Miracle extensions: Difference between revisions

Revision as of 23:32, 10 November 2012

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This revision was by author genewardsmith and made on 2012-11-10 23:32:19 UTC.

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Original Wikitext content:

The basic 7-limit [[miracle]] temperament has various extensions to the 11 and 13 limits.

=Tuning Spectra=
==Spectrum of Miraculous Tunings by Eigenmonzos== 

Gencom: [2 15/14; 105/104 144/143 196/195 275/273]
Gencom map: [<1 1 3 3 2 4|, <0 6 -7 -2 15 -3|]
||~ Eigenmonzo ||~ Secor ||
|| 16/15 || 111.731 ||
|| 13/10 || 113.553 ||
|| 8/7 || 115.587 ||
|| 11/9 || 115.803 ||
|| 5/4 || 116.241 ||
|| 15/11 || 116.441 ||
|| 7/5 || 116.502 ||
|| |0 -27 25 5> || 116.573 (7 limit least squares) ||
|| |0 -19 20> || 116.578 (5 limit least squares) ||
|| 6/5 || 116.588 (5 and 7 limit minimax) ||
|| 11/10 || 116.591 ||
|| 12/11 || 116.596 ||
|| 14/11 || 116.617 ||
|| 7/6 || 116.641 ||
|| |0 17 -11 -6 11> || 116.672 (11 limit least squares) ||
|| 10/9 || 116.716 (9, 11 and 13 limit minimax) ||
|| |0 117 -44 -19> || 116.721 (9 limit least squares) ||
|| 11/8 || 116.755 ||
|| 9/7 || 116.792 ||
|| |0 127 -84 -36 100 -44> || 116.820 (15 limit least squares) ||
|| |0 141 -70 -35 84 -42> || 116.846 (13 limit least squares) ||
|| 4/3 || 116.993 (15 limit minimax) ||
|| 13/11 || 117.266 ||
|| 18/13 || 117.559 ||
|| 13/12 || 117.936 ||
|| 15/14 || 119.443 ||
|| 16/13 || 119.824 ||
|| 15/13 || 123.871 ||
|| 14/13 || 128.298 ||

==Spectrum of Benediction Tunings by Eigenmonzos== 

Gencom: [2 15/14 225/224 243/242 351/350 441/440]
Gencom map: [<1 1 3 3 2 7|, <0 6 -7 -2 15 -34|]
||~ Eigenmonzo ||~ Secor ||
|| 16/15 || 111.731 ||
|| 8/7 || 115.587 ||
|| 11/9 || 115.803 ||
|| 5/4 || 116.241 ||
|| 15/11 || 116.441 ||
|| 16/13 || 116.455 ||
|| 7/5 || 116.502 ||
|| 14/13 || 116.509 ||
|| 13/10 || 116.511 ||
|| 13/12 || 116.536 ||
|| 13/11 || 116.547 ||
|| |0 -234 39 4 -115 228> || 116.56309 (13 limit least squares) ||
|| |0 -251 22 5 -131 261> || 116.56348 (15 limit least squares) ||
|| |0 -27 25 5> || 116.573 (7 limit least squares) ||
|| |0 -19 20> || 116.578 (5 limit least squares) ||
|| 6/5 || 116.588 (5, 7 and 15 limit minimax) ||
|| 11/10 || 116.591 ||
|| 18/13 || 116.595 (13 limit minimax) ||
|| 12/11 || 116.596 ||
|| 15/13 || 116.598 ||
|| 14/11 || 116.617 ||
|| 7/6 || 116.641 ||
|| |0 17 -11 -6 11> || 116.672 (11 limit least squares) ||
|| 10/9 || 116.716 (9 and 11 limit minimax) ||
|| |0 117 -44 -19> || 116.721 (9 limit least squares) ||
|| 11/8 || 116.755 ||
|| 9/7 || 116.792 ||
|| 4/3 || 116.993 ||
|| 15/14 || 119.443 ||

==Spectrum of Manna Tunings by Eigenmonzos== 

Gencom: [2 15/14; 225/224 243/242 325/324 385/384]
Gencom map: [<1 1 3 3 2 0|, <0 6 -7 -2 15 38|]
||~ Eigenmonzo ||~ Secor ||
|| 16/15 || 111.731 ||
|| 8/7 || 115.587 ||
|| 11/9 || 115.803 ||
|| 5/4 || 116.241 ||
|| 15/11 || 116.441 ||
|| 7/5 || 116.502 ||
|| |0 -27 25 5> || 116.573 (7 limit least squares) ||
|| |0 -19 20> || 116.578 (5 limit least squares) ||
|| 6/5 || 116.588 (5 and 7 limit minimax) ||
|| 11/10 || 116.591 ||
|| 12/11 || 116.596 ||
|| 14/11 || 116.617 ||
|| 7/6 || 116.641 ||
|| |0 17 -11 -6 11> || 116.672 (11 limit least squares) ||
|| 10/9 || 116.716 (9 and 11 limit minimax) ||
|| |0 117 -44 -19> || 116.721 (9 limit least squares) ||
|| 15/13 || 116.725 (15 limit minimax) ||
|| 11/8 || 116.755 ||
|| 13/10 || 116.760 (13 limit minimax) ||
|| |0 -37 -166 -77 59 243> || 116.764 (15 limit least squares) ||
|| |0 18 -111 -76 43 204> || 116.780 (13 limit least squares) ||
|| 9/7 || 116.792 ||
|| 14/13 || 116.793 ||
|| 18/13 || 116.793 ||
|| 13/12 || 116.830 ||
|| 16/13 || 116.856 ||
|| 13/11 || 116.922 ||
|| 4/3 || 116.993 ||
|| 15/14 || 119.443 ||

==Spectrum of Revelation Tunings by Eigenmonzos== 

Gencom: [2 15/14; 66/65 99/98 105/104 1001/1000]
Gencom map: [<1 1 3 3 5 4|, <0 6 -7 -2 -16 -3|]
||~ Eigenmonzo ||~ Secor ||
|| 16/15 || 111.731 ||
|| 13/10 || 113.553 ||
|| 13/11 || 114.555 ||
|| 11/10 || 115.000 ||
|| 14/11 || 115.536 ||
|| 11/8 || 115.543 ||
|| 8/7 || 115.587 ||
|| 15/11 || 115.797 ||
|| 12/11 || 115.938 ||
|| 11/9 || 116.164 (11, 13 and 15 limit minimax) ||
|| |0 -195 35 5 89> || 116.198 (11 limit least squares) ||
|| |0 -251 22 5 117 13> || 116.229 (15 limit least squares) ||
|| 5/4 || 116.241 ||
|| |0 -234 39 4 102 11> || 116.249 (13 limit least squares) ||
|| 7/5 || 116.502 ||
|| |0 -27 25 5> || 116.573 (7 limit least squares) ||
|| |0 -19 20> || 116.578 (5 limit least squares) ||
|| 6/5 || 116.588 (5 and 7 limit minimax) ||
|| 7/6 || 116.641 ||
|| 10/9 || 116.716 (9 limit minimax) ||
|| |0 117 -44 -19> || 116.721 (9 limit least squares) ||
|| 9/7 || 116.792 ||
|| 4/3 || 116.993 ||
|| 18/13 || 117.559 ||
|| 13/12 || 117.936 ||
|| 15/14 || 119.443 ||
|| 16/13 || 119.824 ||
|| 15/13 || 123.871 ||
|| 14/13 || 128.298 ||

Original HTML content:

<html><head><title>Miracle extensions</title></head><body>The basic 7-limit <a class="wiki_link" href="/miracle">miracle</a> temperament has various extensions to the 11 and 13 limits.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Tuning Spectra"></a><!-- ws:end:WikiTextHeadingRule:0 -->Tuning Spectra</h1>
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Tuning Spectra-Spectrum of Miraculous Tunings by Eigenmonzos"></a><!-- ws:end:WikiTextHeadingRule:2 -->Spectrum of Miraculous Tunings by Eigenmonzos</h2>
 <br />
Gencom: [2 15/14; 105/104 144/143 196/195 275/273]<br />
Gencom map: [&lt;1 1 3 3 2 4|, &lt;0 6 -7 -2 15 -3|]<br />


<table class="wiki_table">
    <tr>
        <th>Eigenmonzo<br />
</th>
        <th>Secor<br />
</th>
    </tr>
    <tr>
        <td>16/15<br />
</td>
        <td>111.731<br />
</td>
    </tr>
    <tr>
        <td>13/10<br />
</td>
        <td>113.553<br />
</td>
    </tr>
    <tr>
        <td>8/7<br />
</td>
        <td>115.587<br />
</td>
    </tr>
    <tr>
        <td>11/9<br />
</td>
        <td>115.803<br />
</td>
    </tr>
    <tr>
        <td>5/4<br />
</td>
        <td>116.241<br />
</td>
    </tr>
    <tr>
        <td>15/11<br />
</td>
        <td>116.441<br />
</td>
    </tr>
    <tr>
        <td>7/5<br />
</td>
        <td>116.502<br />
</td>
    </tr>
    <tr>
        <td>|0 -27 25 5&gt;<br />
</td>
        <td>116.573 (7 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>|0 -19 20&gt;<br />
</td>
        <td>116.578 (5 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>6/5<br />
</td>
        <td>116.588 (5 and 7 limit minimax)<br />
</td>
    </tr>
    <tr>
        <td>11/10<br />
</td>
        <td>116.591<br />
</td>
    </tr>
    <tr>
        <td>12/11<br />
</td>
        <td>116.596<br />
</td>
    </tr>
    <tr>
        <td>14/11<br />
</td>
        <td>116.617<br />
</td>
    </tr>
    <tr>
        <td>7/6<br />
</td>
        <td>116.641<br />
</td>
    </tr>
    <tr>
        <td>|0 17 -11 -6 11&gt;<br />
</td>
        <td>116.672 (11 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>10/9<br />
</td>
        <td>116.716 (9, 11 and 13 limit minimax)<br />
</td>
    </tr>
    <tr>
        <td>|0 117 -44 -19&gt;<br />
</td>
        <td>116.721 (9 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>11/8<br />
</td>
        <td>116.755<br />
</td>
    </tr>
    <tr>
        <td>9/7<br />
</td>
        <td>116.792<br />
</td>
    </tr>
    <tr>
        <td>|0 127 -84 -36 100 -44&gt;<br />
</td>
        <td>116.820 (15 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>|0 141 -70 -35 84 -42&gt;<br />
</td>
        <td>116.846 (13 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>4/3<br />
</td>
        <td>116.993 (15 limit minimax)<br />
</td>
    </tr>
    <tr>
        <td>13/11<br />
</td>
        <td>117.266<br />
</td>
    </tr>
    <tr>
        <td>18/13<br />
</td>
        <td>117.559<br />
</td>
    </tr>
    <tr>
        <td>13/12<br />
</td>
        <td>117.936<br />
</td>
    </tr>
    <tr>
        <td>15/14<br />
</td>
        <td>119.443<br />
</td>
    </tr>
    <tr>
        <td>16/13<br />
</td>
        <td>119.824<br />
</td>
    </tr>
    <tr>
        <td>15/13<br />
</td>
        <td>123.871<br />
</td>
    </tr>
    <tr>
        <td>14/13<br />
</td>
        <td>128.298<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Tuning Spectra-Spectrum of Benediction Tunings by Eigenmonzos"></a><!-- ws:end:WikiTextHeadingRule:4 -->Spectrum of Benediction Tunings by Eigenmonzos</h2>
 <br />
Gencom: [2 15/14 225/224 243/242 351/350 441/440]<br />
Gencom map: [&lt;1 1 3 3 2 7|, &lt;0 6 -7 -2 15 -34|]<br />


<table class="wiki_table">
    <tr>
        <th>Eigenmonzo<br />
</th>
        <th>Secor<br />
</th>
    </tr>
    <tr>
        <td>16/15<br />
</td>
        <td>111.731<br />
</td>
    </tr>
    <tr>
        <td>8/7<br />
</td>
        <td>115.587<br />
</td>
    </tr>
    <tr>
        <td>11/9<br />
</td>
        <td>115.803<br />
</td>
    </tr>
    <tr>
        <td>5/4<br />
</td>
        <td>116.241<br />
</td>
    </tr>
    <tr>
        <td>15/11<br />
</td>
        <td>116.441<br />
</td>
    </tr>
    <tr>
        <td>16/13<br />
</td>
        <td>116.455<br />
</td>
    </tr>
    <tr>
        <td>7/5<br />
</td>
        <td>116.502<br />
</td>
    </tr>
    <tr>
        <td>14/13<br />
</td>
        <td>116.509<br />
</td>
    </tr>
    <tr>
        <td>13/10<br />
</td>
        <td>116.511<br />
</td>
    </tr>
    <tr>
        <td>13/12<br />
</td>
        <td>116.536<br />
</td>
    </tr>
    <tr>
        <td>13/11<br />
</td>
        <td>116.547<br />
</td>
    </tr>
    <tr>
        <td>|0 -234 39 4 -115 228&gt;<br />
</td>
        <td>116.56309 (13 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>|0 -251 22 5 -131 261&gt;<br />
</td>
        <td>116.56348 (15 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>|0 -27 25 5&gt;<br />
</td>
        <td>116.573 (7 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>|0 -19 20&gt;<br />
</td>
        <td>116.578 (5 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>6/5<br />
</td>
        <td>116.588 (5, 7 and 15 limit minimax)<br />
</td>
    </tr>
    <tr>
        <td>11/10<br />
</td>
        <td>116.591<br />
</td>
    </tr>
    <tr>
        <td>18/13<br />
</td>
        <td>116.595 (13 limit minimax)<br />
</td>
    </tr>
    <tr>
        <td>12/11<br />
</td>
        <td>116.596<br />
</td>
    </tr>
    <tr>
        <td>15/13<br />
</td>
        <td>116.598<br />
</td>
    </tr>
    <tr>
        <td>14/11<br />
</td>
        <td>116.617<br />
</td>
    </tr>
    <tr>
        <td>7/6<br />
</td>
        <td>116.641<br />
</td>
    </tr>
    <tr>
        <td>|0 17 -11 -6 11&gt;<br />
</td>
        <td>116.672 (11 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>10/9<br />
</td>
        <td>116.716 (9 and 11 limit minimax)<br />
</td>
    </tr>
    <tr>
        <td>|0 117 -44 -19&gt;<br />
</td>
        <td>116.721 (9 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>11/8<br />
</td>
        <td>116.755<br />
</td>
    </tr>
    <tr>
        <td>9/7<br />
</td>
        <td>116.792<br />
</td>
    </tr>
    <tr>
        <td>4/3<br />
</td>
        <td>116.993<br />
</td>
    </tr>
    <tr>
        <td>15/14<br />
</td>
        <td>119.443<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Tuning Spectra-Spectrum of Manna Tunings by Eigenmonzos"></a><!-- ws:end:WikiTextHeadingRule:6 -->Spectrum of Manna Tunings by Eigenmonzos</h2>
 <br />
Gencom: [2 15/14; 225/224 243/242 325/324 385/384]<br />
Gencom map: [&lt;1 1 3 3 2 0|, &lt;0 6 -7 -2 15 38|]<br />


<table class="wiki_table">
    <tr>
        <th>Eigenmonzo<br />
</th>
        <th>Secor<br />
</th>
    </tr>
    <tr>
        <td>16/15<br />
</td>
        <td>111.731<br />
</td>
    </tr>
    <tr>
        <td>8/7<br />
</td>
        <td>115.587<br />
</td>
    </tr>
    <tr>
        <td>11/9<br />
</td>
        <td>115.803<br />
</td>
    </tr>
    <tr>
        <td>5/4<br />
</td>
        <td>116.241<br />
</td>
    </tr>
    <tr>
        <td>15/11<br />
</td>
        <td>116.441<br />
</td>
    </tr>
    <tr>
        <td>7/5<br />
</td>
        <td>116.502<br />
</td>
    </tr>
    <tr>
        <td>|0 -27 25 5&gt;<br />
</td>
        <td>116.573 (7 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>|0 -19 20&gt;<br />
</td>
        <td>116.578 (5 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>6/5<br />
</td>
        <td>116.588 (5 and 7 limit minimax)<br />
</td>
    </tr>
    <tr>
        <td>11/10<br />
</td>
        <td>116.591<br />
</td>
    </tr>
    <tr>
        <td>12/11<br />
</td>
        <td>116.596<br />
</td>
    </tr>
    <tr>
        <td>14/11<br />
</td>
        <td>116.617<br />
</td>
    </tr>
    <tr>
        <td>7/6<br />
</td>
        <td>116.641<br />
</td>
    </tr>
    <tr>
        <td>|0 17 -11 -6 11&gt;<br />
</td>
        <td>116.672 (11 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>10/9<br />
</td>
        <td>116.716 (9 and 11 limit minimax)<br />
</td>
    </tr>
    <tr>
        <td>|0 117 -44 -19&gt;<br />
</td>
        <td>116.721 (9 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>15/13<br />
</td>
        <td>116.725 (15 limit minimax)<br />
</td>
    </tr>
    <tr>
        <td>11/8<br />
</td>
        <td>116.755<br />
</td>
    </tr>
    <tr>
        <td>13/10<br />
</td>
        <td>116.760 (13 limit minimax)<br />
</td>
    </tr>
    <tr>
        <td>|0 -37 -166 -77 59 243&gt;<br />
</td>
        <td>116.764 (15 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>|0 18 -111 -76 43 204&gt;<br />
</td>
        <td>116.780 (13 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>9/7<br />
</td>
        <td>116.792<br />
</td>
    </tr>
    <tr>
        <td>14/13<br />
</td>
        <td>116.793<br />
</td>
    </tr>
    <tr>
        <td>18/13<br />
</td>
        <td>116.793<br />
</td>
    </tr>
    <tr>
        <td>13/12<br />
</td>
        <td>116.830<br />
</td>
    </tr>
    <tr>
        <td>16/13<br />
</td>
        <td>116.856<br />
</td>
    </tr>
    <tr>
        <td>13/11<br />
</td>
        <td>116.922<br />
</td>
    </tr>
    <tr>
        <td>4/3<br />
</td>
        <td>116.993<br />
</td>
    </tr>
    <tr>
        <td>15/14<br />
</td>
        <td>119.443<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Tuning Spectra-Spectrum of Revelation Tunings by Eigenmonzos"></a><!-- ws:end:WikiTextHeadingRule:8 -->Spectrum of Revelation Tunings by Eigenmonzos</h2>
 <br />
Gencom: [2 15/14; 66/65 99/98 105/104 1001/1000]<br />
Gencom map: [&lt;1 1 3 3 5 4|, &lt;0 6 -7 -2 -16 -3|]<br />


<table class="wiki_table">
    <tr>
        <th>Eigenmonzo<br />
</th>
        <th>Secor<br />
</th>
    </tr>
    <tr>
        <td>16/15<br />
</td>
        <td>111.731<br />
</td>
    </tr>
    <tr>
        <td>13/10<br />
</td>
        <td>113.553<br />
</td>
    </tr>
    <tr>
        <td>13/11<br />
</td>
        <td>114.555<br />
</td>
    </tr>
    <tr>
        <td>11/10<br />
</td>
        <td>115.000<br />
</td>
    </tr>
    <tr>
        <td>14/11<br />
</td>
        <td>115.536<br />
</td>
    </tr>
    <tr>
        <td>11/8<br />
</td>
        <td>115.543<br />
</td>
    </tr>
    <tr>
        <td>8/7<br />
</td>
        <td>115.587<br />
</td>
    </tr>
    <tr>
        <td>15/11<br />
</td>
        <td>115.797<br />
</td>
    </tr>
    <tr>
        <td>12/11<br />
</td>
        <td>115.938<br />
</td>
    </tr>
    <tr>
        <td>11/9<br />
</td>
        <td>116.164 (11, 13 and 15 limit minimax)<br />
</td>
    </tr>
    <tr>
        <td>|0 -195 35 5 89&gt;<br />
</td>
        <td>116.198 (11 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>|0 -251 22 5 117 13&gt;<br />
</td>
        <td>116.229 (15 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>5/4<br />
</td>
        <td>116.241<br />
</td>
    </tr>
    <tr>
        <td>|0 -234 39 4 102 11&gt;<br />
</td>
        <td>116.249 (13 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>7/5<br />
</td>
        <td>116.502<br />
</td>
    </tr>
    <tr>
        <td>|0 -27 25 5&gt;<br />
</td>
        <td>116.573 (7 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>|0 -19 20&gt;<br />
</td>
        <td>116.578 (5 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>6/5<br />
</td>
        <td>116.588 (5 and 7 limit minimax)<br />
</td>
    </tr>
    <tr>
        <td>7/6<br />
</td>
        <td>116.641<br />
</td>
    </tr>
    <tr>
        <td>10/9<br />
</td>
        <td>116.716 (9 limit minimax)<br />
</td>
    </tr>
    <tr>
        <td>|0 117 -44 -19&gt;<br />
</td>
        <td>116.721 (9 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>9/7<br />
</td>
        <td>116.792<br />
</td>
    </tr>
    <tr>
        <td>4/3<br />
</td>
        <td>116.993<br />
</td>
    </tr>
    <tr>
        <td>18/13<br />
</td>
        <td>117.559<br />
</td>
    </tr>
    <tr>
        <td>13/12<br />
</td>
        <td>117.936<br />
</td>
    </tr>
    <tr>
        <td>15/14<br />
</td>
        <td>119.443<br />
</td>
    </tr>
    <tr>
        <td>16/13<br />
</td>
        <td>119.824<br />
</td>
    </tr>
    <tr>
        <td>15/13<br />
</td>
        <td>123.871<br />
</td>
    </tr>
    <tr>
        <td>14/13<br />
</td>
        <td>128.298<br />
</td>
    </tr>
</table>

</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>2012-11-10 14:23:32 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-11-10 23:32:19 UTC</tt>.<br>
-: The original revision id was <tt>381110574</tt>.<br>
+: The original revision id was <tt>381177888</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 60: / Line 60: @@
 || 13/12 || 116.536 ||
 || 13/11 || 116.547 ||
+|| |0 -234 39 4 -115 228&gt; || 116.56309 (13 limit least squares) ||
+|| |0 -251 22 5 -131 261&gt; || 116.56348 (15 limit least squares) ||
+|| |0 -27 25 5&gt; || 116.573 (7 limit least squares) ||
+|| |0 -19 20&gt; || 116.578 (5 limit least squares) ||
 || 6/5 || 116.588 (5, 7 and 15 limit minimax) ||
 || 11/10 || 116.591 ||
@@ Line 67: / Line 71: @@
 || 14/11 || 116.617 ||
 || 7/6 || 116.641 ||
+|| |0 17 -11 -6 11&gt; || 116.672 (11 limit least squares) ||
 || 10/9 || 116.716 (9 and 11 limit minimax) ||
+|| |0 117 -44 -19&gt; || 116.721 (9 limit least squares) ||
 || 11/8 || 116.755 ||
 || 9/7 || 116.792 ||
@@ Line 84: / Line 90: @@
 || 15/11 || 116.441 ||
 || 7/5 || 116.502 ||
+|| |0 -27 25 5&gt; || 116.573 (7 limit least squares) ||
+|| |0 -19 20&gt; || 116.578 (5 limit least squares) ||
 || 6/5 || 116.588 (5 and 7 limit minimax) ||
 || 11/10 || 116.591 ||
@@ Line 89: / Line 97: @@
 || 14/11 || 116.617 ||
 || 7/6 || 116.641 ||
+|| |0 17 -11 -6 11&gt; || 116.672 (11 limit least squares) ||
 || 10/9 || 116.716 (9 and 11 limit minimax) ||
+|| |0 117 -44 -19&gt; || 116.721 (9 limit least squares) ||
 || 15/13 || 116.725 (15 limit minimax) ||
 || 11/8 || 116.755 ||
 || 13/10 || 116.760 (13 limit minimax) ||
+|| |0 -37 -166 -77 59 243&gt; || 116.764 (15 limit least squares) ||
+|| |0 18 -111 -76 43 204&gt; || 116.780 (13 limit least squares) ||
 || 9/7 || 116.792 ||
 || 14/13 || 116.793 ||
@@ Line 117: / Line 129: @@
 || 12/11 || 115.938 ||
 || 11/9 || 116.164 (11, 13 and 15 limit minimax) ||
+|| |0 -195 35 5 89&gt; || 116.198 (11 limit least squares) ||
+|| |0 -251 22 5 117 13&gt; || 116.229 (15 limit least squares) ||
 || 5/4 || 116.241 ||
+|| |0 -234 39 4 102 11&gt; || 116.249 (13 limit least squares) ||
 || 7/5 || 116.502 ||
+|| |0 -27 25 5&gt; || 116.573 (7 limit least squares) ||
+|| |0 -19 20&gt; || 116.578 (5 limit least squares) ||
 || 6/5 || 116.588 (5 and 7 limit minimax) ||
 || 7/6 || 116.641 ||
 || 10/9 || 116.716 (9 limit minimax) ||
+|| |0 117 -44 -19&gt; || 116.721 (9 limit least squares) ||
 || 9/7 || 116.792 ||
 || 4/3 || 116.993 ||
@@ Line 129: / Line 147: @@
 || 16/13 || 119.824 ||
 || 15/13 || 123.871 ||
-|| 14/13 || 128.298 ||
+|| 14/13 || 128.298 ||</pre></div>
-</pre></div>
 <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;Miracle extensions&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The basic 7-limit &lt;a class="wiki_link" href="/miracle"&gt;miracle&lt;/a&gt; temperament has various extensions to the 11 and 13 limits.&lt;br /&gt;
@@ Line 402: / Line 419: @@
 &lt;/td&gt;
          &lt;td&gt;116.547&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;|0 -234 39 4 -115 228&amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;116.56309 (13 limit least squares)&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;|0 -251 22 5 -131 261&amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;116.56348 (15 limit least squares)&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;|0 -27 25 5&amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;116.573 (7 limit least squares)&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;|0 -19 20&amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;116.578 (5 limit least squares)&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 444: / Line 485: @@
 &lt;/td&gt;
          &lt;td&gt;116.641&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;|0 17 -11 -6 11&amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;116.672 (11 limit least squares)&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 450: / Line 497: @@
 &lt;/td&gt;
          &lt;td&gt;116.716 (9 and 11 limit minimax)&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;|0 117 -44 -19&amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;116.721 (9 limit least squares)&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 526: / Line 579: @@
 &lt;/td&gt;
          &lt;td&gt;116.502&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;|0 -27 25 5&amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;116.573 (7 limit least squares)&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;|0 -19 20&amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;116.578 (5 limit least squares)&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 556: / Line 621: @@
 &lt;/td&gt;
          &lt;td&gt;116.641&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;|0 17 -11 -6 11&amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;116.672 (11 limit least squares)&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 562: / Line 633: @@
 &lt;/td&gt;
          &lt;td&gt;116.716 (9 and 11 limit minimax)&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;|0 117 -44 -19&amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;116.721 (9 limit least squares)&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 580: / Line 657: @@
 &lt;/td&gt;
          &lt;td&gt;116.760 (13 limit minimax)&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;|0 -37 -166 -77 59 243&amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;116.764 (15 limit least squares)&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;|0 18 -111 -76 43 204&amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;116.780 (13 limit least squares)&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 704: / Line 793: @@
 &lt;/td&gt;
          &lt;td&gt;116.164 (11, 13 and 15 limit minimax)&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;|0 -195 35 5 89&amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;116.198 (11 limit least squares)&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;|0 -251 22 5 117 13&amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;116.229 (15 limit least squares)&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 710: / Line 811: @@
 &lt;/td&gt;
          &lt;td&gt;116.241&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;|0 -234 39 4 102 11&amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;116.249 (13 limit least squares)&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 716: / Line 823: @@
 &lt;/td&gt;
          &lt;td&gt;116.502&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;|0 -27 25 5&amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;116.573 (7 limit least squares)&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;|0 -19 20&amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;116.578 (5 limit least squares)&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 734: / Line 853: @@
 &lt;/td&gt;
          &lt;td&gt;116.716 (9 limit minimax)&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;|0 117 -44 -19&amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;116.721 (9 limit least squares)&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;

Miracle extensions: Difference between revisions

Revision as of 23:32, 10 November 2012

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

Navigation menu

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