Semaphoresmic family: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
__FORCETOC__
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
Semiphore 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". Related to this is the 2.3.7-limit 49/48 temperament called "[[Chromatic_pairs#Semaphore|semaphore]]," and the 2.3.5.7 49/48 and 81/80 temperament called [[Meantone_family|"godzilla"]].
: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2013-08-03 11:40:08 UTC</tt>.<br>
: The original revision id was <tt>443283010</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]]
Semiphore 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". Related to this is the 2.3.7-limit 49/48 temperament called "[[xenharmonic/Chromatic pairs#Semaphore|semaphore]]," and the 2.3.5.7 49/48 and 81/80 temperament called [[meantone family|"godzilla"]].


Comma: 49/48
Comma: 49/48


Lattice basis: 7/6 0.7627 5/4 2.322
Lattice basis: 7/6 0.7627 5/4 2.322
Angle(7/6, 5/4) = 90 degrees
Angle(7/6, 5/4) = 90 degrees


Map: [&lt;1 0 2 2|, &lt;0 2 0 1|, &lt;0 0 1 0|]
Map: [&lt;1 0 2 2|, &lt;0 2 0 1|, &lt;0 0 1 0|]
Generators: 2, 7/4, 5
Generators: 2, 7/4, 5
EDOs: 4, 5, 9, 10, 15, 19
EDOs: 4, 5, 9, 10, 15, 19
Badness: 0.000116
Badness: 0.000116


=Selenium=  
=Selenium=
Commas: 49/48, 56/55
Commas: 49/48, 56/55


Map: [&lt;1 0 2 2 5|, &lt;0 2 0 1 1|, &lt;0 0 1 0 -1|]
Map: [&lt;1 0 2 2 5|, &lt;0 2 0 1 1|, &lt;0 0 1 0 -1|]
EDOs: 4, 5, 9, 10, 15, 19, 24, 34
EDOs: 4, 5, 9, 10, 15, 19, 24, 34
Badness: 0.000665
Badness: 0.000665


==13-limit==  
==13-limit==
Commas: 49/48, 56/55, 91/90
Commas: 49/48, 56/55, 91/90


Map: [&lt;1 0 2 2 5 -1|, &lt;0 2 0 1 1 3|, &lt;0 0 1 0 -1 1|]
Map: [&lt;1 0 2 2 5 -1|, &lt;0 2 0 1 1 3|, &lt;0 0 1 0 -1 1|]
EDOs: 5, 9, 10, 15, 19, 24, 34
EDOs: 5, 9, 10, 15, 19, 24, 34
Badness: 0.000787
Badness: 0.000787


=Negric=  
=Negric=
Commas: 49/48, 225/224
Commas: 49/48, 225/224


Map: [&lt;1 2 2 3 0|, &lt;0 -4 3 -2 0|, &lt;0 0 0 0 1|]
Map: [&lt;1 2 2 3 0|, &lt;0 -4 3 -2 0|, &lt;0 0 0 0 1|]
EDOs: 9, 10, 19, 29, 38d, 67cde
EDOs: 9, 10, 19, 29, 38d, 67cde
Badness: 0.001087
Badness: 0.001087


==13-limit==  
==13-limit==
Commas: 49/48, 65/64, 91/90
Commas: 49/48, 65/64, 91/90


Map: [&lt;1 2 2 3 0 4|, &lt;0 -4 3 -2 0 -3|, &lt;0 0 0 0 1 0|]
Map: [&lt;1 2 2 3 0 4|, &lt;0 -4 3 -2 0 -3|, &lt;0 0 0 0 1 0|]
EDOs: 9, 10, 19, 29, 38df, 67cdef
EDOs: 9, 10, 19, 29, 38df, 67cdef
Badness: 80.756</pre></div>
 
<h4>Original HTML content:</h4>
Badness: 80.756
<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;&lt;!-- ws:start:WikiTextTocRule:8:&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:8 --&gt;&lt;!-- ws:start:WikiTextTocRule:9: --&gt;&lt;a href="#Selenium"&gt;Selenium&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:9 --&gt;&lt;!-- ws:start:WikiTextTocRule:10: --&gt;&lt;!-- ws:end:WikiTextTocRule:10 --&gt;&lt;!-- ws:start:WikiTextTocRule:11: --&gt; | &lt;a href="#Negric"&gt;Negric&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:11 --&gt;&lt;!-- ws:start:WikiTextTocRule:12: --&gt;&lt;!-- ws:end:WikiTextTocRule:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&gt;
&lt;!-- ws:end:WikiTextTocRule:13 --&gt;Semiphore 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;. Related to this is the 2.3.7-limit 49/48 temperament called &amp;quot;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Chromatic%20pairs#Semaphore"&gt;semaphore&lt;/a&gt;,&amp;quot; and the 2.3.5.7 49/48 and 81/80 temperament called &lt;a class="wiki_link" href="/meantone%20family"&gt;&amp;quot;godzilla&amp;quot;&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
Comma: 49/48&lt;br /&gt;
&lt;br /&gt;
Lattice basis: 7/6 0.7627 5/4 2.322&lt;br /&gt;
Angle(7/6, 5/4) = 90 degrees&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 2 2|, &amp;lt;0 2 0 1|, &amp;lt;0 0 1 0|]&lt;br /&gt;
Generators: 2, 7/4, 5&lt;br /&gt;
EDOs: 4, 5, 9, 10, 15, 19&lt;br /&gt;
Badness: 0.000116&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Selenium"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Selenium&lt;/h1&gt;
Commas: 49/48, 56/55&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 2 2 5|, &amp;lt;0 2 0 1 1|, &amp;lt;0 0 1 0 -1|]&lt;br /&gt;
EDOs: 4, 5, 9, 10, 15, 19, 24, 34&lt;br /&gt;
Badness: 0.000665&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Selenium-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;13-limit&lt;/h2&gt;
Commas: 49/48, 56/55, 91/90&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 2 2 5 -1|, &amp;lt;0 2 0 1 1 3|, &amp;lt;0 0 1 0 -1 1|]&lt;br /&gt;
EDOs: 5, 9, 10, 15, 19, 24, 34&lt;br /&gt;
Badness: 0.000787&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Negric"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Negric&lt;/h1&gt;
Commas: 49/48, 225/224&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 3 0|, &amp;lt;0 -4 3 -2 0|, &amp;lt;0 0 0 0 1|]&lt;br /&gt;
EDOs: 9, 10, 19, 29, 38d, 67cde&lt;br /&gt;
Badness: 0.001087&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Negric-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;13-limit&lt;/h2&gt;
Commas: 49/48, 65/64, 91/90&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 3 0 4|, &amp;lt;0 -4 3 -2 0 -3|, &amp;lt;0 0 0 0 1 0|]&lt;br /&gt;
EDOs: 9, 10, 19, 29, 38df, 67cdef&lt;br /&gt;
Badness: 80.756&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

Semiphore 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". Related to this is the 2.3.7-limit 49/48 temperament called "semaphore," and the 2.3.5.7 49/48 and 81/80 temperament called "godzilla".

Comma: 49/48

Lattice basis: 7/6 0.7627 5/4 2.322

Angle(7/6, 5/4) = 90 degrees

Map: [<1 0 2 2|, <0 2 0 1|, <0 0 1 0|]

Generators: 2, 7/4, 5

EDOs: 4, 5, 9, 10, 15, 19

Badness: 0.000116

Selenium

Commas: 49/48, 56/55

Map: [<1 0 2 2 5|, <0 2 0 1 1|, <0 0 1 0 -1|]

EDOs: 4, 5, 9, 10, 15, 19, 24, 34

Badness: 0.000665

13-limit

Commas: 49/48, 56/55, 91/90

Map: [<1 0 2 2 5 -1|, <0 2 0 1 1 3|, <0 0 1 0 -1 1|]

EDOs: 5, 9, 10, 15, 19, 24, 34

Badness: 0.000787

Negric

Commas: 49/48, 225/224

Map: [<1 2 2 3 0|, <0 -4 3 -2 0|, <0 0 0 0 1|]

EDOs: 9, 10, 19, 29, 38d, 67cde

Badness: 0.001087

13-limit

Commas: 49/48, 65/64, 91/90

Map: [<1 2 2 3 0 4|, <0 -4 3 -2 0 -3|, <0 0 0 0 1 0|]

EDOs: 9, 10, 19, 29, 38df, 67cdef

Badness: 80.756

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