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Wizmic microtemperaments: Difference between revisions

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- witcher (more properly addressed in amity family)
 
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Technical data page}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This is a collection of [[rank-2 temperament|rank-2]] [[microtemperament]]s which [[tempering out|temper out]] the [[wizma]] ({{monzo|legend=1| -6 -8 2 5 }}, [[ratio]]: 420175/419904).
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-16 15:37:13 UTC</tt>.<br>
: The original revision id was <tt>302519978</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>
<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]]


Microtemperaments which don't fit in elsewhere.
Temperaments discussed elsewhere are:
* [[Superpyth]] (+64/63 or 245/243) → [[Archytas clan #Superpyth|Archytas clan]]
* ''[[Gariwizmic]]'' (+33554432/33480783) → [[Garischismic clan #Gariwizmic|Garischismic clan]]
* ''[[Cloudtone]]'' (+81/80) → [[Meantone family #Cloudtone|Meantone family]]
* [[Tsaharuk]] (+32805/32768) → [[Schismatic family #Tsaharuk|Schismatic family]]
* ''[[Hemiseven]]'' (+1029/1024) → [[Gamelismic clan #Hemiseven|Gamelismic clan]]
* ''[[Septiquarter]]'' (+5120/5103) → [[Hemifamity temperaments #Septiquarter|Hemifamity temperaments]]
* ''[[Hendecatonic (temperament)|Hendecatonic]]'' (+6144/6125 or 10976/10935) → [[Porwell temperaments #Hendecatonic|Porwell temperaments]]
* [[Wizard]] (+225/224) → [[Marvel temperaments #Wizard|Marvel temperaments]]
* ''[[Witcher]]'' (+1600000/1594323) → [[Amity family #Witcher|Amity family]]
* [[Oolong]] (+126/125) → [[Starling temperaments #Oolong|Starling temperaments]]
* [[Ennealimmal]] (+2401/2400 or 4375/4374) → [[Septiennealimmal clan #Ennealimmal|Septiennealimmal clan]]
* ''[[Fifthplus]]'' (+65625/65536) → [[Horwell temperaments #Fifthplus|Horwell temperaments]]
* ''[[Octowerck]]'' (+321489/320000) → [[Varunismic temperaments #Octowerck|Varunismic temperaments]]
* ''[[Sengagen]]'' (+3136/3125) → [[Hemimean clan #Sengagen|Hemimean clan]]
* [[Sqrtphi]] (+15625/15552 or 16875/16807) → [[Kleismic family #Sqrtphi|Kleismic family]]
* ''[[Quinwell]]'' (+2109375/2097152) → [[Semicomma family #Quinwell|Semicomma family]]
* ''[[Decavish]]'' (+2202927104/2197265625) → [[Vishnuzmic family #Decavish|Vishnuzmic family]]


=Qak=
Considered below are qak, tokko, and tertiathirds, in the order of increasing [[badness]].
Commas: 420175/419904, 703125/702464


POTE generator: ~125/96 = 456.144
== Qak ==
Qak tempers out the [[meter]] in addition to the wizma, and may be described as the {{nowrap| 50 & 171 }} temperament.  


Map: [&lt;1 27 11 40|, &lt;0 -41 -14 -60|]
[[Subgroup]]: 2.3.5.7
Wedgie: &lt;&lt;41 14 60 -73 -20 100||
EDOs: 50, 121, 171, 976, 1147, 1318, 1489, 1660, 1831, 2002c, 3833cd
Badness: 0.0293


=Tokko=
[[Comma list]]: 420175/419904, 703125/702464
Commas: 420175/419904, 5250987/5242880


POTE generator: ~147/128 = 238.599
{{Mapping|legend=1| 1 -14 -3 -20 | 0 41 14 60 }}
: mapping generators: ~2, ~125/96


Map: [&lt;1 12 56 -2|, &lt;0 -13 -67 6|]
[[Optimal tuning]]s:  
Wedgie: &lt;&lt;13 67 -6 76 -46 -202||
* [[WE]]: ~2 = 1200.0566{{c}}, ~125/96 = 456.1655{{c}}
EDOs: 5, 166, 171, 1544d, 1715d, 1886d, 2057d
: [[error map]]: {{val| +0.057 +0.039 -0.166 -0.027 }}
Badness: 0.0444
* [[CWE]]: ~2 = 1200.0000{{c}}, ~125/96 = 456.1450{{c}}
: error map: {{val| 0.000 -0.009 -0.283 -0.125 }}


</pre></div>
{{Optimal ET sequence|legend=1| 50, 121, 171, 976, 1147, 1318, 1489, 1660, 1831, 2002c, 3833cd }}
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Wizmic microtemperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:4:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:4 --&gt;&lt;!-- ws:start:WikiTextTocRule:5: --&gt;&lt;a href="#Qak"&gt;Qak&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:5 --&gt;&lt;!-- ws:start:WikiTextTocRule:6: --&gt; | &lt;a href="#Tokko"&gt;Tokko&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:6 --&gt;&lt;!-- ws:start:WikiTextTocRule:7: --&gt;
[[Badness]] (Sintel): 0.741
&lt;!-- ws:end:WikiTextTocRule:7 --&gt;&lt;br /&gt;
 
Microtemperaments which don't fit in elsewhere.&lt;br /&gt;
== Tokko ==
&lt;br /&gt;
: ''For the 5-limit version, see [[Syntonic–diatonic equivalence continuum #Tokko (5-limit)]].''
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Qak"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Qak&lt;/h1&gt;
 
Commas: 420175/419904, 703125/702464&lt;br /&gt;
Tokko tempers out the [[mitonisma]] in addition to the wizma, and may be described as the {{nowrap| 5 & 171 }} temperament.
&lt;br /&gt;
 
POTE generator: ~125/96 = 456.144&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
&lt;br /&gt;
 
Map: [&amp;lt;1 27 11 40|, &amp;lt;0 -41 -14 -60|]&lt;br /&gt;
[[Comma list]]: 420175/419904, 5250987/5242880
Wedgie: &amp;lt;&amp;lt;41 14 60 -73 -20 100||&lt;br /&gt;
 
EDOs: 50, 121, 171, 976, 1147, 1318, 1489, 1660, 1831, 2002c, 3833cd&lt;br /&gt;
{{Mapping|legend=1| 1 -1 -11 4 | 0 13 67 -6 }}
Badness: 0.0293&lt;br /&gt;
: mapping generators: ~2, ~147/128
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Tokko"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Tokko&lt;/h1&gt;
[[Optimal tuning]]s:  
Commas: 420175/419904, 5250987/5242880&lt;br /&gt;
* [[WE]]: ~2 = 1200.0850{{c}}, ~147/128 = 238.6157{{c}}
&lt;br /&gt;
: [[error map]]: {{val| +0.085 -0.036 +0.004 -0.180 }}
POTE generator: ~147/128 = 238.599&lt;br /&gt;
* [[CWE]]: ~2 = 1200.0000{{c}}, ~147/128 = 238.5997{{c}}
&lt;br /&gt;
: error map: {{val| 0.000 -0.159 -0.133 -0.424 }}
Map: [&amp;lt;1 12 56 -2|, &amp;lt;0 -13 -67 6|]&lt;br /&gt;
 
Wedgie: &amp;lt;&amp;lt;13 67 -6 76 -46 -202||&lt;br /&gt;
{{Optimal ET sequence|legend=1| 5, 161c, 166, 171, 1544d, 1715d, …, 2912dd, 3083cdd }}
EDOs: 5, 166, 171, 1544d, 1715d, 1886d, 2057d&lt;br /&gt;
 
Badness: 0.0444&lt;/body&gt;&lt;/html&gt;</pre></div>
[[Badness]] (Sintel): 1.12
 
== Tertiathirds ==
Tertiathirds tempers out the quasiorwellisma, [[29360128/29296875]] in the 7-limit, and may be described as the {{nowrap| 121 & 149 }} temperament. It splits the interval of [[5/4]] into three [[14/13]] generators.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 420175/419904, 29360128/29296875
 
{{Mapping|legend=1| 1 -4 2 -6 | 0 52 3 82 }}
: mapping generators: ~2, ~3375/3136
 
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1199.9305{{c}}, ~3375/3136 = 128.8804{{c}}
: [[error map]]: {{val| -0.070 +0.104 +0.188 -0.216 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3375/3136 = 128.8871{{c}}
: error map: {{val| 0.000 +0.173 +0.348 -0.085 }}
 
{{Optimal ET sequence|legend=1| 121, 149, 270, 2309c, 2579c }}
 
[[Badness]] (Sintel): 2.35
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 3025/3024, 5632/5625, 117649/117612
 
Mapping: {{mapping| 1 -4 2 -6 -9 | 0 52 3 82 116 }}
 
Optimal tunings:
* WE: ~2 = 1199.9251{{c}}, ~264/245 = 128.8818{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~264/245 = 128.8890{{c}}
 
{{Optimal ET sequence|legend=0| 121, 149, 270 }}
 
Badness (Sintel): 1.10
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 676/675, 1716/1715, 3025/3024, 4225/4224
 
Mapping: {{mapping| 1 -4 2 -6 -9 -5 | 0 52 3 82 116 81 }}
 
Optimal tunings:  
* WE: ~2 = 1199.9510{{c}}, ~14/13 = 128.8849{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 128.8896{{c}}
 
{{Optimal ET sequence|legend=0| 121, 149, 270 }}
 
Badness (Sintel): 0.806
 
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 676/675, 715/714, 936/935, 1225/1224, 4225/4224
 
Mapping: {{mapping| 1 -4 2 -6 -9 -5 -3 | 0 52 3 82 116 81 66 }}
 
Optimal tunings:
* WE: ~2 = 1199.8754{{c}}, ~14/13 = 128.8778{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 128.8898{{c}}
 
{{Optimal ET sequence|legend=0| 121, 149, 270 }}
 
Badness (Sintel): 0.973
 
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 676/675, 715/714, 936/935, 1225/1224, 1540/1539, 2128/2125
 
Mapping: {{mapping| 1 -4 2 -6 -9 -5 -3 5 | 0 52 3 82 116 81 66 -7 }}
 
Optimal tunings:
* WE: ~2 = 1199.8964{{c}}, ~14/13 = 128.8793{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 128.8896{{c}}
 
{{Optimal ET sequence|legend=0| 121, 149, 270 }}
 
Badness (Sintel): 0.950
 
[[Category:Temperament collections]]
[[Category:Wizmic microtemperaments| ]] <!-- main article -->
[[Category:Rank 2]]
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