Marvel family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 394589030 - Original comment: ** |
Wikispaces>x31eq **Imported revision 401590092 - 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:x31eq|x31eq]] and made on <tt>2013-01-26 07:09:35 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>401590092</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]] | <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;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]] | ||
=Marvel= | |||
The head of the marvel family is marvel, which tempers out [[225_224|225/224]], the [[septimal kleisma]] or [[marvel comma]]. Marvel has a [[Normal lists|normal list basis]] of [2, 3, 5]; hence a [[Harmonic Limit|5-limit]] scale can be converted to marvel simply by tempering it. One way to do that, and an excellent marvel tuning, is given by [[197edo]]. | |||
Little is gained in tuning accuracy by not tempering out 4375/4374 as well as 225/224, leading to [[Kleismic family|catakleismic temperament]]. Another temperament which does little damage to tuning accuracy is [[Pythagorean family|compton temperament]], for which [[240edo]] may be used. | |||
See also [[Marvel temperaments]]. | |||
==Vital statistics== | ==Vital statistics== | ||
[[Comma]] c = 225/224 | [[Comma]] c = 225/224 | ||
Related linear temperament: [[Kleismic family|catakleismic temperament]] | Related linear temperament: [[Kleismic family|catakleismic temperament]] | ||
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41: 34171875/33554432, 3125/3072 | 41: 34171875/33554432, 3125/3072 | ||
==Music== | ==Music== | ||
[[http://chrisvaisvil.com/?p=314|Semimarvelous Blue Drawf]] by [[Chris Vaisvil]] | [[http://chrisvaisvil.com/?p=314|Semimarvelous Blue Drawf]] by [[Chris Vaisvil]] | ||
==11-limit (Unimarv)== | ==11-limit (Unimarv)== | ||
[[Comma|Commas]]: 225/224, 385/384 | [[Comma|Commas]]: 225/224, 385/384 | ||
Related linear temperament: [[Kleismic family|catakleismic temperament]] | Related linear temperament: [[Kleismic family|catakleismic temperament]] | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
[|1 0 0 0 0>, |4/3 8/9 -1/3 0 -1/9>, |8/3 -2/9 1/3 0 -2/9>, | [|1 0 0 0 0>, |4/3 8/9 -1/3 0 -1/9>, |8/3 -2/9 1/3 0 -2/9>, | ||
|3 4/3 0 0 -2/3>, |8/3 -2/9 -2/3 0 7/9>] | |3 4/3 0 0 -2/3>, |8/3 -2/9 -2/3 0 7/9>] | ||
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Scales: [[marvel22_11]], [[unimarv19]], [[unimarv22]] | Scales: [[marvel22_11]], [[unimarv19]], [[unimarv22]] | ||
===Hobbit bases=== | ===Hobbit bases=== | ||
{2, 3, 5} subgroup | {2, 3, 5} subgroup | ||
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41: 3125/3072, 34171875/33554432 | 41: 3125/3072, 34171875/33554432 | ||
==13-limit== | ==13-limit== | ||
Commas: 225/224, 385/384, 351/350 | Commas: 225/224, 385/384, 351/350 | ||
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[[Spectrum of a temperament|Spectrum]]: 5/4, 4/3, 16/15, 15/14, 9/7, 6/5, 7/6, 11/8, 7/5, 9/8, 8/7, 10/9, 12/11, 13/10, 11/10, 15/11, 16/13, 11/9, 15/13, 14/13, 13/12, 14/11, 18/13, 13/11 | [[Spectrum of a temperament|Spectrum]]: 5/4, 4/3, 16/15, 15/14, 9/7, 6/5, 7/6, 11/8, 7/5, 9/8, 8/7, 10/9, 12/11, 13/10, 11/10, 15/11, 16/13, 11/9, 15/13, 14/13, 13/12, 14/11, 18/13, 13/11 | ||
==Other eleven limit children== | ==Other eleven limit children== | ||
The second comma of the [[Normal lists|normal comma list]] defines which 11-limit family member we are looking at. Adding 4125/4096 gives unidecimal marvel, 91125/90112 gives prodigy, 5632/5625 minerva and 243/242 spectacle. | The second comma of the [[Normal lists|normal comma list]] defines which 11-limit family member we are looking at. Adding 4125/4096 gives unidecimal marvel, 91125/90112 gives prodigy, 5632/5625 minerva and 243/242 spectacle. | ||
=Hecate= | =Hecate= | ||
Commas: 225/224, 385/384, 325/324 | Commas: 225/224, 385/384, 325/324 | ||
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[[Spectrum of a temperament|Spectrum]]: 4/3, 5/4, 16/15, 15/14, 6/5, 9/8, 7/5, 9/7, 7/6, 10/9, 8/7, 18/13, 11/8, 12/11, 13/12, 11/9, 11/10, 15/13, 15/11, 16/13, 13/11, 14/13, 13/10, 14/11 | [[Spectrum of a temperament|Spectrum]]: 4/3, 5/4, 16/15, 15/14, 6/5, 9/8, 7/5, 9/7, 7/6, 10/9, 8/7, 18/13, 11/8, 12/11, 13/12, 11/9, 11/10, 15/13, 15/11, 16/13, 13/11, 14/13, 13/10, 14/11 | ||
==17-limit== | ==17-limit== | ||
Commas: 225/224, 385/384, 325/324, 595/594 | Commas: 225/224, 385/384, 325/324, 595/594 | ||
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Badness: 0.000869 | Badness: 0.000869 | ||
==Enodia== | ==Enodia== | ||
Commas: 225/224, 385/384, 325/324, 375/374 | Commas: 225/224, 385/384, 325/324, 375/374 | ||
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Badness: .000917 | Badness: .000917 | ||
=Marvell= | =Marvell= | ||
Commas: 225/224, 385/384, 1573/1568 | Commas: 225/224, 385/384, 1573/1568 | ||
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Badness: 0.000862 | Badness: 0.000862 | ||
=Isis= | =Isis= | ||
Commas: 225/224, 385/384, 275/273 | Commas: 225/224, 385/384, 275/273 | ||
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Projection pairs: 7 225/32 11 4096/375 13 131072/10125 | Projection pairs: 7 225/32 11 4096/375 13 131072/10125 | ||
=Deecee= | =Deecee= | ||
Commas: 225/224, 385/384, 364/363 | Commas: 225/224, 385/384, 364/363 | ||
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Projection pairs: 7 225/32 11 4096/375 13 134217728/10546875 | Projection pairs: 7 225/32 11 4096/375 13 134217728/10546875 | ||
=Tripod= | =Tripod= | ||
Commas: 105/104, 144/143, 196/195 | Commas: 105/104, 144/143, 196/195 | ||
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Projection pairs: 7 225/32 11 4096/375 13 3375/256 | Projection pairs: 7 225/32 11 4096/375 13 3375/256 | ||
=Prodigy= | =Prodigy= | ||
Prodigy shrinks 1024/1029, 243/242, 384/385 and 2400/2401 down to the same tiny interval. Hence in practice it probably makes the most sense to temper this out as well, leading to [[Gamelismic clan|miracle temperament]]. This, however, does not render it pointless to consider prodigy; for one thing, scales in prodigy such as hobbit scales translate into interesting scales for miracle. | Prodigy shrinks 1024/1029, 243/242, 384/385 and 2400/2401 down to the same tiny interval. Hence in practice it probably makes the most sense to temper this out as well, leading to [[Gamelismic clan|miracle temperament]]. This, however, does not render it pointless to consider prodigy; for one thing, scales in prodigy such as hobbit scales translate into interesting scales for miracle. | ||
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[[Minimax tuning]]: | [[Minimax tuning]]: | ||
[|1 0 0 0 0>, |13/12 1/2 -1/4 0 1/12>, | [|1 0 0 0 0>, |13/12 1/2 -1/4 0 1/12>, | ||
|13/6 -1 1/2 0 1/6>, | |13/6 -1 1/2 0 1/6>, | ||
|3/2 -1 1/2 0 1/2>, |0 0 0 0 1>] | |3/2 -1 1/2 0 1/2>, |0 0 0 0 1>] | ||
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Badness: 0.000344 | Badness: 0.000344 | ||
[[Projection pair]]s: 7 225/32 11 91125/8192 | [[Projection pair]]s: 7 225/32 11 91125/8192 | ||
Scales: [[prodigy11]], [[prodigy12]], [[prodigy29]] | Scales: [[prodigy11]], [[prodigy12]], [[prodigy29]] | ||
==Hobbit bases== | ==Hobbit bases== | ||
{2, 3, 5} subgroup | {2, 3, 5} subgroup | ||
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41: 34171875/33554432, 32805/32768 | 41: 34171875/33554432, 32805/32768 | ||
==13-limit== | ==13-limit== | ||
Commas: 105/104, 196/195, 352/351 | Commas: 105/104, 196/195, 352/351 | ||
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Badness: 0.000736 | Badness: 0.000736 | ||
==Prodigious== | ==Prodigious== | ||
Commas: 225/224, 441/440, 364/363 | Commas: 225/224, 441/440, 364/363 | ||
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Badness: 0.000900 | Badness: 0.000900 | ||
==Prodigal== | ==Prodigal== | ||
Commas: 225/224, 441/440, 351/350 | Commas: 225/224, 441/440, 351/350 | ||
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Badness: 0.000889 | Badness: 0.000889 | ||
=Mirage= | =Mirage= | ||
Commas: 225/224, 243/242, 385/384 | Commas: 225/224, 243/242, 385/384 | ||
Map: [<1 1 3 3 2 0|, <0 6 -7 -2 15 0|, <0 0 0 0 0 1|] | Map: [<1 1 3 3 2 0|, <0 6 -7 -2 15 0|, <0 0 0 0 0 1|] | ||
EDOs: 10, 31, 41, 62, 72, 103, 175f, 216c, 288cdf, 391bcdef | EDOs: 10, 31, 41, 62, 72, 103, 175f, 216c, 288cdf, 391bcdef | ||
Badness: 0.000738 | Badness: 0.000738 | ||
=Minerva= | =Minerva= | ||
[[Comma|Commas]]: 99/98, 176/175 | [[Comma|Commas]]: 99/98, 176/175 | ||
Related linear temperament: [[Semicomma family|orwell]] | Related linear temperament: [[Semicomma family|orwell]] | ||
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[[Eigenmonzo subgroup]]: 2.7/5.11/9 | [[Eigenmonzo subgroup]]: 2.7/5.11/9 | ||
Lattice basis: 16/15 length 0.8997 5/4 length 1.0457 | Lattice basis: 16/15 length 0.8997 5/4 length 1.0457 | ||
Angle(16/15, 5/4) = 98.6044 degrees | Angle(16/15, 5/4) = 98.6044 degrees | ||
Map to lattice: [<0 -1 0 -2 -2|, <0 -1 1 0 2|] | Map to lattice: [<0 -1 0 -2 -2|, <0 -1 1 0 2|] | ||
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Badness: 0.000381 | Badness: 0.000381 | ||
[[Projection pair]]s: 7 225/32 11 5625/512 | [[Projection pair]]s: 7 225/32 11 5625/512 | ||
Scales: [[minerva12]], [[minerva22x]] | Scales: [[minerva12]], [[minerva22x]] | ||
==Athene== | ==Athene== | ||
Commas: 99/98, 176/175, 275/273 | Commas: 99/98, 176/175, 275/273 | ||
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[[Projection pair]]s: 7 225/32 11 5625/512 13 625/48 | [[Projection pair]]s: 7 225/32 11 5625/512 13 625/48 | ||
=Spectacle= | =Spectacle= | ||
[[Comma|Commas]]: 225/224, 243/242 | [[Comma|Commas]]: 225/224, 243/242 | ||
Related linear temperament: [[Marvel temperaments|marvo]] | Related linear temperament: [[Marvel temperaments|marvo]] | ||
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Scales: [[spectacle31]] | Scales: [[spectacle31]] | ||
=Apollo= | =Apollo= | ||
[[Comma|Commas]]: 100/99, 225/224 | [[Comma|Commas]]: 100/99, 225/224 | ||
Related linear temperament: [[Magic family|Magic]] | Related linear temperament: [[Magic family|Magic]] | ||
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Projection pairs: 7 225/32 11 100/9 | Projection pairs: 7 225/32 11 100/9 | ||
=Potassium= | =Potassium= | ||
Commas: 45/44, 56/55 | Commas: 45/44, 56/55 | ||
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Projection pairs: 7 225/32 11 45/4 | Projection pairs: 7 225/32 11 45/4 | ||
==13-limit== | ==13-limit== | ||
Commas: 45/44, 56/55, 78/77 | Commas: 45/44, 56/55, 78/77 | ||
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Projection pairs: 7 225/32 11 45/4 13 3375/256 | Projection pairs: 7 225/32 11 45/4 13 3375/256 | ||
=Catakleismoid= | =Catakleismoid= | ||
Commas: 225/224, 4375/4374 | Commas: 225/224, 4375/4374 | ||
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Badness: 0.001275 | Badness: 0.001275 | ||
==13-limit== | ==13-limit== | ||
Commas: 169/168, 225/224, 325/324 | Commas: 169/168, 225/224, 325/324 | ||
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Badness: 0.000916 | Badness: 0.000916 | ||
=Hestia= | =Hestia= | ||
Commas: 225/224, 125000/124509 | Commas: 225/224, 125000/124509 | ||
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Badness: 0.00154 | Badness: 0.00154 | ||
==13-limit== | ==13-limit== | ||
Commas: 169/168, 225/224, 1001/1000 | Commas: 169/168, 225/224, 1001/1000 | ||
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Badness: 0.001062 | Badness: 0.001062 | ||
=Malcolm= | =Malcolm= | ||
Commas: 225/224, 2200/2187 | Commas: 225/224, 2200/2187 | ||
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Badness: 0.001250 | Badness: 0.001250 | ||
==13-limit== | ==13-limit== | ||
commas: 225/224, 275/273, 325/324 | commas: 225/224, 275/273, 325/324 | ||
Map: [<1 0 0 -5 -3 2|, <0 1 0 2 7 4|, <0 0 1 2 -2 -2|] | Map: [<1 0 0 -5 -3 2|, <0 1 0 2 7 4|, <0 0 1 2 -2 -2|] | ||
EDOs: 41, 53, 94, 429cdef, 523cdef | EDOs: 41, 53, 94, 429cdef, 523cdef | ||
Badness: 0.001075 | Badness: 0.001075</pre></div> | ||
</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>Marvel family</title></head><body><!-- ws:start:WikiTextTocRule:66:&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:66 --><!-- ws:start:WikiTextTocRule:67: --><a href="#Marvel">Marvel</a><!-- ws:end:WikiTextTocRule:67 --><!-- ws:start:WikiTextTocRule:68: --><!-- ws:end:WikiTextTocRule:68 --><!-- ws:start:WikiTextTocRule:69: --><!-- ws:end:WikiTextTocRule:69 --><!-- ws:start:WikiTextTocRule:70: --><!-- ws:end:WikiTextTocRule:70 --><!-- ws:start:WikiTextTocRule:71: --><!-- ws:end:WikiTextTocRule:71 --><!-- ws:start:WikiTextTocRule:72: --><!-- ws:end:WikiTextTocRule:72 --><!-- ws:start:WikiTextTocRule:73: --><!-- ws:end:WikiTextTocRule:73 --><!-- ws:start:WikiTextTocRule:74: --><!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --> | <a href="#Hecate">Hecate</a><!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --><!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --><!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --> | <a href="#Marvell">Marvell</a><!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --> | <a href="#Isis">Isis</a><!-- ws:end:WikiTextTocRule:79 --><!-- ws:start:WikiTextTocRule:80: --> | <a href="#Deecee">Deecee</a><!-- ws:end:WikiTextTocRule:80 --><!-- ws:start:WikiTextTocRule:81: --> | <a href="#Tripod">Tripod</a><!-- ws:end:WikiTextTocRule:81 --><!-- ws:start:WikiTextTocRule:82: --> | <a href="#Prodigy">Prodigy</a><!-- ws:end:WikiTextTocRule:82 --><!-- ws:start:WikiTextTocRule:83: --><!-- 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: --> | <a href="#Mirage">Mirage</a><!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextTocRule:88: --> | <a href="#Minerva">Minerva</a><!-- ws:end:WikiTextTocRule:88 --><!-- ws:start:WikiTextTocRule:89: --><!-- ws:end:WikiTextTocRule:89 --><!-- ws:start:WikiTextTocRule:90: --> | <a href="#Spectacle">Spectacle</a><!-- ws:end:WikiTextTocRule:90 --><!-- ws:start:WikiTextTocRule:91: --> | <a href="#Apollo">Apollo</a><!-- ws:end:WikiTextTocRule:91 --><!-- ws:start:WikiTextTocRule:92: --> | <a href="#Potassium">Potassium</a><!-- ws:end:WikiTextTocRule:92 --><!-- ws:start:WikiTextTocRule:93: --><!-- ws:end:WikiTextTocRule:93 --><!-- ws:start:WikiTextTocRule:94: --> | <a href="#Catakleismoid">Catakleismoid</a><!-- ws:end:WikiTextTocRule:94 --><!-- ws:start:WikiTextTocRule:95: --><!-- ws:end:WikiTextTocRule:95 --><!-- ws:start:WikiTextTocRule:96: --> | <a href="#Hestia">Hestia</a><!-- ws:end:WikiTextTocRule:96 --><!-- ws:start:WikiTextTocRule:97: --><!-- ws:end:WikiTextTocRule:97 --><!-- ws:start:WikiTextTocRule:98: --> | <a href="#Malcolm">Malcolm</a><!-- ws:end:WikiTextTocRule:98 --><!-- ws:start:WikiTextTocRule:99: --><!-- ws:end:WikiTextTocRule:99 --><!-- ws:start:WikiTextTocRule:100: --> | <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>Marvel family</title></head><body><!-- ws:start:WikiTextTocRule:66:&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:66 --><!-- ws:start:WikiTextTocRule:67: --><a href="#Marvel">Marvel</a><!-- ws:end:WikiTextTocRule:67 --><!-- ws:start:WikiTextTocRule:68: --><!-- ws:end:WikiTextTocRule:68 --><!-- ws:start:WikiTextTocRule:69: --><!-- ws:end:WikiTextTocRule:69 --><!-- ws:start:WikiTextTocRule:70: --><!-- ws:end:WikiTextTocRule:70 --><!-- ws:start:WikiTextTocRule:71: --><!-- ws:end:WikiTextTocRule:71 --><!-- ws:start:WikiTextTocRule:72: --><!-- ws:end:WikiTextTocRule:72 --><!-- ws:start:WikiTextTocRule:73: --><!-- ws:end:WikiTextTocRule:73 --><!-- ws:start:WikiTextTocRule:74: --><!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --> | <a href="#Hecate">Hecate</a><!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --><!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --><!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --> | <a href="#Marvell">Marvell</a><!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --> | <a href="#Isis">Isis</a><!-- ws:end:WikiTextTocRule:79 --><!-- ws:start:WikiTextTocRule:80: --> | <a href="#Deecee">Deecee</a><!-- ws:end:WikiTextTocRule:80 --><!-- ws:start:WikiTextTocRule:81: --> | <a href="#Tripod">Tripod</a><!-- ws:end:WikiTextTocRule:81 --><!-- ws:start:WikiTextTocRule:82: --> | <a href="#Prodigy">Prodigy</a><!-- ws:end:WikiTextTocRule:82 --><!-- ws:start:WikiTextTocRule:83: --><!-- 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: --> | <a href="#Mirage">Mirage</a><!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextTocRule:88: --> | <a href="#Minerva">Minerva</a><!-- ws:end:WikiTextTocRule:88 --><!-- ws:start:WikiTextTocRule:89: --><!-- ws:end:WikiTextTocRule:89 --><!-- ws:start:WikiTextTocRule:90: --> | <a href="#Spectacle">Spectacle</a><!-- ws:end:WikiTextTocRule:90 --><!-- ws:start:WikiTextTocRule:91: --> | <a href="#Apollo">Apollo</a><!-- ws:end:WikiTextTocRule:91 --><!-- ws:start:WikiTextTocRule:92: --> | <a href="#Potassium">Potassium</a><!-- ws:end:WikiTextTocRule:92 --><!-- ws:start:WikiTextTocRule:93: --><!-- ws:end:WikiTextTocRule:93 --><!-- ws:start:WikiTextTocRule:94: --> | <a href="#Catakleismoid">Catakleismoid</a><!-- ws:end:WikiTextTocRule:94 --><!-- ws:start:WikiTextTocRule:95: --><!-- ws:end:WikiTextTocRule:95 --><!-- ws:start:WikiTextTocRule:96: --> | <a href="#Hestia">Hestia</a><!-- ws:end:WikiTextTocRule:96 --><!-- ws:start:WikiTextTocRule:97: --><!-- ws:end:WikiTextTocRule:97 --><!-- ws:start:WikiTextTocRule:98: --> | <a href="#Malcolm">Malcolm</a><!-- ws:end:WikiTextTocRule:98 --><!-- ws:start:WikiTextTocRule:99: --><!-- ws:end:WikiTextTocRule:99 --><!-- ws:start:WikiTextTocRule:100: --> | ||
<!-- ws:end:WikiTextTocRule:100 --> | <!-- ws:end:WikiTextTocRule:100 --><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Marvel"></a><!-- ws:end:WikiTextHeadingRule:0 -->Marvel</h1> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Marvel"></a><!-- ws:end:WikiTextHeadingRule:0 -->Marvel</h1> | The head of the marvel family is marvel, which tempers out <a class="wiki_link" href="/225_224">225/224</a>, the <a class="wiki_link" href="/septimal%20kleisma">septimal kleisma</a> or <a class="wiki_link" href="/marvel%20comma">marvel comma</a>. Marvel has a <a class="wiki_link" href="/Normal%20lists">normal list basis</a> of [2, 3, 5]; hence a <a class="wiki_link" href="/Harmonic%20Limit">5-limit</a> scale can be converted to marvel simply by tempering it. One way to do that, and an excellent marvel tuning, is given by <a class="wiki_link" href="/197edo">197edo</a>.<br /> | ||
The head of the marvel family is marvel, which tempers out <a class="wiki_link" href="/225_224">225/224</a>, the <a class="wiki_link" href="/septimal%20kleisma">septimal kleisma</a> or <a class="wiki_link" href="/marvel%20comma">marvel comma</a>. Marvel has a <a class="wiki_link" href="/Normal%20lists">normal list basis</a> of [2, 3, 5]; hence a <a class="wiki_link" href="/Harmonic%20Limit">5-limit</a> scale can be converted to marvel simply by tempering it. One way to do that, and an excellent marvel tuning, is given by <a class="wiki_link" href="/197edo">197edo</a>. <br /> | |||
<br /> | <br /> | ||
Little is gained in tuning accuracy by not tempering out 4375/4374 as well as 225/224, leading to <a class="wiki_link" href="/Kleismic%20family">catakleismic temperament</a>. Another temperament which does little damage to tuning accuracy is <a class="wiki_link" href="/Pythagorean%20family">compton temperament</a>, for which <a class="wiki_link" href="/240edo">240edo</a> may be used.<br /> | Little is gained in tuning accuracy by not tempering out 4375/4374 as well as 225/224, leading to <a class="wiki_link" href="/Kleismic%20family">catakleismic temperament</a>. Another temperament which does little damage to tuning accuracy is <a class="wiki_link" href="/Pythagorean%20family">compton temperament</a>, for which <a class="wiki_link" href="/240edo">240edo</a> may be used.<br /> | ||
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See also <a class="wiki_link" href="/Marvel%20temperaments">Marvel temperaments</a>.<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Marvel-Vital statistics"></a><!-- ws:end:WikiTextHeadingRule:2 -->Vital statistics</h2> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Marvel-Vital statistics"></a><!-- ws:end:WikiTextHeadingRule:2 -->Vital statistics</h2> | ||
<a class="wiki_link" href="/Comma">Comma</a> c = 225/224<br /> | <a class="wiki_link" href="/Comma">Comma</a> c = 225/224<br /> | ||
Related linear temperament: <a class="wiki_link" href="/Kleismic%20family">catakleismic temperament</a><br /> | Related linear temperament: <a class="wiki_link" href="/Kleismic%20family">catakleismic temperament</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Marvel-Music"></a><!-- ws:end:WikiTextHeadingRule:6 -->Music</h2> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Marvel-Music"></a><!-- ws:end:WikiTextHeadingRule:6 -->Music</h2> | ||
<a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=314" rel="nofollow">Semimarvelous Blue Drawf</a> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br /> | <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=314" rel="nofollow">Semimarvelous Blue Drawf</a> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Marvel-11-limit (Unimarv)"></a><!-- ws:end:WikiTextHeadingRule:8 -->11-limit (Unimarv)</h2> | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Marvel-11-limit (Unimarv)"></a><!-- ws:end:WikiTextHeadingRule:8 -->11-limit (Unimarv)</h2> | ||
<a class="wiki_link" href="/Comma">Commas</a>: 225/224, 385/384<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 225/224, 385/384<br /> | ||
Related linear temperament: <a class="wiki_link" href="/Kleismic%20family">catakleismic temperament</a><br /> | Related linear temperament: <a class="wiki_link" href="/Kleismic%20family">catakleismic temperament</a><br /> | ||
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<a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>: <br /> | <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br /> | ||
[|1 0 0 0 0&gt;, |4/3 8/9 -1/3 0 -1/9&gt;, |8/3 -2/9 1/3 0 -2/9&gt;,<br /> | [|1 0 0 0 0&gt;, |4/3 8/9 -1/3 0 -1/9&gt;, |8/3 -2/9 1/3 0 -2/9&gt;,<br /> | ||
|3 4/3 0 0 -2/3&gt;, |8/3 -2/9 -2/3 0 7/9&gt;]<br /> | |3 4/3 0 0 -2/3&gt;, |8/3 -2/9 -2/3 0 7/9&gt;]<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="Marvel-11-limit (Unimarv)-Hobbit bases"></a><!-- ws:end:WikiTextHeadingRule:10 -->Hobbit bases</h3> | <!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="Marvel-11-limit (Unimarv)-Hobbit bases"></a><!-- ws:end:WikiTextHeadingRule:10 -->Hobbit bases</h3> | ||
{2, 3, 5} subgroup<br /> | {2, 3, 5} subgroup<br /> | ||
<br /> | <br /> | ||
12: 128/125, 2048/2025<br /> | 12: 128/125, 2048/2025<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Marvel-13-limit"></a><!-- ws:end:WikiTextHeadingRule:12 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Marvel-13-limit"></a><!-- ws:end:WikiTextHeadingRule:12 -->13-limit</h2> | ||
Commas: 225/224, 385/384, 351/350<br /> | Commas: 225/224, 385/384, 351/350<br /> | ||
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13-limit eigenmonzo subgroup: 2.11/9.13/9<br /> | 13-limit eigenmonzo subgroup: 2.11/9.13/9<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Marvel-Other eleven limit children"></a><!-- ws:end:WikiTextHeadingRule:14 -->Other eleven limit children</h2> | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Marvel-Other eleven limit children"></a><!-- ws:end:WikiTextHeadingRule:14 -->Other eleven limit children</h2> | ||
The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which 11-limit family member we are looking at. Adding 4125/4096 gives unidecimal marvel, 91125/90112 gives prodigy, 5632/5625 minerva and 243/242 spectacle.<br /> | The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which 11-limit family member we are looking at. Adding 4125/4096 gives unidecimal marvel, 91125/90112 gives prodigy, 5632/5625 minerva and 243/242 spectacle.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="Hecate"></a><!-- ws:end:WikiTextHeadingRule:16 -->Hecate</h1> | <!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="Hecate"></a><!-- ws:end:WikiTextHeadingRule:16 -->Hecate</h1> | ||
Commas: 225/224, 385/384, 325/324<br /> | Commas: 225/224, 385/384, 325/324<br /> | ||
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13-limit eigenmonzo subgroup: 2.7.13/5<br /> | 13-limit eigenmonzo subgroup: 2.7.13/5<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Hecate-17-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->17-limit</h2> | <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Hecate-17-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->17-limit</h2> | ||
Commas: 225/224, 385/384, 325/324, 595/594<br /> | Commas: 225/224, 385/384, 325/324, 595/594<br /> | ||
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Map: [&lt;1 0 0 -5 12 2 18|, &lt;0 1 0 2 -1 4 0|, &lt;0 0 1 2 -3 -2 -6|]<br /> | Map: [&lt;1 0 0 -5 12 2 18|, &lt;0 1 0 2 -1 4 0|, &lt;0 0 1 2 -3 -2 -6|]<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Hecate-Enodia"></a><!-- ws:end:WikiTextHeadingRule:20 -->Enodia</h2> | <!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Hecate-Enodia"></a><!-- ws:end:WikiTextHeadingRule:20 -->Enodia</h2> | ||
Commas: 225/224, 385/384, 325/324, 375/374<br /> | Commas: 225/224, 385/384, 325/324, 375/374<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 0 -5 12 2 18|, &lt;0 1 0 2 -1 4 0|, &lt;0 0 1 2 -3 -2 6|]<br /> | Map: [&lt;1 0 0 -5 12 2 18|, &lt;0 1 0 2 -1 4 0|, &lt;0 0 1 2 -3 -2 6|]<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="Marvell"></a><!-- ws:end:WikiTextHeadingRule:22 -->Marvell</h1> | <!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="Marvell"></a><!-- ws:end:WikiTextHeadingRule:22 -->Marvell</h1> | ||
Commas: 225/224, 385/384, 1573/1568<br /> | Commas: 225/224, 385/384, 1573/1568<br /> | ||
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13-limit eigenmonzo subgroup: 2.9/5.11/9<br /> | 13-limit eigenmonzo subgroup: 2.9/5.11/9<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc12"><a name="Isis"></a><!-- ws:end:WikiTextHeadingRule:24 -->Isis</h1> | <!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc12"><a name="Isis"></a><!-- ws:end:WikiTextHeadingRule:24 -->Isis</h1> | ||
Commas: 225/224, 385/384, 275/273<br /> | Commas: 225/224, 385/384, 275/273<br /> | ||
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Map: [&lt;1 0 0 -5 12 17|, &lt;0 1 0 2 -1 4|, &lt;0 0 1 2 -3 -3|]<br /> | Map: [&lt;1 0 0 -5 12 17|, &lt;0 1 0 2 -1 4|, &lt;0 0 1 2 -3 -3|]<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc13"><a name="Deecee"></a><!-- ws:end:WikiTextHeadingRule:26 -->Deecee</h1> | <!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc13"><a name="Deecee"></a><!-- ws:end:WikiTextHeadingRule:26 -->Deecee</h1> | ||
Commas: 225/224, 385/384, 364/363<br /> | Commas: 225/224, 385/384, 364/363<br /> | ||
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13-limit eigenmonzo subgroup: 2.9/5.13/9<br /> | 13-limit eigenmonzo subgroup: 2.9/5.13/9<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:28:&lt;h1&gt; --><h1 id="toc14"><a name="Tripod"></a><!-- ws:end:WikiTextHeadingRule:28 -->Tripod</h1> | <!-- ws:start:WikiTextHeadingRule:28:&lt;h1&gt; --><h1 id="toc14"><a name="Tripod"></a><!-- ws:end:WikiTextHeadingRule:28 -->Tripod</h1> | ||
Commas: 105/104, 144/143, 196/195<br /> | Commas: 105/104, 144/143, 196/195<br /> | ||
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13-limit eigenmonzo subgroup: 2.9/7.13/11<br /> | 13-limit eigenmonzo subgroup: 2.9/7.13/11<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:30:&lt;h1&gt; --><h1 id="toc15"><a name="Prodigy"></a><!-- ws:end:WikiTextHeadingRule:30 -->Prodigy</h1> | <!-- ws:start:WikiTextHeadingRule:30:&lt;h1&gt; --><h1 id="toc15"><a name="Prodigy"></a><!-- ws:end:WikiTextHeadingRule:30 -->Prodigy</h1> | ||
Prodigy shrinks 1024/1029, 243/242, 384/385 and 2400/2401 down to the same tiny interval. Hence in practice it probably makes the most sense to temper this out as well, leading to <a class="wiki_link" href="/Gamelismic%20clan">miracle temperament</a>. This, however, does not render it pointless to consider prodigy; for one thing, scales in prodigy such as hobbit scales translate into interesting scales for miracle.<br /> | Prodigy shrinks 1024/1029, 243/242, 384/385 and 2400/2401 down to the same tiny interval. Hence in practice it probably makes the most sense to temper this out as well, leading to <a class="wiki_link" href="/Gamelismic%20clan">miracle temperament</a>. This, however, does not render it pointless to consider prodigy; for one thing, scales in prodigy such as hobbit scales translate into interesting scales for miracle.<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/Comma">Commas</a>: 225/224, 441/440<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 225/224, 441/440<br /> | ||
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<a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br /> | <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br /> | ||
[|1 0 0 0 0&gt;, |13/12 1/2 -1/4 0 1/12&gt;, <br /> | [|1 0 0 0 0&gt;, |13/12 1/2 -1/4 0 1/12&gt;,<br /> | ||
|13/6 -1 1/2 0 1/6&gt;,<br /> | |13/6 -1 1/2 0 1/6&gt;,<br /> | ||
|3/2 -1 1/2 0 1/2&gt;, |0 0 0 0 1&gt;]<br /> | |3/2 -1 1/2 0 1/2&gt;, |0 0 0 0 1&gt;]<br /> | ||
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Badness: 0.000344<br /> | Badness: 0.000344<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/Projection%20pair">Projection pair</a>s: 7 225/32 11 91125/8192 <br /> | <a class="wiki_link" href="/Projection%20pair">Projection pair</a>s: 7 225/32 11 91125/8192<br /> | ||
<br /> | <br /> | ||
Scales: <a class="wiki_link" href="/prodigy11">prodigy11</a>, <a class="wiki_link" href="/prodigy12">prodigy12</a>, <a class="wiki_link" href="/prodigy29">prodigy29</a><br /> | Scales: <a class="wiki_link" href="/prodigy11">prodigy11</a>, <a class="wiki_link" href="/prodigy12">prodigy12</a>, <a class="wiki_link" href="/prodigy29">prodigy29</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Prodigy-Hobbit bases"></a><!-- ws:end:WikiTextHeadingRule:32 -->Hobbit bases</h2> | <!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Prodigy-Hobbit bases"></a><!-- ws:end:WikiTextHeadingRule:32 -->Hobbit bases</h2> | ||
{2, 3, 5} subgroup<br /> | {2, 3, 5} subgroup<br /> | ||
<br /> | <br /> | ||
31: 81/80, 34171875/33554432<br /> | 31: 81/80, 34171875/33554432<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="Prodigy-13-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="Prodigy-13-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->13-limit</h2> | ||
Commas: 105/104, 196/195, 352/351<br /> | Commas: 105/104, 196/195, 352/351<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 0 -5 -13 -8|, &lt;0 1 0 2 6 3|, &lt;0 0 1 2 3 3|]<br /> | Map: [&lt;1 0 0 -5 -13 -8|, &lt;0 1 0 2 6 3|, &lt;0 0 1 2 3 3|]<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Prodigy-Prodigious"></a><!-- ws:end:WikiTextHeadingRule:36 -->Prodigious</h2> | <!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Prodigy-Prodigious"></a><!-- ws:end:WikiTextHeadingRule:36 -->Prodigious</h2> | ||
Commas: 225/224, 441/440, 364/363<br /> | Commas: 225/224, 441/440, 364/363<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 0 -5 -13 -23|, &lt;0 1 0 2 6 11|, &lt;0 0 1 2 3 4|]<br /> | Map: [&lt;1 0 0 -5 -13 -23|, &lt;0 1 0 2 6 11|, &lt;0 0 1 2 3 4|]<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="Prodigy-Prodigal"></a><!-- ws:end:WikiTextHeadingRule:38 -->Prodigal</h2> | <!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="Prodigy-Prodigal"></a><!-- ws:end:WikiTextHeadingRule:38 -->Prodigal</h2> | ||
Commas: 225/224, 441/440, 351/350<br /> | Commas: 225/224, 441/440, 351/350<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 0 -5 -13 -4|, &lt;0 1 0 2 6 -1|, &lt;0 0 1 2 3 4|]<br /> | Map: [&lt;1 0 0 -5 -13 -4|, &lt;0 1 0 2 6 -1|, &lt;0 0 1 2 3 4|]<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:40:&lt;h1&gt; --><h1 id="toc20"><a name="Mirage"></a><!-- ws:end:WikiTextHeadingRule:40 -->Mirage</h1> | <!-- ws:start:WikiTextHeadingRule:40:&lt;h1&gt; --><h1 id="toc20"><a name="Mirage"></a><!-- ws:end:WikiTextHeadingRule:40 -->Mirage</h1> | ||
Commas: 225/224, 243/242, 385/384<br /> | Commas: 225/224, 243/242, 385/384<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 1 3 3 2 0|, &lt;0 6 -7 -2 15 0|, &lt;0 0 0 0 0 1|]<br /> | Map: [&lt;1 1 3 3 2 0|, &lt;0 6 -7 -2 15 0|, &lt;0 0 0 0 0 1|]<br /> | ||
EDOs: 10, 31, 41, 62, 72, 103, 175f, 216c, 288cdf, 391bcdef <br /> | EDOs: 10, 31, 41, 62, 72, 103, 175f, 216c, 288cdf, 391bcdef<br /> | ||
Badness: 0.000738<br /> | Badness: 0.000738<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:42:&lt;h1&gt; --><h1 id="toc21"><a name="Minerva"></a><!-- ws:end:WikiTextHeadingRule:42 -->Minerva</h1> | <!-- ws:start:WikiTextHeadingRule:42:&lt;h1&gt; --><h1 id="toc21"><a name="Minerva"></a><!-- ws:end:WikiTextHeadingRule:42 -->Minerva</h1> | ||
<a class="wiki_link" href="/Comma">Commas</a>: 99/98, 176/175<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 99/98, 176/175<br /> | ||
Related linear temperament: <a class="wiki_link" href="/Semicomma%20family">orwell</a><br /> | Related linear temperament: <a class="wiki_link" href="/Semicomma%20family">orwell</a><br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/Eigenmonzo%20subgroup">Eigenmonzo subgroup</a>: 2.7/5.11/9<br /> | <a class="wiki_link" href="/Eigenmonzo%20subgroup">Eigenmonzo subgroup</a>: 2.7/5.11/9<br /> | ||
<br /> | <br /> | ||
Lattice basis: 16/15 length 0.8997 5/4 length 1.0457 <br /> | Lattice basis: 16/15 length 0.8997 5/4 length 1.0457<br /> | ||
Angle(16/15, 5/4) = 98.6044 degrees<br /> | Angle(16/15, 5/4) = 98.6044 degrees<br /> | ||
Map to lattice: [&lt;0 -1 0 -2 -2|, &lt;0 -1 1 0 2|]<br /> | Map to lattice: [&lt;0 -1 0 -2 -2|, &lt;0 -1 1 0 2|]<br /> | ||
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Badness: 0.000381<br /> | Badness: 0.000381<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/Projection%20pair">Projection pair</a>s: 7 225/32 11 5625/512 <br /> | <a class="wiki_link" href="/Projection%20pair">Projection pair</a>s: 7 225/32 11 5625/512<br /> | ||
<br /> | <br /> | ||
Scales: <a class="wiki_link" href="/minerva12">minerva12</a>, <a class="wiki_link" href="/minerva22x">minerva22x</a><br /> | Scales: <a class="wiki_link" href="/minerva12">minerva12</a>, <a class="wiki_link" href="/minerva22x">minerva22x</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:44:&lt;h2&gt; --><h2 id="toc22"><a name="Minerva-Athene"></a><!-- ws:end:WikiTextHeadingRule:44 -->Athene</h2> | <!-- ws:start:WikiTextHeadingRule:44:&lt;h2&gt; --><h2 id="toc22"><a name="Minerva-Athene"></a><!-- ws:end:WikiTextHeadingRule:44 -->Athene</h2> | ||
Commas: 99/98, 176/175, 275/273<br /> | Commas: 99/98, 176/175, 275/273<br /> | ||
<br /> | <br /> | ||
13-limit eigenmonzo subgroup: 2.11/9.13/7<br /> | 13-limit eigenmonzo subgroup: 2.11/9.13/7<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:46:&lt;h1&gt; --><h1 id="toc23"><a name="Spectacle"></a><!-- ws:end:WikiTextHeadingRule:46 -->Spectacle</h1> | <!-- ws:start:WikiTextHeadingRule:46:&lt;h1&gt; --><h1 id="toc23"><a name="Spectacle"></a><!-- ws:end:WikiTextHeadingRule:46 -->Spectacle</h1> | ||
<a class="wiki_link" href="/Comma">Commas</a>: 225/224, 243/242<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 225/224, 243/242<br /> | ||
Related linear temperament: <a class="wiki_link" href="/Marvel%20temperaments">marvo</a><br /> | Related linear temperament: <a class="wiki_link" href="/Marvel%20temperaments">marvo</a><br /> | ||
<br /> | <br /> | ||
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<!-- ws:start:WikiTextHeadingRule:48:&lt;h1&gt; --><h1 id="toc24"><a name="Apollo"></a><!-- ws:end:WikiTextHeadingRule:48 -->Apollo</h1> | <!-- ws:start:WikiTextHeadingRule:48:&lt;h1&gt; --><h1 id="toc24"><a name="Apollo"></a><!-- ws:end:WikiTextHeadingRule:48 -->Apollo</h1> | ||
<a class="wiki_link" href="/Comma">Commas</a>: 100/99, 225/224<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 100/99, 225/224<br /> | ||
Related linear temperament: <a class="wiki_link" href="/Magic%20family">Magic</a><br /> | Related linear temperament: <a class="wiki_link" href="/Magic%20family">Magic</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule:50:&lt;h1&gt; --><h1 id="toc25"><a name="Potassium"></a><!-- ws:end:WikiTextHeadingRule:50 -->Potassium</h1> | <!-- ws:start:WikiTextHeadingRule:50:&lt;h1&gt; --><h1 id="toc25"><a name="Potassium"></a><!-- ws:end:WikiTextHeadingRule:50 -->Potassium</h1> | ||
Commas: 45/44, 56/55<br /> | Commas: 45/44, 56/55<br /> | ||
<br /> | <br /> | ||
Eigenmonzo subgroup: 2.9/7.11<br /> | Eigenmonzo subgroup: 2.9/7.11<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:52:&lt;h2&gt; --><h2 id="toc26"><a name="Potassium-13-limit"></a><!-- ws:end:WikiTextHeadingRule:52 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:52:&lt;h2&gt; --><h2 id="toc26"><a name="Potassium-13-limit"></a><!-- ws:end:WikiTextHeadingRule:52 -->13-limit</h2> | ||
Commas: 45/44, 56/55, 78/77<br /> | Commas: 45/44, 56/55, 78/77<br /> | ||
<br /> | <br /> | ||
13-limit eigenmonzo subgroup: 2.9/7.13/9<br /> | 13-limit eigenmonzo subgroup: 2.9/7.13/9<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:54:&lt;h1&gt; --><h1 id="toc27"><a name="Catakleismoid"></a><!-- ws:end:WikiTextHeadingRule:54 -->Catakleismoid</h1> | <!-- ws:start:WikiTextHeadingRule:54:&lt;h1&gt; --><h1 id="toc27"><a name="Catakleismoid"></a><!-- ws:end:WikiTextHeadingRule:54 -->Catakleismoid</h1> | ||
Commas: 225/224, 4375/4374<br /> | Commas: 225/224, 4375/4374<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 1 -3 0|, &lt;0 6 5 22 0|, &lt;0 0 0 0 1|]<br /> | Map: [&lt;1 0 1 -3 0|, &lt;0 6 5 22 0|, &lt;0 0 0 0 1|]<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:56:&lt;h2&gt; --><h2 id="toc28"><a name="Catakleismoid-13-limit"></a><!-- ws:end:WikiTextHeadingRule:56 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:56:&lt;h2&gt; --><h2 id="toc28"><a name="Catakleismoid-13-limit"></a><!-- ws:end:WikiTextHeadingRule:56 -->13-limit</h2> | ||
Commas: 169/168, 225/224, 325/324<br /> | Commas: 169/168, 225/224, 325/324<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 1 -3 0 0|, &lt;0 6 5 22 0 14|, &lt;0 0 0 0 1 0|]<br /> | Map: [&lt;1 0 1 -3 0 0|, &lt;0 6 5 22 0 14|, &lt;0 0 0 0 1 0|]<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:58:&lt;h1&gt; --><h1 id="toc29"><a name="Hestia"></a><!-- ws:end:WikiTextHeadingRule:58 -->Hestia</h1> | <!-- ws:start:WikiTextHeadingRule:58:&lt;h1&gt; --><h1 id="toc29"><a name="Hestia"></a><!-- ws:end:WikiTextHeadingRule:58 -->Hestia</h1> | ||
Commas: 225/224, 125000/124509<br /> | Commas: 225/224, 125000/124509<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 0 -5 9|, &lt;0 2 0 4 -7|, &lt;0 0 1 2 0|]<br /> | Map: [&lt;1 0 0 -5 9|, &lt;0 2 0 4 -7|, &lt;0 0 1 2 0|]<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:60:&lt;h2&gt; --><h2 id="toc30"><a name="Hestia-13-limit"></a><!-- ws:end:WikiTextHeadingRule:60 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:60:&lt;h2&gt; --><h2 id="toc30"><a name="Hestia-13-limit"></a><!-- ws:end:WikiTextHeadingRule:60 -->13-limit</h2> | ||
Commas: 169/168, 225/224, 1001/1000<br /> | Commas: 169/168, 225/224, 1001/1000<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 0 -5 9 -1|, &lt;0 2 0 4 -7 3|, &lt;0 0 1 2 0 1|]<br /> | Map: [&lt;1 0 0 -5 9 -1|, &lt;0 2 0 4 -7 3|, &lt;0 0 1 2 0 1|]<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:62:&lt;h1&gt; --><h1 id="toc31"><a name="Malcolm"></a><!-- ws:end:WikiTextHeadingRule:62 -->Malcolm</h1> | <!-- ws:start:WikiTextHeadingRule:62:&lt;h1&gt; --><h1 id="toc31"><a name="Malcolm"></a><!-- ws:end:WikiTextHeadingRule:62 -->Malcolm</h1> | ||
Commas: 225/224, 2200/2187<br /> | Commas: 225/224, 2200/2187<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 0 -5 -3|, &lt;0 1 0 2 7|, &lt;0 0 1 2 -2|]<br /> | Map: [&lt;1 0 0 -5 -3|, &lt;0 1 0 2 7|, &lt;0 0 1 2 -2|]<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:64:&lt;h2&gt; --><h2 id="toc32"><a name="Malcolm-13-limit"></a><!-- ws:end:WikiTextHeadingRule:64 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:64:&lt;h2&gt; --><h2 id="toc32"><a name="Malcolm-13-limit"></a><!-- ws:end:WikiTextHeadingRule:64 -->13-limit</h2> | ||
commas: 225/224, 275/273, 325/324<br /> | commas: 225/224, 275/273, 325/324<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 0 -5 -3 2|, &lt;0 1 0 2 7 4|, &lt;0 0 1 2 -2 -2|]<br /> | Map: [&lt;1 0 0 -5 -3 2|, &lt;0 1 0 2 7 4|, &lt;0 0 1 2 -2 -2|]<br /> | ||
EDOs: 41, 53, 94, 429cdef, 523cdef<br /> | EDOs: 41, 53, 94, 429cdef, 523cdef<br /> | ||
Badness: 0.001075</body></html></pre></div> | Badness: 0.001075</body></html></pre></div> | ||