Gravity 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>
=Gravity=
: This revision was by author [[User:phylingual|phylingual]] and made on <tt>2012-06-14 20:44:00 UTC</tt>.<br>
The gravity family tempers out [[graviton|graviton]], the 5-limit comma 129140163/128000000 = |-13 17 -6&gt;. The graviton equals (81/80)^4/(25/24), so that four 81/80 commas come to a chromatic semitone. The generator of gravity temperament is a grave fifth of 40/27, and hence the name. It is part of the Whitewood -&gt; Mavila -&gt; Dicot -&gt; Porcupine -&gt; Tetracot -&gt; Amity -&gt; ..... (Meantone) continuum, whereby (81/80)^n = 25/24.
: The original revision id was <tt>345484602</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]]
=Gravity=  
The gravity family tempers out [[graviton]], the 5-limit comma 129140163/128000000 = |-13 17 -6&gt;. The graviton equals (81/80)^4/(25/24), so that four 81/80 commas come to a chromatic semitone. The generator of gravity temperament is a grave fifth of 40/27, and hence the name. It is part of the Whitewood -&gt; Mavila -&gt; Dicot -&gt; Porcupine -&gt; Tetracot -&gt; Amity -&gt; ..... (Meantone) continuum, whereby (81/80)^n = 25/24.


Comma: 129140163/128000000
Comma: 129140163/128000000
Line 15: Line 8:


Map: [&lt;1 5 12|, &lt;0 -6 -17|]
Map: [&lt;1 5 12|, &lt;0 -6 -17|]
EDOs: [[7edo|7]], [[58edo|58]], [[65edo|65]], [[137edo|137]], [[202edo|202]], [[267edo|267]], [[469edo|469]]
EDOs: [[7edo|7]], [[58edo|58]], [[65edo|65]], [[137edo|137]], [[202edo|202]], [[267edo|267]], [[469edo|469]]
Badness: 0.0932
Badness: 0.0932


=Harry=  
=Harry=
Commas: 2401/2400, 19683/19600
Commas: 2401/2400, 19683/19600


Line 24: Line 19:


Map: [&lt;2 4 7 7|, &lt;0 -6 -17 -10|]
Map: [&lt;2 4 7 7|, &lt;0 -6 -17 -10|]
Wedgie: &lt;&lt;12 34 20 26 -2 -49||
Wedgie: &lt;&lt;12 34 20 26 -2 -49||
EDOs: 58, 72, 130, 202, 534
EDOs: 58, 72, 130, 202, 534
Badness: 0.0341
Badness: 0.0341


==11-limit==  
==11-limit==
Commas: 243/242, 441/440, 4000/3993
Commas: 243/242, 441/440, 4000/3993


Line 34: Line 32:


Map: [&lt;2 4 7 7 9|, &lt;0 -6 -17 -10 -15|]
Map: [&lt;2 4 7 7 9|, &lt;0 -6 -17 -10 -15|]
EDOs: 58, 72, 130, 202
EDOs: 58, 72, 130, 202
Badness: 0.0159
Badness: 0.0159


==13-limit==  
==13-limit==
Commas: 243/242, 351/350, 441/440, 676/675
Commas: 243/242, 351/350, 441/440, 676/675


Line 43: Line 43:


Map: [&lt;2 4 7 7 9 11|, &lt;0 -6 -17 -10 -15 -26|]
Map: [&lt;2 4 7 7 9 11|, &lt;0 -6 -17 -10 -15 -26|]
EDOs: 58, 72, 130
EDOs: 58, 72, 130
Badness: 0.0130
Badness: 0.0130


=Gravid=  
=Gravid=
Commas: 126/125, 1605632/1594323
Commas: 126/125, 1605632/1594323


Line 52: Line 54:


Map: [&lt;1 5 12 25|, &lt;0 -6 -17 -39|]
Map: [&lt;1 5 12 25|, &lt;0 -6 -17 -39|]
Wedgie: &lt;&lt;6 17 39 13 45 43||
Wedgie: &lt;&lt;6 17 39 13 45 43||
EDOs: 58, 123, 181c
EDOs: 58, 123, 181c
Badness: 0.1312
Badness: 0.1312


==11-limit==  
==11-limit==
Commas: 126/125, 243/242, 896/891
Commas: 126/125, 243/242, 896/891


Line 62: Line 67:


Map: [&lt;1 5 12 25 12|, &lt;0 -6 -17 -39 -15|]
Map: [&lt;1 5 12 25 12|, &lt;0 -6 -17 -39 -15|]
EDOs: 58, 123, 181ce, 239ce
EDOs: 58, 123, 181ce, 239ce
Badness: 0.0473</pre></div>
 
<h4>Original HTML content:</h4>
Badness: 0.0473
<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;Gravity 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="#Gravity"&gt;Gravity&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;!-- ws:start:WikiTextTocRule:14: --&gt; | &lt;a href="#Harry"&gt;Harry&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;a href="#Gravid"&gt;Gravid&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt;&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;
[[Category:family]]
&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Gravity"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Gravity&lt;/h1&gt;
[[Category:gravity]]
The gravity family tempers out &lt;a class="wiki_link" href="/graviton"&gt;graviton&lt;/a&gt;, the 5-limit comma 129140163/128000000 = |-13 17 -6&amp;gt;. The graviton equals (81/80)^4/(25/24), so that four 81/80 commas come to a chromatic semitone. The generator of gravity temperament is a grave fifth of 40/27, and hence the name. It is part of the Whitewood -&amp;gt; Mavila -&amp;gt; Dicot -&amp;gt; Porcupine -&amp;gt; Tetracot -&amp;gt; Amity -&amp;gt; ..... (Meantone) continuum, whereby (81/80)^n = 25/24.&lt;br /&gt;
[[Category:temperament_family]]
&lt;br /&gt;
Comma: 129140163/128000000&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~40/27 = 683.156&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 12|, &amp;lt;0 -6 -17|]&lt;br /&gt;
EDOs: &lt;a class="wiki_link" href="/7edo"&gt;7&lt;/a&gt;, &lt;a class="wiki_link" href="/58edo"&gt;58&lt;/a&gt;, &lt;a class="wiki_link" href="/65edo"&gt;65&lt;/a&gt;, &lt;a class="wiki_link" href="/137edo"&gt;137&lt;/a&gt;, &lt;a class="wiki_link" href="/202edo"&gt;202&lt;/a&gt;, &lt;a class="wiki_link" href="/267edo"&gt;267&lt;/a&gt;, &lt;a class="wiki_link" href="/469edo"&gt;469&lt;/a&gt;&lt;br /&gt;
Badness: 0.0932&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="Harry"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Harry&lt;/h1&gt;
Commas: 2401/2400, 19683/19600&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~21/20 = 83.156&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 4 7 7|, &amp;lt;0 -6 -17 -10|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;12 34 20 26 -2 -49||&lt;br /&gt;
EDOs: 58, 72, 130, 202, 534&lt;br /&gt;
Badness: 0.0341&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="Harry-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;11-limit&lt;/h2&gt;
Commas: 243/242, 441/440, 4000/3993&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~21/20 = 83.167&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 4 7 7 9|, &amp;lt;0 -6 -17 -10 -15|]&lt;br /&gt;
EDOs: 58, 72, 130, 202&lt;br /&gt;
Badness: 0.0159&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="Harry-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;13-limit&lt;/h2&gt;
Commas: 243/242, 351/350, 441/440, 676/675&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~21/20 = 83.116&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 4 7 7 9 11|, &amp;lt;0 -6 -17 -10 -15 -26|]&lt;br /&gt;
EDOs: 58, 72, 130&lt;br /&gt;
Badness: 0.0130&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Gravid"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Gravid&lt;/h1&gt;
Commas: 126/125, 1605632/1594323&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~27/20 = 517.140&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 12 25|, &amp;lt;0 -6 -17 -39|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;6 17 39 13 45 43||&lt;br /&gt;
EDOs: 58, 123, 181c&lt;br /&gt;
Badness: 0.1312&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Gravid-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;11-limit&lt;/h2&gt;
Commas: 126/125, 243/242, 896/891&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~27/20 = 517.155&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 12 25 12|, &amp;lt;0 -6 -17 -39 -15|]&lt;br /&gt;
EDOs: 58, 123, 181ce, 239ce&lt;br /&gt;
Badness: 0.0473&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

Gravity

The gravity family tempers out graviton, the 5-limit comma 129140163/128000000 = |-13 17 -6>. The graviton equals (81/80)^4/(25/24), so that four 81/80 commas come to a chromatic semitone. The generator of gravity temperament is a grave fifth of 40/27, and hence the name. It is part of the Whitewood -> Mavila -> Dicot -> Porcupine -> Tetracot -> Amity -> ..... (Meantone) continuum, whereby (81/80)^n = 25/24.

Comma: 129140163/128000000

POTE generator: ~40/27 = 683.156

Map: [<1 5 12|, <0 -6 -17|]

EDOs: 7, 58, 65, 137, 202, 267, 469

Badness: 0.0932

Harry

Commas: 2401/2400, 19683/19600

POTE generator: ~21/20 = 83.156

Map: [<2 4 7 7|, <0 -6 -17 -10|]

Wedgie: <<12 34 20 26 -2 -49||

EDOs: 58, 72, 130, 202, 534

Badness: 0.0341

11-limit

Commas: 243/242, 441/440, 4000/3993

POTE generator: ~21/20 = 83.167

Map: [<2 4 7 7 9|, <0 -6 -17 -10 -15|]

EDOs: 58, 72, 130, 202

Badness: 0.0159

13-limit

Commas: 243/242, 351/350, 441/440, 676/675

POTE generator: ~21/20 = 83.116

Map: [<2 4 7 7 9 11|, <0 -6 -17 -10 -15 -26|]

EDOs: 58, 72, 130

Badness: 0.0130

Gravid

Commas: 126/125, 1605632/1594323

POTE generator: ~27/20 = 517.140

Map: [<1 5 12 25|, <0 -6 -17 -39|]

Wedgie: <<6 17 39 13 45 43||

EDOs: 58, 123, 181c

Badness: 0.1312

11-limit

Commas: 126/125, 243/242, 896/891

POTE generator: ~27/20 = 517.155

Map: [<1 5 12 25 12|, <0 -6 -17 -39 -15|]

EDOs: 58, 123, 181ce, 239ce

Badness: 0.0473

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