temperament: [[xenharmonic/Breedsmic temperaments|Hemififths]] | Related temperament: [[xenharmonic/Breedsmic temperaments|Hemififths]] | ||
[[Lp tuning|POL2 generator]]: ~11/9 = 351.691 | |||
[[Gencom]]: | [[Gencom]]: [2 11/9; 144/143 243/242 364/363] | ||
Gencom map: | Gencom map: [<1 1 0 -1 2 4|, <0 2 0 13 5 -1|] | ||
Map: [<1 1 -1 2 4|, <0 2 13 5 -1|] | Map: [<1 1 -1 2 4|, <0 2 13 5 -1|] | ||
EDOs: 7, 10, 17, 24, 41, 58 | EDOs: 7, 10, 17, 24, 41, 58 | ||
[[Lp tuning#L2 tuning|L2 error]]: 1.756 cents | |||
[[image:hemif_58edo.jpg]] | [[image:hemif_58edo.jpg]] | ||
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Related temperament: [[xenharmonic/Meantone family|squares]] | Related temperament: [[xenharmonic/Meantone family|squares]] | ||
[[Lp tuning|POL2 generator]]: ~9/7 = 425.244 | |||
[[Gencom]]: | [[Gencom]]: [2 9/7; 99/98 243/242] | ||
Gencom map: | Gencom map: [<1 3 0 6 7|, <0 -4 0 -9 -10|] | ||
Map: [<1 3 6 7|, <0 -4 -9 -10|] | Map: [<1 3 6 7|, <0 -4 -9 -10|] | ||
EDOs: 5, 8, 11, 14, 17, 31, 48, 79, 127, | EDOs: 5, 8, 11, 14, 17, 31, 48, 79, 127, 206bcd | ||
* [[Lp tuning#L2 tuning|L2 error]]: 2.457 cents | |||
[[image:skwares_206edo.png]] | [[image:skwares_206edo.png]] | ||
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Map: [&lt;1 0 -4 -13|, &lt;0 1 4 10|]<br /> | Map: [&lt;1 0 -4 -13|, &lt;0 1 4 10|]<br /> | ||
EDOs: 5, 7, 12, 19, 31, 81, 112b, 143b<br /> | EDOs: 5, 7, 12, 19, 31, 81, 112b, 143b<br /> | ||
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 2.763 cents<br /> | |||
<br /> | |||
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<br /> | <br /> | ||
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Svalname: 4&amp;15<br /> | Svalname: 4&amp;15<br /> | ||
Related temperaments: starling; becomes myna<br /> | Related temperaments: starling; becomes myna<br /> | ||
<a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~6/5 = 311.154<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/Gencom">Gencom</a>:<br /> | <a class="wiki_link" href="/Gencom">Gencom</a>: [2 6/5; 126/125]<br /> | ||
Gencom map:<br /> | Gencom map: [&lt;1 -1 0 1|, &lt;0 4/3 1/3 -5/3|]<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 -1|, &lt;0 1 3|]<br /> | Map: [&lt;1 0 -1|, &lt;0 1 3|]<br /> | ||
EDOs: 15, 19, 23, 27, 239b, 266b, 293b, 320b, 347b, 374b, 401b<br /> | EDOs: 15, 19, 23, 27, 239b, 266b, 293b, 320b, 347b, 374b, 401b<br /> | ||
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1.680 cents<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/starlingtet4">Four note haplotonic scale</a><br /> | <a class="wiki_link" href="http://xenharmonic.wikispaces.com/starlingtet4">Four note haplotonic scale</a><br /> | ||
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Sval name: 8&amp;33<br /> | Sval name: 8&amp;33<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~12/11 = 147.010<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/Gencom">Gencom</a>:<br /> | <a class="wiki_link" href="/Gencom">Gencom</a>: [2 12/11; 3025/3024 3125/3087]<br /> | ||
Gencom map:<br /> | Gencom map: [&lt;1 -1/2 -1/2 -1/2 3/2|, &lt;0 -15/4 9/4 25/4 -19/4|]<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 0 2|, &lt;0 6 10 -1|]<br /> | Map: [&lt;1 0 0 2|, &lt;0 6 10 -1|]<br /> | ||
EDOs: 33, 41, 49, 57, 106, 204, 253<br /> | EDOs: 33, 41, 49, 57, 106, 204, 253<br /> | ||
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1.741 cents<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule:214:&lt;img src=&quot;/file/view/indium_253edo.png/284867050/indium_253edo.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/indium_253edo.png/284867050/indium_253edo.png" alt="indium_253edo.png" title="indium_253edo.png" /><!-- ws:end:WikiTextLocalImageRule:214 --><br /> | <!-- ws:start:WikiTextLocalImageRule:214:&lt;img src=&quot;/file/view/indium_253edo.png/284867050/indium_253edo.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/indium_253edo.png/284867050/indium_253edo.png" alt="indium_253edo.png" title="indium_253edo.png" /><!-- ws:end:WikiTextLocalImageRule:214 --><br /> | ||
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Val name: 19&amp;22<br /> | Val name: 19&amp;22<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~5/4 = 380.696<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/Gencom">Gencom</a>:<br /> | <a class="wiki_link" href="/Gencom">Gencom</a>: [2 5/4; 100/99 225/224 245/243]<br /> | ||
Gencom map:<br /> | Gencom map: [&lt;1 0 2 -1 6|, &lt;0 5 1 12 -8|]<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 2 -1 6|, &lt;0 5 1 12 -8|]<br /> | Map: [&lt;1 0 2 -1 6|, &lt;0 5 1 12 -8|]<br /> | ||
EDOs: 19, 22, 41, 104, 145<br /> | EDOs: 19, 22, 41, 104, 145<br /> | ||
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 2.741 cents<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule:215:&lt;img src=&quot;http://xenharmonic.wikispaces.com/file/view/magic_145edo.jpg/270820174/magic_145edo.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://xenharmonic.wikispaces.com/file/view/magic_145edo.jpg/270820174/magic_145edo.jpg" alt="magic_145edo.jpg" title="magic_145edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:215 --><br /> | <!-- ws:start:WikiTextLocalImageRule:215:&lt;img src=&quot;http://xenharmonic.wikispaces.com/file/view/magic_145edo.jpg/270820174/magic_145edo.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://xenharmonic.wikispaces.com/file/view/magic_145edo.jpg/270820174/magic_145edo.jpg" alt="magic_145edo.jpg" title="magic_145edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:215 --><br /> | ||
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Svalname: 4&amp;29<br /> | Svalname: 4&amp;29<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~13/11 = 293.679<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/Gencom">Gencom</a>:<br /> | <a class="wiki_link" href="/Gencom">Gencom</a>: [2 13/11; 275/273 847/845]<br /> | ||
Gencom map:<br /> | Gencom map: [&lt;1 0 0 0 0 0|, &lt;0 -8/3 1/3 7/3 -1/2 1/2|]<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 0 0|, &lt;0 3 5 1|]<br /> | Map: [&lt;1 0 0 0|, &lt;0 3 5 1|]<br /> | ||
EDOs: 29, 33, 37, 41, 78<br /> | EDOs: 29, 33, 37, 41, 45, 49, 78, 94, 143d, 237bd, 380bd<br /> | ||
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1.694 cents<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/gariberttet5">Five note haplotonic scale</a><br /> | <a class="wiki_link" href="http://xenharmonic.wikispaces.com/gariberttet5">Five note haplotonic scale</a><br /> | ||
Line 1,716: | Line 1,717: | ||
Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Breedsmic%20temperaments">Hemififths</a><br /> | Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Breedsmic%20temperaments">Hemififths</a><br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~11/9 = 351.691<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/Gencom">Gencom</a>:<br /> | <a class="wiki_link" href="/Gencom">Gencom</a>: [2 11/9; 144/143 243/242 364/363]<br /> | ||
Gencom map:<br /> | Gencom map: [&lt;1 1 0 -1 2 4|, &lt;0 2 0 13 5 -1|]<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 1 -1 2 4|, &lt;0 2 13 5 -1|]<br /> | Map: [&lt;1 1 -1 2 4|, &lt;0 2 13 5 -1|]<br /> | ||
EDOs: 7, 10, 17, 24, 41, 58<br /> | EDOs: 7, 10, 17, 24, 41, 58<br /> | ||
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1.756 cents<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule:216:&lt;img src=&quot;/file/view/hemif_58edo.jpg/272176886/hemif_58edo.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/hemif_58edo.jpg/272176886/hemif_58edo.jpg" alt="hemif_58edo.jpg" title="hemif_58edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:216 --><br /> | <!-- ws:start:WikiTextLocalImageRule:216:&lt;img src=&quot;/file/view/hemif_58edo.jpg/272176886/hemif_58edo.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/hemif_58edo.jpg/272176886/hemif_58edo.jpg" alt="hemif_58edo.jpg" title="hemif_58edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:216 --><br /> | ||
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Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Meantone%20family">squares</a><br /> | Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Meantone%20family">squares</a><br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~9/7 = 425.244<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/Gencom">Gencom</a>:<br /> | <a class="wiki_link" href="/Gencom">Gencom</a>: [2 9/7; 99/98 243/242]<br /> | ||
Gencom map:<br /> | Gencom map: [&lt;1 3 0 6 7|, &lt;0 -4 0 -9 -10|]<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 3 6 7|, &lt;0 -4 -9 -10|]<br /> | Map: [&lt;1 3 6 7|, &lt;0 -4 -9 -10|]<br /> | ||
EDOs: 5, 8, 11, 14, 17, 31, 48, 79, 127, | EDOs: 5, 8, 11, 14, 17, 31, 48, 79, 127, 206bcd<br /> | ||
<ul><li><a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 2.457 cents</li></ul><br /> | |||
<br /> | |||
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<br /> | <br /> |