Sensipent family
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[[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 temperament= 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 Badness:
Original HTML content:
<html><head><title>Sensipent family</title></head><body><!-- ws:start:WikiTextTocRule:20:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --><a href="#Sensipent">Sensipent</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> | <a href="#Sensi temperament">Sensi temperament</a><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --> | <a href="#Heinz">Heinz</a><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --> <!-- ws:end:WikiTextTocRule:31 --><br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><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: [<1 6 8|, <0 -7 -9|]<br /> EDOs: 8, 19, 46, 65, 539<br /> <br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Sensi temperament"></a><!-- ws:end:WikiTextHeadingRule:2 -->Sensi temperament</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 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 /> <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: Calista, the <a class="wiki_link" href="/Algebraic%20number">real root</a> of x^7-2x^2-1, at 340.6467 cents. <br /> <br /> Map: [<1 6 8 11|, <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 /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="Sensi temperament-Sensor"></a><!-- ws:end:WikiTextHeadingRule:4 -->Sensor</h2> Commas: 126/125, 245/243, 385/384<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~9/7 = 443.294<br /> <br /> Map: [<1 6 8 11 -6|, <0 -7 -9 -13 15|]<br /> EDOs: 8, 19, 27, 46, 111, 157<br /> Badness: 0.0379<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h3> --><h3 id="toc3"><a name="Sensi temperament-Sensor-13-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-limit</h3> Commas: 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 /> Map: [<1 6 8 11 -6 10|, <0 -7 -9 -13 15 -10|]<br /> EDOs: 8, 19, 27, 46, 157<br /> Badness: 0.0256<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h2> --><h2 id="toc4"><a name="Sensi temperament-Sensis"></a><!-- ws:end:WikiTextHeadingRule:8 -->Sensis</h2> Commas: 56/55, 100/99, 245/243<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 443.962<br /> <br /> Map: [<1 6 8 11 6|, <0 -7 -9 -13 -4|]<br /> EDOs: 19, 27, 73, 100<br /> Badness: 0.0287<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h3> --><h3 id="toc5"><a name="Sensi temperament-Sensis-13-limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->13-limit</h3> Commas: 56/55, 78/77, 91/90, 100/99<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 443.945<br /> <br /> Map: [<1 6 8 11 6 10|, <0 -7 -9 -13 -4 -10|]<br /> EDOs: 19, 27, 73, 100<br /> Badness: 0.0200<br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h2> --><h2 id="toc6"><a name="Sensi temperament-Sensus"></a><!-- ws:end:WikiTextHeadingRule:12 -->Sensus</h2> Commas: 126/125, 176/175, 245/243<br /> <br /> POTE generator: ~9/7 = 443.626<br /> <br /> Map: [<1 6 8 11 23|, <0 -7 -9 -13 -31|]<br /> EDOs: 8, 19, 27, 46, 165<br /> Badness: 0.0295<br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h3> --><h3 id="toc7"><a name="Sensi temperament-Sensus-13-limit"></a><!-- ws:end:WikiTextHeadingRule:14 -->13-limit</h3> Commas: 91/90, 126/125, 169/168, 352/351<br /> <br /> POTE generator: ~9/7 = 443.559<br /> <br /> Map: [<1 6 8 11 23 10|, <0 -7 -9 -13 -31 -10|]<br /> EDOs: 8, 19, 27, 46, 303<br /> Badness: 0.0208<br /> <br /> <!-- ws:start:WikiTextHeadingRule:16:<h1> --><h1 id="toc8"><a name="Heinz"></a><!-- ws:end:WikiTextHeadingRule:16 -->Heinz</h1> Commas: 78732/78125, 1029/1024<br /> <br /> POTE generator: ~48/35 = 546.815<br /> <br /> Map: [<1 13 17 -1|, <0 -21 -27 7|]<br /> EDOs: 46, 103, 149<br /> Badness: 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> Commas: 385/384, 441/440, 88208/87500<br /> <br /> POTE generator: ~11/8 = 547.631<br /> <br /> Map: [<1 13 17 -1 4|, <0 -21 -27 7 -1|]<br /> EDOs: 46, 103, 149<br /> Badness: 0.0424<br /> Badness:</body></html>