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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 hemimean comma, 3136/3125, is the ratio between the diesis and the tritonic diesis, or jubilisma; that is, (128/125)/(50/49). This is a no-threes comma, with [[Spectrum_of_a_temperament|spectrum]] 5/4, 7/5, 4/3, 6/5, 8/7, 7/6, 9/8, 10/9, 9/7.
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-11-12 01:24:27 UTC</tt>.<br>
: The original revision id was <tt>274570068</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]]


[[Comma|Comma]]: 3136/3125, hemimean


The hemimean comma, 3136/3125, is the ratio between the diesis and the tritonic diesis, or jubilisma; that is, (128/125)/(50/49). This is a no-threes comma, with [[Spectrum of a temperament|spectrum]] 5/4, 7/5, 4/3, 6/5, 8/7, 7/6, 9/8, 10/9, 9/7.
7 and 9 limit minimax


[|1 0 0 0&gt;, |0 1 0 0&gt;, |6/5 0 0 2/5&gt;, |0 0 0 1&gt;]


[[Comma]]: 3136/3125, hemimean
7 and 9 limit minimax
[|1 0 0 0&gt;, |0 1 0 0&gt;, |6/5 0 0 2/5&gt;, |0 0 0 1&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 7/6, 4/3
[[Eigenmonzo|Eigenmonzos]]: 2, 7/6, 4/3


Lattice basis: 28/25 length 0.5055 3/2 length 1.5849
Lattice basis: 28/25 length 0.5055 3/2 length 1.5849
Angle(28/25, 3/2) = 90 degrees
Angle(28/25, 3/2) = 90 degrees
Map to lattice: [&lt;0 0 2 5|, &lt;0 1 0 0|]
Map to lattice: [&lt;0 0 2 5|, &lt;0 1 0 0|]


Map: [&lt;1 0 0 -3|, &lt;0 1 0 0|, &lt;0 0 2 5|]  
Map: [&lt;1 0 0 -3|, &lt;0 1 0 0|, &lt;0 0 2 5|]  
[[Generator|Generators]]: 2, 3, 56/25
 
[[edo|Edos]]: [[217edo|217]], [[229edo|229]], [[328edo|328]], [[359edo|359]], [[446edo|446]], [[545edo|545c]], [[675edo|675c]]
[[generator|Generators]]: 2, 3, 56/25
 
[[EDO|Edos]]: [[217edo|217]], [[229edo|229]], [[328edo|328]], [[359edo|359]], [[446edo|446]], [[545edo|545c]], [[675edo|675c]]
 
Badness: 0.000160
Badness: 0.000160


[[Projection pair]]s: 5 3136/625 7 68841472/9765625 to 2.3.25/7
[[Projection_pair|Projection pair]]s: 5 3136/625 7 68841472/9765625 to 2.3.25/7


=Belobog=
=Belobog=
Line 33: Line 30:


11 limit minimax
11 limit minimax
[|1 0 0 0 0&gt;, |27/22 6/11 -5/22 -3/11 5/22&gt;,  
[|1 0 0 0 0&gt;, |27/22 6/11 -5/22 -3/11 5/22&gt;,  
|24/11 -4/11 -2/11 2/11 2/11&gt;,  
|24/11 -4/11 -2/11 2/11 2/11&gt;,  
|27/11 -10/11 -5/11 5/11 5/11&gt;,  
|27/11 -10/11 -5/11 5/11 5/11&gt;,  
|24/11 -4/11 -13/11 2/11 13/11&gt;]
|24/11 -4/11 -13/11 2/11 13/11&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 11/10, 9/7
[[Eigenmonzo|Eigenmonzos]]: 2, 11/10, 9/7


Lattice basis: 28/25 0.3829 16/15 1.1705
Lattice basis: 28/25 0.3829 16/15 1.1705
Angle(28/25, 16/15) = 93.2696
Angle(28/25, 16/15) = 93.2696
Map to lattice: [&lt;0 -2 2 5 4|, &lt;0 -1 0 0 -2|]
Map to lattice: [&lt;0 -2 2 5 4|, &lt;0 -1 0 0 -2|]


Map: [&lt;1 0 0 -3 -9|, &lt;0 1 0 0 2|, [0 0 2 5 8|]
Map: [&lt;1 0 0 -3 -9|, &lt;0 1 0 0 2|, [0 0 2 5 8|]
[[Generator|Generators]]: 2, 3, 56/25
 
[[edo|Edos]]: 12, 31, 87, 118, 130, 217, [[248edo|248]], [[378edo|378]], [[626edo|626]], [[961edo|961cd]]
[[generator|Generators]]: 2, 3, 56/25
 
[[EDO|Edos]]: 12, 31, 87, 118, 130, 217, [[248edo|248]], [[378edo|378]], [[626edo|626]], [[961edo|961cd]]
 
Badness: 0.000609
Badness: 0.000609


Projection pairs: 5 3136/625 7 68841472/9765625 11 1700108992512/152587890625 to 2.3.25/7
Projection pairs: 5 3136/625 7 68841472/9765625 11 1700108992512/152587890625 to 2.3.25/7


Scales: [[belobog31]]
Scales: [[belobog31|belobog31]]


==13-limit==
==13-limit==
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Map: [&lt;1 0 0 -3 -9 15|, &lt;0 1 0 0 2 -2|, &lt;0 0 2 5 8 -7|]
Map: [&lt;1 0 0 -3 -9 15|, &lt;0 1 0 0 2 -2|, &lt;0 0 2 5 8 -7|]
EDOs: 12, 31, 43, 56, 74, 87, 118, 130, 217, 248, 347e, 378, 465, 595e
EDOs: 12, 31, 43, 56, 74, 87, 118, 130, 217, 248, 347e, 378, 465, 595e
Badness: 0.00111
Badness: 0.00111


Line 63: Line 69:


Map: [&lt;1 0 0 -3 -9 -4|, &lt;0 1 0 0 2 -1|, &lt;0 0 2 5 8 8|]
Map: [&lt;1 0 0 -3 -9 -4|, &lt;0 1 0 0 2 -1|, &lt;0 0 2 5 8 8|]
EDOs: 31, 56, 87, 118, 205d, 263f, 304f, 391df, 509df
EDOs: 31, 56, 87, 118, 205d, 263f, 304f, 391df, 509df
Badness: 0.00126
Badness: 0.00126


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11 limit minimax
11 limit minimax
[|1 0 0 0 0&gt;, |0 1 0 0 0&gt;, |8/5 3/5 1/5 0 -1/5&gt;,  
[|1 0 0 0 0&gt;, |0 1 0 0 0&gt;, |8/5 3/5 1/5 0 -1/5&gt;,  
|1 3/2 1/2 0 -1/2&gt;, |8/5 3/5 -4/5 0 4/5&gt;]
|1 3/2 1/2 0 -1/2&gt;, |8/5 3/5 -4/5 0 4/5&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 11/10, 4/3
[[Eigenmonzo|Eigenmonzos]]: 2, 11/10, 4/3


Map: [&lt;1 0 0 -3 8|, &lt;0 1 0 0 3|, &lt;0 0 2 5 -8|]
Map: [&lt;1 0 0 -3 8|, &lt;0 1 0 0 3|, &lt;0 0 2 5 -8|]
[[Generator|Generators]]: 2, 3, 768/343
 
[[edo|Edos]]: 19, 31, 80, 99d, 111, [[130edo|130]], [[241edo|241]], 340ce, 371ce, 470cde, 711cde
[[generator|Generators]]: 2, 3, 768/343
 
[[EDO|Edos]]: 19, 31, 80, 99d, 111, [[130edo|130]], [[241edo|241]], 340ce, 371ce, 470cde, 711cde
 
Badness: 0.000870
Badness: 0.000870


Line 83: Line 96:


Map: [&lt;1 0 2 2 1|, &lt;0 1 2 5 2|, &lt;0 0 -4 -10 -1|]
Map: [&lt;1 0 2 2 1|, &lt;0 1 2 5 2|, &lt;0 0 -4 -10 -1|]
EDOs: 31, 80, 87, 111, 118, 198, 316, 545c, 861ce
EDOs: 31, 80, 87, 111, 118, 198, 316, 545c, 861ce
Badness: 0.000819</pre></div>
 
<h4>Original HTML content:</h4>
Badness: 0.000819
<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;Hemimean family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:10:&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:10 --&gt;&lt;!-- ws:start:WikiTextTocRule:11: --&gt;&lt;a href="#Belobog"&gt;Belobog&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:11 --&gt;&lt;!-- ws:start:WikiTextTocRule:12: --&gt;&lt;!-- ws:end:WikiTextTocRule:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&gt;&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;!-- ws:start:WikiTextTocRule:14: --&gt; | &lt;a href="#Siebog"&gt;Siebog&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt; | &lt;a href="#Triglav"&gt;Triglav&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt;
[[Category:family]]
&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;br /&gt;
[[Category:hemimean]]
&lt;br /&gt;
[[Category:planar]]
The hemimean comma, 3136/3125, is the ratio between the diesis and the tritonic diesis, or jubilisma; that is, (128/125)/(50/49). This is a no-threes comma, with &lt;a class="wiki_link" href="/Spectrum%20of%20a%20temperament"&gt;spectrum&lt;/a&gt; 5/4, 7/5, 4/3, 6/5, 8/7, 7/6, 9/8, 10/9, 9/7.&lt;br /&gt;
[[Category:theory]]
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;: 3136/3125, hemimean&lt;br /&gt;
&lt;br /&gt;
7 and 9 limit minimax&lt;br /&gt;
[|1 0 0 0&amp;gt;, |0 1 0 0&amp;gt;, |6/5 0 0 2/5&amp;gt;, |0 0 0 1&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 7/6, 4/3&lt;br /&gt;
&lt;br /&gt;
Lattice basis: 28/25 length 0.5055 3/2 length 1.5849&lt;br /&gt;
Angle(28/25, 3/2) = 90 degrees&lt;br /&gt;
Map to lattice: [&amp;lt;0 0 2 5|, &amp;lt;0 1 0 0|]&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -3|, &amp;lt;0 1 0 0|, &amp;lt;0 0 2 5|] &lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 3, 56/25&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: &lt;a class="wiki_link" href="/217edo"&gt;217&lt;/a&gt;, &lt;a class="wiki_link" href="/229edo"&gt;229&lt;/a&gt;, &lt;a class="wiki_link" href="/328edo"&gt;328&lt;/a&gt;, &lt;a class="wiki_link" href="/359edo"&gt;359&lt;/a&gt;, &lt;a class="wiki_link" href="/446edo"&gt;446&lt;/a&gt;, &lt;a class="wiki_link" href="/545edo"&gt;545c&lt;/a&gt;, &lt;a class="wiki_link" href="/675edo"&gt;675c&lt;/a&gt;&lt;br /&gt;
Badness: 0.000160&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Projection%20pair"&gt;Projection pair&lt;/a&gt;s: 5 3136/625 7 68841472/9765625 to 2.3.25/7&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="Belobog"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Belobog&lt;/h1&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 3136/3125, 441/440&lt;br /&gt;
&lt;br /&gt;
11 limit minimax&lt;br /&gt;
[|1 0 0 0 0&amp;gt;, |27/22 6/11 -5/22 -3/11 5/22&amp;gt;, &lt;br /&gt;
|24/11 -4/11 -2/11 2/11 2/11&amp;gt;, &lt;br /&gt;
|27/11 -10/11 -5/11 5/11 5/11&amp;gt;, &lt;br /&gt;
|24/11 -4/11 -13/11 2/11 13/11&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 11/10, 9/7&lt;br /&gt;
&lt;br /&gt;
Lattice basis: 28/25 0.3829 16/15 1.1705&lt;br /&gt;
Angle(28/25, 16/15) = 93.2696&lt;br /&gt;
Map to lattice: [&amp;lt;0 -2 2 5 4|, &amp;lt;0 -1 0 0 -2|]&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -3 -9|, &amp;lt;0 1 0 0 2|, [0 0 2 5 8|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 3, 56/25&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: 12, 31, 87, 118, 130, 217, &lt;a class="wiki_link" href="/248edo"&gt;248&lt;/a&gt;, &lt;a class="wiki_link" href="/378edo"&gt;378&lt;/a&gt;, &lt;a class="wiki_link" href="/626edo"&gt;626&lt;/a&gt;, &lt;a class="wiki_link" href="/961edo"&gt;961cd&lt;/a&gt;&lt;br /&gt;
Badness: 0.000609&lt;br /&gt;
&lt;br /&gt;
Projection pairs: 5 3136/625 7 68841472/9765625 11 1700108992512/152587890625 to 2.3.25/7&lt;br /&gt;
&lt;br /&gt;
Scales: &lt;a class="wiki_link" href="/belobog31"&gt;belobog31&lt;/a&gt;&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="Belobog-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;13-limit&lt;/h2&gt;
Commas: 441/440, 1001/1000, 3136/3125&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -3 -9 15|, &amp;lt;0 1 0 0 2 -2|, &amp;lt;0 0 2 5 8 -7|]&lt;br /&gt;
EDOs: 12, 31, 43, 56, 74, 87, 118, 130, 217, 248, 347e, 378, 465, 595e&lt;br /&gt;
Badness: 0.00111&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="Belobog-Bellowblog"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Bellowblog&lt;/h2&gt;
Commas: 196/195, 352/351, 625/624&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -3 -9 -4|, &amp;lt;0 1 0 0 2 -1|, &amp;lt;0 0 2 5 8 8|]&lt;br /&gt;
EDOs: 31, 56, 87, 118, 205d, 263f, 304f, 391df, 509df&lt;br /&gt;
Badness: 0.00126&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="Siebog"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Siebog&lt;/h1&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 3136/3125, 540/539&lt;br /&gt;
&lt;br /&gt;
11 limit minimax&lt;br /&gt;
[|1 0 0 0 0&amp;gt;, |0 1 0 0 0&amp;gt;, |8/5 3/5 1/5 0 -1/5&amp;gt;, &lt;br /&gt;
|1 3/2 1/2 0 -1/2&amp;gt;, |8/5 3/5 -4/5 0 4/5&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 11/10, 4/3&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -3 8|, &amp;lt;0 1 0 0 3|, &amp;lt;0 0 2 5 -8|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 3, 768/343&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: 19, 31, 80, 99d, 111, &lt;a class="wiki_link" href="/130edo"&gt;130&lt;/a&gt;, &lt;a class="wiki_link" href="/241edo"&gt;241&lt;/a&gt;, 340ce, 371ce, 470cde, 711cde&lt;br /&gt;
Badness: 0.000870&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="Triglav"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Triglav&lt;/h1&gt;
Commas: 3136/3125, 3025/3024&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 2 2 1|, &amp;lt;0 1 2 5 2|, &amp;lt;0 0 -4 -10 -1|]&lt;br /&gt;
EDOs: 31, 80, 87, 111, 118, 198, 316, 545c, 861ce&lt;br /&gt;
Badness: 0.000819&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

The hemimean comma, 3136/3125, is the ratio between the diesis and the tritonic diesis, or jubilisma; that is, (128/125)/(50/49). This is a no-threes comma, with spectrum 5/4, 7/5, 4/3, 6/5, 8/7, 7/6, 9/8, 10/9, 9/7.

Comma: 3136/3125, hemimean

7 and 9 limit minimax

[|1 0 0 0>, |0 1 0 0>, |6/5 0 0 2/5>, |0 0 0 1>]

Eigenmonzos: 2, 7/6, 4/3

Lattice basis: 28/25 length 0.5055 3/2 length 1.5849

Angle(28/25, 3/2) = 90 degrees

Map to lattice: [<0 0 2 5|, <0 1 0 0|]

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

Generators: 2, 3, 56/25

Edos: 217, 229, 328, 359, 446, 545c, 675c

Badness: 0.000160

Projection pairs: 5 3136/625 7 68841472/9765625 to 2.3.25/7

Belobog

Commas: 3136/3125, 441/440

11 limit minimax

[|1 0 0 0 0>, |27/22 6/11 -5/22 -3/11 5/22>, |24/11 -4/11 -2/11 2/11 2/11>, |27/11 -10/11 -5/11 5/11 5/11>, |24/11 -4/11 -13/11 2/11 13/11>]

Eigenmonzos: 2, 11/10, 9/7

Lattice basis: 28/25 0.3829 16/15 1.1705

Angle(28/25, 16/15) = 93.2696

Map to lattice: [<0 -2 2 5 4|, <0 -1 0 0 -2|]

Map: [<1 0 0 -3 -9|, <0 1 0 0 2|, [0 0 2 5 8|]

Generators: 2, 3, 56/25

Edos: 12, 31, 87, 118, 130, 217, 248, 378, 626, 961cd

Badness: 0.000609

Projection pairs: 5 3136/625 7 68841472/9765625 11 1700108992512/152587890625 to 2.3.25/7

Scales: belobog31

13-limit

Commas: 441/440, 1001/1000, 3136/3125

Map: [<1 0 0 -3 -9 15|, <0 1 0 0 2 -2|, <0 0 2 5 8 -7|]

EDOs: 12, 31, 43, 56, 74, 87, 118, 130, 217, 248, 347e, 378, 465, 595e

Badness: 0.00111

Bellowblog

Commas: 196/195, 352/351, 625/624

Map: [<1 0 0 -3 -9 -4|, <0 1 0 0 2 -1|, <0 0 2 5 8 8|]

EDOs: 31, 56, 87, 118, 205d, 263f, 304f, 391df, 509df

Badness: 0.00126

Siebog

Commas: 3136/3125, 540/539

11 limit minimax

[|1 0 0 0 0>, |0 1 0 0 0>, |8/5 3/5 1/5 0 -1/5>, |1 3/2 1/2 0 -1/2>, |8/5 3/5 -4/5 0 4/5>]

Eigenmonzos: 2, 11/10, 4/3

Map: [<1 0 0 -3 8|, <0 1 0 0 3|, <0 0 2 5 -8|]

Generators: 2, 3, 768/343

Edos: 19, 31, 80, 99d, 111, 130, 241, 340ce, 371ce, 470cde, 711cde

Badness: 0.000870

Triglav

Commas: 3136/3125, 3025/3024

Map: [<1 0 2 2 1|, <0 1 2 5 2|, <0 0 -4 -10 -1|]

EDOs: 31, 80, 87, 111, 118, 198, 316, 545c, 861ce

Badness: 0.000819

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