Archytas family: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
Archytas temperament [[tempering_out|tempers out]] [[64/63|64/63]], and thereby identifies the [[otonal|otonal]] [[tetrad|tetrad]] with the [[dominant_seventh_chord|dominant seventh chord]], which is familiar from [[12edo|12edo]] and also a feature of [[22edo|22edo]] and [[27edo|27edo]].
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-03-12 00:20:21 UTC</tt>.<br>
: The original revision id was <tt>309944576</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">Archytas temperament [[tempering out|tempers out]] [[64_63|64/63]], and thereby identifies the [[otonal]] [[tetrad]] with the [[dominant seventh chord]], which is familiar from [[12edo]] and also a feature of [[22edo]] and [[27edo]].


[[Comma]]: 64/63
[[Comma|Comma]]: 64/63


7-limit minimax
7-limit minimax
[|1 0 0 0&gt;, |2 1/3 0 -1/3&gt;,  
[|1 0 0 0&gt;, |2 1/3 0 -1/3&gt;,  
|2 -2/3 1 -1/3&gt;, |2 -2/3 0 2/3&gt;]
|2 -2/3 1 -1/3&gt;, |2 -2/3 0 2/3&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 6/5, 7/5
[[Eigenmonzo|Eigenmonzos]]: 2, 6/5, 7/5


9-limit minimax
9-limit minimax
[|1 0 0 0&gt;, |3/2 1/2 0 -1/4&gt;,  
[|1 0 0 0&gt;, |3/2 1/2 0 -1/4&gt;,  
|3/2 -1/2 1 -1/4&gt;, |3 -1 0 1/2&gt;]
|3/2 -1/2 1 -1/4&gt;, |3 -1 0 1/2&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 6/5, 9/7
[[Eigenmonzo|Eigenmonzos]]: 2, 6/5, 9/7


Lattice basis: 3/2 length 1.0508 5/4 length 2.3219
Lattice basis: 3/2 length 1.0508 5/4 length 2.3219
Angle(3/2, 5/4) = 90 degrees
Angle(3/2, 5/4) = 90 degrees
Map to lattice: [&lt;0 1 0 -2|, &lt;0 0 1 0|]
Map to lattice: [&lt;0 1 0 -2|, &lt;0 0 1 0|]


Map: [&lt;1 0 0 6|, &lt;0 1 0 -2|, &lt;0 0 1 0|]
Map: [&lt;1 0 0 6|, &lt;0 1 0 -2|, &lt;0 0 1 0|]
[[Generator|Generators]]: 2, 3, 5
 
[[edo|Edos]]: [[7edo|7]], [[10edo|10]], [[12edo|12]], [[15edo|15]], [[22edo|22]], [[27edo|27]], [[37edo|37]], [[49edo|49]], [[59edo|59]]
[[generator|Generators]]: 2, 3, 5
Scales: [[archytas12]], [[archytas12synch]]
 
[[EDO|Edos]]: [[7edo|7]], [[10edo|10]], [[12edo|12]], [[15edo|15]], [[22edo|22]], [[27edo|27]], [[37edo|37]], [[49edo|49]], [[59edo|59]]
 
Scales: [[archytas12|archytas12]], [[archytas12synch|archytas12synch]]


Music: Chris Vaisvil  
Music: Chris Vaisvil  
[[http://micro.soonlabel.com/hobbit_scales/daily201031--hobbit-archytas12.mp3|12 archytas hobbits with ale]]
 
[http://micro.soonlabel.com/hobbit_scales/daily201031--hobbit-archytas12.mp3 12 archytas hobbits with ale]
 
Joel Taylor
Joel Taylor
[[http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/Archytas12%20sync%20Study%203.mp3|Portrait of a Tragedy (Death of a Son) - Archytas12 sync Study 3]]
 
[http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/Archytas12%20sync%20Study%203.mp3 Portrait of a Tragedy (Death of a Son) - Archytas12 sync Study 3]


==11 limit children==
==11 limit children==
Line 39: Line 44:
[[Comma|Commas]]: 64/63, 100/99
[[Comma|Commas]]: 64/63, 100/99


[[Minimax tuning]]
[[Minimax_tuning|Minimax tuning]]
 
[|1 0 0 0 0&gt;, |3/2 1/2 0 -1/4 0&gt;,  
[|1 0 0 0 0&gt;, |3/2 1/2 0 -1/4 0&gt;,  
|2 0 0 -1/2 1/2&gt;, |3 -1 0 1/2 0&gt;,  
|2 0 0 -1/2 1/2&gt;, |3 -1 0 1/2 0&gt;,  
|3 -1 0 -1/2 1&gt;]
|3 -1 0 -1/2 1&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 11/9, 9/7
[[Eigenmonzo|Eigenmonzos]]: 2, 11/9, 9/7


Lattice basis: 3/2 0.9878 6/5 1.4312
Lattice basis: 3/2 0.9878 6/5 1.4312
Angle(3/2, 6/5) = 75.0475 degrees
Angle(3/2, 6/5) = 75.0475 degrees
Map to lattice: [&lt;0 1 1 -2 0|, &lt;0 0 -1 0 -2|]
Map to lattice: [&lt;0 1 1 -2 0|, &lt;0 0 -1 0 -2|]


Map: [&lt;1 0 0 6 2|, &lt;0 1 0 -2 -2|, &lt;0 0 1 0 2|]
Map: [&lt;1 0 0 6 2|, &lt;0 1 0 -2 -2|, &lt;0 0 1 0 2|]
[[Generator|Generators]]: 2, 3, 5
 
[[edo|Edos]]: [[12edo|12]], [[15edo|15]], [[22edo|22]], [[37edo|37]], [[49edo|49]]
[[generator|Generators]]: 2, 3, 5
 
[[EDO|Edos]]: [[12edo|12]], [[15edo|15]], [[22edo|22]], [[37edo|37]], [[49edo|49]]
 
Badness: 0.000469
Badness: 0.000469


Scales: [[ares12]]
Scales: [[ares12|ares12]]


==Vulcan==
==Vulcan==
Line 60: Line 72:


Map: [&lt;1 0 0 6 9|, &lt;0 1 0 -2 -2|, &lt;0 0 1 0 -1|]
Map: [&lt;1 0 0 6 9|, &lt;0 1 0 -2 -2|, &lt;0 0 1 0 -1|]
Generators: 2, 3, 5
Generators: 2, 3, 5
EDOs: 5, 10, 12, 15
EDOs: 5, 10, 12, 15
Badness: 0.000577</pre></div>
 
<h4>Original HTML content:</h4>
Badness: 0.000577
<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;Archytas family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Archytas temperament &lt;a class="wiki_link" href="/tempering%20out"&gt;tempers out&lt;/a&gt; &lt;a class="wiki_link" href="/64_63"&gt;64/63&lt;/a&gt;, and thereby identifies the &lt;a class="wiki_link" href="/otonal"&gt;otonal&lt;/a&gt; &lt;a class="wiki_link" href="/tetrad"&gt;tetrad&lt;/a&gt; with the &lt;a class="wiki_link" href="/dominant%20seventh%20chord"&gt;dominant seventh chord&lt;/a&gt;, which is familiar from &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt; and also a feature of &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt; and &lt;a class="wiki_link" href="/27edo"&gt;27edo&lt;/a&gt;.&lt;br /&gt;
[[Category:archytas]]
&lt;br /&gt;
[[Category:family]]
&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;: 64/63&lt;br /&gt;
[[Category:rank_3]]
&lt;br /&gt;
[[Category:theory]]
7-limit minimax&lt;br /&gt;
[|1 0 0 0&amp;gt;, |2 1/3 0 -1/3&amp;gt;, &lt;br /&gt;
|2 -2/3 1 -1/3&amp;gt;, |2 -2/3 0 2/3&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 6/5, 7/5&lt;br /&gt;
&lt;br /&gt;
9-limit minimax&lt;br /&gt;
[|1 0 0 0&amp;gt;, |3/2 1/2 0 -1/4&amp;gt;, &lt;br /&gt;
|3/2 -1/2 1 -1/4&amp;gt;, |3 -1 0 1/2&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 6/5, 9/7&lt;br /&gt;
&lt;br /&gt;
Lattice basis: 3/2 length 1.0508 5/4 length 2.3219&lt;br /&gt;
Angle(3/2, 5/4) = 90 degrees&lt;br /&gt;
Map to lattice: [&amp;lt;0 1 0 -2|, &amp;lt;0 0 1 0|]&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 6|, &amp;lt;0 1 0 -2|, &amp;lt;0 0 1 0|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 3, 5&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: &lt;a class="wiki_link" href="/7edo"&gt;7&lt;/a&gt;, &lt;a class="wiki_link" href="/10edo"&gt;10&lt;/a&gt;, &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/15edo"&gt;15&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22&lt;/a&gt;, &lt;a class="wiki_link" href="/27edo"&gt;27&lt;/a&gt;, &lt;a class="wiki_link" href="/37edo"&gt;37&lt;/a&gt;, &lt;a class="wiki_link" href="/49edo"&gt;49&lt;/a&gt;, &lt;a class="wiki_link" href="/59edo"&gt;59&lt;/a&gt;&lt;br /&gt;
Scales: &lt;a class="wiki_link" href="/archytas12"&gt;archytas12&lt;/a&gt;, &lt;a class="wiki_link" href="/archytas12synch"&gt;archytas12synch&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
Music: Chris Vaisvil &lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/hobbit_scales/daily201031--hobbit-archytas12.mp3" rel="nofollow"&gt;12 archytas hobbits with ale&lt;/a&gt;&lt;br /&gt;
Joel Taylor&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/Archytas12%20sync%20Study%203.mp3" rel="nofollow"&gt;Portrait of a Tragedy (Death of a Son) - Archytas12 sync Study 3&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-11 limit children"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;11 limit children&lt;/h2&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-Ares"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Ares&lt;/h2&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 64/63, 100/99&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Minimax%20tuning"&gt;Minimax tuning&lt;/a&gt;&lt;br /&gt;
[|1 0 0 0 0&amp;gt;, |3/2 1/2 0 -1/4 0&amp;gt;, &lt;br /&gt;
|2 0 0 -1/2 1/2&amp;gt;, |3 -1 0 1/2 0&amp;gt;, &lt;br /&gt;
|3 -1 0 -1/2 1&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 11/9, 9/7&lt;br /&gt;
&lt;br /&gt;
Lattice basis: 3/2 0.9878 6/5 1.4312&lt;br /&gt;
Angle(3/2, 6/5) = 75.0475 degrees&lt;br /&gt;
Map to lattice: [&amp;lt;0 1 1 -2 0|, &amp;lt;0 0 -1 0 -2|]&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 6 2|, &amp;lt;0 1 0 -2 -2|, &amp;lt;0 0 1 0 2|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 3, 5&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/15edo"&gt;15&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22&lt;/a&gt;, &lt;a class="wiki_link" href="/37edo"&gt;37&lt;/a&gt;, &lt;a class="wiki_link" href="/49edo"&gt;49&lt;/a&gt;&lt;br /&gt;
Badness: 0.000469&lt;br /&gt;
&lt;br /&gt;
Scales: &lt;a class="wiki_link" href="/ares12"&gt;ares12&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x-Vulcan"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Vulcan&lt;/h2&gt;
Commas: 56/55, 64/63&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 6 9|, &amp;lt;0 1 0 -2 -2|, &amp;lt;0 0 1 0 -1|]&lt;br /&gt;
Generators: 2, 3, 5&lt;br /&gt;
EDOs: 5, 10, 12, 15&lt;br /&gt;
Badness: 0.000577&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

Archytas temperament tempers out 64/63, and thereby identifies the otonal tetrad with the dominant seventh chord, which is familiar from 12edo and also a feature of 22edo and 27edo.

Comma: 64/63

7-limit minimax

[|1 0 0 0>, |2 1/3 0 -1/3>, |2 -2/3 1 -1/3>, |2 -2/3 0 2/3>]

Eigenmonzos: 2, 6/5, 7/5

9-limit minimax

[|1 0 0 0>, |3/2 1/2 0 -1/4>, |3/2 -1/2 1 -1/4>, |3 -1 0 1/2>]

Eigenmonzos: 2, 6/5, 9/7

Lattice basis: 3/2 length 1.0508 5/4 length 2.3219

Angle(3/2, 5/4) = 90 degrees

Map to lattice: [<0 1 0 -2|, <0 0 1 0|]

Map: [<1 0 0 6|, <0 1 0 -2|, <0 0 1 0|]

Generators: 2, 3, 5

Edos: 7, 10, 12, 15, 22, 27, 37, 49, 59

Scales: archytas12, archytas12synch

Music: Chris Vaisvil

12 archytas hobbits with ale

Joel Taylor

Portrait of a Tragedy (Death of a Son) - Archytas12 sync Study 3

11 limit children

Ares

Commas: 64/63, 100/99

Minimax tuning

[|1 0 0 0 0>, |3/2 1/2 0 -1/4 0>, |2 0 0 -1/2 1/2>, |3 -1 0 1/2 0>, |3 -1 0 -1/2 1>]

Eigenmonzos: 2, 11/9, 9/7

Lattice basis: 3/2 0.9878 6/5 1.4312

Angle(3/2, 6/5) = 75.0475 degrees

Map to lattice: [<0 1 1 -2 0|, <0 0 -1 0 -2|]

Map: [<1 0 0 6 2|, <0 1 0 -2 -2|, <0 0 1 0 2|]

Generators: 2, 3, 5

Edos: 12, 15, 22, 37, 49

Badness: 0.000469

Scales: ares12

Vulcan

Commas: 56/55, 64/63

Map: [<1 0 0 6 9|, <0 1 0 -2 -2|, <0 0 1 0 -1|]

Generators: 2, 3, 5

EDOs: 5, 10, 12, 15

Badness: 0.000577

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