Subgroup temperaments: Difference between revisions
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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>2014-02-20 16: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-02-20 16:41:53 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>490847064</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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[[Tp tuning#T2%20tuning|RMS error]]: 0.6108 cents | [[Tp tuning#T2%20tuning|RMS error]]: 0.6108 cents | ||
== | ==Bleu== | ||
Commas: 99/98, 864/847 | Commas: 99/98, 864/847 | ||
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<a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.6108 cents<br /> | <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.6108 cents<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="x2.3.7.11- | <!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="x2.3.7.11-Bleu"></a><!-- ws:end:WikiTextHeadingRule:34 -->Bleu</h2> | ||
Commas: 99/98, 864/847<br /> | Commas: 99/98, 864/847<br /> | ||
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Revision as of 16:41, 20 February 2014
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 2014-02-20 16:41:53 UTC.
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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 [[Tp tuning#T2%20tuning|RMS error]]: 2.523 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 [[Tp tuning#T2%20tuning|RMS error]]: 1.856 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 [[Tp tuning#T2%20tuning|RMS error]]: 0.3202 cents ==Lee== Comma: 177147/175616 [[Lp tuning|POL2 generator]]: ~81/56 = 633.525 Map: [<1 0 -3|, <0 3 11|] EDOs: 17, 36, 89, 125, 161, 358, 519b [[Tp tuning#T2%20tuning|RMS error]]: 0.3519 cents ==Skwares== Comma: 19683/19208 [[Lp tuning|POL2 generator]]: ~9/7 = 425.365 cents Map: [<1 3 6|, <0 -4 -9|] EDOs: 14, 17, 31, 48, 79, 189b, 268bc, 347bc [[Tp tuning#T2%20tuning|RMS error]]: 1.149 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 [[Tp tuning#T2%20tuning|RMS error]]: 0.3021 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 [[Tp tuning#T2%20tuning|RMS error]]: 2.287 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, 55, 69d, 100d, 131bd [[Tp tuning#T2%20tuning|RMS error]]: 1.392 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 [[Tp tuning#T2%20tuning|RMS error]]: 0.0383 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 [[Tp tuning#T2%20tuning|RMS error]]: 1.977 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 [[Tp tuning#T2%20tuning|RMS error]]: 1.099 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 [[Tp tuning#T2%20tuning|RMS error]]: 0.6108 cents ==Bleu== Commas: 99/98, 864/847 POTE generator: ~12/11 = 140.005 Map: [<1 1 2 3|, <0 5 7 4|] EDOs: 9, 17, 43, 60c RMS error: 1.829 cents =2.3.7.11.13= ==Suhajira== Commas: 64/63, 78/77, 144/143 Gencom: [2 11/9; 64/63 78/77 144/143] Gencom map: [<1 1 0 4 2 4|, <0 2 0 -4 5 -1|] [[Tp tuning|POT2 generator]]: ~11/9 = 353.775 Map: [<1 1 4 2 4|, <0 2 -4 5 -1|] EDOs: 7, 10, 17, 44d, 61cd, 78cd [[Tp tuning#T2%20tuning|RMS error]]: 1.953 cents ==Hemif== Commas: 144/143, 243/242, 364/363 Related temperament: [[xenharmonic/Breedsmic temperaments|Hemififths]], namo [[Tp tuning|POT2 generator]]: ~11/9 = 351.691 [[Gencom]]: [2 11/9; 144/143 243/242 364/363] 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|] EDOs: 7, 10, 17, 24, 41, 58 [[Tp tuning#T2%20tuning|RMS error]]: 0.7167 cents ==Skwares== Commas: 78/77, 99/98, 243/242 [[Tp tuning|POT2 generator]]: ~9/7 = 424.457 Map: [<1 3 6 7 9|, <0 -4 -9 -10 -15|] EDOs: 17, 48e, 65de, 82c, 147ce [[Tp tuning#T2%20tuning|RMS error]]: 1.769 cents ==Leapfrog== Commas: 169/168, 352/351, 364/363 [[Lp tuning|POL2 generator]]: ~3/2 = 704.745 cents Gencom: [2 3/2; 169/169 352/351 364/363] Gencom mapping: [<1 1 0 -6 -3 -1|, <0 1 0 15 11 8|] Sval map: [<1 0 -21 -14 -9|, <0 1 15 11 8|] EDOs: 17, 46, 63 [[Tp tuning#T2%20tuning|RMS error]]: 0.7541 cents ==Bleu== Group: 2.3.7.11.13 Commas: 78/77, 99/98, 144/143 Sval name: 9&17 [[Tp tuning|POL2 generator]]: ~13/12 = 139.990 [[Gencom]]: [2 13/12; 78/77 99/98 144/143] Gencom map: [<1 1 0 2 3 3|, <0 5 0 7 4 6|] Map: [<1 1 2 3 3|, <0 5 7 4 6|] EDOs: [[xenharmonic/17edo|17]], [[xenharmonic/43edo|43]], [[xenharmonic/60edo|60c]] [[Tp tuning#T2%20tuning|RMS error]]: 1.752 cents ==Parapyth (Rank 3)== Commas: 352/351, 364/363 [[Lp tuning|POL2 tuning]]: <1200.000 1903.856 (2787.774) 3369.907 4154.482 4442.913| The gencom below gives [[Margo Schulter]]'s favored basis Gencom: [2 3/2 28/27; 352/351 364/363] Gencom mapping: [<1 1 0 1 4 6|, <0 1 0 3 -1 -4|, <0 0 0 1 1 1|] Sval map: [<1 0 0 7 12|, <0 1 0 -4 -7|, <0 0 1 1 1|] EDOs: 17, 41, 46, 58, 87, 104 [[Tp tuning#T2%20tuning|RMS error]]: 0.3789 cents =2.3.5.11= ==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 [[Tp tuning#T2%20tuning|RMS error]]: 0.3025 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 [[Tp tuning#T2%20tuning|RMS error]]: 1.977 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 [[Tp tuning#T2%20tuning|RMS error]]: 0.0673 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 [[Tp tuning#T2%20tuning|RMS error]]: 0.4262 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 [[Tp tuning#T2%20tuning|RMS error]]: 1.540 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, [[Tp tuning#T2%20tuning|RMS error]]: 1.226 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 [[Tp tuning#T2%20tuning|RMS error]]: 1.074 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 [[Tp tuning#T2%20tuning|RMS error]]: 0.3202 cents =2.3.7/5.11/5.13/5= ==Historical== Subgroup: 2.3.7/5.11/5.13/5 Commas: 364/363, 441/440, 1001/1000 [[Lp tuning|POL2 generator]]: ~21/20 = 83.016 [[Gencom]]: [2 21/20; 364/363 441/440 1001/1000] Gencom map: [<1 2 -3/4 -3/4 1/4 5/4|, <0 -6 0 7 2 -9|] Sval map: [<1 2 0 1 2|, <0 -6 7 2 -9|] EDOs: 14, 29, 72, 101, 130, 159 [[Tp tuning#T2%20tuning|RMS error]]: 0.2562 cents =2.3.7.11/5.13= ==Hypnosis== Subgroup: 2.3.7.11/5.13 Commas: 169/168, 540/539, 729/728 Related temperament: [[Swetismic temperaments#Hypnos-13-limit|hypnos]], [[Hemifamity temperaments#Tricot-13-limit|tricot]] [[Gencom]]: [2 13/9; 169/168, 540/539, 729/728] Gencom map: [<1 0 -4 -3 4 0|, <0 3 13/2 11 -13/2 7|] Sval map: [<1 0 -3 8 0|, <0 3 11 -13 7|] EDOs: 17, 36, 118e, 125e, 161e, 197e [[Tp tuning#T2%20tuning|RMS error]]: 0.5379 cents
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<html><head><title>Subgroup temperaments</title></head><body><!-- ws:start:WikiTextTocRule:82:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:82 --><!-- ws:start:WikiTextTocRule:83: --><a href="#x2.3.7">2.3.7</a><!-- ws:end:WikiTextTocRule:83 --><!-- ws:start:WikiTextTocRule:84: --><!-- ws:end:WikiTextTocRule:84 --><!-- ws:start:WikiTextTocRule:85: --><!-- ws:end:WikiTextTocRule:85 --><!-- ws:start:WikiTextTocRule:86: --><!-- ws:end:WikiTextTocRule:86 --><!-- ws:start:WikiTextTocRule:87: --><!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextTocRule:88: --><!-- ws:end:WikiTextTocRule:88 --><!-- ws:start:WikiTextTocRule:89: --> | <a href="#x2.3.11">2.3.11</a><!-- ws:end:WikiTextTocRule:89 --><!-- ws:start:WikiTextTocRule:90: --><!-- ws:end:WikiTextTocRule:90 --><!-- ws:start:WikiTextTocRule:91: --> | <a href="#x2.3.5.11">2.3.5.11</a><!-- ws:end:WikiTextTocRule:91 --><!-- ws:start:WikiTextTocRule:92: --><!-- ws:end:WikiTextTocRule:92 --><!-- ws:start:WikiTextTocRule:93: --><!-- ws:end:WikiTextTocRule:93 --><!-- ws:start:WikiTextTocRule:94: --><!-- ws:end:WikiTextTocRule:94 --><!-- ws:start:WikiTextTocRule:95: --> | <a href="#x2.3.7.11">2.3.7.11</a><!-- ws:end:WikiTextTocRule:95 --><!-- ws:start:WikiTextTocRule:96: --><!-- ws:end:WikiTextTocRule:96 --><!-- ws:start:WikiTextTocRule:97: --><!-- ws:end:WikiTextTocRule:97 --><!-- ws:start:WikiTextTocRule:98: --><!-- ws:end:WikiTextTocRule:98 --><!-- ws:start:WikiTextTocRule:99: --><!-- ws:end:WikiTextTocRule:99 --><!-- ws:start:WikiTextTocRule:100: --><!-- ws:end:WikiTextTocRule:100 --><!-- ws:start:WikiTextTocRule:101: --> | <a href="#x2.3.7.11.13">2.3.7.11.13</a><!-- ws:end:WikiTextTocRule:101 --><!-- ws:start:WikiTextTocRule:102: --><!-- ws:end:WikiTextTocRule:102 --><!-- ws:start:WikiTextTocRule:103: --><!-- ws:end:WikiTextTocRule:103 --><!-- ws:start:WikiTextTocRule:104: --><!-- ws:end:WikiTextTocRule:104 --><!-- ws:start:WikiTextTocRule:105: --><!-- ws:end:WikiTextTocRule:105 --><!-- ws:start:WikiTextTocRule:106: --><!-- ws:end:WikiTextTocRule:106 --><!-- ws:start:WikiTextTocRule:107: --><!-- ws:end:WikiTextTocRule:107 --><!-- ws:start:WikiTextTocRule:108: --> | <a href="#x2.3.5.11">2.3.5.11</a><!-- ws:end:WikiTextTocRule:108 --><!-- ws:start:WikiTextTocRule:109: --><!-- ws:end:WikiTextTocRule:109 --><!-- ws:start:WikiTextTocRule:110: --> | <a href="#x2.9.7.11">2.9.7.11</a><!-- ws:end:WikiTextTocRule:110 --><!-- ws:start:WikiTextTocRule:111: --><!-- ws:end:WikiTextTocRule:111 --><!-- ws:start:WikiTextTocRule:112: --><!-- ws:end:WikiTextTocRule:112 --><!-- ws:start:WikiTextTocRule:113: --><!-- ws:end:WikiTextTocRule:113 --><!-- ws:start:WikiTextTocRule:114: --> | <a href="#x2.9.15.7.11.13">2.9.15.7.11.13</a><!-- ws:end:WikiTextTocRule:114 --><!-- ws:start:WikiTextTocRule:115: --><!-- ws:end:WikiTextTocRule:115 --><!-- ws:start:WikiTextTocRule:116: --><!-- ws:end:WikiTextTocRule:116 --><!-- ws:start:WikiTextTocRule:117: --><!-- ws:end:WikiTextTocRule:117 --><!-- ws:start:WikiTextTocRule:118: --> | <a href="#x2.9.21">2.9.21</a><!-- ws:end:WikiTextTocRule:118 --><!-- ws:start:WikiTextTocRule:119: --><!-- ws:end:WikiTextTocRule:119 --><!-- ws:start:WikiTextTocRule:120: --> | <a href="#x2.3.7/5.11/5.13/5">2.3.7/5.11/5.13/5</a><!-- ws:end:WikiTextTocRule:120 --><!-- ws:start:WikiTextTocRule:121: --><!-- ws:end:WikiTextTocRule:121 --><!-- ws:start:WikiTextTocRule:122: --> | <a href="#x2.3.7.11/5.13">2.3.7.11/5.13</a><!-- ws:end:WikiTextTocRule:122 --><!-- ws:start:WikiTextTocRule:123: --><!-- ws:end:WikiTextTocRule:123 --><!-- ws:start:WikiTextTocRule:124: --> <!-- ws:end:WikiTextTocRule:124 -->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="/Tp%20tuning#T2%20tuning">RMS error</a>: 2.523 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="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.856 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="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.3202 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h2> --><h2 id="toc4"><a name="x2.3.7-Lee"></a><!-- ws:end:WikiTextHeadingRule:8 -->Lee</h2> Comma: 177147/175616<br /> <br /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~81/56 = 633.525<br /> <br /> Map: [<1 0 -3|, <0 3 11|]<br /> EDOs: 17, 36, 89, 125, 161, 358, 519b<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.3519 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="x2.3.7-Skwares"></a><!-- ws:end:WikiTextHeadingRule:10 -->Skwares</h2> Comma: 19683/19208<br /> <br /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~9/7 = 425.365 cents<br /> <br /> Map: [<1 3 6|, <0 -4 -9|]<br /> EDOs: 14, 17, 31, 48, 79, 189b, 268bc, 347bc<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.149 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h1> --><h1 id="toc6"><a name="x2.3.11"></a><!-- ws:end:WikiTextHeadingRule:12 -->2.3.11</h1> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h2> --><h2 id="toc7"><a name="x2.3.11-Neutraltet"></a><!-- ws:end:WikiTextHeadingRule:14 -->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="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.3021 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:16:<h1> --><h1 id="toc8"><a name="x2.3.5.11"></a><!-- ws:end:WikiTextHeadingRule:16 -->2.3.5.11</h1> <br /> <!-- ws:start:WikiTextHeadingRule:18:<h2> --><h2 id="toc9"><a name="x2.3.5.11-Porkypine"></a><!-- ws:end:WikiTextHeadingRule:18 -->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="/Tp%20tuning#T2%20tuning">RMS error</a>: 2.287 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:20:<h2> --><h2 id="toc10"><a name="x2.3.5.11-Mohaha"></a><!-- ws:end:WikiTextHeadingRule:20 -->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, 55, 69d, 100d, 131bd<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.392 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:22:<h3> --><h3 id="toc11"><a name="x2.3.5.11-Mohaha-Music"></a><!-- ws:end:WikiTextHeadingRule:22 -->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:24:<h1> --><h1 id="toc12"><a name="x2.3.7.11"></a><!-- ws:end:WikiTextHeadingRule:24 -->2.3.7.11</h1> <br /> <!-- ws:start:WikiTextHeadingRule:26:<h2> --><h2 id="toc13"><a name="x2.3.7.11-Ennea"></a><!-- ws:end:WikiTextHeadingRule:26 -->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="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.0383 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:28:<h2> --><h2 id="toc14"><a name="x2.3.7.11-Supra"></a><!-- ws:end:WikiTextHeadingRule:28 -->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="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.977 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:30:<h2> --><h2 id="toc15"><a name="x2.3.7.11-Skwares"></a><!-- ws:end:WikiTextHeadingRule:30 -->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="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.099 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:32:<h2> --><h2 id="toc16"><a name="x2.3.7.11-Hemif"></a><!-- ws:end:WikiTextHeadingRule:32 -->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="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.6108 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:34:<h2> --><h2 id="toc17"><a name="x2.3.7.11-Bleu"></a><!-- ws:end:WikiTextHeadingRule:34 -->Bleu</h2> Commas: 99/98, 864/847<br /> <br /> POTE generator: ~12/11 = 140.005<br /> <br /> Map: [<1 1 2 3|, <0 5 7 4|]<br /> EDOs: 9, 17, 43, 60c<br /> RMS error: 1.829 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:36:<h1> --><h1 id="toc18"><a name="x2.3.7.11.13"></a><!-- ws:end:WikiTextHeadingRule:36 -->2.3.7.11.13</h1> <br /> <!-- ws:start:WikiTextHeadingRule:38:<h2> --><h2 id="toc19"><a name="x2.3.7.11.13-Suhajira"></a><!-- ws:end:WikiTextHeadingRule:38 -->Suhajira</h2> Commas: 64/63, 78/77, 144/143<br /> <br /> Gencom: [2 11/9; 64/63 78/77 144/143]<br /> Gencom map: [<1 1 0 4 2 4|, <0 2 0 -4 5 -1|]<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~11/9 = 353.775<br /> <br /> Map: [<1 1 4 2 4|, <0 2 -4 5 -1|]<br /> EDOs: 7, 10, 17, 44d, 61cd, 78cd<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.953 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:40:<h2> --><h2 id="toc20"><a name="x2.3.7.11.13-Hemif"></a><!-- ws:end:WikiTextHeadingRule:40 -->Hemif</h2> Commas: 144/143, 243/242, 364/363<br /> Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Breedsmic%20temperaments">Hemififths</a>, namo<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~11/9 = 351.691<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 11/9; 144/143 243/242 364/363]<br /> Gencom map: [<1 1 0 -1 2 4|, <0 2 0 13 5 -1|]<br /> <br /> Map: [<1 1 -1 2 4|, <0 2 13 5 -1|]<br /> EDOs: 7, 10, 17, 24, 41, 58<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.7167 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:42:<h2> --><h2 id="toc21"><a name="x2.3.7.11.13-Skwares"></a><!-- ws:end:WikiTextHeadingRule:42 -->Skwares</h2> Commas: 78/77, 99/98, 243/242<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~9/7 = 424.457<br /> <br /> Map: [<1 3 6 7 9|, <0 -4 -9 -10 -15|]<br /> EDOs: 17, 48e, 65de, 82c, 147ce<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.769 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:44:<h2> --><h2 id="toc22"><a name="x2.3.7.11.13-Leapfrog"></a><!-- ws:end:WikiTextHeadingRule:44 -->Leapfrog</h2> Commas: 169/168, 352/351, 364/363<br /> <br /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~3/2 = 704.745 cents<br /> <br /> Gencom: [2 3/2; 169/169 352/351 364/363]<br /> Gencom mapping: [<1 1 0 -6 -3 -1|, <0 1 0 15 11 8|]<br /> <br /> Sval map: [<1 0 -21 -14 -9|, <0 1 15 11 8|]<br /> EDOs: 17, 46, 63<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.7541 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:46:<h2> --><h2 id="toc23"><a name="x2.3.7.11.13-Bleu"></a><!-- ws:end:WikiTextHeadingRule:46 -->Bleu</h2> Group: 2.3.7.11.13<br /> Commas: 78/77, 99/98, 144/143<br /> Sval name: 9&17<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POL2 generator</a>: ~13/12 = 139.990<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 13/12; 78/77 99/98 144/143]<br /> Gencom map: [<1 1 0 2 3 3|, <0 5 0 7 4 6|]<br /> <br /> Map: [<1 1 2 3 3|, <0 5 7 4 6|]<br /> EDOs: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/17edo">17</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/43edo">43</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/60edo">60c</a><br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.752 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:48:<h2> --><h2 id="toc24"><a name="x2.3.7.11.13-Parapyth (Rank 3)"></a><!-- ws:end:WikiTextHeadingRule:48 -->Parapyth (Rank 3)</h2> Commas: 352/351, 364/363<br /> <br /> <a class="wiki_link" href="/Lp%20tuning">POL2 tuning</a>: <1200.000 1903.856 (2787.774) 3369.907 4154.482 4442.913|<br /> <br /> The gencom below gives <a class="wiki_link" href="/Margo%20Schulter">Margo Schulter</a>'s favored basis<br /> Gencom: [2 3/2 28/27; 352/351 364/363]<br /> Gencom mapping: [<1 1 0 1 4 6|, <0 1 0 3 -1 -4|, <0 0 0 1 1 1|]<br /> <br /> Sval map: [<1 0 0 7 12|, <0 1 0 -4 -7|, <0 0 1 1 1|]<br /> EDOs: 17, 41, 46, 58, 87, 104<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.3789 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:50:<h1> --><h1 id="toc25"><a name="x2.3.5.11"></a><!-- ws:end:WikiTextHeadingRule:50 -->2.3.5.11</h1> <br /> <!-- ws:start:WikiTextHeadingRule:52:<h2> --><h2 id="toc26"><a name="x2.3.5.11-Larry"></a><!-- ws:end:WikiTextHeadingRule:52 -->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="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.3025 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:54:<h1> --><h1 id="toc27"><a name="x2.9.7.11"></a><!-- ws:end:WikiTextHeadingRule:54 -->2.9.7.11</h1> <br /> <!-- ws:start:WikiTextHeadingRule:56:<h2> --><h2 id="toc28"><a name="x2.9.7.11-Machine"></a><!-- ws:end:WikiTextHeadingRule:56 -->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="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.977 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:58:<h2> --><h2 id="toc29"><a name="x2.9.7.11-Apparatus"></a><!-- ws:end:WikiTextHeadingRule:58 -->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="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.0673 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:60:<h2> --><h2 id="toc30"><a name="x2.9.7.11-Mechanism"></a><!-- ws:end:WikiTextHeadingRule:60 -->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="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.4262 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:62:<h1> --><h1 id="toc31"><a name="x2.9.15.7.11.13"></a><!-- ws:end:WikiTextHeadingRule:62 -->2.9.15.7.11.13</h1> <br /> <!-- ws:start:WikiTextHeadingRule:64:<h2> --><h2 id="toc32"><a name="x2.9.15.7.11.13-Stacks (aka 2magic)"></a><!-- ws:end:WikiTextHeadingRule:64 -->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="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.540 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:66:<h3> --><h3 id="toc33"><a name="x2.9.15.7.11.13-Stacks (aka 2magic)-2.9.15.7.11 stacks"></a><!-- ws:end:WikiTextHeadingRule:66 -->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="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.226 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:68:<h3> --><h3 id="toc34"><a name="x2.9.15.7.11.13-Stacks (aka 2magic)-2.9.15.7 stacks"></a><!-- ws:end:WikiTextHeadingRule:68 -->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="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.074 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:70:<h1> --><h1 id="toc35"><a name="x2.9.21"></a><!-- ws:end:WikiTextHeadingRule:70 -->2.9.21</h1> <!-- ws:start:WikiTextHeadingRule:72:<h2> --><h2 id="toc36"><a name="x2.9.21-A-team"></a><!-- ws:end:WikiTextHeadingRule:72 -->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="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.3202 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:74:<h1> --><h1 id="toc37"><a name="x2.3.7/5.11/5.13/5"></a><!-- ws:end:WikiTextHeadingRule:74 -->2.3.7/5.11/5.13/5</h1> <!-- ws:start:WikiTextHeadingRule:76:<h2> --><h2 id="toc38"><a name="x2.3.7/5.11/5.13/5-Historical"></a><!-- ws:end:WikiTextHeadingRule:76 -->Historical</h2> Subgroup: 2.3.7/5.11/5.13/5<br /> Commas: 364/363, 441/440, 1001/1000<br /> <br /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~21/20 = 83.016<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 21/20; 364/363 441/440 1001/1000]<br /> Gencom map: [<1 2 -3/4 -3/4 1/4 5/4|, <0 -6 0 7 2 -9|]<br /> <br /> Sval map: [<1 2 0 1 2|, <0 -6 7 2 -9|]<br /> EDOs: 14, 29, 72, 101, 130, 159<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.2562 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:78:<h1> --><h1 id="toc39"><a name="x2.3.7.11/5.13"></a><!-- ws:end:WikiTextHeadingRule:78 -->2.3.7.11/5.13</h1> <!-- ws:start:WikiTextHeadingRule:80:<h2> --><h2 id="toc40"><a name="x2.3.7.11/5.13-Hypnosis"></a><!-- ws:end:WikiTextHeadingRule:80 -->Hypnosis</h2> Subgroup: 2.3.7.11/5.13<br /> Commas: 169/168, 540/539, 729/728<br /> Related temperament: <a class="wiki_link" href="/Swetismic%20temperaments#Hypnos-13-limit">hypnos</a>, <a class="wiki_link" href="/Hemifamity%20temperaments#Tricot-13-limit">tricot</a><br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 13/9; 169/168, 540/539, 729/728]<br /> Gencom map: [<1 0 -4 -3 4 0|, <0 3 13/2 11 -13/2 7|]<br /> <br /> Sval map: [<1 0 -3 8 0|, <0 3 11 -13 7|]<br /> EDOs: 17, 36, 118e, 125e, 161e, 197e<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.5379 cents</body></html>