Bug 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>
The 5-limit parent of the bug family is bug, a temperament of sorts which tempers out 27/25, the large limma, or approximately one step of [[9edo|9edo]]. The monzo for 27/25 is |0 3 -2&gt;, the dual of which is &lt;&lt;2 3 0||. The generator for bug is 5/3, two of which give the 3, and three of which give the 5. Bug may be described as the 4&amp;5 temperament, and [[14edo|14edo]] is a good bug tuning, though wide latitude in these matters is possible. 4, 5, or 9 note MOS are a place to start with it.
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-04-22 15:46:55 UTC</tt>.<br>
: The original revision id was <tt>323899992</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]]


The 5-limit parent of the bug family is bug, a temperament of sorts which tempers out 27/25, the large limma, or approximately one step of [[9edo]]. The monzo for 27/25 is |0 3 -2&gt;, the dual of which is &lt;&lt;2 3 0||. The generator for bug is 5/3, two of which give the 3, and three of which give the 5. Bug may be described as the 4&amp;5 temperament, and [[14edo]] is a good bug tuning, though wide latitude in these matters is possible. 4, 5, or 9 note MOS are a place to start with it.
Bug has a 7-limit extension, beep, via the normal comma list [27/25, 36/35] which can also be obtained by adding 21/20. Beep has the curious property that if we know what the beep tempering is, and we know what the [[Ragismic_microtemperaments|ennealimmal]] tempering is, we can reconstruct 7-limit JI.


Bug has a 7-limit extension, beep, via the normal comma list [27/25, 36/35] which can also be obtained by adding 21/20. Beep has the curious property that if we know what the beep tempering is, and we know what the [[Ragismic microtemperaments|ennealimmal]] tempering is, we can reconstruct 7-limit JI.
=Bug=
 
=Bug=  
Comma: 27/25
Comma: 27/25


[[POTE tuning|POTE temperament]]: 260.388
[[POTE_tuning|POTE temperament]]: 260.388


Map: [&lt;1 0 0|, &lt;0 2 3|]
Map: [&lt;1 0 0|, &lt;0 2 3|]
EDOs: 4, 5, 9, 14, 23, 106
EDOs: 4, 5, 9, 14, 23, 106
Badness: 0.0328
Badness: 0.0328


=Beep=  
=Beep=
Commas: 21/20, 27/25
Commas: 21/20, 27/25


[[POTE tuning|POTE temperament]]: ~6/5 = 263.395
[[POTE_tuning|POTE temperament]]: ~6/5 = 263.395


Map: [&lt;1 0 0 2|, &lt;0 2 3 1|]
Map: [&lt;1 0 0 2|, &lt;0 2 3 1|]
Wedgie: &lt;&lt;2 3 1 0 -4 -6||
Wedgie: &lt;&lt;2 3 1 0 -4 -6||
EDOs: 4, 5, 9, 32, 41
EDOs: 4, 5, 9, 32, 41
Badness: 0.0186
Badness: 0.0186


==Pentoid==  
==Pentoid==
Commas: 21/20, 27/25, 99/98
Commas: 21/20, 27/25, 99/98


[[POTE tuning|POTE temperament]]: ~6/5 = 264.312
[[POTE_tuning|POTE temperament]]: ~6/5 = 264.312


Map: [&lt;1 0 0 2 5|, &lt;0 2 3 1 -2|]
Map: [&lt;1 0 0 2 5|, &lt;0 2 3 1 -2|]
EDOs: 4, 5, 9, 50, 59
EDOs: 4, 5, 9, 50, 59
Badness: 0.0226
Badness: 0.0226


Line 46: Line 45:


Map: [&lt;1 0 0 2 5 -1|, &lt;0 2 3 1 -2 6|]
Map: [&lt;1 0 0 2 5 -1|, &lt;0 2 3 1 -2 6|]
EDOs: 5,9, 32bcde, 41bcdef, 50bcdef
EDOs: 5,9, 32bcde, 41bcdef, 50bcdef
Badness: 0.0212
Badness: 0.0212


==Pento==  
==Pento==
Commas: 21/20, 27/25, 45/44
Commas: 21/20, 27/25, 45/44


Line 55: Line 56:


Map: [&lt;1 0 0 2 -2|, &lt;0 2 3 1 7|]
Map: [&lt;1 0 0 2 -2|, &lt;0 2 3 1 7|]
EDOs: 9
EDOs: 9
Badness: 0.0228
Badness: 0.0228


=Mite=  
=Mite=
Commas: 27/25, 28/25
Commas: 27/25, 28/25


Line 64: Line 67:


Map: [&lt;1 0 0 -2|, &lt;0 2 3 6|]
Map: [&lt;1 0 0 -2|, &lt;0 2 3 6|]
Wedgie: &lt;&lt;2 3 6 0 4 6||
Wedgie: &lt;&lt;2 3 6 0 4 6||
EDOs: 1cdd, 5
EDOs: 1cdd, 5
Badness: 0.0548</pre></div>
 
<h4>Original HTML content:</h4>
Badness: 0.0548
<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;Bug family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:12:&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:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&gt;&lt;a href="#Bug"&gt;Bug&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;!-- ws:start:WikiTextTocRule:14: --&gt; | &lt;a href="#Beep"&gt;Beep&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt;&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt;&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt;&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt; | &lt;a href="#Mite"&gt;Mite&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;
&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;br /&gt;
The 5-limit parent of the bug family is bug, a temperament of sorts which tempers out 27/25, the large limma, or approximately one step of &lt;a class="wiki_link" href="/9edo"&gt;9edo&lt;/a&gt;. The monzo for 27/25 is |0 3 -2&amp;gt;, the dual of which is &amp;lt;&amp;lt;2 3 0||. The generator for bug is 5/3, two of which give the 3, and three of which give the 5. Bug may be described as the 4&amp;amp;5 temperament, and &lt;a class="wiki_link" href="/14edo"&gt;14edo&lt;/a&gt; is a good bug tuning, though wide latitude in these matters is possible. 4, 5, or 9 note MOS are a place to start with it.&lt;br /&gt;
&lt;br /&gt;
Bug has a 7-limit extension, beep, via the normal comma list [27/25, 36/35] which can also be obtained by adding 21/20. Beep has the curious property that if we know what the beep tempering is, and we know what the &lt;a class="wiki_link" href="/Ragismic%20microtemperaments"&gt;ennealimmal&lt;/a&gt; tempering is, we can reconstruct 7-limit JI.&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="Bug"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Bug&lt;/h1&gt;
Comma: 27/25&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 260.388&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0|, &amp;lt;0 2 3|]&lt;br /&gt;
EDOs: 4, 5, 9, 14, 23, 106&lt;br /&gt;
Badness: 0.0328&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Beep"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Beep&lt;/h1&gt;
Commas: 21/20, 27/25&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: ~6/5 = 263.395&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 2|, &amp;lt;0 2 3 1|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;2 3 1 0 -4 -6||&lt;br /&gt;
EDOs: 4, 5, 9, 32, 41&lt;br /&gt;
Badness: 0.0186&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="Beep-Pentoid"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Pentoid&lt;/h2&gt;
Commas: 21/20, 27/25, 99/98&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: ~6/5 = 264.312&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 2 5|, &amp;lt;0 2 3 1 -2|]&lt;br /&gt;
EDOs: 4, 5, 9, 50, 59&lt;br /&gt;
Badness: 0.0226&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="Beep-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;13-limit&lt;/h2&gt;
Commas: 21/20, 26/25, 27/25, 33/32&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~6/5 = 263.935&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 2 5 -1|, &amp;lt;0 2 3 1 -2 6|]&lt;br /&gt;
EDOs: 5,9, 32bcde, 41bcdef, 50bcdef&lt;br /&gt;
Badness: 0.0212&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Beep-Pento"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Pento&lt;/h2&gt;
Commas: 21/20, 27/25, 45/44&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~6/5 = 265.847&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 2 -2|, &amp;lt;0 2 3 1 7|]&lt;br /&gt;
EDOs: 9&lt;br /&gt;
Badness: 0.0228&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Mite"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Mite&lt;/h1&gt;
Commas: 27/25, 28/25&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~6/5 = 240.712&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -2|, &amp;lt;0 2 3 6|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;2 3 6 0 4 6||&lt;br /&gt;
EDOs: 1cdd, 5&lt;br /&gt;
Badness: 0.0548&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

The 5-limit parent of the bug family is bug, a temperament of sorts which tempers out 27/25, the large limma, or approximately one step of 9edo. The monzo for 27/25 is |0 3 -2>, the dual of which is <<2 3 0||. The generator for bug is 5/3, two of which give the 3, and three of which give the 5. Bug may be described as the 4&5 temperament, and 14edo is a good bug tuning, though wide latitude in these matters is possible. 4, 5, or 9 note MOS are a place to start with it.

Bug has a 7-limit extension, beep, via the normal comma list [27/25, 36/35] which can also be obtained by adding 21/20. Beep has the curious property that if we know what the beep tempering is, and we know what the ennealimmal tempering is, we can reconstruct 7-limit JI.

Bug

Comma: 27/25

POTE temperament: 260.388

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

EDOs: 4, 5, 9, 14, 23, 106

Badness: 0.0328

Beep

Commas: 21/20, 27/25

POTE temperament: ~6/5 = 263.395

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

Wedgie: <<2 3 1 0 -4 -6||

EDOs: 4, 5, 9, 32, 41

Badness: 0.0186

Pentoid

Commas: 21/20, 27/25, 99/98

POTE temperament: ~6/5 = 264.312

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

EDOs: 4, 5, 9, 50, 59

Badness: 0.0226

13-limit

Commas: 21/20, 26/25, 27/25, 33/32

POTE generator: ~6/5 = 263.935

Map: [<1 0 0 2 5 -1|, <0 2 3 1 -2 6|]

EDOs: 5,9, 32bcde, 41bcdef, 50bcdef

Badness: 0.0212

Pento

Commas: 21/20, 27/25, 45/44

POTE generator: ~6/5 = 265.847

Map: [<1 0 0 2 -2|, <0 2 3 1 7|]

EDOs: 9

Badness: 0.0228

Mite

Commas: 27/25, 28/25

POTE generator: ~6/5 = 240.712

Map: [<1 0 0 -2|, <0 2 3 6|]

Wedgie: <<2 3 6 0 4 6||

EDOs: 1cdd, 5

Badness: 0.0548

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