Sensipent family: Difference between revisions

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**Imported revision 212006708 - Original comment: **
 
Wikispaces>genewardsmith
**Imported revision 212007488 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-19 14:37:48 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-19 14:43:47 UTC</tt>.<br>
: The original revision id was <tt>212006708</tt>.<br>
: The original revision id was <tt>212007488</tt>.<br>
: The revision comment was: <tt></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>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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=Sensi temperament=
=Sensi=
Sensi tempers out 686/675, 245/243 and 4375/4374 in addition to 126/125, and can be described as the 19&amp;27 temperament. It has as a generator half of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 13-limit sensi tempers out 91/90. 22/17, in the middle, is even closer to the generator. [[46edo]] is an excellent sensi tuning, and MOS of size 11, 19 and 27 are available.
Sensi tempers out 686/675, 245/243 and 4375/4374 in addition to 126/125, and can be described as the 19&amp;27 temperament. It has as a generator half of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 13-limit sensi tempers out 91/90. 22/17, in the middle, is even closer to the generator. [[46edo]] is an excellent sensi tuning, and MOS of size 11, 19 and 27 are available.


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EDOs: 46, 103, 149
EDOs: 46, 103, 149
Badness: 0.0424
Badness: 0.0424
Badness:</pre></div>
 
==13-limit==
Commas: 351/350, 385/384, 441/440, 847/845
 
POTE generator: ~11/8 = 547.629
 
Map: [&lt;1 13 17 -1 4 -5|, &lt;0 -21 -27 7 -1 16|]
EDOs: 46, 103, 149
Badness: 0.0258
 
==17-limit==</pre></div>
<h4>Original HTML content:</h4>
<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;Sensipent family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:20:&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:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt;&lt;a href="#Sensipent"&gt;Sensipent&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt; | &lt;a href="#Sensi temperament"&gt;Sensi temperament&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;!-- ws:start:WikiTextTocRule:23: --&gt;&lt;!-- ws:end:WikiTextTocRule:23 --&gt;&lt;!-- ws:start:WikiTextTocRule:24: --&gt;&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt;&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;!-- ws:start:WikiTextTocRule:26: --&gt;&lt;!-- ws:end:WikiTextTocRule:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt;&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt;&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;!-- ws:start:WikiTextTocRule:29: --&gt; | &lt;a href="#Heinz"&gt;Heinz&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:29 --&gt;&lt;!-- ws:start:WikiTextTocRule:30: --&gt;&lt;!-- ws:end:WikiTextTocRule:30 --&gt;&lt;!-- ws:start:WikiTextTocRule:31: --&gt;
<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;Sensipent family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:24:&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:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt;&lt;a href="#Sensipent"&gt;Sensipent&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;!-- ws:start:WikiTextTocRule:26: --&gt; | &lt;a href="#Sensi"&gt;Sensi&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt;&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt;&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;!-- ws:start:WikiTextTocRule:29: --&gt;&lt;!-- ws:end:WikiTextTocRule:29 --&gt;&lt;!-- ws:start:WikiTextTocRule:30: --&gt;&lt;!-- ws:end:WikiTextTocRule:30 --&gt;&lt;!-- ws:start:WikiTextTocRule:31: --&gt;&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;!-- ws:start:WikiTextTocRule:32: --&gt;&lt;!-- ws:end:WikiTextTocRule:32 --&gt;&lt;!-- ws:start:WikiTextTocRule:33: --&gt; | &lt;a href="#Heinz"&gt;Heinz&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:33 --&gt;&lt;!-- ws:start:WikiTextTocRule:34: --&gt;&lt;!-- ws:end:WikiTextTocRule:34 --&gt;&lt;!-- ws:start:WikiTextTocRule:35: --&gt;&lt;!-- ws:end:WikiTextTocRule:35 --&gt;&lt;!-- ws:start:WikiTextTocRule:36: --&gt;&lt;!-- ws:end:WikiTextTocRule:36 --&gt;&lt;!-- ws:start:WikiTextTocRule:37: --&gt;
&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;br /&gt;
&lt;!-- ws:end:WikiTextTocRule:37 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Sensipent"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Sensipent&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Sensipent"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Sensipent&lt;/h1&gt;
Comma: 78732/78125&lt;br /&gt;
Comma: 78732/78125&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&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="Sensi temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Sensi temperament&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Sensi"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Sensi&lt;/h1&gt;
Sensi tempers out 686/675, 245/243 and 4375/4374 in addition to 126/125, and can be described as the 19&amp;amp;27 temperament. It has as a generator half of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 13-limit sensi tempers out 91/90. 22/17, in the middle, is even closer to the generator. &lt;a class="wiki_link" href="/46edo"&gt;46edo&lt;/a&gt; is an excellent sensi tuning, and MOS of size 11, 19 and 27 are available.&lt;br /&gt;
Sensi tempers out 686/675, 245/243 and 4375/4374 in addition to 126/125, and can be described as the 19&amp;amp;27 temperament. It has as a generator half of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 13-limit sensi tempers out 91/90. 22/17, in the middle, is even closer to the generator. &lt;a class="wiki_link" href="/46edo"&gt;46edo&lt;/a&gt; is an excellent sensi tuning, and MOS of size 11, 19 and 27 are available.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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Badness: 0.0256&lt;br /&gt;
Badness: 0.0256&lt;br /&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="Sensi temperament-Sensor"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Sensor&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Sensi-Sensor"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Sensor&lt;/h2&gt;
Commas: 126/125, 245/243, 385/384&lt;br /&gt;
Commas: 126/125, 245/243, 385/384&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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Badness: 0.0379&lt;br /&gt;
Badness: 0.0379&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="Sensi temperament-Sensor-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;13-limit&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="Sensi-Sensor-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;13-limit&lt;/h3&gt;
Commas: 91/90, 126/125, 169/168, 385/384&lt;br /&gt;
Commas: 91/90, 126/125, 169/168, 385/384&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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Badness: 0.0256&lt;br /&gt;
Badness: 0.0256&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Sensi temperament-Sensis"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Sensis&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Sensi-Sensis"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Sensis&lt;/h2&gt;
Commas: 56/55, 100/99, 245/243&lt;br /&gt;
Commas: 56/55, 100/99, 245/243&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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Badness: 0.0287&lt;br /&gt;
Badness: 0.0287&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="Sensi temperament-Sensis-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;13-limit&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="Sensi-Sensis-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;13-limit&lt;/h3&gt;
Commas: 56/55, 78/77, 91/90, 100/99&lt;br /&gt;
Commas: 56/55, 78/77, 91/90, 100/99&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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Badness: 0.0200&lt;br /&gt;
Badness: 0.0200&lt;br /&gt;
&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="Sensi temperament-Sensus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Sensus&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Sensi-Sensus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Sensus&lt;/h2&gt;
Commas: 126/125, 176/175, 245/243&lt;br /&gt;
Commas: 126/125, 176/175, 245/243&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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Badness: 0.0295&lt;br /&gt;
Badness: 0.0295&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc7"&gt;&lt;a name="Sensi temperament-Sensus-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;13-limit&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc7"&gt;&lt;a name="Sensi-Sensus-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;13-limit&lt;/h3&gt;
Commas: 91/90, 126/125, 169/168, 352/351&lt;br /&gt;
Commas: 91/90, 126/125, 169/168, 352/351&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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EDOs: 46, 103, 149&lt;br /&gt;
EDOs: 46, 103, 149&lt;br /&gt;
Badness: 0.0424&lt;br /&gt;
Badness: 0.0424&lt;br /&gt;
Badness:&lt;/body&gt;&lt;/html&gt;</pre></div>
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Heinz-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;13-limit&lt;/h2&gt;
Commas: 351/350, 385/384, 441/440, 847/845&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~11/8 = 547.629&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 13 17 -1 4 -5|, &amp;lt;0 -21 -27 7 -1 16|]&lt;br /&gt;
EDOs: 46, 103, 149&lt;br /&gt;
Badness: 0.0258&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="Heinz-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;17-limit&lt;/h2&gt;
&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 14:43, 19 March 2011

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author genewardsmith and made on 2011-03-19 14:43:47 UTC.
The original revision id was 212007488.
The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

[[toc|flat]]

=Sensipent=
Comma: 78732/78125

[[POTE tuning|POTE generator]]: 162/125 =

Map: [<1 6 8|, <0 -7 -9|]
EDOs: 8, 19, 46, 65, 539


=Sensi=
Sensi tempers out 686/675, 245/243 and 4375/4374 in addition to 126/125, and can be described as the 19&27 temperament. It has as a generator half of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 13-limit sensi tempers out 91/90. 22/17, in the middle, is even closer to the generator. [[46edo]] is an excellent sensi tuning, and MOS of size 11, 19 and 27 are available.

[[Comma|Commas]]: 126/125, 245/243

7-limit minimax
[|1 0 0 0>, |1/13 0 0 7/13>, |5/13 0 0 9/13>, |0 0 0 1>]
[[Eigenmonzo|Eigenmonzos]]: 2, 7

9-limit minimax
[|1 0 0 0>, |2/5 14/5 -7/5 0>, 
|4/5 18/5 -9/5 0>, |3/5 26/5 -13/5 0>]
[[Eigenmonzo|Eigenmonzos]]: 2, 9/5

[[POTE tuning|POTE generator]]: ~9/7 = 443.383
Algebraic generator: Calista, the [[Algebraic number|real root]] of x^7-2x^2-1, at 340.6467 cents. 

Map: [<1 6 8 11|, <0 -7 -9 -13|]
[[Generator|Generators]]: 2, 14/9
EDOs: 19, 27, 46, 249, 295
Badness: 0.0256

==Sensor==
Commas: 126/125, 245/243, 385/384

[[POTE tuning|POTE generator]]: ~9/7 = 443.294

Map: [<1 6 8 11 -6|, <0 -7 -9 -13 15|]
EDOs: 8, 19, 27, 46, 111, 157
Badness: 0.0379

===13-limit===
Commas: 91/90, 126/125, 169/168, 385/384

[[POTE tuning|POTE generator]]: ~9/7 = 443.321

Map: [<1 6 8 11 -6 10|, <0 -7 -9 -13 15 -10|]
EDOs: 8, 19, 27, 46, 157
Badness: 0.0256

==Sensis==
Commas: 56/55, 100/99, 245/243

[[POTE tuning|POTE generator]]:  443.962

Map: [<1 6 8 11 6|, <0 -7 -9 -13 -4|]
EDOs: 19, 27, 73, 100
Badness: 0.0287

===13-limit===
Commas: 56/55, 78/77, 91/90, 100/99

[[POTE tuning|POTE generator]]: 443.945

Map: [<1 6 8 11 6 10|, <0 -7 -9 -13 -4 -10|]
EDOs: 19, 27, 73, 100
Badness: 0.0200

==Sensus==
Commas: 126/125, 176/175, 245/243

POTE generator: ~9/7 = 443.626

Map: [<1 6 8 11 23|, <0 -7 -9 -13 -31|]
EDOs: 8, 19, 27, 46, 165
Badness: 0.0295

===13-limit===
Commas: 91/90, 126/125, 169/168, 352/351

POTE generator: ~9/7 = 443.559

Map: [<1 6 8 11 23 10|, <0 -7 -9 -13 -31 -10|]
EDOs: 8, 19, 27, 46, 303
Badness: 0.0208

=Heinz=
Commas: 78732/78125, 1029/1024

POTE generator: ~48/35 = 546.815

Map: [<1 13 17 -1|, <0 -21 -27 7|]
EDOs: 46, 103, 149
Badness: 0.1154

==11-limit==
Commas: 385/384, 441/440, 88208/87500

POTE generator: ~11/8 = 547.631

Map: [<1 13 17 -1 4|, <0 -21 -27 7 -1|]
EDOs: 46, 103, 149
Badness: 0.0424

==13-limit==
Commas: 351/350, 385/384, 441/440, 847/845

POTE generator: ~11/8 = 547.629

Map: [<1 13 17 -1 4 -5|, <0 -21 -27 7 -1 16|]
EDOs: 46, 103, 149
Badness: 0.0258

==17-limit==

Original HTML content:

<html><head><title>Sensipent family</title></head><body><!-- ws:start:WikiTextTocRule:24:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --><a href="#Sensipent">Sensipent</a><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --> | <a href="#Sensi">Sensi</a><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --> | <a href="#Heinz">Heinz</a><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: -->
<!-- ws:end:WikiTextTocRule:37 --><br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Sensipent"></a><!-- ws:end:WikiTextHeadingRule:0 -->Sensipent</h1>
Comma: 78732/78125<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 162/125 =<br />
<br />
Map: [&lt;1 6 8|, &lt;0 -7 -9|]<br />
EDOs: 8, 19, 46, 65, 539<br />
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Sensi"></a><!-- ws:end:WikiTextHeadingRule:2 -->Sensi</h1>
Sensi tempers out 686/675, 245/243 and 4375/4374 in addition to 126/125, and can be described as the 19&amp;27 temperament. It has as a generator half of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 13-limit sensi tempers out 91/90. 22/17, in the middle, is even closer to the generator. <a class="wiki_link" href="/46edo">46edo</a> is an excellent sensi tuning, and MOS of size 11, 19 and 27 are available.<br />
<br />
<a class="wiki_link" href="/Comma">Commas</a>: 126/125, 245/243<br />
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7-limit minimax<br />
[|1 0 0 0&gt;, |1/13 0 0 7/13&gt;, |5/13 0 0 9/13&gt;, |0 0 0 1&gt;]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 7<br />
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9-limit minimax<br />
[|1 0 0 0&gt;, |2/5 14/5 -7/5 0&gt;, <br />
|4/5 18/5 -9/5 0&gt;, |3/5 26/5 -13/5 0&gt;]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 9/5<br />
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<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~9/7 = 443.383<br />
Algebraic generator: Calista, the <a class="wiki_link" href="/Algebraic%20number">real root</a> of x^7-2x^2-1, at 340.6467 cents. <br />
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Map: [&lt;1 6 8 11|, &lt;0 -7 -9 -13|]<br />
<a class="wiki_link" href="/Generator">Generators</a>: 2, 14/9<br />
EDOs: 19, 27, 46, 249, 295<br />
Badness: 0.0256<br />
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<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Sensi-Sensor"></a><!-- ws:end:WikiTextHeadingRule:4 -->Sensor</h2>
Commas: 126/125, 245/243, 385/384<br />
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<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~9/7 = 443.294<br />
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Map: [&lt;1 6 8 11 -6|, &lt;0 -7 -9 -13 15|]<br />
EDOs: 8, 19, 27, 46, 111, 157<br />
Badness: 0.0379<br />
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<!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="Sensi-Sensor-13-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-limit</h3>
Commas: 91/90, 126/125, 169/168, 385/384<br />
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<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~9/7 = 443.321<br />
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Map: [&lt;1 6 8 11 -6 10|, &lt;0 -7 -9 -13 15 -10|]<br />
EDOs: 8, 19, 27, 46, 157<br />
Badness: 0.0256<br />
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<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Sensi-Sensis"></a><!-- ws:end:WikiTextHeadingRule:8 -->Sensis</h2>
Commas: 56/55, 100/99, 245/243<br />
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<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>:  443.962<br />
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Map: [&lt;1 6 8 11 6|, &lt;0 -7 -9 -13 -4|]<br />
EDOs: 19, 27, 73, 100<br />
Badness: 0.0287<br />
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<!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="Sensi-Sensis-13-limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->13-limit</h3>
Commas: 56/55, 78/77, 91/90, 100/99<br />
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<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 443.945<br />
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Map: [&lt;1 6 8 11 6 10|, &lt;0 -7 -9 -13 -4 -10|]<br />
EDOs: 19, 27, 73, 100<br />
Badness: 0.0200<br />
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<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Sensi-Sensus"></a><!-- ws:end:WikiTextHeadingRule:12 -->Sensus</h2>
Commas: 126/125, 176/175, 245/243<br />
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POTE generator: ~9/7 = 443.626<br />
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Map: [&lt;1 6 8 11 23|, &lt;0 -7 -9 -13 -31|]<br />
EDOs: 8, 19, 27, 46, 165<br />
Badness: 0.0295<br />
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<!-- ws:start:WikiTextHeadingRule:14:&lt;h3&gt; --><h3 id="toc7"><a name="Sensi-Sensus-13-limit"></a><!-- ws:end:WikiTextHeadingRule:14 -->13-limit</h3>
Commas: 91/90, 126/125, 169/168, 352/351<br />
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POTE generator: ~9/7 = 443.559<br />
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Map: [&lt;1 6 8 11 23 10|, &lt;0 -7 -9 -13 -31 -10|]<br />
EDOs: 8, 19, 27, 46, 303<br />
Badness: 0.0208<br />
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<!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="Heinz"></a><!-- ws:end:WikiTextHeadingRule:16 -->Heinz</h1>
Commas: 78732/78125, 1029/1024<br />
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POTE generator: ~48/35 = 546.815<br />
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Map: [&lt;1 13 17 -1|, &lt;0 -21 -27 7|]<br />
EDOs: 46, 103, 149<br />
Badness: 0.1154<br />
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<!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Heinz-11-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->11-limit</h2>
Commas: 385/384, 441/440, 88208/87500<br />
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POTE generator: ~11/8 = 547.631<br />
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Map: [&lt;1 13 17 -1 4|, &lt;0 -21 -27 7 -1|]<br />
EDOs: 46, 103, 149<br />
Badness: 0.0424<br />
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<!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Heinz-13-limit"></a><!-- ws:end:WikiTextHeadingRule:20 -->13-limit</h2>
Commas: 351/350, 385/384, 441/440, 847/845<br />
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POTE generator: ~11/8 = 547.629<br />
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Map: [&lt;1 13 17 -1 4 -5|, &lt;0 -21 -27 7 -1 16|]<br />
EDOs: 46, 103, 149<br />
Badness: 0.0258<br />
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<!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="Heinz-17-limit"></a><!-- ws:end:WikiTextHeadingRule:22 -->17-limit</h2>
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