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Ditonmic family: Difference between revisions

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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>
The '''ditonmic family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[ditonma]] ([[ratio]]: 1220703125/1207959552, {{monzo|legend=1| -27 -2 13 }}).
: This revision was by author [[User:guest|guest]] and made on <tt>2012-08-10 04:14:50 UTC</tt>.<br>
: The original revision id was <tt>357159938</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">This tempers out the ditonma, 1220703125/1207959552.


=Ditonic=  
== Ditonic ==
Commas: 1220703125/1207959552
Named by [[Petr Pařízek]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>, ditonic can be described as the 50 & 53 temperament. It splits [[~]][[8/5]] in two for a generator, which happens to be an interval very close in size to the [[ditone]], ~81/64. Note that the ditone itself is 52 generator steps away.


POTE generator: ~15625/12288 = 407.574
[[Subgroup]]: 2.3.5


Map: [&lt;1 6 3|, &lt;0 -13 -2|]
[[Comma list]]: 1220703125/1207959552
EDOs: 47, 50, 53, 474c, 527c
Badness: 0.1671


=Coditone=
{{Mapping|legend=1| 1 6 3 | 0 -13 -2 }}
Commas: 225/224, 2125764/2100875


POTE generator: ~1225/972 = 407.690
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~15625/12288 = 407.534
: [[error map]]: {{val| 0.000 +0.099 -1.382 }}
* [[POTE]]: ~2 = 1200.000, ~15625/12288 = 407.574
: error map: {{val| 0.000 -0.416 -1.462 }}


Map: [&lt;1 6 3 13|, &lt;0 -13 -2 -30|]
{{Optimal ET sequence|legend=1| 3, …, 47, 50, 53, 474c, 527c, 580c, 633c, 686c, 739c, 792c, 845cc }}
EDOs: 50, 53, 103, 156


==11-limit==
[[Badness]] (Smith): 0.167086
Commas: 99/98, 176/175, 6655/6561


POTE generator: ~242/189 = 407.567
== Coditone ==
[[Subgroup]]: 2.3.5.7


Map: [&lt;1 6 3 13 15|, &lt;0 -13 -2 -30 -34|]
[[Comma list]]: 225/224, 2125764/2100875
EDOs: 53
Badness: 0.0639


==13-limit==
{{Mapping|legend=1| 1 6 3 13 | 0 -13 -2 -30 }}
Commas: 99/98, 176/175, 325/324, 847/845


POTE generator: ~33/26 = 407.541
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~1225/972 = 407.642
: [[error map]]: {{val| 0.000 -1.298 -1.597 +1.921 }}
* [[POTE]]: ~2 = 1200.000, ~1225/972 = 407.690
: error map: {{val| 0.000 -1.921 -1.693 +0.483 }}


Map: [&lt;1 6 3 13 15 20|, &lt;0 -13 -2 -30 -34 -48|]
{{Optimal ET sequence|legend=1| 3d, 50, 53, 103, 156 }}
EDOs: 53
 
Badness: 0.0440</pre></div>
[[Badness]] (Smith): 0.064356
<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;Ditonmic family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This tempers out the ditonma, 1220703125/1207959552.&lt;br /&gt;
=== 11-limit ===
&lt;br /&gt;
Subgroup: 2.3.5.7.11
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Ditonic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Ditonic&lt;/h1&gt;
 
Commas: 1220703125/1207959552&lt;br /&gt;
Comma list: 225/224, 385/384, 78408/78125
&lt;br /&gt;
 
POTE generator: ~15625/12288 = 407.574&lt;br /&gt;
Mapping: {{mapping| 1 6 3 13 -3 | 0 -13 -2 -30 19 }}
&lt;br /&gt;
 
Map: [&amp;lt;1 6 3|, &amp;lt;0 -13 -2|]&lt;br /&gt;
Optimal tunings:  
EDOs: 47, 50, 53, 474c, 527c&lt;br /&gt;
* CTE: ~2 = 1200.000, ~1225/972 = 407.688
Badness: 0.1671&lt;br /&gt;
* POTE: ~2 = 1200.000, ~1225/972 = 407.741
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Coditone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Coditone&lt;/h1&gt;
{{Optimal ET sequence|legend=0| 50, 53, 103 }}
Commas: 225/224, 2125764/2100875&lt;br /&gt;
 
&lt;br /&gt;
Badness (Smith): 0.044329
POTE generator: ~1225/972 = 407.690&lt;br /&gt;
 
&lt;br /&gt;
==== 13-limit ====
Map: [&amp;lt;1 6 3 13|, &amp;lt;0 -13 -2 -30|]&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
EDOs: 50, 53, 103, 156&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 225/224, 351/350, 385/384, 847/845
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Coditone-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;11-limit&lt;/h2&gt;
 
Commas: 99/98, 176/175, 6655/6561&lt;br /&gt;
Mapping: {{mapping| 1 6 3 13 -3 2 | 0 -13 -2 -30 19 5 }}
&lt;br /&gt;
 
POTE generator: ~242/189 = 407.567&lt;br /&gt;
Optimal tunings:
&lt;br /&gt;
* CTE: ~2 = 1200.000, ~325/256 = 407.691
Map: [&amp;lt;1 6 3 13 15|, &amp;lt;0 -13 -2 -30 -34|]&lt;br /&gt;
* POTE: ~2 = 1200.000, ~325/256 = 407.736
EDOs: 53&lt;br /&gt;
 
Badness: 0.0639&lt;br /&gt;
{{Optimal ET sequence|legend=0| 50, 53, 103 }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Coditone-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;13-limit&lt;/h2&gt;
Badness (Smith): 0.024352
Commas: 99/98, 176/175, 325/324, 847/845&lt;br /&gt;
 
&lt;br /&gt;
=== Coditonic ===
POTE generator: ~33/26 = 407.541&lt;br /&gt;
Subgroup: 2.3.5.7.11
&lt;br /&gt;
 
Map: [&amp;lt;1 6 3 13 15 20|, &amp;lt;0 -13 -2 -30 -34 -48|]&lt;br /&gt;
Comma list: 99/98, 176/175, 6655/6561
EDOs: 53&lt;br /&gt;
 
Badness: 0.0440&lt;/body&gt;&lt;/html&gt;</pre></div>
Mapping: {{mapping| 1 6 3 13 15 | 0 -13 -2 -30 -34 }}
 
Optimal tunings:
* CTE: ~2 = 1200.000, ~242/189 = 407.528
* POTE: ~2 = 1200.000, ~242/189 = 407.567
 
{{Optimal ET sequence|legend=0| 3de, 50e, 53 }}
 
Badness (Smith): 0.063876
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 99/98, 176/175, 325/324, 847/845
 
Mapping: {{mapping| 1 6 3 13 15 20 | 0 -13 -2 -30 -34 -48 }}
 
Optimal tunings:
* CTE: ~2 = 1200.000, ~242/189 = 407.514
* POTE: ~2 = 1200.000, ~33/26 = 407.541
 
{{Optimal ET sequence|legend=0| 3def, 50eff, 53 }}
 
Badness (Smith): 0.043989
 
== Diton ==
This extension is known as ''ditonic'' in [[Graham Breed]]'s temperament finder.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 126/125, 8751645/8388608
 
{{Mapping|legend=1| 1 6 3 -4 | 0 -13 -2 20 }}
 
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~2625/2048 = 407.922
: [[error map]]: {{val| 0.000 -4.939 -2.157 -10.388 }}
* [[POTE]]: ~2 = 1200.000, ~2625/2048 = 407.954
: error map: {{val| 0.000 -5.353 -2.221 -9.751 }}
 
{{Optimal ET sequence|legend=1| 3, 47, 50 }}
 
[[Badness]] (Smith): 0.242101
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 126/125, 245/242, 2079/2048
 
Mapping: {{mapping| 1 6 3 -4 -3 | 0 -13 -2 20 19 }}
 
Optimal tunings:
* CTE: ~2 = 1200.000, ~14/11 = 407.930
* POTE: ~2 = 1200.000, ~14/11 = 407.892
 
{{Optimal ET sequence|legend=0| 3, 47, 50 }}
 
Badness (Smith): 0.100884
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 105/104, 126/125, 245/242, 1287/1280
 
Mapping: {{mapping| 1 6 3 -4 -3 2 | 0 -13 -2 20 19 5 }}
 
Optimal tunings:
* CTE: ~2 = 1200.000, ~14/11 = 407.933
* POTE: ~2 = 1200.000, ~14/11 = 407.887
 
{{Optimal ET sequence|legend=0| 3, 47, 50 }}
 
Badness (Smith): 0.054997
 
== Notes ==
 
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Ditonmic family| ]] <!-- main article -->
[[Category:Ditonmic]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Ditonmic_family"