Jubilismic family: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
Jubilismic temperament tempers out the interval 50/49, variously called the tritonic diesis, jubilisma or [http://en.wikipedia.org/wiki/Septimal_sixth-tone septimal sixth-tone]. It therefore identifies the two septimal tritones [[7/5|7/5]] and [[10/7|10/7]], an identification familiar from [[12edo|12edo]]. While most rank three temperaments are planar, jubilismic temperament divides the octave in two.
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>2011-01-03 19:01:58 UTC</tt>.<br>
: The original revision id was <tt>190748144</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">Jubilismic temperament tempers out the interval 50/49, variously called the tritonic diesis, jubilisma or [[http://en.wikipedia.org/wiki/Septimal_sixth-tone|septimal sixth-tone]]. It therefore identifies the two septimal tritones [[7_5|7/5]] and [[10_7|10/7]], an identification familiar from [[12edo]]. While most rank three temperaments are planar, jubilismic temperament divides the octave in two.


[[Comma]]: 50/49
[[Comma|Comma]]: 50/49


7 and 9 limit minimax tuning
7 and 9 limit minimax tuning
[|1 0 0 0&gt;, |0 1 0 0&gt;, |-1/4 0 1/2 1/2&gt;,  
[|1 0 0 0&gt;, |0 1 0 0&gt;, |-1/4 0 1/2 1/2&gt;,  
|1/4 0 1/2 1/2&gt;]
|1/4 0 1/2 1/2&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 3/2, 35/32
[[Eigenmonzo|Eigenmonzos]]: 2, 3/2, 35/32


Map: [&lt;2 0 0 1|, &lt;0 1 0 0|, &lt;0 0 1 1|]
Map: [&lt;2 0 0 1|, &lt;0 1 0 0|, &lt;0 0 1 1|]
[[Generator|Generators]]: 7/5, 3, 5
 
[[edo|Edos]]: [[10edo|10]], [[12edo|12]], [[22edo|22]], [[26edo|26]], [[38edo|38]], [[48edo|48]]
[[generator|Generators]]: 7/5, 3, 5
Scales: [[jubilismic10]]
 
[[EDO|Edos]]: [[10edo|10]], [[12edo|12]], [[22edo|22]], [[26edo|26]], [[38edo|38]], [[48edo|48]]
 
Scales: [[jubilismic10|jubilismic10]]


==Jubilee==
==Jubilee==
Line 24: Line 22:


Map: [&lt;2 0 0 1 4|, &lt;0 1 0 0 -2|, &lt;0 0 1 1 2|]
Map: [&lt;2 0 0 1 4|, &lt;0 1 0 0 -2|, &lt;0 0 1 1 2|]
EDOS: 12, 22, 48
EDOS: 12, 22, 48
Badness: 0.000600
Badness: 0.000600


Line 31: Line 31:


Map: [&lt;2 0 0 1 -4|, &lt;0 1 0 0 2|, &lt;0 0 1 1 1|]
Map: [&lt;2 0 0 1 -4|, &lt;0 1 0 0 2|, &lt;0 0 1 1 1|]
EDOs: 10, 12, 26
EDOs: 10, 12, 26
Badness: 0.000689
Badness: 0.000689


Line 38: Line 40:


Map: [&lt;2 0 0 1 7|, &lt;0 1 0 0 0|, &lt;0 0 1 1 0|]
Map: [&lt;2 0 0 1 7|, &lt;0 1 0 0 0|, &lt;0 0 1 1 0|]
EDOs: 10, 12
EDOs: 10, 12
Badness: 0.000717
Badness: 0.000717


Line 45: Line 49:


Map: [&lt;2 0 0 1 2|, &lt;0 1 0 0 3|, &lt;0 0 1 1 -1|]
Map: [&lt;2 0 0 1 2|, &lt;0 1 0 0 3|, &lt;0 0 1 1 -1|]
EDOs: 10, 22
EDOs: 10, 22
Badness: 0.000781
Badness: 0.000781
</pre></div>
[[Category:jubilismic]]
<h4>Original HTML content:</h4>
[[Category:temperament]]
<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;Jubilismic family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Jubilismic temperament tempers out the interval 50/49, variously called the tritonic diesis, jubilisma or &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_sixth-tone" rel="nofollow"&gt;septimal sixth-tone&lt;/a&gt;. It therefore identifies the two septimal tritones &lt;a class="wiki_link" href="/7_5"&gt;7/5&lt;/a&gt; and &lt;a class="wiki_link" href="/10_7"&gt;10/7&lt;/a&gt;, an identification familiar from &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;. While most rank three temperaments are planar, jubilismic temperament divides the octave in two.&lt;br /&gt;
[[Category:theory]]
&lt;br /&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;: 50/49&lt;br /&gt;
&lt;br /&gt;
7 and 9 limit minimax tuning&lt;br /&gt;
[|1 0 0 0&amp;gt;, |0 1 0 0&amp;gt;, |-1/4 0 1/2 1/2&amp;gt;, &lt;br /&gt;
|1/4 0 1/2 1/2&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 3/2, 35/32&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 0 0 1|, &amp;lt;0 1 0 0|, &amp;lt;0 0 1 1|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 7/5, 3, 5&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;Edos&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="/22edo"&gt;22&lt;/a&gt;, &lt;a class="wiki_link" href="/26edo"&gt;26&lt;/a&gt;, &lt;a class="wiki_link" href="/38edo"&gt;38&lt;/a&gt;, &lt;a class="wiki_link" href="/48edo"&gt;48&lt;/a&gt;&lt;br /&gt;
Scales: &lt;a class="wiki_link" href="/jubilismic10"&gt;jubilismic10&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-Jubilee"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Jubilee&lt;/h2&gt;
Commas: 50/49, 99/98&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 0 0 1 4|, &amp;lt;0 1 0 0 -2|, &amp;lt;0 0 1 1 2|]&lt;br /&gt;
EDOS: 12, 22, 48&lt;br /&gt;
Badness: 0.000600&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="x-Festival"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Festival&lt;/h2&gt;
Commas: 50/49, 45/44&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 0 0 1 -4|, &amp;lt;0 1 0 0 2|, &amp;lt;0 0 1 1 1|]&lt;br /&gt;
EDOs: 10, 12, 26&lt;br /&gt;
Badness: 0.000689&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-Fiesta"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Fiesta&lt;/h2&gt;
Commas: 50/49, 56/55&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 0 0 1 7|, &amp;lt;0 1 0 0 0|, &amp;lt;0 0 1 1 0|]&lt;br /&gt;
EDOs: 10, 12&lt;br /&gt;
Badness: 0.000717&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="x-Jamboree"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Jamboree&lt;/h2&gt;
Commas: 50/49, 55/54&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 0 0 1 2|, &amp;lt;0 1 0 0 3|, &amp;lt;0 0 1 1 -1|]&lt;br /&gt;
EDOs: 10, 22&lt;br /&gt;
Badness: 0.000781&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

Jubilismic temperament tempers out the interval 50/49, variously called the tritonic diesis, jubilisma or septimal sixth-tone. It therefore identifies the two septimal tritones 7/5 and 10/7, an identification familiar from 12edo. While most rank three temperaments are planar, jubilismic temperament divides the octave in two.

Comma: 50/49

7 and 9 limit minimax tuning

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

Eigenmonzos: 2, 3/2, 35/32

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

Generators: 7/5, 3, 5

Edos: 10, 12, 22, 26, 38, 48

Scales: jubilismic10

Jubilee

Commas: 50/49, 99/98

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

EDOS: 12, 22, 48

Badness: 0.000600

Festival

Commas: 50/49, 45/44

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

EDOs: 10, 12, 26

Badness: 0.000689

Fiesta

Commas: 50/49, 56/55

Map: [<2 0 0 1 7|, <0 1 0 0 0|, <0 0 1 1 0|]

EDOs: 10, 12

Badness: 0.000717

Jamboree

Commas: 50/49, 55/54

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

EDOs: 10, 22

Badness: 0.000781

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