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]] '''greenwoodmic temperaments''', which [[tempering out|temper out]] [[405/392]], the [[greenwoodma]].
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-08 14:42:28 UTC</tt>.<br>
-: The original revision id was <tt>299827428</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
+Considered below are secund and semishallowtone.
-Map: [&lt;7 11 1 12|, &lt;0 0 2 1|]
+== Secund ==
-Wedgie: &lt;&lt;0 14 7 22 11 -23||
+Secund tempers out the greendwoodma, the [[avicennma]], and the [[orwellisma]]. It may be described as the {{nowrap| 9 & 26 }} temperament, with a [[ploidacot]] signature of pentacot. It divides the [[3/2|perfect fifth]] into five [[~]][[16/15]] generators, two for [[7/6]] and three for [[9/7]].
-EDOs: 14c, 21, 35, 84bcd
-Badness: 0.1218
-</pre></div>
+[[Subgroup]]: 2.3.5.7
-<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;
+[[Comma list]]: 405/392, 525/512
-&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;
+{{Mapping|legend=1| 1 1 3 2 | 0 5 -6 7 }}
-Commas: 405/392, 1323/1280&lt;br /&gt;
+: mapping generators: ~2, ~16/15
-&lt;br /&gt;
-POTE generator: ~8/7 = 241.490&lt;br /&gt;
+[[Optimal tuning]]s:
-&lt;br /&gt;
+* [[WE]]: ~2 = 1203.6786{{c}}, ~16/15 = 138.3805{{c}}
-Map: [&amp;lt;7 11 1 12|, &amp;lt;0 0 2 1|]&lt;br /&gt;
+: [[error map]]: {{val| +3.679 -6.374 -5.561 +7.195 }}
-Wedgie: &amp;lt;&amp;lt;0 14 7 22 11 -23||&lt;br /&gt;
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~16/15 = 138.0648{{c}}
-EDOs: 14c, 21, 35, 84bcd&lt;br /&gt;
+: error map: {{val| 0.000 -11.631 -14.702 -2.372 }}
-Badness: 0.1218&lt;/body&gt;&lt;/html&gt;</pre></div>
+{{Optimal ET sequence|legend=1| 9, 17, 26, 61bc, 87bcc }}
+[[Badness]] (Sintel): 2.27
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 45/44, 99/98, 385/384
+Mapping: {{mapping| 1 1 3 2 3 | 0 5 -6 7 4 }}
+Optimal tunings:
+* WE: ~2 = 1202.9415{{c}}, ~12/11 = 138.2377{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~12/11 = 137.9970{{c}}
+{{Optimal ET sequence|legend=0| 9, 17, 26, 61bc }}
+Badness (Sintel): 1.41
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 27/26, 45/44, 99/98, 385/384
+Mapping: {{mapping| 1 1 3 2 3 2 | 0 5 -6 7 4 15 }}
+Optimal tunings:
+* WE: ~2 = 1202.4465{{c}}, ~12/11 = 137.2165{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~12/11 = 137.0309{{c}}
+{{Optimal ET sequence|legend=0| 9, 35 }}
+Badness (Sintel): 2.05
+==== Secundly ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 45/44, 65/64, 78/77, 99/98
+Mapping: {{mapping| 1 1 3 2 3 3 | 0 5 -6 7 4 6 }}
+Optimal tunings:
+* WE: ~2 = 1203.0195{{c}}, ~13/12 = 138.2642{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 138.0317{{c}}
+{{Optimal ET sequence|legend=0| 9, 17, 26, 61bcf }}
+Badness (Sintel): 1.08
+== Semishallowtone ==
+{{See also| Shallowtone }}
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 405/392, 35721/32768
+{{Mapping|legend=1| 2 0 36 15 | 0 1 -10 -3 }}
+: mapping generators: ~189/128, ~3
+[[Optimal tuning]]s:
+* [[WE]]: ~189/128 = 603.1653{{c}}, ~3/2 = 686.6365{{c}} (~64/63 = 83.4712{{c}})
+: [[error map]]: {{val| +6.331 -8.988 -2.034 -0.248 }}
+* [[CWE]]: ~189/128 = 600.0000{{c}}, ~3/2 = 682.6498{{c}} (~64/63 = 82.6498{{c}})
+: error map: {{val| 0.000 -19.305 -12.811 -16.775 }}
+{{Optimal ET sequence|legend=1| 14c, 44bd, 58bcd }}
+[[Badness]] (Sintel): 8.42
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 45/44, 99/98, 35721/32768
+Mapping: {{mapping| 2 0 36 15 32 | 0 1 -10 -3 -8 }}
+Optimal tunings:
+* WE: ~189/128 = 603.0536{{c}}, ~3/2 = 686.6175{{c}} (~64/63 = 83.5640{{c}})
+* CWE: ~189/128 = 600.0000{{c}}, ~3/2 = 682.7238{{c}} (~64/63 = 82.7238{{c}})
+{{Optimal ET sequence|legend=0| 14c, 44bd, 58bcde, 72bbccddee }}
+Badness (Sintel): 4.15
+=== 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:
+* WE: ~91/64 = 601.8872{{c}}, ~3/2 = 684.4774{{c}} (~64/63 = 82.5902{{c}})
+* CWE: ~91/64 = 600.0000{{c}}, ~3/2 = 682.1676{{c}} (~64/63 = 82.1676{{c}})
+{{Optimal ET sequence|legend=0| 14c, 30b }}
+Badness (Sintel): 4.38
+[[Category:Temperament collections]]
+[[Category:Greenwoodmic temperaments| ]] <!-- main article -->
+[[Category:Rank 2]]