Kleismic family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 234998158 - Original comment: ** |
Wikispaces>xenwolf **Imported revision 235943316 - 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: | : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-11 12:51:42 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>235943316</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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The 5-limit parent comma for the kleismic family is 15625/15552, the kleisma. Its monzo is |-6 -5 6>, and flipping that yields <<6 5 -6|| for the wedgie. This tells us the generator is a minor third, and that to get to the interval class of major thirds will require five of these, and so to get to fifths will require six. In fact, (6/5)^5 = 5/2 * 15625/15552. This 5-limit temperament is commonly called hanson, and 14\53 is about perfect as a hanson generator, though 9\34 also makes sense and 5\19 is possible. Other tunings include [[72edo]], [[87edo]] and [[140edo]]. | The [[5-limit]] parent comma for the kleismic family is 15625/15552, the kleisma. Its monzo is |-6 -5 6>, and flipping that yields <<6 5 -6|| for the wedgie. This tells us the generator is a minor third, and that to get to the interval class of major thirds will require five of these, and so to get to fifths will require six. In fact, (6/5)^5 = 5/2 * 15625/15552. This 5-limit temperament is commonly called hanson, and 14\53 is about perfect as a hanson generator, though 9\34 also makes sense and 5\19 is possible. Other tunings include [[72edo]], [[87edo]] and [[140edo]]. | ||
[[POTE tuning|POTE generator]]: 317.007 | [[POTE tuning|POTE generator]]: 317.007 | ||
Map: [<1 0 1|, <0 6 5|] | Map: [<1 0 1|, <0 6 5|] | ||
EDOs: 15, 19, 34, 53, 458 | EDOs: [[15edo|15]], [[19edo|19]], [[34edo|34]], [[53edo|53]], [[458edo|458]] | ||
Music: | Music: | ||
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=Seven limit children= | =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 keemun, 4375/4374, the ragisma, gives catakleismic, 5120/5103, hemifamity, gives countercata, 6144/6125, the porwell comma, gives hemikleismic, 245/243, sensamagic, gives clyde, 1029/1024, the gamelisma, gives tritikleismic, and 2401/2400, the breedsma, gives quadritikleismic. Keemun, catakleismic and countercata all have octave period and use the minor third as a generator; catakleismic and countercata define the 7/4 more complexly but more accurately than keemun. Hemikleismic splits the 6/5 in half to get a neutral second generator of 35/32, and clyde similarly splits the 5/3 in half to get a 9/7 generator. Finally, tritikleismic has a 1/3 octave period with minor third generator, and quadritikleismic a 1/4 octave period with the minor third generator. | 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 keemun, 4375/4374, the ragisma, gives catakleismic, 5120/5103, hemifamity, gives countercata, 6144/6125, the porwell comma, gives hemikleismic, 245/243, sensamagic, gives clyde, 1029/1024, the gamelisma, gives tritikleismic, and 2401/2400, the breedsma, gives quadritikleismic. Keemun, catakleismic and countercata all have octave period and use the minor third as a generator; catakleismic and countercata define the 7/4 more complexly but more accurately than keemun. Hemikleismic splits the 6/5 in half to get a neutral second generator of 35/32, and clyde similarly splits the 5/3 in half to get a 9/7 generator. Finally, tritikleismic has a 1/3 octave period with minor third generator, and quadritikleismic a 1/4 octave period with the minor third generator. | ||
=Keemun= | =Keemun= | ||
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Map: [<1 0 1 2|, <0 6 5 3|] | Map: [<1 0 1 2|, <0 6 5 3|] | ||
Wedgie: <<6 5 3 -6 -12 -7|| | [[Wedgie]]: <<6 5 3 -6 -12 -7|| | ||
EDOs: [[15edo|15]], [[19edo|19]], [[91edo|91]] | EDOs: [[15edo|15]], [[19edo|19]], [[91edo|91]] | ||
Badness: 0.0274 | [[Badness]]: 0.0274 | ||
==11-limit== | ==11-limit== | ||
[[Comma]]s: 49/48, 56/55, 100/99 | |||
[[POTE tuning|POTE generator]]: ~6/5 = 317.576 | [[POTE tuning|POTE generator]]: ~6/5 = 317.576 | ||
Map: [<1 0 1 2 4|, <0 6 5 3 -2|] | Map: [<1 0 1 2 4|, <0 6 5 3 -2|] | ||
EDOs: 4, 15, 19, 34 | EDOs: [[4edo|4]], [[15edo|15]], [[19edo|19]], [[34edo|34]] | ||
Badness: 0.0274 | [[Badness]]: 0.0274 | ||
==13-limit== | ==13-limit== | ||
[[Comma]]s: 49/48, 56/55, 78/77, 100/99 | |||
[[POTE tuning|POTE generator]]: ~6/5 = 316.611 | [[POTE tuning|POTE generator]]: ~6/5 = 316.611 | ||
Map: [<1 0 1 2 4 5|, <0 6 5 3 -2 -5|] | Map: [<1 0 1 2 4 5|, <0 6 5 3 -2 -5|] | ||
EDOs: 4, 15, 19, 72 | EDOs: [[4edo|4]], [[15edo|15]], [[19edo|19]], [[72edo|72]] | ||
Badness: 0.0297 | [[Badness]]: 0.0297 | ||
=Catakleismic= | =Catakleismic= | ||
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Map: [<1 0 1 -3|, <0 6 5 22|] | Map: [<1 0 1 -3|, <0 6 5 22|] | ||
Wedgie: <<6 5 22 -6 18 37|| | [[Wedgie]]: <<6 5 22 -6 18 37|| | ||
EDOs: [[19edo|19]], [[53edo|15]], [[72edo|72]], [[197edo|197]], [[269edo|269]] | EDOs: [[19edo|19]], [[53edo|15]], [[72edo|72]], [[197edo|197]], [[269edo|269]] | ||
Badness: 0.0215 | [[Badness]]: 0.0215 | ||
==11-limit== | ==11-limit== | ||
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Map: [<1 0 1 -3 9|, <0 6 5 22 -21|] | Map: [<1 0 1 -3 9|, <0 6 5 22 -21|] | ||
EDOs: [[15edo|15]], [[19edo|19]], [[53edo|53]], [[72edo|72]], [[269edo|269]], [[341edo|341]] | EDOs: [[15edo|15]], [[19edo|19]], [[53edo|53]], [[72edo|72]], [[269edo|269]], [[341edo|341]] | ||
Badness: 0.0218 | [[Badness]]: 0.0218 | ||
==13-limit== | ==13-limit== | ||
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Map: [<1 0 1 -3 9 0|, <0 6 5 22 -21 14|] | Map: [<1 0 1 -3 9 0|, <0 6 5 22 -21 14|] | ||
EDOs: [[15edo|15]], [[19edo|19]], [[53edo|53]], [[72edo|72]], [[197edo|197]], [[269edo|269]], [[466edo|466]] | EDOs: [[15edo|15]], [[19edo|19]], [[53edo|53]], [[72edo|72]], [[197edo|197]], [[269edo|269]], [[466edo|466]] | ||
Badness: 0.0169 | [[Badness]]: 0.0169 | ||
=Countercata= | =Countercata= | ||
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Map: [<1 0 1 11|, <0 6 5 -31|] | Map: [<1 0 1 11|, <0 6 5 -31|] | ||
Wedgie: <<6 5 -31 -6 -66 -86|| | [[Wedgie]]: <<6 5 -31 -6 -66 -86|| | ||
EDOs: 15, 19, 34, 53, 87, 140, 333, 473, 806 | EDOs: [[15edo|15]], [[19edo|19]], [[34edo|34]], [[53edo|53]], [[87edo|87]], [[140edo|140]], [[333edo|333]], [[473edo|473]], [[806edo|806]] | ||
Badness: 0.0521 | [[Badness]]: 0.0521 | ||
==11-limit== | ==11-limit== | ||
[[Comma]]s: 385/384, 2200/2187, 3388/3375 | |||
POTE generator: ~6/5 = 317.162 | POTE generator: ~6/5 = 317.162 | ||
Map: [<1 0 1 11 -5|, <0 6 5 -31 32|] | Map: [<1 0 1 11 -5|, <0 6 5 -31 32|] | ||
EDOs: 34, 53, 87, 140, 227 | EDOs: [[34edo|34]], [[53edo|53]], [[87edo|87]], [[140edo|140]], [[227edo|227]] | ||
Badness: 0.0398 | [[Badness]]: 0.0398 | ||
==13-limit== | ==13-limit== | ||
[[Comma]]s: 325/324, 352/351, 385/384, 625/624 | |||
POTE generator: ~6/5 = 317.162 | POTE generator: ~6/5 = 317.162 | ||
Map: [<1 0 1 11 -5 0|, <0 6 5 -31 32 14|] | Map: [<1 0 1 11 -5 0|, <0 6 5 -31 32 14|] | ||
EDOs: 34, 53, 87, 140, 367 | EDOs: [[34edo|34]], [[53edo|53]], [[87edo|87]], [[140edo|140]], [[367edo|367]] | ||
Badness: 0.0202 | [[Badness]]: 0.0202 | ||
=Metakleismic= | =Metakleismic= | ||
[[Comma]]s: 15625/15552, 179200/177147 | |||
POTE generator: ~6/5 = 317.314 | POTE generator: ~6/5 = 317.314 | ||
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Map: [<1 0 1 -12|, <0 6 5 56|] | Map: [<1 0 1 -12|, <0 6 5 56|] | ||
Wedgie: <<6 5 56 -6 72 116|| | Wedgie: <<6 5 56 -6 72 116|| | ||
EDOs: 15, 19, 34, 87, 121, 208 | EDOs: [[15edo|15]], [[19edo|19]], [[34edo|34]], [[87edo|87]], [[121edo|121]], [[208edo|208]] | ||
Badness: 0.1635 | [[Badness]]: 0.1635 | ||
==11-limit== | ==11-limit== | ||
[[Comma]]s: 896/891, 2200/2187, 14700/14641 | |||
POTE generator: ~6/5 = 317.311 | POTE generator: ~6/5 = 317.311 | ||
Map: [<1 0 1 -12 -5|, <0 6 5 56 32|] | Map: [<1 0 1 -12 -5|, <0 6 5 56 32|] | ||
EDOs: 15, 19, 34, 87, 121, 208 | EDOs: [[15edo|15]], [[19edo|19]], [[34edo|34]], [[87edo|87]], [[121edo|121]], [[208edo|208]] | ||
Badness: 0.0486 | [[Badness]]: 0.0486 | ||
==13-limit== | ==13-limit== | ||
[[Comma]]s: 325/324, 352/351, 364/363, 625/624 | |||
POTE generator: ~6/5 = 317.311 | POTE generator: ~6/5 = 317.311 | ||
Map: [<1 0 1 -12 -5 0|, <0 6 5 56 32 14|] | Map: [<1 0 1 -12 -5 0|, <0 6 5 56 32 14|] | ||
EDOs: 15, 19, 34, 87, 121, 208 | EDOs: [[15edo|15]], [[19edo|19]], [[34edo|34]], [[87edo|87]], [[121edo|121]], [[208edo|208]] | ||
Badness: 0.0244 | [[Badness]]: 0.0244 | ||
=Hemikleismic= | =Hemikleismic= | ||
| Line 141: | Line 141: | ||
Map: [<1 0 1 4|, <0 12 10 -9|] | Map: [<1 0 1 4|, <0 12 10 -9|] | ||
EDOs: 53, 121 | EDOs: [[53edo|53]], [[121edo|121]] | ||
=Clyde= | =Clyde= | ||
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=Tritikleismic= | =Tritikleismic= | ||
[[Comma]]s: 15625/15552, 1029/1024 | |||
[[POTE tuning|POTE generator]]: 316.872 | [[POTE tuning|POTE generator]]: 316.872 | ||
Map: [<3 0 3 10|, <0 6 5 -2|] | Map: [<3 0 3 10|, <0 6 5 -2|] | ||
Wedgie: <<18 15 -6 -18 -60 -56|| | [[Wedgie]]: <<18 15 -6 -18 -60 -56|| | ||
EDOs: 12, 15, 57, 72, 159, 231 | EDOs: [[12edo|12]], [[15edo|15]], [[57edo|57]], [[72edo|72]], [[159edo|159]], [[231edo|231]] | ||
Badness: 0.0563 | [[Badness]]: 0.0563 | ||
==11-limit== | ==11-limit== | ||
[[Comma]]s: 385/384, 441/440, 4000/3993 | |||
[[POTE tuning|POTE generator]]: 316.881 | [[POTE tuning|POTE generator]]: 316.881 | ||
Map: [<3 0 3 10 8|, <0 6 5 -2 3|] | Map: [<3 0 3 10 8|, <0 6 5 -2 3|] | ||
EDOs: 12, 15, 57, 72, 159, 231 | EDOs: [[12edo|12]], [[15edo|15]], [[57edo|57]], [[72edo|72]], [[159edo|159]], [[231edo|231]] | ||
Badness: 0.0193 | [[Badness]]: 0.0193 | ||
==13-limit== | ==13-limit== | ||
[[Comma]]s: 325/324, 364/363, 441/440, 625/624 | |||
[[POTE tuning|POTE generator]]: 316.959 | [[POTE tuning|POTE generator]]: 316.959 | ||
Map: [<3 0 3 10 8 0|, <0 6 5 -2 3 14|] | Map: [<3 0 3 10 8 0|, <0 6 5 -2 3 14|] | ||
EDOs: 12, 15, 72, 87, 159, 867, 1026 | EDOs: [[12edo|12]], [[15edo|15]], [[72edo|72]], 87, 159, 867, 1026 | ||
Badness: 0.0157 | [[Badness]]: 0.0157 | ||
=Quadritikleismic= | =Quadritikleismic= | ||
[[Comma]]s: 15625/15552, 2401/2400 | |||
[[POTE tuning|POTE generator]]: 316.9999 | [[POTE tuning|POTE generator]]: 316.9999 | ||
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Wedgie: <<24 20 16 -24 -42 -19|| | Wedgie: <<24 20 16 -24 -42 -19|| | ||
EDOs: [[68edo|68]], [[72edo|72]], [[140edo|140]], [[212edo|212]], [[1200edo|1200]] | EDOs: [[68edo|68]], [[72edo|72]], [[140edo|140]], [[212edo|212]], [[1200edo|1200]] | ||
Badness: 0.0392 | [[Badness]]: 0.0392 | ||
==11-limit== | ==11-limit== | ||
| Line 203: | Line 203: | ||
Map: [<4 0 4 7 17|, <0 6 5 4 -3|] | Map: [<4 0 4 7 17|, <0 6 5 4 -3|] | ||
EDOs: [[68edo|68]], [[72edo|72]], [[140edo|140]], [[212edo|212]], [[284edo|284]], [[496edo|496]], [[780edo|780]] | EDOs: [[68edo|68]], [[72edo|72]], [[140edo|140]], [[212edo|212]], [[284edo|284]], [[496edo|496]], [[780edo|780]] | ||
Badness: 0.0234 | [[Badness]]: 0.0234 | ||
==13-limit== | ==13-limit== | ||
| Line 211: | Line 211: | ||
Map: [<4 0 4 7 17 0|, <0 6 5 4 -3 14|] | Map: [<4 0 4 7 17 0|, <0 6 5 4 -3 14|] | ||
EDOs: 68, 72, 140, 212 | EDOs: [[68edo|68]], [[72edo|72]], [[140edo|140]], [[212edo|212]] | ||
Badness: 0.0187</pre></div> | [[Badness]]: 0.0187</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>Kleismic family</title></head><body><!-- ws:start:WikiTextTocRule:42:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><a href="#Seven limit children">Seven limit children</a><!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --> | <a href="#Keemun">Keemun</a><!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --><!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --><!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --> | <a href="#Catakleismic">Catakleismic</a><!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --><!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --><!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --> | <a href="#Countercata">Countercata</a><!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --><!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --><!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --> | <a href="#Metakleismic">Metakleismic</a><!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --><!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --><!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --> | <a href="#Hemikleismic">Hemikleismic</a><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --> | <a href="#Clyde">Clyde</a><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --> | <a href="#Tritikleismic">Tritikleismic</a><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --> | <a href="#Quadritikleismic">Quadritikleismic</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: --> | <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>Kleismic family</title></head><body><!-- ws:start:WikiTextTocRule:42:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><a href="#Seven limit children">Seven limit children</a><!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --> | <a href="#Keemun">Keemun</a><!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --><!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --><!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --> | <a href="#Catakleismic">Catakleismic</a><!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --><!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --><!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --> | <a href="#Countercata">Countercata</a><!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --><!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --><!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --> | <a href="#Metakleismic">Metakleismic</a><!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --><!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --><!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --> | <a href="#Hemikleismic">Hemikleismic</a><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --> | <a href="#Clyde">Clyde</a><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --> | <a href="#Tritikleismic">Tritikleismic</a><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --> | <a href="#Quadritikleismic">Quadritikleismic</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 --><br /> | <!-- ws:end:WikiTextTocRule:64 --><br /> | ||
<br /> | <br /> | ||
The 5-limit parent comma for the kleismic family is 15625/15552, the kleisma. Its monzo is |-6 -5 6&gt;, and flipping that yields &lt;&lt;6 5 -6|| for the wedgie. This tells us the generator is a minor third, and that to get to the interval class of major thirds will require five of these, and so to get to fifths will require six. In fact, (6/5)^5 = 5/2 * 15625/15552. This 5-limit temperament is commonly called hanson, and 14\53 is about perfect as a hanson generator, though 9\34 also makes sense and 5\19 is possible. Other tunings include <a class="wiki_link" href="/72edo">72edo</a>, <a class="wiki_link" href="/87edo">87edo</a> and <a class="wiki_link" href="/140edo">140edo</a>.<br /> | The <a class="wiki_link" href="/5-limit">5-limit</a> parent comma for the kleismic family is 15625/15552, the kleisma. Its monzo is |-6 -5 6&gt;, and flipping that yields &lt;&lt;6 5 -6|| for the wedgie. This tells us the generator is a minor third, and that to get to the interval class of major thirds will require five of these, and so to get to fifths will require six. In fact, (6/5)^5 = 5/2 * 15625/15552. This 5-limit temperament is commonly called hanson, and 14\53 is about perfect as a hanson generator, though 9\34 also makes sense and 5\19 is possible. Other tunings include <a class="wiki_link" href="/72edo">72edo</a>, <a class="wiki_link" href="/87edo">87edo</a> and <a class="wiki_link" href="/140edo">140edo</a>.<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 317.007<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 317.007<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 1|, &lt;0 6 5|]<br /> | Map: [&lt;1 0 1|, &lt;0 6 5|]<br /> | ||
EDOs: 15, 19, 34, 53, 458<br /> | EDOs: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/34edo">34</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/458edo">458</a><br /> | ||
<br /> | <br /> | ||
Music:<br /> | Music:<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Seven limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->Seven limit children</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Seven limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->Seven limit children</h1> | ||
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 keemun, 4375/4374, the ragisma, gives catakleismic, 5120/5103, hemifamity, gives countercata, 6144/6125, the porwell comma, gives hemikleismic, 245/243, sensamagic, gives clyde, 1029/1024, the gamelisma, gives tritikleismic, and 2401/2400, the breedsma, gives quadritikleismic. Keemun, catakleismic and countercata all have octave period and use the minor third as a generator; catakleismic and countercata define the 7/4 more complexly but more accurately than keemun. Hemikleismic splits the 6/5 in half to get a neutral second generator of 35/32, and clyde similarly splits the 5/3 in half to get a 9/7 generator. Finally, tritikleismic has a 1/3 octave period with minor third generator, and quadritikleismic a 1/4 octave period with the minor third generator.<br /> | The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which <a class="wiki_link" href="/7-limit">7-limit</a> family member we are looking at. 875/864, the keemic comma, gives keemun, 4375/4374, the ragisma, gives catakleismic, 5120/5103, hemifamity, gives countercata, 6144/6125, the porwell comma, gives hemikleismic, 245/243, sensamagic, gives clyde, 1029/1024, the gamelisma, gives tritikleismic, and 2401/2400, the breedsma, gives quadritikleismic. Keemun, catakleismic and countercata all have octave period and use the minor third as a generator; catakleismic and countercata define the 7/4 more complexly but more accurately than keemun. Hemikleismic splits the 6/5 in half to get a neutral second generator of 35/32, and clyde similarly splits the 5/3 in half to get a 9/7 generator. Finally, tritikleismic has a 1/3 octave period with minor third generator, and quadritikleismic a 1/4 octave period with the minor third generator.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Keemun"></a><!-- ws:end:WikiTextHeadingRule:2 -->Keemun</h1> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Keemun"></a><!-- ws:end:WikiTextHeadingRule:2 -->Keemun</h1> | ||
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Map: [&lt;1 0 1 2|, &lt;0 6 5 3|]<br /> | Map: [&lt;1 0 1 2|, &lt;0 6 5 3|]<br /> | ||
Wedgie: &lt;&lt;6 5 3 -6 -12 -7||<br /> | <a class="wiki_link" href="/Wedgie">Wedgie</a>: &lt;&lt;6 5 3 -6 -12 -7||<br /> | ||
EDOs: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/91edo">91</a><br /> | EDOs: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/91edo">91</a><br /> | ||
Badness: 0.0274<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0274<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Keemun-11-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->11-limit</h2> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Keemun-11-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->11-limit</h2> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 49/48, 56/55, 100/99<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~6/5 = 317.576<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~6/5 = 317.576<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 1 2 4|, &lt;0 6 5 3 -2|]<br /> | Map: [&lt;1 0 1 2 4|, &lt;0 6 5 3 -2|]<br /> | ||
EDOs: 4, 15, 19, 34<br /> | EDOs: <a class="wiki_link" href="/4edo">4</a>, <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/34edo">34</a><br /> | ||
Badness: 0.0274<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0274<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Keemun-13-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Keemun-13-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-limit</h2> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 49/48, 56/55, 78/77, 100/99<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~6/5 = 316.611<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~6/5 = 316.611<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 1 2 4 5|, &lt;0 6 5 3 -2 -5|]<br /> | Map: [&lt;1 0 1 2 4 5|, &lt;0 6 5 3 -2 -5|]<br /> | ||
EDOs: 4, 15, 19, 72<br /> | EDOs: <a class="wiki_link" href="/4edo">4</a>, <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/72edo">72</a><br /> | ||
Badness: 0.0297<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0297<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Catakleismic"></a><!-- ws:end:WikiTextHeadingRule:8 -->Catakleismic</h1> | <!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Catakleismic"></a><!-- ws:end:WikiTextHeadingRule:8 -->Catakleismic</h1> | ||
| Line 265: | Line 265: | ||
<br /> | <br /> | ||
Map: [&lt;1 0 1 -3|, &lt;0 6 5 22|]<br /> | Map: [&lt;1 0 1 -3|, &lt;0 6 5 22|]<br /> | ||
Wedgie: &lt;&lt;6 5 22 -6 18 37||<br /> | <a class="wiki_link" href="/Wedgie">Wedgie</a>: &lt;&lt;6 5 22 -6 18 37||<br /> | ||
EDOs: <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/53edo">15</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/197edo">197</a>, <a class="wiki_link" href="/269edo">269</a><br /> | EDOs: <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/53edo">15</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/197edo">197</a>, <a class="wiki_link" href="/269edo">269</a><br /> | ||
Badness: 0.0215<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0215<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Catakleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->11-limit</h2> | <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Catakleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->11-limit</h2> | ||
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Map: [&lt;1 0 1 -3 9|, &lt;0 6 5 22 -21|]<br /> | Map: [&lt;1 0 1 -3 9|, &lt;0 6 5 22 -21|]<br /> | ||
EDOs: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/269edo">269</a>, <a class="wiki_link" href="/341edo">341</a><br /> | EDOs: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/269edo">269</a>, <a class="wiki_link" href="/341edo">341</a><br /> | ||
Badness: 0.0218<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0218<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Catakleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:12 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Catakleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:12 -->13-limit</h2> | ||
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Map: [&lt;1 0 1 -3 9 0|, &lt;0 6 5 22 -21 14|]<br /> | Map: [&lt;1 0 1 -3 9 0|, &lt;0 6 5 22 -21 14|]<br /> | ||
EDOs: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/197edo">197</a>, <a class="wiki_link" href="/269edo">269</a>, <a class="wiki_link" href="/466edo">466</a><br /> | EDOs: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/197edo">197</a>, <a class="wiki_link" href="/269edo">269</a>, <a class="wiki_link" href="/466edo">466</a><br /> | ||
Badness: 0.0169<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0169<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="Countercata"></a><!-- ws:end:WikiTextHeadingRule:14 -->Countercata</h1> | <!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="Countercata"></a><!-- ws:end:WikiTextHeadingRule:14 -->Countercata</h1> | ||
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Map: [&lt;1 0 1 11|, &lt;0 6 5 -31|]<br /> | Map: [&lt;1 0 1 11|, &lt;0 6 5 -31|]<br /> | ||
Wedgie: &lt;&lt;6 5 -31 -6 -66 -86||<br /> | <a class="wiki_link" href="/Wedgie">Wedgie</a>: &lt;&lt;6 5 -31 -6 -66 -86||<br /> | ||
EDOs: 15, 19, 34, 53, 87, 140, 333, 473, 806<br /> | EDOs: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/34edo">34</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/140edo">140</a>, <a class="wiki_link" href="/333edo">333</a>, <a class="wiki_link" href="/473edo">473</a>, <a class="wiki_link" href="/806edo">806</a><br /> | ||
Badness: 0.0521<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0521<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="Countercata-11-limit"></a><!-- ws:end:WikiTextHeadingRule:16 -->11-limit</h2> | <!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="Countercata-11-limit"></a><!-- ws:end:WikiTextHeadingRule:16 -->11-limit</h2> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 385/384, 2200/2187, 3388/3375<br /> | |||
<br /> | <br /> | ||
POTE generator: ~6/5 = 317.162<br /> | POTE generator: ~6/5 = 317.162<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 1 11 -5|, &lt;0 6 5 -31 32|]<br /> | Map: [&lt;1 0 1 11 -5|, &lt;0 6 5 -31 32|]<br /> | ||
EDOs: 34, 53, 87, 140, 227<br /> | EDOs: <a class="wiki_link" href="/34edo">34</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/140edo">140</a>, <a class="wiki_link" href="/227edo">227</a><br /> | ||
Badness: 0.0398<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0398<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Countercata-13-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Countercata-13-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->13-limit</h2> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 325/324, 352/351, 385/384, 625/624<br /> | |||
<br /> | <br /> | ||
POTE generator: ~6/5 = 317.162<br /> | POTE generator: ~6/5 = 317.162<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 1 11 -5 0|, &lt;0 6 5 -31 32 14|]<br /> | Map: [&lt;1 0 1 11 -5 0|, &lt;0 6 5 -31 32 14|]<br /> | ||
EDOs: 34, 53, 87, 140, 367<br /> | EDOs: <a class="wiki_link" href="/34edo">34</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/140edo">140</a>, <a class="wiki_link" href="/367edo">367</a><br /> | ||
Badness: 0.0202<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0202<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="Metakleismic"></a><!-- ws:end:WikiTextHeadingRule:20 -->Metakleismic</h1> | <!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="Metakleismic"></a><!-- ws:end:WikiTextHeadingRule:20 -->Metakleismic</h1> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 15625/15552, 179200/177147<br /> | |||
<br /> | <br /> | ||
POTE generator: ~6/5 = 317.314<br /> | POTE generator: ~6/5 = 317.314<br /> | ||
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Map: [&lt;1 0 1 -12|, &lt;0 6 5 56|]<br /> | Map: [&lt;1 0 1 -12|, &lt;0 6 5 56|]<br /> | ||
Wedgie: &lt;&lt;6 5 56 -6 72 116||<br /> | Wedgie: &lt;&lt;6 5 56 -6 72 116||<br /> | ||
EDOs: 15, 19, 34, 87, 121, 208<br /> | EDOs: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/34edo">34</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/121edo">121</a>, <a class="wiki_link" href="/208edo">208</a><br /> | ||
Badness: 0.1635<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.1635<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="Metakleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:22 -->11-limit</h2> | <!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="Metakleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:22 -->11-limit</h2> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 896/891, 2200/2187, 14700/14641<br /> | |||
<br /> | <br /> | ||
POTE generator: ~6/5 = 317.311<br /> | POTE generator: ~6/5 = 317.311<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 1 -12 -5|, &lt;0 6 5 56 32|]<br /> | Map: [&lt;1 0 1 -12 -5|, &lt;0 6 5 56 32|]<br /> | ||
EDOs: 15, 19, 34, 87, 121, 208<br /> | EDOs: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/34edo">34</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/121edo">121</a>, <a class="wiki_link" href="/208edo">208</a><br /> | ||
Badness: 0.0486<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0486<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Metakleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Metakleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->13-limit</h2> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 325/324, 352/351, 364/363, 625/624<br /> | |||
<br /> | <br /> | ||
POTE generator: ~6/5 = 317.311<br /> | POTE generator: ~6/5 = 317.311<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 1 -12 -5 0|, &lt;0 6 5 56 32 14|]<br /> | Map: [&lt;1 0 1 -12 -5 0|, &lt;0 6 5 56 32 14|]<br /> | ||
EDOs: 15, 19, 34, 87, 121, 208<br /> | EDOs: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/34edo">34</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/121edo">121</a>, <a class="wiki_link" href="/208edo">208</a><br /> | ||
Badness: 0.0244<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0244<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc13"><a name="Hemikleismic"></a><!-- ws:end:WikiTextHeadingRule:26 -->Hemikleismic</h1> | <!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc13"><a name="Hemikleismic"></a><!-- ws:end:WikiTextHeadingRule:26 -->Hemikleismic</h1> | ||
| Line 349: | Line 349: | ||
<br /> | <br /> | ||
Map: [&lt;1 0 1 4|, &lt;0 12 10 -9|]<br /> | Map: [&lt;1 0 1 4|, &lt;0 12 10 -9|]<br /> | ||
EDOs: 53, 121<br /> | EDOs: <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/121edo">121</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:28:&lt;h1&gt; --><h1 id="toc14"><a name="Clyde"></a><!-- ws:end:WikiTextHeadingRule:28 -->Clyde</h1> | <!-- ws:start:WikiTextHeadingRule:28:&lt;h1&gt; --><h1 id="toc14"><a name="Clyde"></a><!-- ws:end:WikiTextHeadingRule:28 -->Clyde</h1> | ||
| Line 367: | Line 367: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:30:&lt;h1&gt; --><h1 id="toc15"><a name="Tritikleismic"></a><!-- ws:end:WikiTextHeadingRule:30 -->Tritikleismic</h1> | <!-- ws:start:WikiTextHeadingRule:30:&lt;h1&gt; --><h1 id="toc15"><a name="Tritikleismic"></a><!-- ws:end:WikiTextHeadingRule:30 -->Tritikleismic</h1> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 15625/15552, 1029/1024<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.872<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.872<br /> | ||
<br /> | <br /> | ||
Map: [&lt;3 0 3 10|, &lt;0 6 5 -2|]<br /> | Map: [&lt;3 0 3 10|, &lt;0 6 5 -2|]<br /> | ||
Wedgie: &lt;&lt;18 15 -6 -18 -60 -56||<br /> | <a class="wiki_link" href="/Wedgie">Wedgie</a>: &lt;&lt;18 15 -6 -18 -60 -56||<br /> | ||
EDOs: 12, 15, 57, 72, 159, 231<br /> | EDOs: <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/57edo">57</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/159edo">159</a>, <a class="wiki_link" href="/231edo">231</a><br /> | ||
Badness: 0.0563<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0563<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Tritikleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->11-limit</h2> | <!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Tritikleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->11-limit</h2> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 385/384, 441/440, 4000/3993<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.881<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.881<br /> | ||
<br /> | <br /> | ||
Map: [&lt;3 0 3 10 8|, &lt;0 6 5 -2 3|]<br /> | Map: [&lt;3 0 3 10 8|, &lt;0 6 5 -2 3|]<br /> | ||
EDOs: 12, 15, 57, 72, 159, 231<br /> | EDOs: <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/57edo">57</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/159edo">159</a>, <a class="wiki_link" href="/231edo">231</a><br /> | ||
Badness: 0.0193<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0193<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="Tritikleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="Tritikleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->13-limit</h2> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 325/324, 364/363, 441/440, 625/624<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.959<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.959<br /> | ||
<br /> | <br /> | ||
Map: [&lt;3 0 3 10 8 0|, &lt;0 6 5 -2 3 14|]<br /> | Map: [&lt;3 0 3 10 8 0|, &lt;0 6 5 -2 3 14|]<br /> | ||
EDOs: 12, 15, 72, 87, 159, 867, 1026<br /> | EDOs: <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/72edo">72</a>, 87, 159, 867, 1026<br /> | ||
Badness: 0.0157<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0157<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:36:&lt;h1&gt; --><h1 id="toc18"><a name="Quadritikleismic"></a><!-- ws:end:WikiTextHeadingRule:36 -->Quadritikleismic</h1> | <!-- ws:start:WikiTextHeadingRule:36:&lt;h1&gt; --><h1 id="toc18"><a name="Quadritikleismic"></a><!-- ws:end:WikiTextHeadingRule:36 -->Quadritikleismic</h1> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 15625/15552, 2401/2400<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.9999<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.9999<br /> | ||
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Wedgie: &lt;&lt;24 20 16 -24 -42 -19||<br /> | Wedgie: &lt;&lt;24 20 16 -24 -42 -19||<br /> | ||
EDOs: <a class="wiki_link" href="/68edo">68</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/140edo">140</a>, <a class="wiki_link" href="/212edo">212</a>, <a class="wiki_link" href="/1200edo">1200</a><br /> | EDOs: <a class="wiki_link" href="/68edo">68</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/140edo">140</a>, <a class="wiki_link" href="/212edo">212</a>, <a class="wiki_link" href="/1200edo">1200</a><br /> | ||
Badness: 0.0392<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0392<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="Quadritikleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:38 -->11-limit</h2> | <!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="Quadritikleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:38 -->11-limit</h2> | ||
| Line 411: | Line 411: | ||
Map: [&lt;4 0 4 7 17|, &lt;0 6 5 4 -3|]<br /> | Map: [&lt;4 0 4 7 17|, &lt;0 6 5 4 -3|]<br /> | ||
EDOs: <a class="wiki_link" href="/68edo">68</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/140edo">140</a>, <a class="wiki_link" href="/212edo">212</a>, <a class="wiki_link" href="/284edo">284</a>, <a class="wiki_link" href="/496edo">496</a>, <a class="wiki_link" href="/780edo">780</a><br /> | EDOs: <a class="wiki_link" href="/68edo">68</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/140edo">140</a>, <a class="wiki_link" href="/212edo">212</a>, <a class="wiki_link" href="/284edo">284</a>, <a class="wiki_link" href="/496edo">496</a>, <a class="wiki_link" href="/780edo">780</a><br /> | ||
Badness: 0.0234<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0234<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:40:&lt;h2&gt; --><h2 id="toc20"><a name="Quadritikleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:40 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:40:&lt;h2&gt; --><h2 id="toc20"><a name="Quadritikleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:40 -->13-limit</h2> | ||
| Line 419: | Line 419: | ||
<br /> | <br /> | ||
Map: [&lt;4 0 4 7 17 0|, &lt;0 6 5 4 -3 14|]<br /> | Map: [&lt;4 0 4 7 17 0|, &lt;0 6 5 4 -3 14|]<br /> | ||
EDOs: 68, 72, 140, 212<br /> | EDOs: <a class="wiki_link" href="/68edo">68</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/140edo">140</a>, <a class="wiki_link" href="/212edo">212</a><br /> | ||
Badness: 0.0187</body></html></pre></div> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0187</body></html></pre></div> | ||