Hemimage temperaments: 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>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-02-18 15:20:44 UTC</tt>.<br>
: The original revision id was <tt>490298826</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]]
 
 
Hemimage temperaments temper out the hemimage comma, |5 -7 -1 3&gt; = 10976/10935.
Hemimage temperaments temper out the hemimage comma, |5 -7 -1 3&gt; = 10976/10935.


Line 19: Line 10:


Map: [&lt;2 3 4 5|, &lt;0 5 19 18|]
Map: [&lt;2 3 4 5|, &lt;0 5 19 18|]
Wedgie: &lt;&lt;10 38 36 37 29 -23||
Wedgie: &lt;&lt;10 38 36 37 29 -23||
EDOs: 58, 118, 294, 412d, 530d
EDOs: 58, 118, 294, 412d, 530d
Badness: 0.0843
Badness: 0.0843


Line 29: Line 23:


Map: [&lt;2 3 4 5 6|, &lt;0 5 19 18 27|]
Map: [&lt;2 3 4 5 6|, &lt;0 5 19 18 27|]
EDOs: 58, 118, 294, 412d
EDOs: 58, 118, 294, 412d
Badness: 0.0305
Badness: 0.0305


Line 38: Line 34:


Map: [&lt;3 4 5 6|, &lt;0 5 13 16|]
Map: [&lt;3 4 5 6|, &lt;0 5 13 16|]
Wedgie: &lt;&lt;15 39 48 27 34 2||
Wedgie: &lt;&lt;15 39 48 27 34 2||
EDOs: 60, 99, 258, 357, 456
EDOs: 60, 99, 258, 357, 456
Badness: 0.0575
Badness: 0.0575


Line 48: Line 47:


Map: [&lt;20 0 -17 -39|, &lt;0 1 2 3|]
Map: [&lt;20 0 -17 -39|, &lt;0 1 2 3|]
Wedgie: &lt;&lt;20 40 60 17 39 27||
Wedgie: &lt;&lt;20 40 60 17 39 27||
EDOs: 60, 80, 140, 640b, 780b, 920b
EDOs: 60, 80, 140, 640b, 780b, 920b
Badness: 0.1065
Badness: 0.1065


Line 58: Line 60:


Map: [&lt;20 0 -17 -39 -26|, &lt;0 1 2 3 3|]
Map: [&lt;20 0 -17 -39 -26|, &lt;0 1 2 3 3|]
EDOs: 80, 140, 360, 500be, 860bde
EDOs: 80, 140, 360, 500be, 860bde
Badness: 0.0468
Badness: 0.0468


Line 67: Line 71:


Map: [&lt;20 0 -17 -39 -26 74|, &lt;0 1 2 3 3 0|]
Map: [&lt;20 0 -17 -39 -26 74|, &lt;0 1 2 3 3 0|]
EDOs: 60e, 80, 140, 500be, 640be, 780be
EDOs: 60e, 80, 140, 500be, 640be, 780be
Badness: 0.0327
Badness: 0.0327


Line 76: Line 82:


Map: [&lt;1 0 17 4|, &lt;0 4 -37 -3|]
Map: [&lt;1 0 17 4|, &lt;0 4 -37 -3|]
EDOs: 58, 121, 179, 300bd, 479bcd
EDOs: 58, 121, 179, 300bd, 479bcd
Badness: 0.1407
Badness: 0.1407


Line 85: Line 93:


Map: [&lt;1 0 17 4 11|, &lt;0 4 -37 -3 -19|]
Map: [&lt;1 0 17 4 11|, &lt;0 4 -37 -3 -19|]
EDOs: 58, 121, 179e, 300bde
EDOs: 58, 121, 179e, 300bde
Badness: 0.0453
Badness: 0.0453


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Map: [&lt;1 0 17 4 11 16|, &lt;0 4 -37 -3 -19 -31|]
Map: [&lt;1 0 17 4 11 16|, &lt;0 4 -37 -3 -19 -31|]
EDOs: 58, 121, 179ef, 300bdef
EDOs: 58, 121, 179ef, 300bdef
Badness: 0.0238
Badness: 0.0238
</pre></div>
<h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Hemimage temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:20:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Commatic"&gt;Commatic&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Commatic-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;!-- ws:start:WikiTextTocRule:23: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Commatic-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:23 --&gt;&lt;!-- ws:start:WikiTextTocRule:24: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Chromat"&gt;Chromat&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Degrees"&gt;Degrees&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;!-- ws:start:WikiTextTocRule:26: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Degrees-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Degrees-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Subfourth"&gt;Subfourth&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;!-- ws:start:WikiTextTocRule:29: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Subfourth-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:29 --&gt;&lt;!-- ws:start:WikiTextTocRule:30: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Subfourth-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:30 --&gt;&lt;!-- ws:start:WikiTextTocRule:31: --&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;br /&gt;
&lt;br /&gt;
Hemimage temperaments temper out the hemimage comma, |5 -7 -1 3&amp;gt; = 10976/10935.&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="Commatic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Commatic&lt;/h1&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Commatic-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;7-limit&lt;/h2&gt;
Commas: 10976/10935, 50421/50000&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~81/80 = 20.377&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 3 4 5|, &amp;lt;0 5 19 18|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;10 38 36 37 29 -23||&lt;br /&gt;
EDOs: 58, 118, 294, 412d, 530d&lt;br /&gt;
Badness: 0.0843&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="Commatic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;11-limit&lt;/h2&gt;
Commas: 441/440, 3388/3375, 8019/8000&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~81/80 = 20.390&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 3 4 5 6|, &amp;lt;0 5 19 18 27|]&lt;br /&gt;
EDOs: 58, 118, 294, 412d&lt;br /&gt;
Badness: 0.0305&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Chromat"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Chromat&lt;/h1&gt;
Commas: 10976/10935, 235298/234375&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~28/27 = 60.528&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;3 4 5 6|, &amp;lt;0 5 13 16|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;15 39 48 27 34 2||&lt;br /&gt;
EDOs: 60, 99, 258, 357, 456&lt;br /&gt;
Badness: 0.0575&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="Degrees"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Degrees&lt;/h1&gt;
Commas: 10976/10935, 390625/388962&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~3/2 = 703.015&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;20 0 -17 -39|, &amp;lt;0 1 2 3|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;20 40 60 17 39 27||&lt;br /&gt;
EDOs: 60, 80, 140, 640b, 780b, 920b&lt;br /&gt;
Badness: 0.1065&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="Degrees-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;11-limit&lt;/h2&gt;
Commas: 1331/1323, 1375/1372, 2200/2187&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~3/2 = 703.231&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;20 0 -17 -39 -26|, &amp;lt;0 1 2 3 3|]&lt;br /&gt;
EDOs: 80, 140, 360, 500be, 860bde&lt;br /&gt;
Badness: 0.0468&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Degrees-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;13-limit&lt;/h2&gt;
Commas: 325/324, 352/351, 1001/1000, 1331/1323&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~3/2 = 703.080&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;20 0 -17 -39 -26 74|, &amp;lt;0 1 2 3 3 0|]&lt;br /&gt;
EDOs: 60e, 80, 140, 500be, 640be, 780be&lt;br /&gt;
Badness: 0.0327&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Subfourth"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Subfourth&lt;/h1&gt;
Commas: 10976/10935, 65536/64827&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~21/16 = 475.991&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 17 4|, &amp;lt;0 4 -37 -3|]&lt;br /&gt;
EDOs: 58, 121, 179, 300bd, 479bcd&lt;br /&gt;
Badness: 0.1407&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Subfourth-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;11-limit&lt;/h2&gt;
Commas: 540/539, 896/891, 12005/11979&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~21/16 = 475.995&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 17 4 11|, &amp;lt;0 4 -37 -3 -19|]&lt;br /&gt;
EDOs: 58, 121, 179e, 300bde&lt;br /&gt;
Badness: 0.0453&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Subfourth-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;13-limit&lt;/h2&gt;
Commas: 352/351, 364/363, 540/539, 676/675&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~21/16 = 475.996&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 17 4 11 16|, &amp;lt;0 4 -37 -3 -19 -31|]&lt;br /&gt;
EDOs: 58, 121, 179ef, 300bdef&lt;br /&gt;
Badness: 0.0238&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

Hemimage temperaments temper out the hemimage comma, |5 -7 -1 3> = 10976/10935.

Commatic

7-limit

Commas: 10976/10935, 50421/50000

POTE generator: ~81/80 = 20.377

Map: [<2 3 4 5|, <0 5 19 18|]

Wedgie: <<10 38 36 37 29 -23||

EDOs: 58, 118, 294, 412d, 530d

Badness: 0.0843

11-limit

Commas: 441/440, 3388/3375, 8019/8000

POTE generator: ~81/80 = 20.390

Map: [<2 3 4 5 6|, <0 5 19 18 27|]

EDOs: 58, 118, 294, 412d

Badness: 0.0305

Chromat

Commas: 10976/10935, 235298/234375

POTE generator: ~28/27 = 60.528

Map: [<3 4 5 6|, <0 5 13 16|]

Wedgie: <<15 39 48 27 34 2||

EDOs: 60, 99, 258, 357, 456

Badness: 0.0575

Degrees

Commas: 10976/10935, 390625/388962

POTE generator: ~3/2 = 703.015

Map: [<20 0 -17 -39|, <0 1 2 3|]

Wedgie: <<20 40 60 17 39 27||

EDOs: 60, 80, 140, 640b, 780b, 920b

Badness: 0.1065

11-limit

Commas: 1331/1323, 1375/1372, 2200/2187

POTE generator: ~3/2 = 703.231

Map: [<20 0 -17 -39 -26|, <0 1 2 3 3|]

EDOs: 80, 140, 360, 500be, 860bde

Badness: 0.0468

13-limit

Commas: 325/324, 352/351, 1001/1000, 1331/1323

POTE generator: ~3/2 = 703.080

Map: [<20 0 -17 -39 -26 74|, <0 1 2 3 3 0|]

EDOs: 60e, 80, 140, 500be, 640be, 780be

Badness: 0.0327

Subfourth

Commas: 10976/10935, 65536/64827

POTE generator: ~21/16 = 475.991

Map: [<1 0 17 4|, <0 4 -37 -3|]

EDOs: 58, 121, 179, 300bd, 479bcd

Badness: 0.1407

11-limit

Commas: 540/539, 896/891, 12005/11979

POTE generator: ~21/16 = 475.995

Map: [<1 0 17 4 11|, <0 4 -37 -3 -19|]

EDOs: 58, 121, 179e, 300bde

Badness: 0.0453

13-limit

Commas: 352/351, 364/363, 540/539, 676/675

POTE generator: ~21/16 = 475.996

Map: [<1 0 17 4 11 16|, <0 4 -37 -3 -19 -31|]

EDOs: 58, 121, 179ef, 300bdef

Badness: 0.0238

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