Subgroup temperaments: Difference between revisions
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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>2012-07-12 13:00:35 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>352834442</tt>.<br> | ||
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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.<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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Revision as of 13:00, 12 July 2012
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
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[[toc|flat]] Below are some subgroups and temperaments for them. Obviously, no attempt has been made at completeness; attention is focused on subgroups containing interesting chords. The reader may also want to consult the page on [[Chromatic pairs]]. =2.3.7= ==[[Semaphore and Godzilla|Semaphore]]== Comma: 49/48 [[Lp tuning|POL2 generator]]: ~8/7~7/6 = 250.385 [[Gencom]]: [2 8/7; 49/48] Gencom mapping: [<1 2 0 3|, <0 -2 0 -1|] Map: [<1 2 3|, <0 -2 -1|] EDOs: 5, 14, 19, 24, 67c, 91c [[Lp tuning#L2 tuning|L2 error]]: 5.046 cents ==Archy== Archy can be thought of as "no-5's [[dominant]]" or "no-5's [[superpyth]]". The name comes from the fact that it tempers out 64/63, the Archytas comma. Comma: 64/63 [[Lp tuning|POL2 generator]]: ~3/2 = 709.321 Gencom: [2 3/2; 64/63] Gencom mapping: [<1 1 0 4|, <0 1 0 -2|] Map: [<1 2 2|, <0 -1 2|] EDOs: 5, 12, 17, 22, 27, 137bc [[Lp tuning#L2 tuning|L2 error]]: 3.713 cents ==[[Slendric]]== Comma: 1029/1024 [[Lp tuning|POL2 generator]]: ~8/7 = 233.688 Gencom: [2 8/7; 1029/1024] Gencom mapping: [<1 1 0 3|, <0 3 0 -1|] Map: [<1 1 3|, <0 3 -1|] EDOs: 5, 21, 26, 31, 36, 77, 113, 190 [[Lp tuning#L2 tuning|L2 error]]: 0.6403 cents =2.3.11= ==Neutraltet== Neutraltet can be thought of as 2.3.11 version of either [[mohajira]] or [[maqamic]], and is the temperament optimizing the [[neutral tetrad]]. Comma: 243/242 [[Lp tuning|POL2 generator]]: ~11/9 = 350.525 Gencom: [2 11/9; 243/242] Gencom mapping: [<1 1 0 0 2|, <0 2 0 0 5|] Map: [<1 1 2|, <0 2 5|] EDOs: 7, 10, 17, 24, 41, 65, 89, 202, 291, 380 [[Lp tuning#L2 tuning|L2 error]]: 0.6756 cents [[xenharmonic/neutraltet7|Seven note albitonic scale]] [[xenharmonic/neutraltet10|Ten note chromatic scale]] [[xenharmonic/neutraltet17|Seventeen note mega chromatic scale]] =2.3.5.11= ==Porkypine== Commas: 55/54, 100/99 [[Lp tuning|POL2 generator]]: ~10/9 = 164.078 Gencom: [2 10/9; 55/54, 100/99] Gencom mapping: [<1 2 3 0 4|, <0 -3 -5 0 -4|] Map: [<1 2 3 4|, <0 -3 -5 -4|] EDOs: 7, 15, 22, 37, 73cd, 95cd, 117bcd [[Lp tuning#L2 tuning|L2 error]]: 5.114 cents ==Mohaha== Commas: 81/80, 121/120 [[Lp tuning|POL2 generator]]: ~11/9 = 348.094 Gencom: [2 11/9; 81/80 121/120] Gencom mapping: [<1 1 0 0 2|, <0 2 8 0 5|] Map: [<1 1 0 2|, <0 2 8 5|] EDOs: 7, 10, 17, 24, 31, 69d, 100d, 131bd [[Lp tuning#L2 tuning|L2 error]]: 3.113 cents ===Music=== [[http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/mohaha10ping2.mp3|Mohaha10ping2]] by [[Billy Stiltner]] =2.3.7.11= ==Ennea== Commas: 41503/41472, 43923/43904 [[Lp tuning|POL2 generator]]: ~99/98 = 17.6258 Gencom: [2 99/98; 41503/41472, 43923/43904] Gencom mapping: [<1 14/9 0 25/9 31/9|, <0 2 0 2 1|] Sval map: [<9 0 11 24|, <0 2 2 1|] EDOs: 54, 63, 68, 72, 135, 342, 477, 525, 613, 681, 749, 817, 2159bcd, 3336bcd, 4153bcd [[Lp tuning#L2 tuning|L2 error]]: 0.0857 cents ==Supra== Commas: 64/63, 99/98 [[POTE tuning|POTE generator]]: ~3/2 = 707.192 Gencom: [2 3/2; 64/63 99/98] Gencom mapping: [<1 1 0 4 7|, <0 1 0 -2 -6|] Sval map: [<1 0 6 13|, <0 1 -2 -6|] EDOs: 5, 12, 17, 39c, 56c [[Lp tuning#L2 tuning|L2 error]]: 4.421 cents ==Skwares== Commas: 99/98, 243/242 [[POTE tuning|POTE generator]]: ~9/7 = 425.244 Gencom: [2 9/7; 99/98 243/242] Gencom mapping: [<1 3 0 6 7|, <0 -4 0 -9 -10]] Sval map: [<1 3 6 7|, <0 -4 -9 -10|] EDOs: 14, 17, 31, 48, 79, 127, 206bcd [[Lp tuning#L2 tuning|L2 error]]: 2.457 cents ==Hemif== Commas: 243/242, 896/891 POTE generator: ~11/9 = 351.535 Gencom: [2 11/9; 243/242 896/891] Gencom mapping: [<1 1 0 -1 2|, <0 2 0 13 5|] Sval map: [<1 1 -1 2|, <0 2 13 5|] EDOs: 7, 17, 41, 58, 99d [[Lp tuning#L2 tuning|L2 error]]: 1.366 cents =2.5.7.11= ==Larry== Commas: 243/242, 4000/3993 Related temperaments: [[Gravity family#Gravity|gravity]], [[Gravity family#Harry|harry]] POTE generator: ~40/27 = 683.166 Gencom: [2 40/27; 243/242 4000/3993] Gencom mapping: [<1 5 12 0 12|, <0 -6 -17 0 -15|] Map: [<1 5 12 12|, <0 -6 -17 -15|] EDOs: 7, 58, 65, 137, 202 [[Lp tuning#L2 tuning|L2 error]]: 0.6765 cents =2.9.7.11= ==Machine== Commas: 64/63, 99/98 [[POTE tuning|POTE generator]]: ~8/7 = 214.384 Gencom: [2 8/7; 64/63 99/98] Gencom mapping: [<1 3/2 0 3 4|, <0 1/2 0 -1 -3|] [[Smonzos and Svals|Sval map]]: [<1 0 6 13|, <0 1 -1 -3|] EDOs: 5, 6, 11, 17, 28 [[Lp tuning#L2 tuning|L2 error]]: 4.421 cents ==Apparatus== Commas: 41503/41472, 322102/321489 [[POTE tuning|POTE generator]]: ~77/72 = 115.570 Gencom: [2 77/72; 41503/41472 322102/321489] Gencom mapping: [<1 5/2 0 3 5|, <0 -19/2 0 -2 -16|] [[Smonzos and Svals|Sval map]]: [<1 5 3 5|, <0 -19 -2 -16|] EDOs: 10, 21, 31, 52, 83, 135, 353, 488, 623 [[Lp tuning#L2 tuning|L2 error]]: 0.1505 cents ==Mechanism== Commas: 896/891, 26411/26244 [[POTE tuning|POTE generator]]: ~9/7 = 438.465 Gencom: [2 9/7; 896/891 26411/26244] Gencom mapping: [<1 5/2 0 5 2|, <0 -5/2 0 -6 4|] [[Smonzos and Svals|Sval map]]: [<1 5 5 2|, <0 -5 -6 4|] EDOs: 8, 11, 30, 41, 52 [[Lp tuning#L2 tuning|L2 error]]: 0.9531 cents =2.9.15.7.11.13= ==Stacks (aka 2magic)== Commas: 100/99, 105/104, 144/143, 196/195 [[Lp tuning|POL2 generator]]: ~9/7 = 438.977 Gencom: [2 9/7; 100/99 105/104 144/143 196/195] Gencom mapping: [<1 5/2 5/2 5 2 7|, <0 -5/2 -1/2 -6 4 -9|] Sval map: [<1 0 2 -1 6 -2|, <0 5 3 6 -4 9|] EDOs: 11, 30, 41, 153cdef, 194cdef, 235cdef [[Lp tuning#L2 tuning|L2 error]]: 3.772 cents ===2.9.15.7.11 stacks=== Commas: 100/99, 225/224, 245/243 [[Lp tuning|POL2 generator]]: ~9/7 = 438.607 Gencom: [2 9/7; 100/99 225/224 245/243] Gencom mapping: [<1 5/2 5/2 5 2|, <0 -5/2 -1/2 -6 4|] Sval map: [<1 0 2 -1 6|, <0 5 3 6 -4|] EDOs: 8, 11, 30, 41, 52, 93, 145, 342bce, [[Lp tuning#L2 tuning|L2 error]]: 2.741 cents ===2.9.15.7 stacks=== Commas: 225/224, 245/243 [[Lp tuning|POL2 generator]]: ~9/7 = 439.296 Gencom: [2 9/7; 225/224 245/243] Gencom mapping: [<1 5/2 5/2 5|, <0 -5/2 -1/2 -6|] Sval map: [<1 0 2 -1|, <0 5 3 6|] EDOs: 8, 11, 30, 41, 71, 93, 112c, 134c, 175c [[Lp tuning#L2 tuning|L2 error]]: 2.149 cents =2.9.21= ==A-team== Commas: 1029/1024 [[Lp tuning|POL2 generator]]: ~21/16 = 467.375 Gencom: [2 21/16; 1029/1024] Gencom mapping: [<1 1 0 3|, <0 3/2 0 -1/2|] Sval map: [<1 2 4|, <0 3 1|] EDOs: 5, 13, 18, 41, 59, 77, 95 [[Lp tuning#L2 tuning|L2 error]]: 0.6403
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<html><head><title>Subgroup temperaments</title></head><body><!-- ws:start:WikiTextTocRule:54:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --><a href="#x2.3.7">2.3.7</a><!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --> | <a href="#x2.3.11">2.3.11</a><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --> | <a href="#x2.3.5.11">2.3.5.11</a><!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --><!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --><!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: --><!-- ws:end:WikiTextTocRule:64 --><!-- ws:start:WikiTextTocRule:65: --> | <a href="#x2.3.7.11">2.3.7.11</a><!-- ws:end:WikiTextTocRule:65 --><!-- ws:start:WikiTextTocRule:66: --><!-- ws:end:WikiTextTocRule:66 --><!-- ws:start:WikiTextTocRule:67: --><!-- ws:end:WikiTextTocRule:67 --><!-- ws:start:WikiTextTocRule:68: --><!-- ws:end:WikiTextTocRule:68 --><!-- ws:start:WikiTextTocRule:69: --><!-- ws:end:WikiTextTocRule:69 --><!-- ws:start:WikiTextTocRule:70: --> | <a href="#x2.5.7.11">2.5.7.11</a><!-- ws:end:WikiTextTocRule:70 --><!-- ws:start:WikiTextTocRule:71: --><!-- ws:end:WikiTextTocRule:71 --><!-- ws:start:WikiTextTocRule:72: --> | <a href="#x2.9.7.11">2.9.7.11</a><!-- ws:end:WikiTextTocRule:72 --><!-- ws:start:WikiTextTocRule:73: --><!-- ws:end:WikiTextTocRule:73 --><!-- ws:start:WikiTextTocRule:74: --><!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --><!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --> | <a href="#x2.9.15.7.11.13">2.9.15.7.11.13</a><!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --><!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --><!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --><!-- ws:end:WikiTextTocRule:79 --><!-- ws:start:WikiTextTocRule:80: --> | <a href="#x2.9.21">2.9.21</a><!-- ws:end:WikiTextTocRule:80 --><!-- ws:start:WikiTextTocRule:81: --><!-- ws:end:WikiTextTocRule:81 --><!-- ws:start:WikiTextTocRule:82: --> <!-- ws:end:WikiTextTocRule:82 -->Below are some subgroups and temperaments for them. Obviously, no attempt has been made at completeness; attention is focused on subgroups containing interesting chords. The reader may also want to consult the page on <a class="wiki_link" href="/Chromatic%20pairs">Chromatic pairs</a>.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="x2.3.7"></a><!-- ws:end:WikiTextHeadingRule:0 -->2.3.7</h1> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="x2.3.7-Semaphore"></a><!-- ws:end:WikiTextHeadingRule:2 --><a class="wiki_link" href="/Semaphore%20and%20Godzilla">Semaphore</a></h2> Comma: 49/48<br /> <br /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~8/7~7/6 = 250.385<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 8/7; 49/48]<br /> Gencom mapping: [<1 2 0 3|, <0 -2 0 -1|]<br /> <br /> Map: [<1 2 3|, <0 -2 -1|]<br /> EDOs: 5, 14, 19, 24, 67c, 91c<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 5.046 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="x2.3.7-Archy"></a><!-- ws:end:WikiTextHeadingRule:4 -->Archy</h2> Archy can be thought of as "no-5's <a class="wiki_link" href="/dominant">dominant</a>" or "no-5's <a class="wiki_link" href="/superpyth">superpyth</a>". The name comes from the fact that it tempers out 64/63, the Archytas comma.<br /> <br /> Comma: 64/63<br /> <br /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~3/2 = 709.321<br /> <br /> Gencom: [2 3/2; 64/63]<br /> Gencom mapping: [<1 1 0 4|, <0 1 0 -2|]<br /> <br /> Map: [<1 2 2|, <0 -1 2|]<br /> EDOs: 5, 12, 17, 22, 27, 137bc<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 3.713 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="x2.3.7-Slendric"></a><!-- ws:end:WikiTextHeadingRule:6 --><a class="wiki_link" href="/Slendric">Slendric</a></h2> Comma: 1029/1024<br /> <br /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~8/7 = 233.688<br /> <br /> Gencom: [2 8/7; 1029/1024]<br /> Gencom mapping: [<1 1 0 3|, <0 3 0 -1|]<br /> <br /> Map: [<1 1 3|, <0 3 -1|]<br /> EDOs: 5, 21, 26, 31, 36, 77, 113, 190<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.6403 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h1> --><h1 id="toc4"><a name="x2.3.11"></a><!-- ws:end:WikiTextHeadingRule:8 -->2.3.11</h1> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="x2.3.11-Neutraltet"></a><!-- ws:end:WikiTextHeadingRule:10 -->Neutraltet</h2> Neutraltet can be thought of as 2.3.11 version of either <a class="wiki_link" href="/mohajira">mohajira</a> or <a class="wiki_link" href="/maqamic">maqamic</a>, and is the temperament optimizing the <a class="wiki_link" href="/neutral%20tetrad">neutral tetrad</a>.<br /> <br /> Comma: 243/242<br /> <br /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~11/9 = 350.525<br /> <br /> Gencom: [2 11/9; 243/242]<br /> Gencom mapping: [<1 1 0 0 2|, <0 2 0 0 5|]<br /> <br /> Map: [<1 1 2|, <0 2 5|]<br /> EDOs: 7, 10, 17, 24, 41, 65, 89, 202, 291, 380<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.6756 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/neutraltet7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/neutraltet10">Ten note chromatic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/neutraltet17">Seventeen note mega chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h1> --><h1 id="toc6"><a name="x2.3.5.11"></a><!-- ws:end:WikiTextHeadingRule:12 -->2.3.5.11</h1> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h2> --><h2 id="toc7"><a name="x2.3.5.11-Porkypine"></a><!-- ws:end:WikiTextHeadingRule:14 -->Porkypine</h2> Commas: 55/54, 100/99<br /> <br /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~10/9 = 164.078<br /> <br /> Gencom: [2 10/9; 55/54, 100/99]<br /> Gencom mapping: [<1 2 3 0 4|, <0 -3 -5 0 -4|]<br /> <br /> Map: [<1 2 3 4|, <0 -3 -5 -4|]<br /> EDOs: 7, 15, 22, 37, 73cd, 95cd, 117bcd<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 5.114 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:16:<h2> --><h2 id="toc8"><a name="x2.3.5.11-Mohaha"></a><!-- ws:end:WikiTextHeadingRule:16 -->Mohaha</h2> Commas: 81/80, 121/120<br /> <br /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~11/9 = 348.094<br /> <br /> Gencom: [2 11/9; 81/80 121/120]<br /> Gencom mapping: [<1 1 0 0 2|, <0 2 8 0 5|]<br /> <br /> Map: [<1 1 0 2|, <0 2 8 5|]<br /> EDOs: 7, 10, 17, 24, 31, 69d, 100d, 131bd<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 3.113 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:18:<h3> --><h3 id="toc9"><a name="x2.3.5.11-Mohaha-Music"></a><!-- ws:end:WikiTextHeadingRule:18 -->Music</h3> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/mohaha10ping2.mp3" rel="nofollow">Mohaha10ping2</a> by <a class="wiki_link" href="/Billy%20Stiltner">Billy Stiltner</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:20:<h1> --><h1 id="toc10"><a name="x2.3.7.11"></a><!-- ws:end:WikiTextHeadingRule:20 -->2.3.7.11</h1> <br /> <!-- ws:start:WikiTextHeadingRule:22:<h2> --><h2 id="toc11"><a name="x2.3.7.11-Ennea"></a><!-- ws:end:WikiTextHeadingRule:22 -->Ennea</h2> Commas: 41503/41472, 43923/43904<br /> <br /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~99/98 = 17.6258<br /> <br /> Gencom: [2 99/98; 41503/41472, 43923/43904]<br /> Gencom mapping: [<1 14/9 0 25/9 31/9|, <0 2 0 2 1|]<br /> <br /> Sval map: [<9 0 11 24|, <0 2 2 1|]<br /> EDOs: 54, 63, 68, 72, 135, 342, 477, 525, 613, 681, 749, 817, 2159bcd, 3336bcd, 4153bcd<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.0857 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:24:<h2> --><h2 id="toc12"><a name="x2.3.7.11-Supra"></a><!-- ws:end:WikiTextHeadingRule:24 -->Supra</h2> Commas: 64/63, 99/98<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~3/2 = 707.192<br /> <br /> Gencom: [2 3/2; 64/63 99/98]<br /> Gencom mapping: [<1 1 0 4 7|, <0 1 0 -2 -6|]<br /> <br /> Sval map: [<1 0 6 13|, <0 1 -2 -6|]<br /> EDOs: 5, 12, 17, 39c, 56c<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 4.421 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:26:<h2> --><h2 id="toc13"><a name="x2.3.7.11-Skwares"></a><!-- ws:end:WikiTextHeadingRule:26 -->Skwares</h2> Commas: 99/98, 243/242<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~9/7 = 425.244<br /> <br /> Gencom: [2 9/7; 99/98 243/242]<br /> Gencom mapping: [<1 3 0 6 7|, <0 -4 0 -9 -10]]<br /> <br /> Sval map: [<1 3 6 7|, <0 -4 -9 -10|]<br /> EDOs: 14, 17, 31, 48, 79, 127, 206bcd<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 2.457 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:28:<h2> --><h2 id="toc14"><a name="x2.3.7.11-Hemif"></a><!-- ws:end:WikiTextHeadingRule:28 -->Hemif</h2> Commas: 243/242, 896/891<br /> <br /> POTE generator: ~11/9 = 351.535<br /> <br /> Gencom: [2 11/9; 243/242 896/891]<br /> Gencom mapping: [<1 1 0 -1 2|, <0 2 0 13 5|]<br /> <br /> Sval map: [<1 1 -1 2|, <0 2 13 5|]<br /> EDOs: 7, 17, 41, 58, 99d<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1.366 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:30:<h1> --><h1 id="toc15"><a name="x2.5.7.11"></a><!-- ws:end:WikiTextHeadingRule:30 -->2.5.7.11</h1> <br /> <!-- ws:start:WikiTextHeadingRule:32:<h2> --><h2 id="toc16"><a name="x2.5.7.11-Larry"></a><!-- ws:end:WikiTextHeadingRule:32 -->Larry</h2> Commas: 243/242, 4000/3993<br /> Related temperaments: <a class="wiki_link" href="/Gravity%20family#Gravity">gravity</a>, <a class="wiki_link" href="/Gravity%20family#Harry">harry</a><br /> <br /> POTE generator: ~40/27 = 683.166<br /> <br /> Gencom: [2 40/27; 243/242 4000/3993]<br /> Gencom mapping: [<1 5 12 0 12|, <0 -6 -17 0 -15|]<br /> <br /> Map: [<1 5 12 12|, <0 -6 -17 -15|]<br /> EDOs: 7, 58, 65, 137, 202<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.6765 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:34:<h1> --><h1 id="toc17"><a name="x2.9.7.11"></a><!-- ws:end:WikiTextHeadingRule:34 -->2.9.7.11</h1> <br /> <!-- ws:start:WikiTextHeadingRule:36:<h2> --><h2 id="toc18"><a name="x2.9.7.11-Machine"></a><!-- ws:end:WikiTextHeadingRule:36 -->Machine</h2> Commas: 64/63, 99/98<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~8/7 = 214.384<br /> <br /> Gencom: [2 8/7; 64/63 99/98]<br /> Gencom mapping: [<1 3/2 0 3 4|, <0 1/2 0 -1 -3|]<br /> <br /> <a class="wiki_link" href="/Smonzos%20and%20Svals">Sval map</a>: [<1 0 6 13|, <0 1 -1 -3|]<br /> EDOs: 5, 6, 11, 17, 28<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 4.421 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:38:<h2> --><h2 id="toc19"><a name="x2.9.7.11-Apparatus"></a><!-- ws:end:WikiTextHeadingRule:38 -->Apparatus</h2> Commas: 41503/41472, 322102/321489<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~77/72 = 115.570<br /> <br /> Gencom: [2 77/72; 41503/41472 322102/321489]<br /> Gencom mapping: [<1 5/2 0 3 5|, <0 -19/2 0 -2 -16|]<br /> <br /> <a class="wiki_link" href="/Smonzos%20and%20Svals">Sval map</a>: [<1 5 3 5|, <0 -19 -2 -16|]<br /> EDOs: 10, 21, 31, 52, 83, 135, 353, 488, 623<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.1505 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:40:<h2> --><h2 id="toc20"><a name="x2.9.7.11-Mechanism"></a><!-- ws:end:WikiTextHeadingRule:40 -->Mechanism</h2> Commas: 896/891, 26411/26244<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~9/7 = 438.465<br /> <br /> Gencom: [2 9/7; 896/891 26411/26244]<br /> Gencom mapping: [<1 5/2 0 5 2|, <0 -5/2 0 -6 4|]<br /> <br /> <a class="wiki_link" href="/Smonzos%20and%20Svals">Sval map</a>: [<1 5 5 2|, <0 -5 -6 4|]<br /> EDOs: 8, 11, 30, 41, 52<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.9531 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:42:<h1> --><h1 id="toc21"><a name="x2.9.15.7.11.13"></a><!-- ws:end:WikiTextHeadingRule:42 -->2.9.15.7.11.13</h1> <br /> <!-- ws:start:WikiTextHeadingRule:44:<h2> --><h2 id="toc22"><a name="x2.9.15.7.11.13-Stacks (aka 2magic)"></a><!-- ws:end:WikiTextHeadingRule:44 -->Stacks (aka 2magic)</h2> Commas: 100/99, 105/104, 144/143, 196/195<br /> <br /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~9/7 = 438.977<br /> <br /> Gencom: [2 9/7; 100/99 105/104 144/143 196/195]<br /> Gencom mapping: [<1 5/2 5/2 5 2 7|, <0 -5/2 -1/2 -6 4 -9|] <br /> <br /> Sval map: [<1 0 2 -1 6 -2|, <0 5 3 6 -4 9|]<br /> EDOs: 11, 30, 41, 153cdef, 194cdef, 235cdef<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 3.772 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:46:<h3> --><h3 id="toc23"><a name="x2.9.15.7.11.13-Stacks (aka 2magic)-2.9.15.7.11 stacks"></a><!-- ws:end:WikiTextHeadingRule:46 -->2.9.15.7.11 stacks</h3> Commas: 100/99, 225/224, 245/243<br /> <br /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~9/7 = 438.607<br /> <br /> Gencom: [2 9/7; 100/99 225/224 245/243]<br /> Gencom mapping: [<1 5/2 5/2 5 2|, <0 -5/2 -1/2 -6 4|]<br /> <br /> Sval map: [<1 0 2 -1 6|, <0 5 3 6 -4|]<br /> EDOs: 8, 11, 30, 41, 52, 93, 145, 342bce, <br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 2.741 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:48:<h3> --><h3 id="toc24"><a name="x2.9.15.7.11.13-Stacks (aka 2magic)-2.9.15.7 stacks"></a><!-- ws:end:WikiTextHeadingRule:48 -->2.9.15.7 stacks</h3> Commas: 225/224, 245/243<br /> <br /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~9/7 = 439.296<br /> <br /> Gencom: [2 9/7; 225/224 245/243]<br /> Gencom mapping: [<1 5/2 5/2 5|, <0 -5/2 -1/2 -6|]<br /> <br /> Sval map: [<1 0 2 -1|, <0 5 3 6|]<br /> EDOs: 8, 11, 30, 41, 71, 93, 112c, 134c, 175c<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 2.149 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:50:<h1> --><h1 id="toc25"><a name="x2.9.21"></a><!-- ws:end:WikiTextHeadingRule:50 -->2.9.21</h1> <!-- ws:start:WikiTextHeadingRule:52:<h2> --><h2 id="toc26"><a name="x2.9.21-A-team"></a><!-- ws:end:WikiTextHeadingRule:52 -->A-team</h2> Commas: 1029/1024<br /> <br /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~21/16 = 467.375<br /> <br /> Gencom: [2 21/16; 1029/1024]<br /> Gencom mapping: [<1 1 0 3|, <0 3/2 0 -1/2|]<br /> <br /> Sval map: [<1 2 4|, <0 3 1|]<br /> EDOs: 5, 13, 18, 41, 59, 77, 95<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.6403</body></html>