Hemimean clan: 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:Gedankenwelt|Gedankenwelt]] and made on <tt>2015-08-10 01:07:25 UTC</tt>.<br>
: The original revision id was <tt>556412395</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]]
The hemimean clan, tempering out the no-threes hemimean comma 3136/3125, contains the temperaments misty and semisept, considered below, as well as [[Meantone|meantone]], [[Hemiwürschmidt|hemiwürschmidt]], [[Parakleismic|parakleismic]], [[Hemithirds|hemithirds]], [[Clyde|clyde]], [[Hemischismic|hemischismic]], [[Passion|passion]], [[Hexe|hexe]] and [[Sycamore|sycamore]] considered elsewhere.
The hemimean clan, tempering out the no-threes hemimean comma 3136/3125, contains the temperaments misty and semisept, considered below, as well as [[Meantone|meantone]], [[Hemiwürschmidt|hemiwürschmidt]], [[Parakleismic|parakleismic]], [[Hemithirds|hemithirds]], [[Clyde|clyde]], [[Hemischismic|hemischismic]], [[Passion|passion]], [[Hexe|hexe]] and [[Sycamore|sycamore]] considered elsewhere.


=2.5.7-limit=  
=2.5.7-limit=
Comma: 3136/3125
Comma: 3136/3125


No-threes [[POTE tuning|POTE generator]] (~28/25): 193.772
No-threes [[POTE_tuning|POTE generator]] (~28/25): 193.772


Map: [&lt;1 0 0 -3|, &lt;0 0 2 5|]
Map: [&lt;1 0 0 -3|, &lt;0 0 2 5|]
EDOs: [[6edo|6]], [[12edo|12]], [[19edo|19]], [[31edo|31]], [[68edo|68]], [[80edo|80]], [[87edo|87]], [[99edo|99]], [[130edo|130]], [[217edo|217]], [[229edo|229]], [[328edo|328]], [[347edo|347]], [[446edo|446]], [[545edo|545c]], [[675edo|675]]
EDOs: [[6edo|6]], [[12edo|12]], [[19edo|19]], [[31edo|31]], [[68edo|68]], [[80edo|80]], [[87edo|87]], [[99edo|99]], [[130edo|130]], [[217edo|217]], [[229edo|229]], [[328edo|328]], [[347edo|347]], [[446edo|446]], [[545edo|545c]], [[675edo|675]]


=Misty=  
=Misty=
Commas: 3136/3125, 5120/5103
Commas: 3136/3125, 5120/5103


[[POTE tuning|POTE generator]]: 703.021
[[POTE_tuning|POTE generator]]: 703.021


Map: [&lt;3 0 26 56|, &lt;0 1 -4 -10|]
Map: [&lt;3 0 26 56|, &lt;0 1 -4 -10|]
Wedgie: &lt;&lt;3 -12 -30 -26 -56 -36||
Wedgie: &lt;&lt;3 -12 -30 -26 -56 -36||
EDOs: [[12edo|12]], [[87edo|87]], [[99edo|99]]
EDOs: [[12edo|12]], [[87edo|87]], [[99edo|99]]


==11-limit==  
==11-limit==
Commas: 441/440, 3136/3125, 4375/4356
Commas: 441/440, 3136/3125, 4375/4356


[[POTE tuning|POTE generator]]: 703.210
[[POTE_tuning|POTE generator]]: 703.210


Map: [&lt;3 0 26 56 77|, &lt;0 1 -4 -10 -14|]
Map: [&lt;3 0 26 56 77|, &lt;0 1 -4 -10 -14|]
EDOs: 12, 87, 99e, 186e
EDOs: 12, 87, 99e, 186e


==13-limit==  
==13-limit==
Commas: 196/195, 352/351, 364/363, 625/624
Commas: 196/195, 352/351, 364/363, 625/624


[[POTE tuning|POTE generator]]: 703.303
[[POTE_tuning|POTE generator]]: 703.303


Map: [&lt;3 0 26 56 77 92|, &lt;0 1 -4 -10 -14 -17|]
Map: [&lt;3 0 26 56 77 92|, &lt;0 1 -4 -10 -14 -17|]
EDOs: 12, 87, 186ef, 273ef
EDOs: 12, 87, 186ef, 273ef


=Mystic=  
=Mystic=
Commas: 325/324, 441/440, 896/891, 1001/1000
Commas: 325/324, 441/440, 896/891, 1001/1000


[[POTE tuning|POTE generator]]: 703.311
[[POTE_tuning|POTE generator]]: 703.311


Map: [&lt;3 0 26 56 77 -46|, &lt;0 1 -4 -10 -14 12|]
Map: [&lt;3 0 26 56 77 -46|, &lt;0 1 -4 -10 -14 12|]
EDOs: 12, 87, 186e, 273e, 633bde
EDOs: 12, 87, 186e, 273e, 633bde


==17-limit==  
==17-limit==
Commas: 196/195, 352/351, 364/363, 625/624
Commas: 196/195, 352/351, 364/363, 625/624


[[POTE tuning|POTE generator]]: 703.233
[[POTE_tuning|POTE generator]]: 703.233


Map: [&lt;3 0 26 56 77 92 -2|, &lt;0 1 -4 -10 -14 -17 3|]
Map: [&lt;3 0 26 56 77 92 -2|, &lt;0 1 -4 -10 -14 -17 3|]
EDOs: 87, 186ef, 273ef
EDOs: 87, 186ef, 273ef


==19-limit==  
==19-limit==
Commas: 154/153, 196/195, 245/243, 273/272, 286/285, 325/324
Commas: 154/153, 196/195, 245/243, 273/272, 286/285, 325/324


[[POTE tuning|POTE generator]]: 703.253
[[POTE_tuning|POTE generator]]: 703.253


Map: [&lt;3 0 26 56 77 92 -2 8|, &lt;0 1 -4 -10 -14 -17 3 1|]
Map: [&lt;3 0 26 56 77 92 -2 8|, &lt;0 1 -4 -10 -14 -17 3 1|]
EDOs: 46, 87, 133, 326de, 413degh
EDOs: 46, 87, 133, 326de, 413degh


=Semisept=  
=Semisept=
Comma: 782757789696/762939453125
Comma: 782757789696/762939453125


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Map: [&lt;1 12 6|, &lt;0 -17 -6|]
Map: [&lt;1 12 6|, &lt;0 -17 -6|]
EDOs: 18, 31, 80, 111
EDOs: 18, 31, 80, 111
Badness: 0.6306
Badness: 0.6306


==7-limit==  
==7-limit==
Commas: 3136/3125, 1728/1715
Commas: 3136/3125, 1728/1715


[[POTE tuning|POTE generator]]: (~75/49) 735.155
[[POTE_tuning|POTE generator]]: (~75/49) 735.155


Map: [&lt;1 12 6 12|, &lt;0 -17 -6 -15|]
Map: [&lt;1 12 6 12|, &lt;0 -17 -6 -15|]
Wedgie: &lt;&lt;17 6 15 -30 -24 18||
Wedgie: &lt;&lt;17 6 15 -30 -24 18||
EDOs: [[18edo|18]], 31, [[80edo|80]], 111
EDOs: [[18edo|18]], 31, [[80edo|80]], 111


==11-limit==  
==11-limit==
Commas: 176/175, 540/539, 1331/1323
Commas: 176/175, 540/539, 1331/1323


[[POTE tuning|POTE generator]]: (~55/36) 735.125
[[POTE_tuning|POTE generator]]: (~55/36) 735.125


Map: [&lt;1 12 6 12 20|, &lt;0 -17 -6 -15 -27|]
Map: [&lt;1 12 6 12 20|, &lt;0 -17 -6 -15 -27|]
EDOs: 18e, 31, 80, 111, 364cd,
EDOs: 18e, 31, 80, 111, 364cd,
Badness: 0.0225
Badness: 0.0225


===Semishly===  
===Semishly===
Commas: 144/143, 176/175, 196/195, 275/273
Commas: 144/143, 176/175, 196/195, 275/273


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Map: [&lt;1 12 6 12 20 8|, &lt;0 -17 -6 -15 -27 -7|]
Map: [&lt;1 12 6 12 20 8|, &lt;0 -17 -6 -15 -27 -7|]
EDOs: 31, 49f, 80f
EDOs: 31, 49f, 80f
Badness: 0.0284
Badness: 0.0284


==13-limit==  
==13-limit==
Commas: 176/175, 351/350, 540/539, 1375/1372
Commas: 176/175, 351/350, 540/539, 1375/1372


[[POTE tuning|POTE generator]]: 735.126
[[POTE_tuning|POTE generator]]: 735.126


Map: [&lt;1 12 6 12 20 -11|, &lt;0 -17 -6 -15 -27 24|]
Map: [&lt;1 12 6 12 20 -11|, &lt;0 -17 -6 -15 -27 24|]
EDOs: 31, 80, 111
EDOs: 31, 80, 111
Badness: 0.0252
Badness: 0.0252


==17-limit==  
==17-limit==
Commas: 176/175, 256/255, 351/350, 640/637, 715/714
Commas: 176/175, 256/255, 351/350, 640/637, 715/714


[[POTE tuning|POTE generator]]: (~26/17) 735.125
[[POTE_tuning|POTE generator]]: (~26/17) 735.125


Map: [&lt;1 12 6 12 20 -11 -10|, &lt;0 -17 -6 -15 -27 24 23|]
Map: [&lt;1 12 6 12 20 -11 -10|, &lt;0 -17 -6 -15 -27 24 23|]
EDOs: 31, 80, 111
EDOs: 31, 80, 111


==19-limit==  
==19-limit==
Commas: 176/175, 286/285, 351/350, 476/475, 540/539, 1331/1323
Commas: 176/175, 286/285, 351/350, 476/475, 540/539, 1331/1323


[[POTE tuning|POTE generator]]: 735.116
[[POTE_tuning|POTE generator]]: 735.116


Map: [&lt;1 12 6 12 20 -11 -10 -8|, &lt;0 -17 -6 -15 -27 24 23 20|]
Map: [&lt;1 12 6 12 20 -11 -10 -8|, &lt;0 -17 -6 -15 -27 24 23 20|]
EDOs: 31, 80, 111
EDOs: 31, 80, 111


==23-limit==  
==23-limit==
Commas: 176/175, 253/252, 286/285, 345/343, 351/350, 391/390, 460/459
Commas: 176/175, 253/252, 286/285, 345/343, 351/350, 391/390, 460/459


[[POTE tuning|POTE generator]]: 435.106
[[POTE_tuning|POTE generator]]: 435.106


Map: [&lt;1 12 6 12 20 -11 -10 -8 18|,
Map: [&lt;1 12 6 12 20 -11 -10 -8 18|,
&lt;0 -17 -6 -15 -27 24 23 20 -22|]
&lt;0 -17 -6 -15 -27 24 23 20 -22|]
EDOs: 31, 80, 111, 191cdh, 302cdgh
EDOs: 31, 80, 111, 191cdh, 302cdgh


=Sengagen=  
=Sengagen=
Commas: 3136/3125, 420175/419904
Commas: 3136/3125, 420175/419904


Line 142: Line 157:


Map: [&lt;1 1 2 2|, &lt;0 29 16 40|]
Map: [&lt;1 1 2 2|, &lt;0 29 16 40|]
Wedgie: &lt;&lt;29 16 40 -42 -18 48||
Wedgie: &lt;&lt;29 16 40 -42 -18 48||
EDOs: 49, 50, 99, 248, 347, 446
EDOs: 49, 50, 99, 248, 347, 446
Badness: 0.0580
Badness: 0.0580


=Subpental=  
=Subpental=
Commas: 3136/3125, 19683/19600
Commas: 3136/3125, 19683/19600


Line 152: Line 170:


Map: [&lt;1 6 8 17|, &lt;0 -14 -18 -45|]
Map: [&lt;1 6 8 17|, &lt;0 -14 -18 -45|]
Wedgie: &lt;&lt;14 18 45 -4 32 54||
Wedgie: &lt;&lt;14 18 45 -4 32 54||
EDOs: 19, 111, 130, 929c, 1059c, 1189bc, 1319bc
EDOs: 19, 111, 130, 929c, 1059c, 1189bc, 1319bc
Badness: 0.0543
Badness: 0.0543


==11-limit==  
==11-limit==
Commas: 540/539, 3136/3125, 8019/8000
Commas: 540/539, 3136/3125, 8019/8000


Line 162: Line 183:


Map: [&lt;1 6 8 17 -6|, &lt;0 -14 -18 -45 30|]
Map: [&lt;1 6 8 17 -6|, &lt;0 -14 -18 -45 30|]
EDOs: 19, 111, 130, 241, 371ce, 501cde, 872cde
EDOs: 19, 111, 130, 241, 371ce, 501cde, 872cde
Badness: 0.0453
Badness: 0.0453


==13-limit==  
==13-limit==
Commas: 351/350, 540/539, 676/675, 3136/3125
Commas: 351/350, 540/539, 676/675, 3136/3125


Line 171: Line 194:


Map: [&lt;1 6 8 17 -6 16|, &lt;0 -14 -18 -45 30 -39|]
Map: [&lt;1 6 8 17 -6 16|, &lt;0 -14 -18 -45 30 -39|]
EDOs: 19, 111, 130, 241, 371ce
EDOs: 19, 111, 130, 241, 371ce
Badness: 0.0239
Badness: 0.0239


=Arch=  
=Arch=
Commas: 3136/3125, 5250987/5242880
Commas: 3136/3125, 5250987/5242880


Line 180: Line 205:


Map: [&lt;1 2 2 2|, &lt;0 -18 14 35|]
Map: [&lt;1 2 2 2|, &lt;0 -18 14 35|]
Wedgie: &lt;&lt;18 -14 -35 -64 -106 -42||
Wedgie: &lt;&lt;18 -14 -35 -64 -106 -42||
EDOs: 43, 87, 130, 217, 347, 824c, 1171c, 1518cd
EDOs: 43, 87, 130, 217, 347, 824c, 1171c, 1518cd
Badness: 0.0943
Badness: 0.0943


==11-limit==  
==11-limit==
Commas: 441/440, 3136/3125, 4000/3993
Commas: 441/440, 3136/3125, 4000/3993


Line 190: Line 218:


Map: [&lt;1 2 2 2 3|, &lt;0 -18 14 35 20|]
Map: [&lt;1 2 2 2 3|, &lt;0 -18 14 35 20|]
EDOs: 43, 87, 130, 217, 347e, 911cde
EDOs: 43, 87, 130, 217, 347e, 911cde
Badness: 0.0365
Badness: 0.0365


==13-limit==  
==13-limit==
Commas: 364/363, 441/440, 676/675, 3136/3125
Commas: 364/363, 441/440, 676/675, 3136/3125


Line 199: Line 229:


Map: [&lt;1 2 2 2 3 4|, &lt;0 -18 14 35 20 -13|]
Map: [&lt;1 2 2 2 3 4|, &lt;0 -18 14 35 20 -13|]
EDOs: 43, 87, 130, 217, 347e, 564e
EDOs: 43, 87, 130, 217, 347e, 564e
Badness: 0.0195
Badness: 0.0195


=Emka=  
=Emka=
Commas: 3136/3125, 84035/82944
Commas: 3136/3125, 84035/82944


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Map: [&lt;1 14 6 12|, &lt;0 -27 -8 -20|]
Map: [&lt;1 14 6 12|, &lt;0 -27 -8 -20|]
EDOs: 37, 50, 87, 137d, 224d
EDOs: 37, 50, 87, 137d, 224d
Badness: 0.1443
Badness: 0.1443


==11-limit==  
==11-limit==
Commas: 385/384, 2401/2376, 3136/3125
Commas: 385/384, 2401/2376, 3136/3125


Line 217: Line 251:


Map: [&lt;1 14 6 12 3|, &lt;0 -27 -8 -20 1|]
Map: [&lt;1 14 6 12 3|, &lt;0 -27 -8 -20 1|]
EDOs: 37, 50, 87, 224d, 311d
EDOs: 37, 50, 87, 224d, 311d
Badness: 0.0547
Badness: 0.0547


==13-limit==  
==13-limit==
Commas: 196/195, 364/363, 385/384, 625/624
Commas: 196/195, 364/363, 385/384, 625/624


Line 226: Line 262:


Map: [&lt;1 14 6 12 3 6|, &lt;0 -27 -8 -20 1 -5|]
Map: [&lt;1 14 6 12 3 6|, &lt;0 -27 -8 -20 1 -5|]
EDOs: 37, 50, 87, 224d, 311d, 398d
EDOs: 37, 50, 87, 224d, 311d, 398d
Badness: 0.0297</pre></div>
 
<h4>Original HTML content:</h4>
Badness: 0.0297
<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 clan&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:50:&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:50 --&gt;&lt;!-- ws:start:WikiTextTocRule:51: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#x2.5.7-limit"&gt;2.5.7-limit&lt;/a&gt;&lt;/div&gt;
[[Category:clan]]
&lt;!-- ws:end:WikiTextTocRule:51 --&gt;&lt;!-- ws:start:WikiTextTocRule:52: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Misty"&gt;Misty&lt;/a&gt;&lt;/div&gt;
[[Category:hemimean]]
&lt;!-- ws:end:WikiTextTocRule:52 --&gt;&lt;!-- ws:start:WikiTextTocRule:53: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Misty-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
[[Category:list]]
&lt;!-- ws:end:WikiTextTocRule:53 --&gt;&lt;!-- ws:start:WikiTextTocRule:54: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Misty-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
[[Category:overview]]
&lt;!-- ws:end:WikiTextTocRule:54 --&gt;&lt;!-- ws:start:WikiTextTocRule:55: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Mystic"&gt;Mystic&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:55 --&gt;&lt;!-- ws:start:WikiTextTocRule:56: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Mystic-17-limit"&gt;17-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:56 --&gt;&lt;!-- ws:start:WikiTextTocRule:57: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Mystic-19-limit"&gt;19-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:57 --&gt;&lt;!-- ws:start:WikiTextTocRule:58: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Semisept"&gt;Semisept&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:58 --&gt;&lt;!-- ws:start:WikiTextTocRule:59: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Semisept-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:59 --&gt;&lt;!-- ws:start:WikiTextTocRule:60: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Semisept-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:60 --&gt;&lt;!-- ws:start:WikiTextTocRule:61: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Semisept-11-limit-Semishly"&gt;Semishly&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:61 --&gt;&lt;!-- ws:start:WikiTextTocRule:62: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Semisept-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:62 --&gt;&lt;!-- ws:start:WikiTextTocRule:63: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Semisept-17-limit"&gt;17-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:63 --&gt;&lt;!-- ws:start:WikiTextTocRule:64: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Semisept-19-limit"&gt;19-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:64 --&gt;&lt;!-- ws:start:WikiTextTocRule:65: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Semisept-23-limit"&gt;23-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:65 --&gt;&lt;!-- ws:start:WikiTextTocRule:66: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Sengagen"&gt;Sengagen&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:66 --&gt;&lt;!-- ws:start:WikiTextTocRule:67: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Subpental"&gt;Subpental&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:67 --&gt;&lt;!-- ws:start:WikiTextTocRule:68: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Subpental-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:68 --&gt;&lt;!-- ws:start:WikiTextTocRule:69: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Subpental-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:69 --&gt;&lt;!-- ws:start:WikiTextTocRule:70: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Arch"&gt;Arch&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:70 --&gt;&lt;!-- ws:start:WikiTextTocRule:71: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Arch-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:71 --&gt;&lt;!-- ws:start:WikiTextTocRule:72: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Arch-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:72 --&gt;&lt;!-- ws:start:WikiTextTocRule:73: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Emka"&gt;Emka&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:73 --&gt;&lt;!-- ws:start:WikiTextTocRule:74: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Emka-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:74 --&gt;&lt;!-- ws:start:WikiTextTocRule:75: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Emka-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:75 --&gt;&lt;!-- ws:start:WikiTextTocRule:76: --&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:76 --&gt;The hemimean clan, tempering out the no-threes hemimean comma 3136/3125, contains the temperaments misty and semisept, considered below, as well as &lt;a class="wiki_link" href="/Meantone"&gt;meantone&lt;/a&gt;, &lt;a class="wiki_link" href="/Hemiw%C3%BCrschmidt"&gt;hemiwürschmidt&lt;/a&gt;, &lt;a class="wiki_link" href="/Parakleismic"&gt;parakleismic&lt;/a&gt;, &lt;a class="wiki_link" href="/Hemithirds"&gt;hemithirds&lt;/a&gt;, &lt;a class="wiki_link" href="/Clyde"&gt;clyde&lt;/a&gt;, &lt;a class="wiki_link" href="/Hemischismic"&gt;hemischismic&lt;/a&gt;, &lt;a class="wiki_link" href="/Passion"&gt;passion&lt;/a&gt;, &lt;a class="wiki_link" href="/Hexe"&gt;hexe&lt;/a&gt; and &lt;a class="wiki_link" href="/Sycamore"&gt;sycamore&lt;/a&gt; considered elsewhere.&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="x2.5.7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;2.5.7-limit&lt;/h1&gt;
Comma: 3136/3125&lt;br /&gt;
&lt;br /&gt;
No-threes &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt; (~28/25): 193.772&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -3|, &amp;lt;0 0 2 5|]&lt;br /&gt;
EDOs: &lt;a class="wiki_link" href="/6edo"&gt;6&lt;/a&gt;, &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/68edo"&gt;68&lt;/a&gt;, &lt;a class="wiki_link" href="/80edo"&gt;80&lt;/a&gt;, &lt;a class="wiki_link" href="/87edo"&gt;87&lt;/a&gt;, &lt;a class="wiki_link" href="/99edo"&gt;99&lt;/a&gt;, &lt;a class="wiki_link" href="/130edo"&gt;130&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="/347edo"&gt;347&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;675&lt;/a&gt;&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="Misty"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Misty&lt;/h1&gt;
Commas: 3136/3125, 5120/5103&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 703.021&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;3 0 26 56|, &amp;lt;0 1 -4 -10|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;3 -12 -30 -26 -56 -36||&lt;br /&gt;
EDOs: &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/87edo"&gt;87&lt;/a&gt;, &lt;a class="wiki_link" href="/99edo"&gt;99&lt;/a&gt;&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="Misty-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;11-limit&lt;/h2&gt;
Commas: 441/440, 3136/3125, 4375/4356&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 703.210&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;3 0 26 56 77|, &amp;lt;0 1 -4 -10 -14|]&lt;br /&gt;
EDOs: 12, 87, 99e, 186e&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="Misty-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;13-limit&lt;/h2&gt;
Commas: 196/195, 352/351, 364/363, 625/624&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 703.303&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;3 0 26 56 77 92|, &amp;lt;0 1 -4 -10 -14 -17|]&lt;br /&gt;
EDOs: 12, 87, 186ef, 273ef&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="Mystic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Mystic&lt;/h1&gt;
Commas: 325/324, 441/440, 896/891, 1001/1000&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 703.311&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;3 0 26 56 77 -46|, &amp;lt;0 1 -4 -10 -14 12|]&lt;br /&gt;
EDOs: 12, 87, 186e, 273e, 633bde&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="Mystic-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;17-limit&lt;/h2&gt;
Commas: 196/195, 352/351, 364/363, 625/624&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 703.233&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;3 0 26 56 77 92 -2|, &amp;lt;0 1 -4 -10 -14 -17 3|]&lt;br /&gt;
EDOs: 87, 186ef, 273ef&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="Mystic-19-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;19-limit&lt;/h2&gt;
Commas: 154/153, 196/195, 245/243, 273/272, 286/285, 325/324&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 703.253&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;3 0 26 56 77 92 -2 8|, &amp;lt;0 1 -4 -10 -14 -17 3 1|]&lt;br /&gt;
EDOs: 46, 87, 133, 326de, 413degh&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="Semisept"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Semisept&lt;/h1&gt;
Comma: 782757789696/762939453125&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~192/125 = 735.146&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 12 6|, &amp;lt;0 -17 -6|]&lt;br /&gt;
EDOs: 18, 31, 80, 111&lt;br /&gt;
Badness: 0.6306&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="Semisept-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;7-limit&lt;/h2&gt;
Commas: 3136/3125, 1728/1715&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: (~75/49) 735.155&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 12 6 12|, &amp;lt;0 -17 -6 -15|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;17 6 15 -30 -24 18||&lt;br /&gt;
EDOs: &lt;a class="wiki_link" href="/18edo"&gt;18&lt;/a&gt;, 31, &lt;a class="wiki_link" href="/80edo"&gt;80&lt;/a&gt;, 111&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="Semisept-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;11-limit&lt;/h2&gt;
Commas: 176/175, 540/539, 1331/1323&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: (~55/36) 735.125&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 12 6 12 20|, &amp;lt;0 -17 -6 -15 -27|]&lt;br /&gt;
EDOs: 18e, 31, 80, 111, 364cd,&lt;br /&gt;
Badness: 0.0225&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc10"&gt;&lt;a name="Semisept-11-limit-Semishly"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Semishly&lt;/h3&gt;
Commas: 144/143, 176/175, 196/195, 275/273&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~13/10 = 464.980&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 12 6 12 20 8|, &amp;lt;0 -17 -6 -15 -27 -7|]&lt;br /&gt;
EDOs: 31, 49f, 80f&lt;br /&gt;
Badness: 0.0284&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="Semisept-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;13-limit&lt;/h2&gt;
Commas: 176/175, 351/350, 540/539, 1375/1372&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 735.126&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 12 6 12 20 -11|, &amp;lt;0 -17 -6 -15 -27 24|]&lt;br /&gt;
EDOs: 31, 80, 111&lt;br /&gt;
Badness: 0.0252&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc12"&gt;&lt;a name="Semisept-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;17-limit&lt;/h2&gt;
Commas: 176/175, 256/255, 351/350, 640/637, 715/714&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: (~26/17) 735.125&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 12 6 12 20 -11 -10|, &amp;lt;0 -17 -6 -15 -27 24 23|]&lt;br /&gt;
EDOs: 31, 80, 111&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Semisept-19-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;19-limit&lt;/h2&gt;
Commas: 176/175, 286/285, 351/350, 476/475, 540/539, 1331/1323&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 735.116&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 12 6 12 20 -11 -10 -8|, &amp;lt;0 -17 -6 -15 -27 24 23 20|]&lt;br /&gt;
EDOs: 31, 80, 111&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc14"&gt;&lt;a name="Semisept-23-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;23-limit&lt;/h2&gt;
Commas: 176/175, 253/252, 286/285, 345/343, 351/350, 391/390, 460/459&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 435.106&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 12 6 12 20 -11 -10 -8 18|,&lt;br /&gt;
&amp;lt;0 -17 -6 -15 -27 24 23 20 -22|]&lt;br /&gt;
EDOs: 31, 80, 111, 191cdh, 302cdgh&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc15"&gt;&lt;a name="Sengagen"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Sengagen&lt;/h1&gt;
Commas: 3136/3125, 420175/419904&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~686/675 = 24.217&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 2 2|, &amp;lt;0 29 16 40|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;29 16 40 -42 -18 48||&lt;br /&gt;
EDOs: 49, 50, 99, 248, 347, 446&lt;br /&gt;
Badness: 0.0580&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc16"&gt;&lt;a name="Subpental"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;Subpental&lt;/h1&gt;
Commas: 3136/3125, 19683/19600&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~56/45 = 378.467&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 6 8 17|, &amp;lt;0 -14 -18 -45|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;14 18 45 -4 32 54||&lt;br /&gt;
EDOs: 19, 111, 130, 929c, 1059c, 1189bc, 1319bc&lt;br /&gt;
Badness: 0.0543&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="Subpental-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;11-limit&lt;/h2&gt;
Commas: 540/539, 3136/3125, 8019/8000&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~56/45 = 378.440&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 6 8 17 -6|, &amp;lt;0 -14 -18 -45 30|]&lt;br /&gt;
EDOs: 19, 111, 130, 241, 371ce, 501cde, 872cde&lt;br /&gt;
Badness: 0.0453&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc18"&gt;&lt;a name="Subpental-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;13-limit&lt;/h2&gt;
Commas: 351/350, 540/539, 676/675, 3136/3125&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~56/45 = 378.437&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 6 8 17 -6 16|, &amp;lt;0 -14 -18 -45 30 -39|]&lt;br /&gt;
EDOs: 19, 111, 130, 241, 371ce&lt;br /&gt;
Badness: 0.0239&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc19"&gt;&lt;a name="Arch"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;Arch&lt;/h1&gt;
Commas: 3136/3125, 5250987/5242880&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~64/63 = 27.668&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 2|, &amp;lt;0 -18 14 35|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;18 -14 -35 -64 -106 -42||&lt;br /&gt;
EDOs: 43, 87, 130, 217, 347, 824c, 1171c, 1518cd&lt;br /&gt;
Badness: 0.0943&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc20"&gt;&lt;a name="Arch-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;11-limit&lt;/h2&gt;
Commas: 441/440, 3136/3125, 4000/3993&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~64/63 = 27.663&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 2 3|, &amp;lt;0 -18 14 35 20|]&lt;br /&gt;
EDOs: 43, 87, 130, 217, 347e, 911cde&lt;br /&gt;
Badness: 0.0365&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc21"&gt;&lt;a name="Arch-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;13-limit&lt;/h2&gt;
Commas: 364/363, 441/440, 676/675, 3136/3125&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~64/63 = 27.660&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 2 3 4|, &amp;lt;0 -18 14 35 20 -13|]&lt;br /&gt;
EDOs: 43, 87, 130, 217, 347e, 564e&lt;br /&gt;
Badness: 0.0195&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc22"&gt;&lt;a name="Emka"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;Emka&lt;/h1&gt;
Commas: 3136/3125, 84035/82944&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~48/35 = 551.782&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 14 6 12|, &amp;lt;0 -27 -8 -20|]&lt;br /&gt;
EDOs: 37, 50, 87, 137d, 224d&lt;br /&gt;
Badness: 0.1443&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc23"&gt;&lt;a name="Emka-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;11-limit&lt;/h2&gt;
Commas: 385/384, 2401/2376, 3136/3125&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~11/8 = 551.765&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 14 6 12 3|, &amp;lt;0 -27 -8 -20 1|]&lt;br /&gt;
EDOs: 37, 50, 87, 224d, 311d&lt;br /&gt;
Badness: 0.0547&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc24"&gt;&lt;a name="Emka-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;13-limit&lt;/h2&gt;
Commas: 196/195, 364/363, 385/384, 625/624&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~11/8 = 551.758&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 14 6 12 3 6|, &amp;lt;0 -27 -8 -20 1 -5|]&lt;br /&gt;
EDOs: 37, 50, 87, 224d, 311d, 398d&lt;br /&gt;
Badness: 0.0297&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

The hemimean clan, tempering out the no-threes hemimean comma 3136/3125, contains the temperaments misty and semisept, considered below, as well as meantone, hemiwürschmidt, parakleismic, hemithirds, clyde, hemischismic, passion, hexe and sycamore considered elsewhere.

2.5.7-limit

Comma: 3136/3125

No-threes POTE generator (~28/25): 193.772

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

EDOs: 6, 12, 19, 31, 68, 80, 87, 99, 130, 217, 229, 328, 347, 446, 545c, 675

Misty

Commas: 3136/3125, 5120/5103

POTE generator: 703.021

Map: [<3 0 26 56|, <0 1 -4 -10|]

Wedgie: <<3 -12 -30 -26 -56 -36||

EDOs: 12, 87, 99

11-limit

Commas: 441/440, 3136/3125, 4375/4356

POTE generator: 703.210

Map: [<3 0 26 56 77|, <0 1 -4 -10 -14|]

EDOs: 12, 87, 99e, 186e

13-limit

Commas: 196/195, 352/351, 364/363, 625/624

POTE generator: 703.303

Map: [<3 0 26 56 77 92|, <0 1 -4 -10 -14 -17|]

EDOs: 12, 87, 186ef, 273ef

Mystic

Commas: 325/324, 441/440, 896/891, 1001/1000

POTE generator: 703.311

Map: [<3 0 26 56 77 -46|, <0 1 -4 -10 -14 12|]

EDOs: 12, 87, 186e, 273e, 633bde

17-limit

Commas: 196/195, 352/351, 364/363, 625/624

POTE generator: 703.233

Map: [<3 0 26 56 77 92 -2|, <0 1 -4 -10 -14 -17 3|]

EDOs: 87, 186ef, 273ef

19-limit

Commas: 154/153, 196/195, 245/243, 273/272, 286/285, 325/324

POTE generator: 703.253

Map: [<3 0 26 56 77 92 -2 8|, <0 1 -4 -10 -14 -17 3 1|]

EDOs: 46, 87, 133, 326de, 413degh

Semisept

Comma: 782757789696/762939453125

POTE generator: ~192/125 = 735.146

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

EDOs: 18, 31, 80, 111

Badness: 0.6306

7-limit

Commas: 3136/3125, 1728/1715

POTE generator: (~75/49) 735.155

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

Wedgie: <<17 6 15 -30 -24 18||

EDOs: 18, 31, 80, 111

11-limit

Commas: 176/175, 540/539, 1331/1323

POTE generator: (~55/36) 735.125

Map: [<1 12 6 12 20|, <0 -17 -6 -15 -27|]

EDOs: 18e, 31, 80, 111, 364cd,

Badness: 0.0225

Semishly

Commas: 144/143, 176/175, 196/195, 275/273

POTE generator: ~13/10 = 464.980

Map: [<1 12 6 12 20 8|, <0 -17 -6 -15 -27 -7|]

EDOs: 31, 49f, 80f

Badness: 0.0284

13-limit

Commas: 176/175, 351/350, 540/539, 1375/1372

POTE generator: 735.126

Map: [<1 12 6 12 20 -11|, <0 -17 -6 -15 -27 24|]

EDOs: 31, 80, 111

Badness: 0.0252

17-limit

Commas: 176/175, 256/255, 351/350, 640/637, 715/714

POTE generator: (~26/17) 735.125

Map: [<1 12 6 12 20 -11 -10|, <0 -17 -6 -15 -27 24 23|]

EDOs: 31, 80, 111

19-limit

Commas: 176/175, 286/285, 351/350, 476/475, 540/539, 1331/1323

POTE generator: 735.116

Map: [<1 12 6 12 20 -11 -10 -8|, <0 -17 -6 -15 -27 24 23 20|]

EDOs: 31, 80, 111

23-limit

Commas: 176/175, 253/252, 286/285, 345/343, 351/350, 391/390, 460/459

POTE generator: 435.106

Map: [<1 12 6 12 20 -11 -10 -8 18|,

<0 -17 -6 -15 -27 24 23 20 -22|]

EDOs: 31, 80, 111, 191cdh, 302cdgh

Sengagen

Commas: 3136/3125, 420175/419904

POTE generator: ~686/675 = 24.217

Map: [<1 1 2 2|, <0 29 16 40|]

Wedgie: <<29 16 40 -42 -18 48||

EDOs: 49, 50, 99, 248, 347, 446

Badness: 0.0580

Subpental

Commas: 3136/3125, 19683/19600

POTE generator: ~56/45 = 378.467

Map: [<1 6 8 17|, <0 -14 -18 -45|]

Wedgie: <<14 18 45 -4 32 54||

EDOs: 19, 111, 130, 929c, 1059c, 1189bc, 1319bc

Badness: 0.0543

11-limit

Commas: 540/539, 3136/3125, 8019/8000

POTE generator: ~56/45 = 378.440

Map: [<1 6 8 17 -6|, <0 -14 -18 -45 30|]

EDOs: 19, 111, 130, 241, 371ce, 501cde, 872cde

Badness: 0.0453

13-limit

Commas: 351/350, 540/539, 676/675, 3136/3125

POTE generator: ~56/45 = 378.437

Map: [<1 6 8 17 -6 16|, <0 -14 -18 -45 30 -39|]

EDOs: 19, 111, 130, 241, 371ce

Badness: 0.0239

Arch

Commas: 3136/3125, 5250987/5242880

POTE generator: ~64/63 = 27.668

Map: [<1 2 2 2|, <0 -18 14 35|]

Wedgie: <<18 -14 -35 -64 -106 -42||

EDOs: 43, 87, 130, 217, 347, 824c, 1171c, 1518cd

Badness: 0.0943

11-limit

Commas: 441/440, 3136/3125, 4000/3993

POTE generator: ~64/63 = 27.663

Map: [<1 2 2 2 3|, <0 -18 14 35 20|]

EDOs: 43, 87, 130, 217, 347e, 911cde

Badness: 0.0365

13-limit

Commas: 364/363, 441/440, 676/675, 3136/3125

POTE generator: ~64/63 = 27.660

Map: [<1 2 2 2 3 4|, <0 -18 14 35 20 -13|]

EDOs: 43, 87, 130, 217, 347e, 564e

Badness: 0.0195

Emka

Commas: 3136/3125, 84035/82944

POTE generator: ~48/35 = 551.782

Map: [<1 14 6 12|, <0 -27 -8 -20|]

EDOs: 37, 50, 87, 137d, 224d

Badness: 0.1443

11-limit

Commas: 385/384, 2401/2376, 3136/3125

POTE generator: ~11/8 = 551.765

Map: [<1 14 6 12 3|, <0 -27 -8 -20 1|]

EDOs: 37, 50, 87, 224d, 311d

Badness: 0.0547

13-limit

Commas: 196/195, 364/363, 385/384, 625/624

POTE generator: ~11/8 = 551.758

Map: [<1 14 6 12 3 6|, <0 -27 -8 -20 1 -5|]

EDOs: 37, 50, 87, 224d, 311d, 398d

Badness: 0.0297

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