Sensipent family: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 250423972 - Original comment: ** |
Wikispaces>Natebedell **Imported revision 251162520 - 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: | : This revision was by author [[User:Natebedell|Natebedell]] and made on <tt>2011-09-06 10:08:40 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>251162520</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]] | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]] | ||
=Sensipent= | |||
=Sensipent= | [[Comma]]: 78732/78125 = |2 9 -7> | ||
[[Comma]]: 78732/78125 | |||
[[POTE tuning|POTE generator]]: 162/125 = 443.058 cents | [[POTE tuning|POTE generator]]: 162/125 = 443.058 cents | ||
| Line 17: | Line 16: | ||
=Sensi= | =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. | 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. | ||
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9-limit minimax | 9-limit minimax | ||
[|1 0 0 0>, |2/5 14/5 -7/5 0>, | [|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>] | |4/5 18/5 -9/5 0>, |3/5 26/5 -13/5 0>] | ||
[[Eigenmonzo|Eigenmonzos]]: 2, 9/5 | [[Eigenmonzo|Eigenmonzos]]: 2, 9/5 | ||
[[POTE tuning|POTE generator]]: ~9/7 = 443.383 | [[POTE tuning|POTE generator]]: ~9/7 = 443.383 | ||
Algebraic generator: The [[Algebraic number|real root]] of x^5+x^4-4x^2+x-1, at 443.3783 cents. | Algebraic generator: The [[Algebraic number|real root]] of x^5+x^4-4x^2+x-1, at 443.3783 cents. | ||
[[Map]]: [<1 6 8 11|, <0 -7 -9 -13|] | [[Map]]: [<1 6 8 11|, <0 -7 -9 -13|] | ||
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[[Badness]]: 0.0256 | [[Badness]]: 0.0256 | ||
==Sensor== | ==Sensor== | ||
[[Comma]]s: 126/125, 245/243, 385/384 | [[Comma]]s: 126/125, 245/243, 385/384 | ||
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[[Badness]]: 0.0379 | [[Badness]]: 0.0379 | ||
===13-limit=== | ===13-limit=== | ||
[[Comma]]s: 91/90, 126/125, 169/168, 385/384 | [[Comma]]s: 91/90, 126/125, 169/168, 385/384 | ||
| Line 57: | Line 56: | ||
[[Badness]]: 0.0256 | [[Badness]]: 0.0256 | ||
==Sensis== | ==Sensis== | ||
[[Comma]]s: 56/55, 100/99, 245/243 | [[Comma]]s: 56/55, 100/99, 245/243 | ||
[[POTE tuning|POTE generator]]: | [[POTE tuning|POTE generator]]: 443.962 | ||
[[Map]]: [<1 6 8 11 6|, <0 -7 -9 -13 -4|] | [[Map]]: [<1 6 8 11 6|, <0 -7 -9 -13 -4|] | ||
| Line 66: | Line 65: | ||
[[Badness]]: 0.0287 | [[Badness]]: 0.0287 | ||
===13-limit=== | ===13-limit=== | ||
[[Comma]]s: 56/55, 78/77, 91/90, 100/99 | [[Comma]]s: 56/55, 78/77, 91/90, 100/99 | ||
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[[Badness]]: 0.0200 | [[Badness]]: 0.0200 | ||
==Sensus== | ==Sensus== | ||
[[Comma]]s: 126/125, 176/175, 245/243 | [[Comma]]s: 126/125, 176/175, 245/243 | ||
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[[Badness]]: 0.0295 | [[Badness]]: 0.0295 | ||
===13-limit=== | ===13-limit=== | ||
[[Comma]]s: 91/90, 126/125, 169/168, 352/351 | [[Comma]]s: 91/90, 126/125, 169/168, 352/351 | ||
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[[Badness]]: 0.0208 | [[Badness]]: 0.0208 | ||
=Heinz= | =Heinz= | ||
[[Comma]]s: 78732/78125, 1029/1024 | [[Comma]]s: 78732/78125, 1029/1024 | ||
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[[Badness]]: 0.1154 | [[Badness]]: 0.1154 | ||
==11-limit== | ==11-limit== | ||
[[Comma]]s: 385/384, 441/440, 88208/87500 | [[Comma]]s: 385/384, 441/440, 88208/87500 | ||
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[[Badness]]: 0.0424 | [[Badness]]: 0.0424 | ||
==13-limit== | ==13-limit== | ||
[[Comma]]s: 351/350, 385/384, 441/440, 847/845 | [[Comma]]s: 351/350, 385/384, 441/440, 847/845 | ||
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[[Badness]]: 0.0258 | [[Badness]]: 0.0258 | ||
==17-limit== | ==17-limit== | ||
[[Comma]]s: 273/272, 351/350, 385/384, 441/440, 847/845 | [[Comma]]s: 273/272, 351/350, 385/384, 441/440, 847/845 | ||
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[[Badness]]: 0.0185 | [[Badness]]: 0.0185 | ||
==19-limit== | ==19-limit== | ||
[[Comma]]s: 171/170, 209/208, 351/350, 385/384, 441/440, 969/968 | [[Comma]]s: 171/170, 209/208, 351/350, 385/384, 441/440, 969/968 | ||
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<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"><html><head><title>Sensipent family</title></head><body><!-- ws:start:WikiTextTocRule:26:&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:26 --><!-- ws:start:WikiTextTocRule:27: --><a href="#Sensipent">Sensipent</a><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --> | <a href="#Sensi">Sensi</a><!-- 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: --><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --> | <a href="#Heinz">Heinz</a><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --> | <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"><html><head><title>Sensipent family</title></head><body><!-- ws:start:WikiTextTocRule:26:&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:26 --><!-- ws:start:WikiTextTocRule:27: --><a href="#Sensipent">Sensipent</a><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --> | <a href="#Sensi">Sensi</a><!-- 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: --><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --> | <a href="#Heinz">Heinz</a><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --> | ||
<!-- ws:end:WikiTextTocRule:40 --> | <!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Sensipent"></a><!-- ws:end:WikiTextHeadingRule:0 -->Sensipent</h1> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Sensipent"></a><!-- ws:end:WikiTextHeadingRule:0 -->Sensipent</h1> | <a class="wiki_link" href="/Comma">Comma</a>: 78732/78125 = |2 9 -7&gt;<br /> | ||
<a class="wiki_link" href="/Comma">Comma</a>: 78732/78125<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 162/125 = 443.058 cents<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 162/125 = 443.058 cents<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Sensi"></a><!-- ws:end:WikiTextHeadingRule:2 -->Sensi</h1> | <!-- 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 <a class="wiki_link" href="/13-limit">13-limit</a> 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 /> | 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 <a class="wiki_link" href="/13-limit">13-limit</a> 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 /> | <br /> | ||
<a class="wiki_link" href="/Comma">Commas</a>: 126/125, 245/243<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 126/125, 245/243<br /> | ||
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<br /> | <br /> | ||
9-limit minimax<br /> | 9-limit minimax<br /> | ||
[|1 0 0 0&gt;, |2/5 14/5 -7/5 0&gt;, <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 /> | |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 /> | <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 9/5<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~9/7 = 443.383<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~9/7 = 443.383<br /> | ||
Algebraic generator: The <a class="wiki_link" href="/Algebraic%20number">real root</a> of x^5+x^4-4x^2+x-1, at 443.3783 cents. <br /> | Algebraic generator: The <a class="wiki_link" href="/Algebraic%20number">real root</a> of x^5+x^4-4x^2+x-1, at 443.3783 cents.<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/Map">Map</a>: [&lt;1 6 8 11|, &lt;0 -7 -9 -13|]<br /> | <a class="wiki_link" href="/Map">Map</a>: [&lt;1 6 8 11|, &lt;0 -7 -9 -13|]<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Sensi-Sensor"></a><!-- ws:end:WikiTextHeadingRule:4 -->Sensor</h2> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Sensi-Sensor"></a><!-- ws:end:WikiTextHeadingRule:4 -->Sensor</h2> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 126/125, 245/243, 385/384<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 126/125, 245/243, 385/384<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~9/7 = 443.294<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~9/7 = 443.294<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="Sensi-Sensor-13-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-limit</h3> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="Sensi-Sensor-13-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-limit</h3> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 91/90, 126/125, 169/168, 385/384<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 91/90, 126/125, 169/168, 385/384<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~9/7 = 443.321<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~9/7 = 443.321<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Sensi-Sensis"></a><!-- ws:end:WikiTextHeadingRule:8 -->Sensis</h2> | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Sensi-Sensis"></a><!-- ws:end:WikiTextHeadingRule:8 -->Sensis</h2> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 56/55, 100/99, 245/243<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 56/55, 100/99, 245/243<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 443.962<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/Map">Map</a>: [&lt;1 6 8 11 6|, &lt;0 -7 -9 -13 -4|]<br /> | <a class="wiki_link" href="/Map">Map</a>: [&lt;1 6 8 11 6|, &lt;0 -7 -9 -13 -4|]<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="Sensi-Sensis-13-limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->13-limit</h3> | <!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="Sensi-Sensis-13-limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->13-limit</h3> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 56/55, 78/77, 91/90, 100/99<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 56/55, 78/77, 91/90, 100/99<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 443.945<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 443.945<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Sensi-Sensus"></a><!-- ws:end:WikiTextHeadingRule:12 -->Sensus</h2> | <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Sensi-Sensus"></a><!-- ws:end:WikiTextHeadingRule:12 -->Sensus</h2> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 126/125, 176/175, 245/243<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 126/125, 176/175, 245/243<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20generator">POTE generator</a>: ~9/7 = 443.626<br /> | <a class="wiki_link" href="/POTE%20generator">POTE generator</a>: ~9/7 = 443.626<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:14:&lt;h3&gt; --><h3 id="toc7"><a name="Sensi-Sensus-13-limit"></a><!-- ws:end:WikiTextHeadingRule:14 -->13-limit</h3> | <!-- ws:start:WikiTextHeadingRule:14:&lt;h3&gt; --><h3 id="toc7"><a name="Sensi-Sensus-13-limit"></a><!-- ws:end:WikiTextHeadingRule:14 -->13-limit</h3> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 91/90, 126/125, 169/168, 352/351<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 91/90, 126/125, 169/168, 352/351<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20generator">POTE generator</a>: ~9/7 = 443.559<br /> | <a class="wiki_link" href="/POTE%20generator">POTE generator</a>: ~9/7 = 443.559<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="Heinz"></a><!-- ws:end:WikiTextHeadingRule:16 -->Heinz</h1> | <!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="Heinz"></a><!-- ws:end:WikiTextHeadingRule:16 -->Heinz</h1> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 78732/78125, 1029/1024<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 78732/78125, 1029/1024<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20generator">POTE generator</a>: ~48/35 = 546.815<br /> | <a class="wiki_link" href="/POTE%20generator">POTE generator</a>: ~48/35 = 546.815<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Heinz-11-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->11-limit</h2> | <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Heinz-11-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->11-limit</h2> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 385/384, 441/440, 88208/87500<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 385/384, 441/440, 88208/87500<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20generator">POTE generator</a>: ~11/8 = 547.631<br /> | <a class="wiki_link" href="/POTE%20generator">POTE generator</a>: ~11/8 = 547.631<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Heinz-13-limit"></a><!-- ws:end:WikiTextHeadingRule:20 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Heinz-13-limit"></a><!-- ws:end:WikiTextHeadingRule:20 -->13-limit</h2> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 351/350, 385/384, 441/440, 847/845<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 351/350, 385/384, 441/440, 847/845<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20generator">POTE generator</a>: ~11/8 = 547.629<br /> | <a class="wiki_link" href="/POTE%20generator">POTE generator</a>: ~11/8 = 547.629<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> | <!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="Heinz-17-limit"></a><!-- ws:end:WikiTextHeadingRule:22 -->17-limit</h2> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 273/272, 351/350, 385/384, 441/440, 847/845<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 273/272, 351/350, 385/384, 441/440, 847/845<br /> | ||
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<a class="wiki_link" href="/POTE%20generator">POTE generator</a>: ~11/8 = 547.635<br /> | <a class="wiki_link" href="/POTE%20generator">POTE generator</a>: ~11/8 = 547.635<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Heinz-19-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->19-limit</h2> | <!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Heinz-19-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->19-limit</h2> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 171/170, 209/208, 351/350, 385/384, 441/440, 969/968<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 171/170, 209/208, 351/350, 385/384, 441/440, 969/968<br /> | ||
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<a class="wiki_link" href="/POTE%20generator">POTE generator</a>: ~11/8 = 547.614<br /> | <a class="wiki_link" href="/POTE%20generator">POTE generator</a>: ~11/8 = 547.614<br /> | ||
Revision as of 10:08, 6 September 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 Natebedell and made on 2011-09-06 10:08:40 UTC.
- The original revision id was 251162520.
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Original Wikitext content:
[[toc|flat]] =Sensipent= [[Comma]]: 78732/78125 = |2 9 -7> [[POTE tuning|POTE generator]]: 162/125 = 443.058 cents [[Map]]: [<1 6 8|, <0 -7 -9|] [[EDO]]s: [[8edo|8]], [[19edo|19]], [[46edo|46]], [[65edo|65]], [[539edo|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: The [[Algebraic number|real root]] of x^5+x^4-4x^2+x-1, at 443.3783 cents. [[Map]]: [<1 6 8 11|, <0 -7 -9 -13|] [[Generator|Generators]]: 2, 14/9 [[EDO]]s: [[19edo|19]], [[27edo|27]], [[46edo|46]], [[249edo|249]], [[295edo|295]] [[Badness]]: 0.0256 ==Sensor== [[Comma]]s: 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|] [[EDO]]s: 8, 19, 27, 46, 111, 157 [[Badness]]: 0.0379 ===13-limit=== [[Comma]]s: 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|] [[EDO]]s: [[8edo|8]], [[19edo|19]], [[27edo|27]], [[46edo|46]], [[157edo|157]] [[Badness]]: 0.0256 ==Sensis== [[Comma]]s: 56/55, 100/99, 245/243 [[POTE tuning|POTE generator]]: 443.962 [[Map]]: [<1 6 8 11 6|, <0 -7 -9 -13 -4|] [[EDO]]s: [[19edo|19]], [[27edo|27]], [[73edo|73]], [[100edo|100]] [[Badness]]: 0.0287 ===13-limit=== [[Comma]]s: 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|] [[EDO]]s: 19, 27, 73, 100 [[Badness]]: 0.0200 ==Sensus== [[Comma]]s: 126/125, 176/175, 245/243 [[POTE generator]]: ~9/7 = 443.626 [[Map]]: [<1 6 8 11 23|, <0 -7 -9 -13 -31|] [[EDO]]s: 8, 19, 27, 46, 165 [[Badness]]: 0.0295 ===13-limit=== [[Comma]]s: 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|] [[EDO]]s: 8, 19, 27, 46, [[303edo|303]] [[Badness]]: 0.0208 =Heinz= [[Comma]]s: 78732/78125, 1029/1024 [[POTE generator]]: ~48/35 = 546.815 [[Map]]: [<1 13 17 -1|, <0 -21 -27 7|] [[EDO]]s: 46, [[103edo|103]], [[149edo|149]] [[Badness]]: 0.1154 ==11-limit== [[Comma]]s: 385/384, 441/440, 88208/87500 [[POTE generator]]: ~11/8 = 547.631 [[Map]]: [<1 13 17 -1 4|, <0 -21 -27 7 -1|] [[EDO]]s: 46, 103, 149 [[Badness]]: 0.0424 ==13-limit== [[Comma]]s: 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|] [[EDO]]s: 46, 57, 103, 149 [[Badness]]: 0.0258 ==17-limit== [[Comma]]s: 273/272, 351/350, 385/384, 441/440, 847/845 [[POTE generator]]: ~11/8 = 547.635 [[Map]]: [<1 13 17 -1 4 -5 3|, <0 -21 -27 7 -1 16 2|] [[EDO]]s: 46, [[57edo|57]], 103, 149 [[Badness]]: 0.0185 ==19-limit== [[Comma]]s: 171/170, 209/208, 351/350, 385/384, 441/440, 969/968 [[POTE generator]]: ~11/8 = 547.614 [[Map]]: [<1 13 17 -1 4 -5 3 -5|, <0 -21 -27 7 -1 16 2 17|] [[EDO]]s: 46, 57, 103, [[252edo|252]] [[Badness]]: 0.0190
Original HTML content:
<html><head><title>Sensipent family</title></head><body><!-- ws:start:WikiTextTocRule:26:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --><a href="#Sensipent">Sensipent</a><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --> | <a href="#Sensi">Sensi</a><!-- 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: --><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --> | <a href="#Heinz">Heinz</a><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --> <!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Sensipent"></a><!-- ws:end:WikiTextHeadingRule:0 -->Sensipent</h1> <a class="wiki_link" href="/Comma">Comma</a>: 78732/78125 = |2 9 -7><br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 162/125 = 443.058 cents<br /> <br /> <a class="wiki_link" href="/Map">Map</a>: [<1 6 8|, <0 -7 -9|]<br /> <a class="wiki_link" href="/EDO">EDO</a>s: <a class="wiki_link" href="/8edo">8</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/46edo">46</a>, <a class="wiki_link" href="/65edo">65</a>, <a class="wiki_link" href="/539edo">539</a><br /> <br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><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&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 <a class="wiki_link" href="/13-limit">13-limit</a> 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 /> <br /> 7-limit minimax<br /> [|1 0 0 0>, |1/13 0 0 7/13>, |5/13 0 0 9/13>, |0 0 0 1>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 7<br /> <br /> 9-limit minimax<br /> [|1 0 0 0>, |2/5 14/5 -7/5 0>,<br /> |4/5 18/5 -9/5 0>, |3/5 26/5 -13/5 0>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 9/5<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~9/7 = 443.383<br /> Algebraic generator: The <a class="wiki_link" href="/Algebraic%20number">real root</a> of x^5+x^4-4x^2+x-1, at 443.3783 cents.<br /> <br /> <a class="wiki_link" href="/Map">Map</a>: [<1 6 8 11|, <0 -7 -9 -13|]<br /> <a class="wiki_link" href="/Generator">Generators</a>: 2, 14/9<br /> <a class="wiki_link" href="/EDO">EDO</a>s: <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/27edo">27</a>, <a class="wiki_link" href="/46edo">46</a>, <a class="wiki_link" href="/249edo">249</a>, <a class="wiki_link" href="/295edo">295</a><br /> <a class="wiki_link" href="/Badness">Badness</a>: 0.0256<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="Sensi-Sensor"></a><!-- ws:end:WikiTextHeadingRule:4 -->Sensor</h2> <a class="wiki_link" href="/Comma">Comma</a>s: 126/125, 245/243, 385/384<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~9/7 = 443.294<br /> <br /> <a class="wiki_link" href="/Map">Map</a>: [<1 6 8 11 -6|, <0 -7 -9 -13 15|]<br /> <a class="wiki_link" href="/EDO">EDO</a>s: 8, 19, 27, 46, 111, 157<br /> <a class="wiki_link" href="/Badness">Badness</a>: 0.0379<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h3> --><h3 id="toc3"><a name="Sensi-Sensor-13-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-limit</h3> <a class="wiki_link" href="/Comma">Comma</a>s: 91/90, 126/125, 169/168, 385/384<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~9/7 = 443.321<br /> <br /> <a class="wiki_link" href="/Map">Map</a>: [<1 6 8 11 -6 10|, <0 -7 -9 -13 15 -10|]<br /> <a class="wiki_link" href="/EDO">EDO</a>s: <a class="wiki_link" href="/8edo">8</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/27edo">27</a>, <a class="wiki_link" href="/46edo">46</a>, <a class="wiki_link" href="/157edo">157</a><br /> <a class="wiki_link" href="/Badness">Badness</a>: 0.0256<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h2> --><h2 id="toc4"><a name="Sensi-Sensis"></a><!-- ws:end:WikiTextHeadingRule:8 -->Sensis</h2> <a class="wiki_link" href="/Comma">Comma</a>s: 56/55, 100/99, 245/243<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 443.962<br /> <br /> <a class="wiki_link" href="/Map">Map</a>: [<1 6 8 11 6|, <0 -7 -9 -13 -4|]<br /> <a class="wiki_link" href="/EDO">EDO</a>s: <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/27edo">27</a>, <a class="wiki_link" href="/73edo">73</a>, <a class="wiki_link" href="/100edo">100</a><br /> <a class="wiki_link" href="/Badness">Badness</a>: 0.0287<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h3> --><h3 id="toc5"><a name="Sensi-Sensis-13-limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->13-limit</h3> <a class="wiki_link" href="/Comma">Comma</a>s: 56/55, 78/77, 91/90, 100/99<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 443.945<br /> <br /> <a class="wiki_link" href="/Map">Map</a>: [<1 6 8 11 6 10|, <0 -7 -9 -13 -4 -10|]<br /> <a class="wiki_link" href="/EDO">EDO</a>s: 19, 27, 73, 100<br /> <a class="wiki_link" href="/Badness">Badness</a>: 0.0200<br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h2> --><h2 id="toc6"><a name="Sensi-Sensus"></a><!-- ws:end:WikiTextHeadingRule:12 -->Sensus</h2> <a class="wiki_link" href="/Comma">Comma</a>s: 126/125, 176/175, 245/243<br /> <br /> <a class="wiki_link" href="/POTE%20generator">POTE generator</a>: ~9/7 = 443.626<br /> <br /> <a class="wiki_link" href="/Map">Map</a>: [<1 6 8 11 23|, <0 -7 -9 -13 -31|]<br /> <a class="wiki_link" href="/EDO">EDO</a>s: 8, 19, 27, 46, 165<br /> <a class="wiki_link" href="/Badness">Badness</a>: 0.0295<br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h3> --><h3 id="toc7"><a name="Sensi-Sensus-13-limit"></a><!-- ws:end:WikiTextHeadingRule:14 -->13-limit</h3> <a class="wiki_link" href="/Comma">Comma</a>s: 91/90, 126/125, 169/168, 352/351<br /> <br /> <a class="wiki_link" href="/POTE%20generator">POTE generator</a>: ~9/7 = 443.559<br /> <br /> <a class="wiki_link" href="/Map">Map</a>: [<1 6 8 11 23 10|, <0 -7 -9 -13 -31 -10|]<br /> <a class="wiki_link" href="/EDO">EDO</a>s: 8, 19, 27, 46, <a class="wiki_link" href="/303edo">303</a><br /> <a class="wiki_link" href="/Badness">Badness</a>: 0.0208<br /> <br /> <!-- ws:start:WikiTextHeadingRule:16:<h1> --><h1 id="toc8"><a name="Heinz"></a><!-- ws:end:WikiTextHeadingRule:16 -->Heinz</h1> <a class="wiki_link" href="/Comma">Comma</a>s: 78732/78125, 1029/1024<br /> <br /> <a class="wiki_link" href="/POTE%20generator">POTE generator</a>: ~48/35 = 546.815<br /> <br /> <a class="wiki_link" href="/Map">Map</a>: [<1 13 17 -1|, <0 -21 -27 7|]<br /> <a class="wiki_link" href="/EDO">EDO</a>s: 46, <a class="wiki_link" href="/103edo">103</a>, <a class="wiki_link" href="/149edo">149</a><br /> <a class="wiki_link" href="/Badness">Badness</a>: 0.1154<br /> <br /> <!-- ws:start:WikiTextHeadingRule:18:<h2> --><h2 id="toc9"><a name="Heinz-11-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->11-limit</h2> <a class="wiki_link" href="/Comma">Comma</a>s: 385/384, 441/440, 88208/87500<br /> <br /> <a class="wiki_link" href="/POTE%20generator">POTE generator</a>: ~11/8 = 547.631<br /> <br /> <a class="wiki_link" href="/Map">Map</a>: [<1 13 17 -1 4|, <0 -21 -27 7 -1|]<br /> <a class="wiki_link" href="/EDO">EDO</a>s: 46, 103, 149<br /> <a class="wiki_link" href="/Badness">Badness</a>: 0.0424<br /> <br /> <!-- ws:start:WikiTextHeadingRule:20:<h2> --><h2 id="toc10"><a name="Heinz-13-limit"></a><!-- ws:end:WikiTextHeadingRule:20 -->13-limit</h2> <a class="wiki_link" href="/Comma">Comma</a>s: 351/350, 385/384, 441/440, 847/845<br /> <br /> <a class="wiki_link" href="/POTE%20generator">POTE generator</a>: ~11/8 = 547.629<br /> <br /> <a class="wiki_link" href="/Map">Map</a>: [<1 13 17 -1 4 -5|, <0 -21 -27 7 -1 16|]<br /> <a class="wiki_link" href="/EDO">EDO</a>s: 46, 57, 103, 149<br /> <a class="wiki_link" href="/Badness">Badness</a>: 0.0258<br /> <br /> <!-- ws:start:WikiTextHeadingRule:22:<h2> --><h2 id="toc11"><a name="Heinz-17-limit"></a><!-- ws:end:WikiTextHeadingRule:22 -->17-limit</h2> <a class="wiki_link" href="/Comma">Comma</a>s: 273/272, 351/350, 385/384, 441/440, 847/845<br /> <br /> <a class="wiki_link" href="/POTE%20generator">POTE generator</a>: ~11/8 = 547.635<br /> <br /> <a class="wiki_link" href="/Map">Map</a>: [<1 13 17 -1 4 -5 3|, <0 -21 -27 7 -1 16 2|]<br /> <a class="wiki_link" href="/EDO">EDO</a>s: 46, <a class="wiki_link" href="/57edo">57</a>, 103, 149<br /> <a class="wiki_link" href="/Badness">Badness</a>: 0.0185<br /> <br /> <!-- ws:start:WikiTextHeadingRule:24:<h2> --><h2 id="toc12"><a name="Heinz-19-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->19-limit</h2> <a class="wiki_link" href="/Comma">Comma</a>s: 171/170, 209/208, 351/350, 385/384, 441/440, 969/968<br /> <br /> <a class="wiki_link" href="/POTE%20generator">POTE generator</a>: ~11/8 = 547.614<br /> <br /> <a class="wiki_link" href="/Map">Map</a>: [<1 13 17 -1 4 -5 3 -5|, <0 -21 -27 7 -1 16 2 17|]<br /> <a class="wiki_link" href="/EDO">EDO</a>s: 46, 57, 103, <a class="wiki_link" href="/252edo">252</a><br /> <a class="wiki_link" href="/Badness">Badness</a>: 0.0190</body></html>