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Greenwoodmic temperaments: 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>
This is a collection of [[rank-2 temperament|rank-2]] [[temperament]]s [[tempering out]] the [[greenwoodma]], 405/392 ({{monzo| -3 4 1 -2 }}).
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-08 14:55:02 UTC</tt>.<br>
: The original revision id was <tt>299834040</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">These temper out the greenwoodma, |-3 4 1 -2&gt; = 405/392.


=Greenwood=
Temperaments discussed elsewhere are
Commas: 405/392, 1323/1280
* ''[[Sidi]]'' (+25/24) → [[Dicot family #Sidi|Dicot family]]
* ''[[August]]'' (+36/35) → [[Augmented family #August|Augmented family]]
* ''[[Superpelog]]'' (+49/48) → [[Semaphoresmic clan #Superpelog|Semaphoresmic clan]]
* ''[[Injera]]'' (+50/49 or 81/80) → [[Meantone family #Injera|Meantone family]]
* ''[[Schism]]'' (+64/63) → [[Archytas clan #Schism|Archytas clan]]
* ''[[Greenwood]]'' (+1323/1280) → [[Whitewood family #Greenwood|Whitewood family]]


POTE generator: ~8/7 = 241.490
== Secund ==
[[Subgroup]]: 2.3.5.7


Map: [&lt;7 11 1 12|, &lt;0 0 2 1|]
[[Comma list]]: 405/392, 525/512
Wedgie: &lt;&lt;0 14 7 22 11 -23||
EDOs: 14c, 21, 35, 84bcd
Badness: 0.1218


==11-limit==
{{Mapping|legend=1| 1 1 3 2 | 0 5 -6 7 }}
Commas: 45/44, 99/98, 1323/1280


POTE generator: ~8/7 = 242.711
: mapping generaators: ~2, ~16/15


Map: [&lt;7 11 1 12 9|, &lt;0 0 2 1 2|]
[[Optimal tuning]]s:
EDOs: 14c, 21, 35, 49bcde, 84bcde
* [[CTE]]: ~2 = 1200.000, ~16/15 = 138.454
Badness: 0.0575
: [[error map]]: {{val| 0.000 -9.684 -17.038 +0.353 }}
* [[POTE]]: ~2 = 1200.000, ~16/15 = 137.958
: error map: {{val| 0.000 -12.167 -14.059 -3.123 }}


==13-limit==
{{Optimal ET sequence|legend=1| 9, 17, 26, 61bc, 87bcc }}
Commas: 27/26, 45/44, 99/98, 640/637


POTE generaor: ~8/7 = 238.607
[[Badness]] (Smith): 0.089840


Map: [&lt;7 11 1 12 9 26|, &lt;0 0 2 1 2 0|]
=== 11-limit ===
EDOs: 14c, 21, 35, 91bf
Subgroup: 2.3.5.7.11
Badness: 0.0540


=Secund=
Comma list: 45/44, 99/98, 385/384
Commas: 405/392, 525/512


POTE generator: ~16/15 = 137.958
Mapping: {{mapping| 1 1 3 2 3 | 0 5 -6 7 4 }}


Map: [&lt;1 1 3 2|, &lt;0 5 -6 7|]
Optimal tunings:  
Wedgie: &lt;&lt;5 -6 7 -21 -3 33||
* CTE: ~2 = 1200.000, ~12/11 = 138.420
EDOs: 9, 17, 26, 61bc, 87bc
* POTE: ~2 = 1200.000, ~12/11 = 137.900
Badness: 0.0898


==11-limit==
{{Optimal ET sequence|legend=0| 9, 17, 26, 61bc }}
Commas: 45/44, 99/98, 385/384


POTE generator: ~12/11 = 137.900
Badness (Smith): 0.042562


Map: [&lt;1 1 3 2 3|, &lt;0 5 -6 7 4|]
==== 13-limit ====
EDOs: 9, 17, 26, 61bc, 87bc
Subgroup: 2.3.5.7.11.13
Badness: 0.0426


==13-limit==
Comma list: 27/26, 45/44, 99/98, 385/384
Commas: 27/26, 45/44, 99/98, 385/384


POTE generator: ~12/11 = 136.937
Mapping: {{mapping| 1 1 3 2 3 2 | 0 5 -6 7 4 15 }}


Map: [&lt;1 1 3 2 3 2|, &lt;0 5 -6 7 4 15|]
Optimal tunings:  
EDOs: 9, 26f, 35
* CTE: ~2 = 1200.000, ~12/11 = 137.455
Badness: 0.0497
* POTE: ~2 = 1200.000, ~12/11 = 136.937


</pre></div>
{{Optimal ET sequence|legend=0| 9, 35 }}
<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;Greenwoodmic temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;These temper out the greenwoodma, |-3 4 1 -2&amp;gt; = 405/392.&lt;br /&gt;
Badness (Smith): 0.049684
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Greenwood"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Greenwood&lt;/h1&gt;
==== Secundly ====
Commas: 405/392, 1323/1280&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
&lt;br /&gt;
 
POTE generator: ~8/7 = 241.490&lt;br /&gt;
Comma list: 45/44, 65/64, 78/77, 99/98
&lt;br /&gt;
 
Map: [&amp;lt;7 11 1 12|, &amp;lt;0 0 2 1|]&lt;br /&gt;
Mapping: {{mapping| 1 1 3 2 3 3 | 0 5 -6 7 4 6 }}
Wedgie: &amp;lt;&amp;lt;0 14 7 22 11 -23||&lt;br /&gt;
 
EDOs: 14c, 21, 35, 84bcd&lt;br /&gt;
Optimal tunings:  
Badness: 0.1218&lt;br /&gt;
* CTE: ~2 = 1200.000, ~13/12 = 138.583
&lt;br /&gt;
* POTE: ~2 = 1200.000, ~13/12 = 137.917
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Greenwood-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;11-limit&lt;/h2&gt;
 
Commas: 45/44, 99/98, 1323/1280&lt;br /&gt;
{{Optimal ET sequence|legend=0| 9, 17, 26, 61bcf }}
&lt;br /&gt;
 
POTE generator: ~8/7 = 242.711&lt;br /&gt;
Badness (Smith): 0.026212
&lt;br /&gt;
 
Map: [&amp;lt;7 11 1 12 9|, &amp;lt;0 0 2 1 2|]&lt;br /&gt;
== Semishallowtone ==
EDOs: 14c, 21, 35, 49bcde, 84bcde&lt;br /&gt;
{{See also| Shallowtone }}
Badness: 0.0575&lt;br /&gt;
 
&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Greenwood-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;13-limit&lt;/h2&gt;
 
Commas: 27/26, 45/44, 99/98, 640/637&lt;br /&gt;
[[Comma list]]: 405/392, 35721/32768
&lt;br /&gt;
 
POTE generaor: ~8/7 = 238.607&lt;br /&gt;
{{Mapping|legend=1| 2 0 36 15 | 0 1 -10 -3 }}
&lt;br /&gt;
 
Map: [&amp;lt;7 11 1 12 9 26|, &amp;lt;0 0 2 1 2 0|]&lt;br /&gt;
: mapping generators: ~189/128, ~3
EDOs: 14c, 21, 35, 91bf&lt;br /&gt;
 
Badness: 0.0540&lt;br /&gt;
[[Optimal tuning]]s:  
&lt;br /&gt;
* [[CTE]]: ~189/128 = 600.000, ~3/2 = 681.532 (~64/63 = 81.532)
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Secund"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Secund&lt;/h1&gt;
: [[error map]]: {{val| 0.000 -20.423 -1.629 -13.421 }}
Commas: 405/392, 525/512&lt;br /&gt;
* [[CWE]]: ~189/128 = 600.000, ~3/2 = 682.650 (~64/63 = 82.650)
&lt;br /&gt;
: error map: {{val| 0.000 -19.305 -12.811 -16.775 }}
POTE generator: ~16/15 = 137.958&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 14c, 44bd, 58bcd }}
Map: [&amp;lt;1 1 3 2|, &amp;lt;0 5 -6 7|]&lt;br /&gt;
 
Wedgie: &amp;lt;&amp;lt;5 -6 7 -21 -3 33||&lt;br /&gt;
[[Badness]]:
EDOs: 9, 17, 26, 61bc, 87bc&lt;br /&gt;
* Smith: 0.333
Badness: 0.0898&lt;br /&gt;
* Dirichlet: 8.420
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Secund-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;11-limit&lt;/h2&gt;
=== 11-limit ===
Commas: 45/44, 99/98, 385/384&lt;br /&gt;
Subgroup: 2.3.5.7.11
&lt;br /&gt;
 
POTE generator: ~12/11 = 137.900&lt;br /&gt;
Comma list: 45/44, 99/98, 35721/32768
&lt;br /&gt;
 
Map: [&amp;lt;1 1 3 2 3|, &amp;lt;0 5 -6 7 4|]&lt;br /&gt;
Mapping: {{mapping| 2 0 36 15 32 | 0 1 -10 -3 -8 }}
EDOs: 9, 17, 26, 61bc, 87bc&lt;br /&gt;
 
Badness: 0.0426&lt;br /&gt;
Optimal tunings:
&lt;br /&gt;
* CTE: ~189/128 = 600.000, ~3/2 = 681.438 (~64/63 = 81.438)
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Secund-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;13-limit&lt;/h2&gt;
* CWE: ~189/128 = 600.000, ~3/2 = 682.724 (~64/63 = 82.724)
Commas: 27/26, 45/44, 99/98, 385/384&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=0| 14c, 44bd, 58bcde, 72bbccddee }}
POTE generator: ~12/11 = 136.937&lt;br /&gt;
 
&lt;br /&gt;
Badness:
Map: [&amp;lt;1 1 3 2 3 2|, &amp;lt;0 5 -6 7 4 15|]&lt;br /&gt;
* Smith: 0.125
EDOs: 9, 26f, 35&lt;br /&gt;
* Dirichlet: 4.148
Badness: 0.0497&lt;/body&gt;&lt;/html&gt;</pre></div>
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 27/26, 45/44, 99/98, 35721/32768
 
Mapping: {{mapping| 2 0 36 15 32 -2 | 0 1 -10 -3 -8 3 }}
 
Optimal tunings:
* CTE: ~91/64 = 600.000, ~3/2 = 681.406 (~64/63 = 81.406)
* CWE: ~91/64 = 600.000, ~3/2 = 682.168 (~64/63 = 82.168)
 
{{Optimal ET sequence|legend=0| 14c, 30b }}
 
Badness:
* Smith: 0.106
* Dirichlet: 4.377
 
[[Category:Temperament collections]]
[[Category:Pages with mostly numerical content]]
[[Category:Greenwoodmic temperaments| ]] <!-- main article -->
[[Category:Greenwoodmic| ]] <!-- key article -->
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Greenwoodmic_temperaments"