Sensipent family: Difference between revisions

Revision as of 20:16, 2 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 genewardsmith and made on 2011-09-02 20:16:08 UTC.

The original revision id was 250423972.

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 = 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:&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 --><br />
<!-- 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<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>: [&lt;1 6 8|, &lt;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:&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 />
<br />
<a class="wiki_link" href="/Comma">Commas</a>: 126/125, 245/243<br />
<br />
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 />
<br />
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 />
<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>: [&lt;1 6 8 11|, &lt;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:&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 />
<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>: [&lt;1 6 8 11 -6|, &lt;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:&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 />
<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>: [&lt;1 6 8 11 -6 10|, &lt;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:&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 />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>:  443.962<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="/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:&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 />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 443.945<br />
<br />
<a class="wiki_link" href="/Map">Map</a>: [&lt;1 6 8 11 6 10|, &lt;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:&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 />
<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>: [&lt;1 6 8 11 23|, &lt;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:&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 />
<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>: [&lt;1 6 8 11 23 10|, &lt;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:&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 />
<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>: [&lt;1 13 17 -1|, &lt;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:&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 />
<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>: [&lt;1 13 17 -1 4|, &lt;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:&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 />
<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>: [&lt;1 13 17 -1 4 -5|, &lt;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:&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 />
<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>: [&lt;1 13 17 -1 4 -5 3|, &lt;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:&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 />
<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>: [&lt;1 13 17 -1 4 -5 3 -5|, &lt;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>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2011-04-22 02:57:14 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-02 20:16:08 UTC</tt>.<br>
-: The original revision id was <tt>222227920</tt>.<br>
+: The original revision id was <tt>250423972</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>
@@ Line 32: / Line 32: @@
 [[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.
+Algebraic generator: The [[Algebraic number|real root]] of x^5+x^4-4x^2+x-1, at 443.3783 cents.
 [[Map]]: [&lt;1 6 8 11|, &lt;0 -7 -9 -13|]
@@ Line 164: / Line 164: @@
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~9/7 = 443.383&lt;br /&gt;
-Algebraic generator: Calista, the &lt;a class="wiki_link" href="/Algebraic%20number"&gt;real root&lt;/a&gt; of x^7-2x^2-1, at 340.6467 cents. &lt;br /&gt;
+Algebraic generator: The &lt;a class="wiki_link" href="/Algebraic%20number"&gt;real root&lt;/a&gt; of x^5+x^4-4x^2+x-1, at 443.3783 cents. &lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/Map"&gt;Map&lt;/a&gt;: [&amp;lt;1 6 8 11|, &amp;lt;0 -7 -9 -13|]&lt;br /&gt;

Sensipent family: Difference between revisions

Revision as of 20:16, 2 September 2011

IMPORTED REVISION FROM WIKISPACES

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