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Orwellismic temperaments: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Technical data page}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
These temper out {{monzo| 6 3 -1 -3 }} = 1728/1715, the orwellisma.
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-05-04 16:45:14 UTC</tt>.<br>
: The original revision id was <tt>330203666</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]]


These temper out |6 3 -1 -3&gt; = 1728/1715, the orwellisma.
Temperaments considered below are secant, infraorwell, quartonic, sentinel, diesic, philips, triskaidekic, and pentorwell. Discussed elsewhere are:
* ''[[Beep]]'' (+21/20 or 27/25) → [[Bug family #Beep|Bug family]]
* ''[[Doublewide]]'' (+50/49) → [[Jubilismic clan #Doublewide|Jubilismic clan]]
* [[Superpyth]] (+64/63) → [[Archytas clan #Superpyth|Archytas clan]]
* ''[[Mothra]]'' (+81/80) → [[Meantone family #Mothra|Meantone family]]
* [[Myna]] (+126/125) → [[Starling temperaments #Myna|Starling temperaments]]
* [[Orwell]] (+225/224) → [[Semicomma family #Orwell|Semicomma family]]
* ''[[Secund]]'' (+405/392 or 525/512) → [[Greenwoodmic temperaments #Secund|Greenwoodmic temperaments]]
* ''[[Quartonic]]'' (+4000/3969) → [[Quartonic family]]
* ''[[Buzzard]]'' (+5120/5103) → [[Vulture family #Buzzard|Vulture family]]
* ''[[Trisensory]]'' (+78732/78125) → [[Sensipent family #Trisensory|Sensipent family]]
* ''[[Trimabila]]'' (+268435456/263671875) → [[Mabila family #Trimabila|Mabila family]]


=Secant=
== Secant ==
Commas: 1728/1715, 177147/175000
[[Subgroup]]: 2.3.5.7


POTE generator: ~10/9 = 185.885
[[Comma list]]: 1728/1715, 177147/175000


Map: [&lt;2 1 0 5|, &lt;0 7 15 2|]
{{Mapping|legend=1| 2 1 0 5 | 0 7 15 2 }}
Wedgie: &lt;&lt;14 30 4 15 -33 -75|
EDOs: 26, 58, 84, 142, 368cd
Badness: 0.0953


==11-limit==
: Mapping generators: ~567/400, ~10/9
Commas: 441/440, 1344/1331, 1728/1715


POTE genertor: ~10/9 = 185.962
[[Optimal tuning]] ([[POTE]]): ~567/400 = 1\2, ~10/9 = 185.885


Map: [&lt;2 1 0 5 6|, &lt;0 7 15 2 3|]
{{Optimal ET sequence|legend=1| 26, 58, 84, 142, 368cd }}
EDOs: 26, 58, 142e, 200cde
Badness: 0.0464


==13-limit==
[[Badness]]: 0.095278
Commas: 144/143, 351/350, 364/363, 441/440


POTE generator: ~10/9 = 185.955
=== 11-limit ===
Subgroup: 2.3.5.7.11


Map: [&lt;2 1 0 5 6 4|, &lt;0 7 15 2 3 11|]
Comma list: 441/440, 1344/1331, 1728/1715
EDOs: 26, 58, 84, 142ef
Badness: 0.0250


=Infraorwell=
Mapping: {{mapping| 2 1 0 5 6 | 0 7 15 2 3 }}
Commas: 1728/1715, 28672/28125


POTE generator: ~7/6 = 269.032
Optimal tuning (POTE): ~99/70 = 1\2, ~10/9 = 185.962


Map: [&lt;1 14 0 16|, &lt;0 -16 3 -17|]
Optimal ET sequence: {{Optimal ET sequence| 26, 58, 142e, 200cdee }}
Wedgie: &lt;&lt;16 -3 17 -42 -18 48||
EDOs: 9, 49, 58, 165cd, 223bcd
Badness: 0.1171


==11-limit==
Badness: 0.046373
Commas: 176/175, 540/539, 1344/1331


POTE generator: ~7/6 = 269.036
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


Map: [&lt;1 14 0 16 12|, &lt;0 -16 3 -17 -11|]
Comma list: 144/143, 351/350, 364/363, 441/440
EDOs: 9, 49, 58, 165cde
Badness: 0.0407


==13-limit==
Mapping: {{mapping| 2 1 0 5 6 4 | 0 7 15 2 3 11 }}
Commas: 144/143, 176/175, 196/195, 364/363


POTE generator: ~7/6 = 269.021
Optimal tuning (POTE): ~99/70 = 1\2, ~10/9 = 185.955


Map: [&lt;1 14 0 16 12 20|, &lt;0 -16 3 -17 -11 -21|]
Optimal ET sequence: {{Optimal ET sequence| 26, 58, 84, 142ef }}
EDOs: 9, 49f, 58
Badness: 0.0237


=Quartonic=
Badness: 0.025035
Comma: 390625000/387420489


POTE generator: ~250/243 = 45.233
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17


Map: [&lt;1 2 3|, &lt;0 -11 -18|]
Comma list: 144/143, 170/169, 221/220, 351/350, 441/440
EDOs: 26, 27, 53, 239, 292, 345, 398, 451
Badness: 0.1172


==7-limit==
Mapping: {{mapping| 2 1 0 5 6 4 6 | 0 7 15 2 3 11 7 }}
Commas: 1728/1715, 4000/3969


POTE generator: ~36/35 = 45.139
Optimal tuning (POTE): ~17/12 = 1\2, ~10/9 = 185.916


Map: [&lt;1 2 3 3|, &lt;0 -11 -18 -5|]
Optimal ET sequence: {{Optimal ET sequence| 26, 58, 84, 142ef }}
Wedgie: &lt;&lt;11 18 5 3 -23 -39||
EDOs: 26, 27, 53, 80, 133d, 186d, 319d
Badness: 0.0426


==11-limit==
Badness: 0.021642
Commas: 176/175, 540/539, 2200/2187


POTE generator: ~36/35 = 45.041
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19


Map: [&lt;1 2 3 3 5|, &lt;0 -11 -18 -5 -41|]
Comma list: 144/143, 153/152, 170/169, 210/209, 221/220, 400/399
EDOs: 53, 80, 213d, 293bcd
Badness: 0.034


==13-limit==
Mapping: {{mapping| 2 1 0 5 6 4 6 2 | 0 7 15 2 3 11 7 21 }}
Commas: 169/168 176/175 325/324 540/539


POTE generator: ~36/35 = 45.080
Optimal tuning (POTE): ~17/12 = 1\2, ~10/9 = 185.858


Map: [&lt;1 2 3 3 5 4|, &lt;0 -11 -18 -5 -41 -8|]
Optimal ET sequence: {{Optimal ET sequence| 26, 58h, 84, 142efh, 226deefgh }}
EDOs: 53, 80, 133d, 213d
Badness: 0.0239


==Quarto==
Badness: 0.018565
Commmas: 100/99 245/242 864/847


POTE generator: ~36/35 = 45.132
== Infraorwell ==
[[Subgroup]]: 2.3.5.7


Map: [&lt;1 2 3 3 4|, &lt;0 -11 -18 -5 -14|]
[[Comma list]]: 1728/1715, 28672/28125
EDOs: 26, 27e, 53e, 80e
Badness: 0.0418


===13-limit===
{{Mapping|legend=1| 1 14 0 16 | 0 -16 3 -17 }}
Commas: 78/77, 100/99, 144/143, 245/242


POTE generator: ~36/35 = 45.205
: Mapping generators: ~2, ~12/7


Map: [&lt;1 2 3 3 4 4|, &lt;0 -11 -18 -5 -14 -8|]
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/6 = 269.032
EDOs: 26, 27e, 53e
Badness: 0.0277


==Quartz==
{{Optimal ET sequence|legend=1| 9, 49, 58, 165cd, 223bcd }}
Commas: 99/98, 385/384, 4000/3969


POTE generator: ~36/35 = 45.385
[[Badness]]: 0.117073


Map: [&lt;1 2 3 3 3|, &lt;0 -11 -18 -5 12|]
=== 11-limit ===
EDOs: 26, 53
Subgroup: 2.3.5.7.11
Badness: 0.0533


===13-limit===
Comma list: 176/175, 540/539, 1344/1331
Commas: 99/98, 169/168, 275/273, 385/384


POTE generator: ~36/35 = 45.387
Mapping: {{mapping| 1 14 0 16 12 | 0 -16 3 -17 -11 }}


Map: [&lt;1 2 3 3 3 4|, &lt;0 -11 -18 -5 12 -8|]
Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 269.036
EDOs: 26, 53, 132e, 185cdef, 238cdef
Badness: 0.0288


=Sentinel=
Optimal ET sequence: {{Optimal ET sequence| 9, 49, 58, 165cdee }}
Comma: 8968066875/8589934592


POTE generator: ~512/405 = 425.474
Badness: 0.040721


Map: [&lt;1 3 -3|, &lt;0 -4 15|]
=== 13-limit ===
EDOs: 14, 17, 31, 79, 110, 361bc
Subgroup: 2.3.5.7.11.13
Badness: 0.7234


==7-limit==
Comma list: 144/143, 176/175, 196/195, 364/363
Commas: 1728/1715, 3645/3584


POTE generator: ~9/7 = 425.596
Mapping: {{mapping| 1 14 0 16 12 20 | 0 -16 3 -17 -11 -21 }}


Map: [&lt;1 3 -3 6|, &lt;0 -4 15 -9|]
Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 269.021
Wedgie: &lt;&lt;4 -15 9 -33 3 63||
EDOs: 14, 17, 31, 110, 141, 172b, 375bc
Badness: 0.0938


==11-limit==
Optimal ET sequence: {{Optimal ET sequence| 9, 49f, 58 }}
Commas: 99/98, 243/242, 385/384


POTE generator: ~9/7 = 425.550
Badness: 0.023683


Map: [&lt;1 3 -3 6 7|, &lt;0 -4 15 -9 -10|]
== Sentinel ==
EDOs: 14, 17, 31, 79, 110e, 141e
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Sentinel]].''
Badness: 0.0396


==13-limit==
[[Subgroup]]: 2.3.5.7
Commas: 99/98, 105/104, 144/143, 243/242


POTE generator: ~9/7 = 425.501
[[Comma list]]: 1728/1715, 3645/3584


Map: [&lt;1 3 -3 6 7 3|, &lt;0 -4 15 -9 -10 2|]
{{Mapping|legend=1| 1 3 -3 6 | 0 -4 15 -9 }}
EDOs: 14, 17, 31, 79f, 110ef, 141ef
Badness: 0.0374


=Diesic=
: Mapping generators: ~2, ~9/7
Comma: 10460353203/9765625000


POTE generator: ~6561/6250 = 38.571
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/7 = 425.596


Map: [&lt;1 2 3|, &lt;0 -13 -21|]
{{Optimal ET sequence|legend=1| 14, 17, 31, 110, 141, 172b, 375bc }}
EDOs: 31, 156c, 187c, 218bc, 249bc, 280bc
Badness: 1.3447


==7-limit==
[[Badness]]: 0.093805
Commas: 1728/1715, 5103/5000


POTE generator: ~36/35 = 38.567
=== 11-limit ===
Subgroup: 2.3.5.7.11


Map: [&lt;1 2 3 3|, &lt;0 -13 -21 -6|]
Comma list: 99/98, 243/242, 385/384
Wedgie: &lt;&lt;13 21 6 3 -27 -45||
EDOs: 31, 156c, 187c, 218bc, 249bc, 280bc
Badness: 0.1073


==11-limit==
Mapping: {{mapping| 1 3 -3 6 7 | 0 -4 15 -9 -10 }}
Commas: 121/120, 441/440, 891/875


POTE generator: ~36/35 = 38.565
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 425.550


Map: [&lt;1 2 3 3 4|, &lt;0 -13 -21 -6 -17|]
Optimal ET sequence: {{Optimal ET sequence| 14, 17, 31, 79, 110e, 141e }}
EDOs: 31, 156ce, 187ce, 218bce, 249bce
Badness: 0.0442


==13-limit==
Badness: 0.039595
Commas: 66/65, 121/120, 343/338, 441/440


POTE generator: ~36/35 = 38.444
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


Map: [&lt;1 2 3 3 4 4|, &lt;0 -13 -21 -6 -17 -9|]
Comma list: 99/98, 105/104, 144/143, 243/242
EDOs: 31, 94cf, 125cf
Badness: 0.0381


Mapping: {{mapping| 1 3 -3 6 7 3 | 0 -4 15 -9 -10 2 }}


Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 425.501


</pre></div>
Optimal ET sequence: {{Optimal ET sequence| 14, 17, 31, 79f, 110ef, 141ef }}
<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;Orwellismic temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:44:&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:44 --&gt;&lt;!-- ws:start:WikiTextTocRule:45: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Secant"&gt;Secant&lt;/a&gt;&lt;/div&gt;
Badness: 0.037408
&lt;!-- ws:end:WikiTextTocRule:45 --&gt;&lt;!-- ws:start:WikiTextTocRule:46: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Secant-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:46 --&gt;&lt;!-- ws:start:WikiTextTocRule:47: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Secant-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
== Diesic ==
&lt;!-- ws:end:WikiTextTocRule:47 --&gt;&lt;!-- ws:start:WikiTextTocRule:48: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Infraorwell"&gt;Infraorwell&lt;/a&gt;&lt;/div&gt;
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Diesic]].''
&lt;!-- ws:end:WikiTextTocRule:48 --&gt;&lt;!-- ws:start:WikiTextTocRule:49: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Infraorwell-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:49 --&gt;&lt;!-- ws:start:WikiTextTocRule:50: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Infraorwell-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
[[Subgroup]]: 2.3.5.7
&lt;!-- ws:end:WikiTextTocRule:50 --&gt;&lt;!-- ws:start:WikiTextTocRule:51: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Quartonic"&gt;Quartonic&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:51 --&gt;&lt;!-- ws:start:WikiTextTocRule:52: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Quartonic-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
[[Comma list]]: 1728/1715, 5103/5000
&lt;!-- ws:end:WikiTextTocRule:52 --&gt;&lt;!-- ws:start:WikiTextTocRule:53: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Quartonic-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:53 --&gt;&lt;!-- ws:start:WikiTextTocRule:54: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Quartonic-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
{{Mapping|legend=1| 1 2 3 3 | 0 -13 -21 -6 }}
&lt;!-- ws:end:WikiTextTocRule:54 --&gt;&lt;!-- ws:start:WikiTextTocRule:55: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Quartonic-Quarto"&gt;Quarto&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:55 --&gt;&lt;!-- ws:start:WikiTextTocRule:56: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Quartonic-Quarto-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
: Mapping generators: ~2, ~36/35
&lt;!-- ws:end:WikiTextTocRule:56 --&gt;&lt;!-- ws:start:WikiTextTocRule:57: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Quartonic-Quartz"&gt;Quartz&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:57 --&gt;&lt;!-- ws:start:WikiTextTocRule:58: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Quartonic-Quartz-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~36/35 = 38.567
&lt;!-- ws:end:WikiTextTocRule:58 --&gt;&lt;!-- ws:start:WikiTextTocRule:59: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Sentinel"&gt;Sentinel&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="#Sentinel-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
{{Optimal ET sequence|legend=1| 31, 156c, 187c, 218bc, 249bc, 280bc }}
&lt;!-- ws:end:WikiTextTocRule:60 --&gt;&lt;!-- ws:start:WikiTextTocRule:61: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Sentinel-11-limit"&gt;11-limit&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="#Sentinel-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
[[Badness]]: 0.107348
&lt;!-- ws:end:WikiTextTocRule:62 --&gt;&lt;!-- ws:start:WikiTextTocRule:63: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Diesic"&gt;Diesic&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="#Diesic-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
=== 11-limit ===
&lt;!-- ws:end:WikiTextTocRule:64 --&gt;&lt;!-- ws:start:WikiTextTocRule:65: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Diesic-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
Subgroup: 2.3.5.7.11
&lt;!-- ws:end:WikiTextTocRule:65 --&gt;&lt;!-- ws:start:WikiTextTocRule:66: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Diesic-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:66 --&gt;&lt;!-- ws:start:WikiTextTocRule:67: --&gt;&lt;/div&gt;
Comma list: 121/120, 441/440, 891/875
&lt;!-- ws:end:WikiTextTocRule:67 --&gt;&lt;br /&gt;
 
These temper out |6 3 -1 -3&amp;gt; = 1728/1715, the orwellisma.&lt;br /&gt;
Mapping: {{mapping| 1 2 3 3 4 | 0 -13 -21 -6 -17 }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Secant"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Secant&lt;/h1&gt;
Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 38.565
Commas: 1728/1715, 177147/175000&lt;br /&gt;
 
&lt;br /&gt;
Optimal ET sequence: {{Optimal ET sequence| 31, 156ce, 187ce, 218bcee, 249bcee }}
POTE generator: ~10/9 = 185.885&lt;br /&gt;
 
&lt;br /&gt;
Badness: 0.044186
Map: [&amp;lt;2 1 0 5|, &amp;lt;0 7 15 2|]&lt;br /&gt;
 
Wedgie: &amp;lt;&amp;lt;14 30 4 15 -33 -75|&lt;br /&gt;
=== 13-limit ===
EDOs: 26, 58, 84, 142, 368cd&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
Badness: 0.0953&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 66/65, 121/120, 343/338, 441/440
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Secant-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;11-limit&lt;/h2&gt;
 
Commas: 441/440, 1344/1331, 1728/1715&lt;br /&gt;
Mapping: {{mapping| 1 2 3 3 4 4 | 0 -13 -21 -6 -17 -9 }}
&lt;br /&gt;
 
POTE genertor: ~10/9 = 185.962&lt;br /&gt;
Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 38.444
&lt;br /&gt;
 
Map: [&amp;lt;2 1 0 5 6|, &amp;lt;0 7 15 2 3|]&lt;br /&gt;
Optimal ET sequence: {{Optimal ET sequence| 31, 94cff, 125cff }}
EDOs: 26, 58, 142e, 200cde&lt;br /&gt;
 
Badness: 0.0464&lt;br /&gt;
Badness: 0.038116
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Secant-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;13-limit&lt;/h2&gt;
== Phillips ==
Commas: 144/143, 351/350, 364/363, 441/440&lt;br /&gt;
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Phillips]].''
&lt;br /&gt;
 
POTE generator: ~10/9 = 185.955&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
&lt;br /&gt;
 
Map: [&amp;lt;2 1 0 5 6 4|, &amp;lt;0 7 15 2 3 11|]&lt;br /&gt;
[[Comma list]]: 1728/1715, 6561/6272
EDOs: 26, 58, 84, 142ef&lt;br /&gt;
 
Badness: 0.0250&lt;br /&gt;
{{Mapping|legend=1| 2 0 33 -7 | 0 1 -9 4 }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Infraorwell"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Infraorwell&lt;/h1&gt;
: Mapping generators: ~81/56, ~3
Commas: 1728/1715, 28672/28125&lt;br /&gt;
 
&lt;br /&gt;
[[Optimal tuning]] ([[POTE]]): ~81/56 = 1\2, ~3/2 = 691.174
POTE generator: ~7/6 = 269.032&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 14, 26, 66b, 92bc }}
Map: [&amp;lt;1 14 0 16|, &amp;lt;0 -16 3 -17|]&lt;br /&gt;
 
Wedgie: &amp;lt;&amp;lt;16 -3 17 -42 -18 48||&lt;br /&gt;
[[Badness]]: 0.228602
EDOs: 9, 49, 58, 165cd, 223bcd&lt;br /&gt;
 
Badness: 0.1171&lt;br /&gt;
=== 11-limit ===
&lt;br /&gt;
Subgroup: 2.3.5.7.11
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Commas: 176/175, 540/539, 1344/1331&lt;br /&gt;
Comma list: 99/98, 385/384, 729/704
&lt;br /&gt;
 
POTE generator: ~7/6 = 269.036&lt;br /&gt;
Mapping: {{mapping| 2 0 33 -7 -12 | 0 1 -9 4 6 }}
&lt;br /&gt;
 
Map: [&amp;lt;1 14 0 16 12|, &amp;lt;0 -16 3 -17 -11|]&lt;br /&gt;
Optimal tuning (POTE): ~63/44 = 1\2, ~3/2 = 691.040
EDOs: 9, 49, 58, 165cde&lt;br /&gt;
 
Badness: 0.0407&lt;br /&gt;
Optimal ET sequence: {{Optimal ET sequence| 14, 26, 40, 66b }}
&lt;br /&gt;
 
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Badness: 0.095777
Commas: 144/143, 176/175, 196/195, 364/363&lt;br /&gt;
 
&lt;br /&gt;
== Triskaidekic ==
POTE generator: ~7/6 = 269.021&lt;br /&gt;
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Triskaidekic]].''
&lt;br /&gt;
 
Map: [&amp;lt;1 14 0 16 12 20|, &amp;lt;0 -16 3 -17 -11 -21|]&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
EDOs: 9, 49f, 58&lt;br /&gt;
 
Badness: 0.0237&lt;br /&gt;
[[Comma list]]: 1728/1715, 1875/1792
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Quartonic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Quartonic&lt;/h1&gt;
{{Mapping|legend=1| 13 0 30 16 | 0 1 0 1 }}
Comma: 390625000/387420489&lt;br /&gt;
 
&lt;br /&gt;
: Mapping generators: ~15/14, ~3
POTE generator: ~250/243 = 45.233&lt;br /&gt;
 
&lt;br /&gt;
[[Optimal tuning]] ([[POTE]]): ~15/14 = 1\13, ~3/2 = 694.143
Map: [&amp;lt;1 2 3|, &amp;lt;0 -11 -18|]&lt;br /&gt;
 
EDOs: 26, 27, 53, 239, 292, 345, 398, 451&lt;br /&gt;
{{Optimal ET sequence|legend=1| 13d, 26 }}
Badness: 0.1172&lt;br /&gt;
 
&lt;br /&gt;
[[Badness]]: 0.219050
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Commas: 1728/1715, 4000/3969&lt;br /&gt;
=== 11-limit ===
&lt;br /&gt;
Subgroup: 2.3.5.7.11
POTE generator: ~36/35 = 45.139&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 99/98, 125/121, 385/384
Map: [&amp;lt;1 2 3 3|, &amp;lt;0 -11 -18 -5|]&lt;br /&gt;
 
Wedgie: &amp;lt;&amp;lt;11 18 5 3 -23 -39||&lt;br /&gt;
Mapping: {{mapping| 13 0 30 16 45 | 0 1 0 1 0 }}
EDOs: 26, 27, 53, 80, 133d, 186d, 319d&lt;br /&gt;
 
Badness: 0.0426&lt;br /&gt;
Optimal tuning (POTE): ~15/14 = 1\13, ~3/2 = 696.296
&lt;br /&gt;
 
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Optimal ET sequence: {{Optimal ET sequence| 13d, 26, 91cd }}
Commas: 176/175, 540/539, 2200/2187&lt;br /&gt;
 
&lt;br /&gt;
Badness: 0.098847
POTE generator: ~36/35 = 45.041&lt;br /&gt;
 
&lt;br /&gt;
=== 13-limit ===
Map: [&amp;lt;1 2 3 3 5|, &amp;lt;0 -11 -18 -5 -41|]&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
EDOs: 53, 80, 213d, 293bcd&lt;br /&gt;
 
Badness: 0.034&lt;br /&gt;
Comma list: 78/77, 99/98, 125/121, 1200/1183
&lt;br /&gt;
 
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Mapping: {{mapping| 13 0 30 16 45 48 | 0 1 0 1 0 0 }}
Commas: 169/168 176/175 325/324 540/539&lt;br /&gt;
 
&lt;br /&gt;
Optimal tuning (POTE): ~15/14 = 1\13, ~3/2 = 695.879
POTE generator: ~36/35 = 45.080&lt;br /&gt;
 
&lt;br /&gt;
Optimal ET sequence: {{Optimal ET sequence| 13d, 26, 91cdf }}
Map: [&amp;lt;1 2 3 3 5 4|, &amp;lt;0 -11 -18 -5 -41 -8|]&lt;br /&gt;
 
EDOs: 53, 80, 133d, 213d&lt;br /&gt;
Badness: 0.059216
Badness: 0.0239&lt;br /&gt;
 
&lt;br /&gt;
== Pentorwell ==
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Quartonic-Quarto"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Quarto&lt;/h2&gt;
[[Subgroup]]: 2.3.5.7
Commmas: 100/99 245/242 864/847&lt;br /&gt;
 
&lt;br /&gt;
[[Comma list]]: 1728/1715, 179200/177147
POTE generator: ~36/35 = 45.132&lt;br /&gt;
 
&lt;br /&gt;
{{Mapping|legend=1| 5 0 -36 22 | 0 1 6 -1 }}
Map: [&amp;lt;1 2 3 3 4|, &amp;lt;0 -11 -18 -5 -14|]&lt;br /&gt;
 
EDOs: 26, 27e, 53e, 80e&lt;br /&gt;
[[Optimal tuning]]s:  
Badness: 0.0418&lt;br /&gt;
* [[CTE]]: ~280/243 = 1\5, ~3/2 = 704.3709 (~64/63 = 15.6291)
&lt;br /&gt;
* [[POTE]]: ~280/243 = 1\5, ~3/2 = 704.9128 (~64/63 = 15.0872)
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Commas: 78/77, 100/99, 144/143, 245/242&lt;br /&gt;
{{Optimal ET sequence|legend=1| 5, 75, 80 }}
&lt;br /&gt;
 
POTE generator: ~36/35 = 45.205&lt;br /&gt;
[[Badness]]: 0.148665
&lt;br /&gt;
 
Map: [&amp;lt;1 2 3 3 4 4|, &amp;lt;0 -11 -18 -5 -14 -8|]&lt;br /&gt;
=== 11-limit ===
EDOs: 26, 27e, 53e&lt;br /&gt;
Subgroup: 2.3.5.7.11
Badness: 0.0277&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 896/891, 1728/1715, 2200/2187
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Commas: 99/98, 385/384, 4000/3969&lt;br /&gt;
Mapping: {{mapping| 5 0 -36 22 57 | 0 1 6 -1 -5 }}
&lt;br /&gt;
 
POTE generator: ~36/35 = 45.385&lt;br /&gt;
Optimal tunings:  
&lt;br /&gt;
* CTE: ~55/48 = 1\5, ~3/2 = 704.8440 (~99/98 = 15.1560)
Map: [&amp;lt;1 2 3 3 3|, &amp;lt;0 -11 -18 -5 12|]&lt;br /&gt;
* POTE: ~55/48 = 1\5, ~3/2 = 704.8788 (~99/98 = 15.1212)
EDOs: 26, 53&lt;br /&gt;
 
Badness: 0.0533&lt;br /&gt;
Optimal ET sequence: {{Optimal ET sequence| 75e, 80, 315bcdddee }}
&lt;br /&gt;
 
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Badness: 0.071702
Commas: 99/98, 169/168, 275/273, 385/384&lt;br /&gt;
 
&lt;br /&gt;
=== 13-limit ===
POTE generator: ~36/35 = 45.387&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
&lt;br /&gt;
 
Map: [&amp;lt;1 2 3 3 3 4|, &amp;lt;0 -11 -18 -5 12 -8|]&lt;br /&gt;
Comma list: 325/324, 352/351, 364/363, 1728/1715
EDOs: 26, 53, 132e, 185cdef, 238cdef&lt;br /&gt;
 
Badness: 0.0288&lt;br /&gt;
Mapping: {{mapping| 5 0 -36 22 57 82 | 0 1 6 -1 -5 -8 }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc14"&gt;&lt;a name="Sentinel"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Sentinel&lt;/h1&gt;
Optimal tunings:  
Comma: 8968066875/8589934592&lt;br /&gt;
* CTE: ~55/48 = 1\5, ~3/2 = 704.7636 (~99/98 = 15.2364)
&lt;br /&gt;
* CWE: ~55/48 = 1\5, ~3/2 = 704.7112 (~99/98 = 15.2882)
POTE generator: ~512/405 = 425.474&lt;br /&gt;
 
&lt;br /&gt;
Optimal ET sequence: {{Optimal ET sequence| 75e, 80, 155de }}
Map: [&amp;lt;1 3 -3|, &amp;lt;0 -4 15|]&lt;br /&gt;
 
EDOs: 14, 17, 31, 79, 110, 361bc&lt;br /&gt;
Badness: 0.0557
Badness: 0.7234&lt;br /&gt;
 
&lt;br /&gt;
[[Category:Temperament collections]]
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[[Category:Pages with mostly numerical content]]
Commas: 1728/1715, 3645/3584&lt;br /&gt;
[[Category:Orwellismic temperaments| ]] <!-- main article -->
&lt;br /&gt;
[[Category:Orwellismic| ]] <!-- key article -->
POTE generator: ~9/7 = 425.596&lt;br /&gt;
[[Category:Rank 2]]
&lt;br /&gt;
Map: [&amp;lt;1 3 -3 6|, &amp;lt;0 -4 15 -9|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;4 -15 9 -33 3 63||&lt;br /&gt;
EDOs: 14, 17, 31, 110, 141, 172b, 375bc&lt;br /&gt;
Badness: 0.0938&lt;br /&gt;
&lt;br /&gt;
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Commas: 99/98, 243/242, 385/384 &lt;br /&gt;
&lt;br /&gt;
POTE generator: ~9/7 = 425.550&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 3 -3 6 7|, &amp;lt;0 -4 15 -9 -10|]&lt;br /&gt;
EDOs: 14, 17, 31, 79, 110e, 141e&lt;br /&gt;
Badness: 0.0396&lt;br /&gt;
&lt;br /&gt;
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Commas: 99/98, 105/104, 144/143, 243/242&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~9/7 = 425.501&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 3 -3 6 7 3|, &amp;lt;0 -4 15 -9 -10 2|]&lt;br /&gt;
EDOs: 14, 17, 31, 79f, 110ef, 141ef&lt;br /&gt;
Badness: 0.0374&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc18"&gt;&lt;a name="Diesic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Diesic&lt;/h1&gt;
Comma: 10460353203/9765625000&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~6561/6250 = 38.571&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 3|, &amp;lt;0 -13 -21|]&lt;br /&gt;
EDOs: 31, 156c, 187c, 218bc, 249bc, 280bc&lt;br /&gt;
Badness: 1.3447&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc19"&gt;&lt;a name="Diesic-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;7-limit&lt;/h2&gt;
Commas: 1728/1715, 5103/5000 &lt;br /&gt;
&lt;br /&gt;
POTE generator: ~36/35 = 38.567&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 3 3|, &amp;lt;0 -13 -21 -6|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;13 21 6 3 -27 -45||&lt;br /&gt;
EDOs: 31, 156c, 187c, 218bc, 249bc, 280bc&lt;br /&gt;
Badness: 0.1073&lt;br /&gt;
&lt;br /&gt;
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Commas: 121/120, 441/440, 891/875 &lt;br /&gt;
&lt;br /&gt;
POTE generator: ~36/35 = 38.565&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 3 3 4|, &amp;lt;0 -13 -21 -6 -17|]&lt;br /&gt;
EDOs: 31, 156ce, 187ce, 218bce, 249bce&lt;br /&gt;
Badness: 0.0442&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="Diesic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;13-limit&lt;/h2&gt;
Commas: 66/65, 121/120, 343/338, 441/440&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~36/35 = 38.444&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 3 3 4 4|, &amp;lt;0 -13 -21 -6 -17 -9|]&lt;br /&gt;
EDOs: 31, 94cf, 125cf&lt;br /&gt;
Badness: 0.0381&lt;/body&gt;&lt;/html&gt;</pre></div>
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