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Semaphoresmic 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 '''semaphoresmic family''' of [[rank-3 temperament|rank-3]] [[regular temperament|temperaments]] [[tempering out|tempers out]] [[49/48]] in the full [[7-limit]], and thereby identifies the septimal minor third, [[7/6]], and the septimal whole tone, [[8/7]]. It also splits the fourth into two of these intervals; hence the name, which sounds like "semi-fourth". Related to this is the 2.3.7-subgroup {49/48} temperament [[Semaphoresmic clan #Semaphore|semaphore]], and the 7-limit {49/48, 81/80} temperament [[Semaphoresmic clan #Godzilla|godzilla]].
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-02-18 13:32:35 UTC</tt>.<br>
: The original revision id was <tt>203159576</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">Semaphore temperament tempers out 49/48 and thereby identifies the septimal minor third, 7/6, and the septimal whole tone, 8/7. It also splits the fourth into two of these intervals; hence the name, which sounds like "semi-fourth". The name [[meantone family|"godzilla"]] identifies a rank two temperament formerly sometimes called "semaphore", for the same reason.


Comma: 49/48
== Semaphoresmic a.k.a. semiphore ==
[[Subgroup]]: 2.3.5.7


Lattice basis: 7/6 0.7627 5/4 2.322
[[Comma list]]: 49/48
Angle(7/6, 5/4) = 90 degrees


Map: [&lt;1 0 2 2|, &lt;0 2 0 1|, &lt;0 0 1 0|]
{{Mapping|legend=1| 1 0 2 2 | 0 2 0 1 | 0 0 1 0 }}
Generators: 2, 7/4, 5
 
EDOs: 4, 5, 9, 10, 15, 19
: mapping generators: ~2, ~7/4, ~5
Badness: 0.000116</pre></div>
 
<h4>Original HTML content:</h4>
Lattice basis:
<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;Semiphore family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Semaphore temperament tempers out 49/48 and thereby identifies the septimal minor third, 7/6, and the septimal whole tone, 8/7. It also splits the fourth into two of these intervals; hence the name, which sounds like &amp;quot;semi-fourth&amp;quot;. The name &lt;a class="wiki_link" href="/meantone%20family"&gt;&amp;quot;godzilla&amp;quot;&lt;/a&gt; identifies a rank two temperament formerly sometimes called &amp;quot;semaphore&amp;quot;, for the same reason.&lt;br /&gt;
: 7/6 length = 0.7627, 5/4 length = 2.322
&lt;br /&gt;
: Angle (7/6, 5/4) = 90 degrees
Comma: 49/48&lt;br /&gt;
 
&lt;br /&gt;
[[Optimal tuning]]s:
Lattice basis: 7/6 0.7627 5/4 2.322&lt;br /&gt;
* [[WE]]: ~2 = 1202.8324{{c}}, ~7/4 = 951.8567{{c}}, ~5/4 = 380.5997{{c}}
Angle(7/6, 5/4) = 90 degrees&lt;br /&gt;
: [[error map]]: {{val| +2.832 +1.758 -0.049 -11.304 }}
&lt;br /&gt;
* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 950.6890{{c}}, ~5/4 = 382.3522{{c}}
Map: [&amp;lt;1 0 2 2|, &amp;lt;0 2 0 1|, &amp;lt;0 0 1 0|]&lt;br /&gt;
: error map: {{val| 0.000 -0.577 -3.962 -18.137 }}
Generators: 2, 7/4, 5&lt;br /&gt;
 
EDOs: 4, 5, 9, 10, 15, 19&lt;br /&gt;
{{Optimal ET sequence|legend=1| 4, 5, 9, 10, 14c, 15, 19, 48d, 53d, 67cdd, 86cdd }}
Badness: 0.000116&lt;/body&gt;&lt;/html&gt;</pre></div>
 
[[Badness]] (Sintel): 0.510
 
=== 2.3.5.7.13 subgroup ===
Subgroup: 2.3.5.7.13
 
Comma list: 49/48, 91/90
 
Sval mapping: {{mapping| 1 0 0 2 -1 | 0 2 0 1 3 | 0 0 1 0 1 }}
 
Optimal tunings:  
* WE: ~2 = 1202.7771{{c}}, ~7/4 = 951.9629{{c}}, ~5/4 = 381.0131{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 950.6703{{c}}, ~5/4 = 382.2972{{c}}
 
{{Optimal ET sequence|legend=0| 5, 9, 10, 14cf, 15, 19, 48df, 53d, 67cddf, 72dd }}
 
Badness (Sintel): 0.380
 
== Selenium ==
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 49/48, 56/55
 
{{Mapping|legend=1| 1 0 2 2 5 | 0 2 0 1 1 | 0 0 1 0 -1 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.0412{{c}}, ~7/4 = 951.7616{{c}}, ~5/4 = 390.6621{{c}}
: [[error map]]: {{val| +0.041 +1.568 +4.431 -16.982 +9.905 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 951.7409{{c}}, ~5/4 = 390.6582{{c}}
: error map: {{val| 0.000 +1.527 +4.344 -17.085 +9.765 }}
 
{{Optimal ET sequence|legend=1| 4, 5, 9, 10, 15, 19, 24, 34 }}
 
[[Badness]] (Sintel): 0.800
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 49/48, 56/55, 91/90
 
Mapping: {{mapping| 1 0 2 2 5 -1 | 0 2 0 1 1 3 | 0 0 1 0 -1 1 }}
 
Optimal tunings:
* WE: ~2 = 1200.0790{{c}}, ~7/4 = 951.3067{{c}}, ~5/4 = 389.6213{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 951.2662{{c}}, ~5/4 = 389.6120{{c}}
 
{{Optimal ET sequence|legend=0| 5, 9, 10, 15, 19, 24, 34 }}
 
Badness (Sintel): 0.736
 
== Negric ==
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 49/48, 225/224
 
{{Mapping|legend=1| 1 2 2 3 0 | 0 -4 3 -2 0 | 0 0 0 0 1 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1203.4810{{c}}, ~15/14 = 125.9724{{c}}, ~11/8 = 540.7985{{c}}
: [[error map]]: {{val| +3.481 +1.118 -1.435 -10.328 -0.076 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~15/14 = 125.4347{{c}}, ~11/8 = 541.8688{{c}}
: error map: {{val| 0.000 -3.694 -10.009 -19.695 -9.449 }}
 
{{Optimal ET sequence|legend=1| 9, 10, 19, 29, 38d, 67cdde, 105cdddee }}
 
[[Badness]] (Sintel): 1.31
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 49/48, 65/64, 91/90
 
Mapping: {{mapping| 1 2 2 3 0 4 | 0 -4 3 -2 0 -3 | 0 0 0 0 1 0 }}
 
Optimal tunings:
* WE: ~2 = 1203.6981{{c}}, ~14/13 = 125.9545{{c}}, ~11/8 = 540.1440{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 125.3543{{c}}, ~11/8 = 540.9490{{c}}
 
{{Optimal ET sequence|legend=0| 9, 10, 19, 29, 38df, 67cddef, 105cdddeefff }}
 
Badness (Sintel): 0.755
 
[[Category:Temperament families]]
[[Category:Semaphoresmic family| ]] <!-- main article -->
[[Category:Rank 3]]
Retrieved from "https://en.xen.wiki/w/Semaphoresmic_family"