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>2012-04-28 01:50:03 UTC</tt>.<br>
: The original revision id was <tt>326263302</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
Commas: 1728/1715, 4000/3969


POTE generator: ~36/35 = 45.139
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17


Map: [&lt;1 2 3 3|, &lt;0 -11 -18 -5|]
Comma list: 144/143, 170/169, 221/220, 351/350, 441/440
Wedgie: &lt;&lt;11 18 5 3 -23 -39||
EDOs: 26, 27, 53, 80, 133d, 186d, 319d
Badness: 0.0426


==11-limit==
Mapping: {{mapping| 2 1 0 5 6 4 6 | 0 7 15 2 3 11 7 }}
Commas: 176/175, 540/539, 2200/2187


POTE generator: ~36/35 = 45.041
Optimal tuning (POTE): ~17/12 = 1\2, ~10/9 = 185.916


Map: [&lt;1 2 3 3 5|, &lt;0 -11 -18 -5 -41|]
Optimal ET sequence: {{Optimal ET sequence| 26, 58, 84, 142ef }}
EDOs: 53, 80, 213d, 293bcd
Badness: 0.034


==13-limit==
Badness: 0.021642
Commas: 169/168 176/175 325/324 540/539


POTE generator: ~36/35 = 45.080
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19


Map: [&lt;1 2 3 3 5 4|, &lt;0 -11 -18 -5 -41 -8|]
Comma list: 144/143, 153/152, 170/169, 210/209, 221/220, 400/399
EDOs: 53, 80, 133d, 213d
Badness: 0.0239


==Quarto==
Mapping: {{mapping| 2 1 0 5 6 4 6 2 | 0 7 15 2 3 11 7 21 }}
Commmas: 100/99 245/242 864/847


POTE generator: ~36/35 = 45.132
Optimal tuning (POTE): ~17/12 = 1\2, ~10/9 = 185.858


Map: [&lt;1 2 3 3 4|, &lt;0 -11 -18 -5 -14|]
Optimal ET sequence: {{Optimal ET sequence| 26, 58h, 84, 142efh, 226deefgh }}
EDOs: 26, 27e, 53e, 80e
Badness: 0.0418


===13-limit===
Badness: 0.018565
Commas: 78/77, 100/99, 144/143, 245/242


POTE generator: ~36/35 = 45.205
== Infraorwell ==
[[Subgroup]]: 2.3.5.7


Map: [&lt;1 2 3 3 4 4|, &lt;0 -11 -18 -5 -14 -8|]
[[Comma list]]: 1728/1715, 28672/28125
EDOs: 26, 27e, 53e
Badness: 0.0277


=Sentinel=
{{Mapping|legend=1| 1 14 0 16 | 0 -16 3 -17 }}
Commas: 1728/1715, 3645/3584


POTE generator: ~9/7 = 425.596
: Mapping generators: ~2, ~12/7


Map: [&lt;1 3 -3 6|, &lt;0 -4 15 -9|]
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/6 = 269.032
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|legend=1| 9, 49, 58, 165cd, 223bcd }}
Commas: 99/98, 243/242, 385/384


POTE generator: ~9/7 = 425.550
[[Badness]]: 0.117073


Map: [&lt;1 3 -3 6 7|, &lt;0 -4 15 -9 -10|]
=== 11-limit ===
EDOs: 14, 17, 31, 79, 110e, 141e
Subgroup: 2.3.5.7.11
Badness: 0.0396


==13-limit==
Comma list: 176/175, 540/539, 1344/1331
Commas: 99/98, 105/104, 144/143, 243/242


POTE generator: ~9/7 = 425.501
Mapping: {{mapping| 1 14 0 16 12 | 0 -16 3 -17 -11 }}


Map: [&lt;1 3 -3 6 7 3|, &lt;0 -4 15 -9 -10 2|]
Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 269.036
EDOs: 14, 17, 31, 79f, 110ef, 141ef
Badness: 0.0374


Optimal ET sequence: {{Optimal ET sequence| 9, 49, 58, 165cdee }}


Badness: 0.040721


=== 13-limit ===
Subgroup: 2.3.5.7.11.13


Comma list: 144/143, 176/175, 196/195, 364/363


Mapping: {{mapping| 1 14 0 16 12 20 | 0 -16 3 -17 -11 -21 }}


</pre></div>
Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 269.021
<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:28:&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:28 --&gt;&lt;!-- ws:start:WikiTextTocRule:29: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Secant"&gt;Secant&lt;/a&gt;&lt;/div&gt;
Optimal ET sequence: {{Optimal ET sequence| 9, 49f, 58 }}
&lt;!-- ws:end:WikiTextTocRule:29 --&gt;&lt;!-- ws:start:WikiTextTocRule:30: --&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:30 --&gt;&lt;!-- ws:start:WikiTextTocRule:31: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Secant-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
Badness: 0.023683
&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;!-- ws:start:WikiTextTocRule:32: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Infraorwell"&gt;Infraorwell&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:32 --&gt;&lt;!-- ws:start:WikiTextTocRule:33: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Infraorwell-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
== Sentinel ==
&lt;!-- ws:end:WikiTextTocRule:33 --&gt;&lt;!-- ws:start:WikiTextTocRule:34: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Infraorwell-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Sentinel]].''
&lt;!-- ws:end:WikiTextTocRule:34 --&gt;&lt;!-- ws:start:WikiTextTocRule:35: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Quartonic"&gt;Quartonic&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:35 --&gt;&lt;!-- ws:start:WikiTextTocRule:36: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Quartonic-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
[[Subgroup]]: 2.3.5.7
&lt;!-- ws:end:WikiTextTocRule:36 --&gt;&lt;!-- ws:start:WikiTextTocRule:37: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Quartonic-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:37 --&gt;&lt;!-- ws:start:WikiTextTocRule:38: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Quartonic-Quarto"&gt;Quarto&lt;/a&gt;&lt;/div&gt;
[[Comma list]]: 1728/1715, 3645/3584
&lt;!-- ws:end:WikiTextTocRule:38 --&gt;&lt;!-- ws:start:WikiTextTocRule:39: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Quartonic-Quarto-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:39 --&gt;&lt;!-- ws:start:WikiTextTocRule:40: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Sentinel"&gt;Sentinel&lt;/a&gt;&lt;/div&gt;
{{Mapping|legend=1| 1 3 -3 6 | 0 -4 15 -9 }}
&lt;!-- ws:end:WikiTextTocRule:40 --&gt;&lt;!-- ws:start:WikiTextTocRule:41: --&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:41 --&gt;&lt;!-- ws:start:WikiTextTocRule:42: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Sentinel-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
: Mapping generators: ~2, ~9/7
&lt;!-- ws:end:WikiTextTocRule:42 --&gt;&lt;!-- ws:start:WikiTextTocRule:43: --&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:43 --&gt;&lt;br /&gt;
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/7 = 425.596
These temper out |6 3 -1 -3&amp;gt; = 1728/1715, the orwellisma.&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 14, 17, 31, 110, 141, 172b, 375bc }}
&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;
 
Commas: 1728/1715, 177147/175000&lt;br /&gt;
[[Badness]]: 0.093805
&lt;br /&gt;
 
POTE generator: ~10/9 = 185.885&lt;br /&gt;
=== 11-limit ===
&lt;br /&gt;
Subgroup: 2.3.5.7.11
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;
Comma list: 99/98, 243/242, 385/384
EDOs: 26, 58, 84, 142, 368cd&lt;br /&gt;
 
Badness: 0.0953&lt;br /&gt;
Mapping: {{mapping| 1 3 -3 6 7 | 0 -4 15 -9 -10 }}
&lt;br /&gt;
 
&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;
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 425.550
Commas: 441/440, 1344/1331, 1728/1715&lt;br /&gt;
 
&lt;br /&gt;
Optimal ET sequence: {{Optimal ET sequence| 14, 17, 31, 79, 110e, 141e }}
POTE genertor: ~10/9 = 185.962&lt;br /&gt;
 
&lt;br /&gt;
Badness: 0.039595
Map: [&amp;lt;2 1 0 5 6|, &amp;lt;0 7 15 2 3|]&lt;br /&gt;
 
EDOs: 26, 58, 142e, 200cde&lt;br /&gt;
=== 13-limit ===
Badness: 0.0464&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
&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;
Comma list: 99/98, 105/104, 144/143, 243/242
Commas: 144/143, 351/350, 364/363, 441/440&lt;br /&gt;
 
&lt;br /&gt;
Mapping: {{mapping| 1 3 -3 6 7 3 | 0 -4 15 -9 -10 2 }}
POTE generator: ~10/9 = 185.955&lt;br /&gt;
 
&lt;br /&gt;
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 425.501
Map: [&amp;lt;2 1 0 5 6 4|, &amp;lt;0 7 15 2 3 11|]&lt;br /&gt;
 
EDOs: 26, 58, 84, 142ef&lt;br /&gt;
Optimal ET sequence: {{Optimal ET sequence| 14, 17, 31, 79f, 110ef, 141ef }}
Badness: 0.0250&lt;br /&gt;
 
&lt;br /&gt;
Badness: 0.037408
&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;
 
Commas: 1728/1715, 28672/28125&lt;br /&gt;
== Diesic ==
&lt;br /&gt;
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Diesic]].''
POTE generator: ~7/6 = 269.032&lt;br /&gt;
 
&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
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;
[[Comma list]]: 1728/1715, 5103/5000
EDOs: 9, 49, 58, 165cd, 223bcd&lt;br /&gt;
 
Badness: 0.1171&lt;br /&gt;
{{Mapping|legend=1| 1 2 3 3 | 0 -13 -21 -6 }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Infraorwell-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;11-limit&lt;/h2&gt;
: Mapping generators: ~2, ~36/35
Commas: 176/175, 540/539, 1344/1331&lt;br /&gt;
 
&lt;br /&gt;
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~36/35 = 38.567
POTE generator: ~7/6 = 269.036&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 31, 156c, 187c, 218bc, 249bc, 280bc }}
Map: [&amp;lt;1 14 0 16 12|, &amp;lt;0 -16 3 -17 -11|]&lt;br /&gt;
 
EDOs: 9, 49, 58, 165cde&lt;br /&gt;
[[Badness]]: 0.107348
Badness: 0.0407&lt;br /&gt;
 
&lt;br /&gt;
=== 11-limit ===
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Infraorwell-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;13-limit&lt;/h2&gt;
Subgroup: 2.3.5.7.11
Commas: 144/143, 176/175, 196/195, 364/363&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 121/120, 441/440, 891/875
POTE generator: ~7/6 = 269.021&lt;br /&gt;
 
&lt;br /&gt;
Mapping: {{mapping| 1 2 3 3 4 | 0 -13 -21 -6 -17 }}
Map: [&amp;lt;1 14 0 16 12 20|, &amp;lt;0 -16 3 -17 -11 -21|]&lt;br /&gt;
 
EDOs: 9, 49f, 58&lt;br /&gt;
Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 38.565
Badness: 0.0237&lt;br /&gt;
 
&lt;br /&gt;
Optimal ET sequence: {{Optimal ET sequence| 31, 156ce, 187ce, 218bcee, 249bcee }}
&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;
 
Commas: 1728/1715, 4000/3969&lt;br /&gt;
Badness: 0.044186
&lt;br /&gt;
 
POTE generator: ~36/35 = 45.139&lt;br /&gt;
=== 13-limit ===
&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
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;
Comma list: 66/65, 121/120, 343/338, 441/440
EDOs: 26, 27, 53, 80, 133d, 186d, 319d&lt;br /&gt;
 
Badness: 0.0426&lt;br /&gt;
Mapping: {{mapping| 1 2 3 3 4 4 | 0 -13 -21 -6 -17 -9 }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Quartonic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;11-limit&lt;/h2&gt;
Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 38.444
Commas: 176/175, 540/539, 2200/2187&lt;br /&gt;
 
&lt;br /&gt;
Optimal ET sequence: {{Optimal ET sequence| 31, 94cff, 125cff }}
POTE generator: ~36/35 = 45.041&lt;br /&gt;
 
&lt;br /&gt;
Badness: 0.038116
Map: [&amp;lt;1 2 3 3 5|, &amp;lt;0 -11 -18 -5 -41|]&lt;br /&gt;
 
EDOs: 53, 80, 213d, 293bcd&lt;br /&gt;
== Phillips ==
Badness: 0.034&lt;br /&gt;
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Phillips]].''
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Quartonic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;13-limit&lt;/h2&gt;
[[Subgroup]]: 2.3.5.7
Commas: 169/168 176/175 325/324 540/539&lt;br /&gt;
 
&lt;br /&gt;
[[Comma list]]: 1728/1715, 6561/6272
POTE generator: ~36/35 = 45.080&lt;br /&gt;
 
&lt;br /&gt;
{{Mapping|legend=1| 2 0 33 -7 | 0 1 -9 4 }}
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;
: Mapping generators: ~81/56, ~3
Badness: 0.0239&lt;br /&gt;
 
&lt;br /&gt;
[[Optimal tuning]] ([[POTE]]): ~81/56 = 1\2, ~3/2 = 691.174
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Quartonic-Quarto"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Quarto&lt;/h2&gt;
 
Commmas: 100/99 245/242 864/847&lt;br /&gt;
{{Optimal ET sequence|legend=1| 14, 26, 66b, 92bc }}
&lt;br /&gt;
 
POTE generator: ~36/35 = 45.132&lt;br /&gt;
[[Badness]]: 0.228602
&lt;br /&gt;
 
Map: [&amp;lt;1 2 3 3 4|, &amp;lt;0 -11 -18 -5 -14|]&lt;br /&gt;
=== 11-limit ===
EDOs: 26, 27e, 53e, 80e&lt;br /&gt;
Subgroup: 2.3.5.7.11
Badness: 0.0418&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 99/98, 385/384, 729/704
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc10"&gt;&lt;a name="Quartonic-Quarto-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;13-limit&lt;/h3&gt;
 
Commas: 78/77, 100/99, 144/143, 245/242&lt;br /&gt;
Mapping: {{mapping| 2 0 33 -7 -12 | 0 1 -9 4 6 }}
&lt;br /&gt;
 
POTE generator: ~36/35 = 45.205&lt;br /&gt;
Optimal tuning (POTE): ~63/44 = 1\2, ~3/2 = 691.040
&lt;br /&gt;
 
Map: [&amp;lt;1 2 3 3 4 4|, &amp;lt;0 -11 -18 -5 -14 -8|]&lt;br /&gt;
Optimal ET sequence: {{Optimal ET sequence| 14, 26, 40, 66b }}
EDOs: 26, 27e, 53e&lt;br /&gt;
 
Badness: 0.0277&lt;br /&gt;
Badness: 0.095777
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc11"&gt;&lt;a name="Sentinel"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Sentinel&lt;/h1&gt;
== Triskaidekic ==
Commas: 1728/1715, 3645/3584&lt;br /&gt;
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Triskaidekic]].''
&lt;br /&gt;
 
POTE generator: ~9/7 = 425.596&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
&lt;br /&gt;
 
Map: [&amp;lt;1 3 -3 6|, &amp;lt;0 -4 15 -9|]&lt;br /&gt;
[[Comma list]]: 1728/1715, 1875/1792
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;
{{Mapping|legend=1| 13 0 30 16 | 0 1 0 1 }}
Badness: 0.0938&lt;br /&gt;
 
&lt;br /&gt;
: Mapping generators: ~15/14, ~3
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc12"&gt;&lt;a name="Sentinel-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;11-limit&lt;/h2&gt;
 
Commas: 99/98, 243/242, 385/384 &lt;br /&gt;
[[Optimal tuning]] ([[POTE]]): ~15/14 = 1\13, ~3/2 = 694.143
&lt;br /&gt;
 
POTE generator: ~9/7 = 425.550&lt;br /&gt;
{{Optimal ET sequence|legend=1| 13d, 26 }}
&lt;br /&gt;
 
Map: [&amp;lt;1 3 -3 6 7|, &amp;lt;0 -4 15 -9 -10|]&lt;br /&gt;
[[Badness]]: 0.219050
EDOs: 14, 17, 31, 79, 110e, 141e&lt;br /&gt;
 
Badness: 0.0396&lt;br /&gt;
=== 11-limit ===
&lt;br /&gt;
Subgroup: 2.3.5.7.11
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Sentinel-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;13-limit&lt;/h2&gt;
 
Commas: 99/98, 105/104, 144/143, 243/242&lt;br /&gt;
Comma list: 99/98, 125/121, 385/384
&lt;br /&gt;
 
POTE generator: ~9/7 = 425.501&lt;br /&gt;
Mapping: {{mapping| 13 0 30 16 45 | 0 1 0 1 0 }}
&lt;br /&gt;
 
Map: [&amp;lt;1 3 -3 6 7 3|, &amp;lt;0 -4 15 -9 -10 2|]&lt;br /&gt;
Optimal tuning (POTE): ~15/14 = 1\13, ~3/2 = 696.296
EDOs: 14, 17, 31, 79f, 110ef, 141ef&lt;br /&gt;
 
Badness: 0.0374&lt;/body&gt;&lt;/html&gt;</pre></div>
Optimal ET sequence: {{Optimal ET sequence| 13d, 26, 91cd }}
 
Badness: 0.098847
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 78/77, 99/98, 125/121, 1200/1183
 
Mapping: {{mapping| 13 0 30 16 45 48 | 0 1 0 1 0 0 }}
 
Optimal tuning (POTE): ~15/14 = 1\13, ~3/2 = 695.879
 
Optimal ET sequence: {{Optimal ET sequence| 13d, 26, 91cdf }}
 
Badness: 0.059216
 
== Pentorwell ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 1728/1715, 179200/177147
 
{{Mapping|legend=1| 5 0 -36 22 | 0 1 6 -1 }}
 
[[Optimal tuning]]s:  
* [[CTE]]: ~280/243 = 1\5, ~3/2 = 704.3709 (~64/63 = 15.6291)
* [[POTE]]: ~280/243 = 1\5, ~3/2 = 704.9128 (~64/63 = 15.0872)
 
{{Optimal ET sequence|legend=1| 5, 75, 80 }}
 
[[Badness]]: 0.148665
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 896/891, 1728/1715, 2200/2187
 
Mapping: {{mapping| 5 0 -36 22 57 | 0 1 6 -1 -5 }}
 
Optimal tunings:
* CTE: ~55/48 = 1\5, ~3/2 = 704.8440 (~99/98 = 15.1560)
* POTE: ~55/48 = 1\5, ~3/2 = 704.8788 (~99/98 = 15.1212)
 
Optimal ET sequence: {{Optimal ET sequence| 75e, 80, 315bcdddee }}
 
Badness: 0.071702
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 325/324, 352/351, 364/363, 1728/1715
 
Mapping: {{mapping| 5 0 -36 22 57 82 | 0 1 6 -1 -5 -8 }}
 
Optimal tunings:  
* CTE: ~55/48 = 1\5, ~3/2 = 704.7636 (~99/98 = 15.2364)
* CWE: ~55/48 = 1\5, ~3/2 = 704.7112 (~99/98 = 15.2882)
 
Optimal ET sequence: {{Optimal ET sequence| 75e, 80, 155de }}
 
Badness: 0.0557
 
[[Category:Temperament collections]]
[[Category:Pages with mostly numerical content]]
[[Category:Orwellismic temperaments| ]] <!-- main article -->
[[Category:Orwellismic| ]] <!-- key article -->
[[Category:Rank 2]]

Latest revision as of 00:29, 24 June 2025

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

These temper out [6 3 -1 -3⟩ = 1728/1715, the orwellisma.

Temperaments considered below are secant, infraorwell, quartonic, sentinel, diesic, philips, triskaidekic, and pentorwell. Discussed elsewhere are:

Secant

Subgroup: 2.3.5.7

Comma list: 1728/1715, 177147/175000

Mapping: [⟨2 1 0 5], ⟨0 7 15 2]]

Mapping generators: ~567/400, ~10/9

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

Optimal ET sequence: 26, 58, 84, 142, 368cd

Badness: 0.095278

11-limit

Subgroup: 2.3.5.7.11

Comma list: 441/440, 1344/1331, 1728/1715

Mapping: [⟨2 1 0 5 6], ⟨0 7 15 2 3]]

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

Optimal ET sequence: 26, 58, 142e, 200cdee

Badness: 0.046373

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 144/143, 351/350, 364/363, 441/440

Mapping: [⟨2 1 0 5 6 4], ⟨0 7 15 2 3 11]]

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

Optimal ET sequence: 26, 58, 84, 142ef

Badness: 0.025035

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 144/143, 170/169, 221/220, 351/350, 441/440

Mapping: [⟨2 1 0 5 6 4 6], ⟨0 7 15 2 3 11 7]]

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

Optimal ET sequence: 26, 58, 84, 142ef

Badness: 0.021642

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 144/143, 153/152, 170/169, 210/209, 221/220, 400/399

Mapping: [⟨2 1 0 5 6 4 6 2], ⟨0 7 15 2 3 11 7 21]]

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

Optimal ET sequence: 26, 58h, 84, 142efh, 226deefgh

Badness: 0.018565

Infraorwell

Subgroup: 2.3.5.7

Comma list: 1728/1715, 28672/28125

Mapping: [⟨1 14 0 16], ⟨0 -16 3 -17]]

Mapping generators: ~2, ~12/7

Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 269.032

Optimal ET sequence: 9, 49, 58, 165cd, 223bcd

Badness: 0.117073

11-limit

Subgroup: 2.3.5.7.11

Comma list: 176/175, 540/539, 1344/1331

Mapping: [⟨1 14 0 16 12], ⟨0 -16 3 -17 -11]]

Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 269.036

Optimal ET sequence: 9, 49, 58, 165cdee

Badness: 0.040721

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 144/143, 176/175, 196/195, 364/363

Mapping: [⟨1 14 0 16 12 20], ⟨0 -16 3 -17 -11 -21]]

Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 269.021

Optimal ET sequence: 9, 49f, 58

Badness: 0.023683

Sentinel

For the 5-limit version of this temperament, see High badness temperaments #Sentinel.

Subgroup: 2.3.5.7

Comma list: 1728/1715, 3645/3584

Mapping: [⟨1 3 -3 6], ⟨0 -4 15 -9]]

Mapping generators: ~2, ~9/7

Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 425.596

Optimal ET sequence: 14, 17, 31, 110, 141, 172b, 375bc

Badness: 0.093805

11-limit

Subgroup: 2.3.5.7.11

Comma list: 99/98, 243/242, 385/384

Mapping: [⟨1 3 -3 6 7], ⟨0 -4 15 -9 -10]]

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

Optimal ET sequence: 14, 17, 31, 79, 110e, 141e

Badness: 0.039595

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 99/98, 105/104, 144/143, 243/242

Mapping: [⟨1 3 -3 6 7 3], ⟨0 -4 15 -9 -10 2]]

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

Optimal ET sequence: 14, 17, 31, 79f, 110ef, 141ef

Badness: 0.037408

Diesic

For the 5-limit version of this temperament, see High badness temperaments #Diesic.

Subgroup: 2.3.5.7

Comma list: 1728/1715, 5103/5000

Mapping: [⟨1 2 3 3], ⟨0 -13 -21 -6]]

Mapping generators: ~2, ~36/35

Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 38.567

Optimal ET sequence: 31, 156c, 187c, 218bc, 249bc, 280bc

Badness: 0.107348

11-limit

Subgroup: 2.3.5.7.11

Comma list: 121/120, 441/440, 891/875

Mapping: [⟨1 2 3 3 4], ⟨0 -13 -21 -6 -17]]

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

Optimal ET sequence: 31, 156ce, 187ce, 218bcee, 249bcee

Badness: 0.044186

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 66/65, 121/120, 343/338, 441/440

Mapping: [⟨1 2 3 3 4 4], ⟨0 -13 -21 -6 -17 -9]]

Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 38.444

Optimal ET sequence: 31, 94cff, 125cff

Badness: 0.038116

Phillips

For the 5-limit version of this temperament, see High badness temperaments #Phillips.

Subgroup: 2.3.5.7

Comma list: 1728/1715, 6561/6272

Mapping: [⟨2 0 33 -7], ⟨0 1 -9 4]]

Mapping generators: ~81/56, ~3

Optimal tuning (POTE): ~81/56 = 1\2, ~3/2 = 691.174

Optimal ET sequence: 14, 26, 66b, 92bc

Badness: 0.228602

11-limit

Subgroup: 2.3.5.7.11

Comma list: 99/98, 385/384, 729/704

Mapping: [⟨2 0 33 -7 -12], ⟨0 1 -9 4 6]]

Optimal tuning (POTE): ~63/44 = 1\2, ~3/2 = 691.040

Optimal ET sequence: 14, 26, 40, 66b

Badness: 0.095777

Triskaidekic

For the 5-limit version of this temperament, see High badness temperaments #Triskaidekic.

Subgroup: 2.3.5.7

Comma list: 1728/1715, 1875/1792

Mapping: [⟨13 0 30 16], ⟨0 1 0 1]]

Mapping generators: ~15/14, ~3

Optimal tuning (POTE): ~15/14 = 1\13, ~3/2 = 694.143

Optimal ET sequence: 13d, 26

Badness: 0.219050

11-limit

Subgroup: 2.3.5.7.11

Comma list: 99/98, 125/121, 385/384

Mapping: [⟨13 0 30 16 45], ⟨0 1 0 1 0]]

Optimal tuning (POTE): ~15/14 = 1\13, ~3/2 = 696.296

Optimal ET sequence: 13d, 26, 91cd

Badness: 0.098847

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 78/77, 99/98, 125/121, 1200/1183

Mapping: [⟨13 0 30 16 45 48], ⟨0 1 0 1 0 0]]

Optimal tuning (POTE): ~15/14 = 1\13, ~3/2 = 695.879

Optimal ET sequence: 13d, 26, 91cdf

Badness: 0.059216

Pentorwell

Subgroup: 2.3.5.7

Comma list: 1728/1715, 179200/177147

Mapping: [⟨5 0 -36 22], ⟨0 1 6 -1]]

Optimal tunings:

  • CTE: ~280/243 = 1\5, ~3/2 = 704.3709 (~64/63 = 15.6291)
  • POTE: ~280/243 = 1\5, ~3/2 = 704.9128 (~64/63 = 15.0872)

Optimal ET sequence: 5, 75, 80

Badness: 0.148665

11-limit

Subgroup: 2.3.5.7.11

Comma list: 896/891, 1728/1715, 2200/2187

Mapping: [⟨5 0 -36 22 57], ⟨0 1 6 -1 -5]]

Optimal tunings:

  • CTE: ~55/48 = 1\5, ~3/2 = 704.8440 (~99/98 = 15.1560)
  • POTE: ~55/48 = 1\5, ~3/2 = 704.8788 (~99/98 = 15.1212)

Optimal ET sequence: 75e, 80, 315bcdddee

Badness: 0.071702

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 325/324, 352/351, 364/363, 1728/1715

Mapping: [⟨5 0 -36 22 57 82], ⟨0 1 6 -1 -5 -8]]

Optimal tunings:

  • CTE: ~55/48 = 1\5, ~3/2 = 704.7636 (~99/98 = 15.2364)
  • CWE: ~55/48 = 1\5, ~3/2 = 704.7112 (~99/98 = 15.2882)

Optimal ET sequence: 75e, 80, 155de

Badness: 0.0557

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