Orwell extensions: Difference between revisions

Revision as of 10:23, 10 November 2012

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The original revision id was 381072162.

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Original Wikitext content:

[[Orwell]] temperament has various extensions to the 13 limit.

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

Gencom: [2 7/6; 99/98 121/120 176/175 275/273]
Gencom map: [<1 0 3 1 3 8|, <0 7 -3 8 2 -19|]
||~ Eigenmonzo ||~ Subminor Third ||
|| 7/6 || 266.871 ||
|| 15/11 || 268.475 ||
|| 14/11 || 269.585 ||
|| 12/11 || 270.127 ||
|| 15/14 || 270.139 ||
|| 11/9 || 271.049 ||
|| 8/7 || 271.103 ||
|| 7/5 || 271.137 ||
|| 5/4 || 271.229 ||
|| 1361367/1000000 || 271.326 (7 limit least squares) ||
|| |0 119 -46 20 -16> || 271.445 (11 limit least squares) ||
|| |0 90 -41 14> || 271.561 (9 limit least squares) ||
|| 6/5 || 271.564 (5 limit minimax) ||
|| |0 -211 30 -47 -5 142> || 271.567 13 limit least squares) ||
|| |0 -236 5 -51 -3 165> || 271.570 (15 limit least squares) ||
|| 1220703125/1033121304 || 271.590 (5 limit least squares) ||
|| 10/9 || 271.623 (9 limit minimax) ||
|| 14/13 || 271.418 (13 and 15 limit minimax) ||
|| 16/13 || 271.551 ||
|| 6/5 || 271.564 ||
|| 13/12 || 271.593 ||
|| 13/10 || 271.612 ||
|| 18/13 || 271.618 ||
|| 10/9 || 271.623 ||
|| 15/13 || 271.641 ||
|| 4/3 || 271.708 ||
|| 13/11 || 271.942 ||
|| 16/15 || 272.067 ||
|| 9/7 || 272.514 ||
|| 11/10 || 273.001 ||
|| 11/8 || 275.659 ||

==Spectrum of Winston Tunings by Eigenmonzos== 

Gencom: [2 7/6; 66/65 99/98 105/104 121/120]
Gencom map: [<1 0 3 1 3 1|, <0 7 -3 8 2 12|]
||~ Eigenmonzo ||~ Subminor Third ||
|| 7/6 || 266.871 ||
|| 13/12 || 267.715 ||
|| 14/13 || 267.925 ||
|| 15/11 || 268.475 ||
|| 13/11 || 268.921 ||
|| 15/13 || 269.032 ||
|| 14/11 || 269.585 ||
|| 16/13 || 270.044 ||
|| 12/11 || 270.127 ||
|| 15/14 || 270.139 ||
|| 13/10 || 270.281 ||
|| |0 112 -67 20 -28 52> || 270.860 (15 limit least squares) ||
|| |0 118 -61 16 -26 44> || 270.933 (13 limit least squares) ||
|| 11/9 || 271.049 (13 and 15 limit minimax) ||
|| 8/7 || 271.103 ||
|| 7/5 || 271.137 ||
|| 5/4 || 271.229 ||
|| 1361367/1000000 || 271.326 (7 limit least squares) ||
|| |0 119 -46 20 -16> || 271.445 (11 limit least squares) ||
|| |0 90 -41 14> || 271.561 (9 limit least squares) ||
|| 6/5 || 271.564 (5 limit minimax) ||
|| 1220703125/1033121304 || 271.590 (5 limit least squares) ||
|| 10/9 || 271.623 (9 limit minimax) ||
|| 4/3 || 271.708 ||
|| 16/15 || 272.067 ||
|| 9/7 || 272.514 ||
|| 11/10 || 273.001 ||
|| 11/8 || 275.659 ||
|| 18/13 || 281.691 ||

==Spectrum of Blair Tunings by Eigenmonzos== 

Gencom: [2 7/6; 65/64 78/77 91/90 99/98]
Gencom map: [<1 0 3 1 3 3|, <0 7 -3 8 2 3|]
||~ Eigenmonzo ||~ Subminor Third ||
|| 15/13 || 247.741 ||
|| 13/12 || 265.357 ||
|| 14/13 || 265.660 ||
|| 7/6 || 266.871 ||
|| 15/11 || 268.475 ||
|| 18/13 || 269.398 ||
|| 14/11 || 269.585 ||
|| 12/11 || 270.127 ||
|| 15/14 || 270.139 ||
|| 11/9 || 271.049 ||
|| 8/7 || 271.103 ||
|| 7/5 || 271.137 (7, 11, 13 and 15 limit minimax) ||
|| 5/4 || 271.229 ||
|| |0 148 -49 29 -19 -11> || 271.231 (15 limit least squares) ||
|| |0 145 -52 25 -17 -10> || 271.261 (13 limit least squares) ||
|| 1361367/1000000 || 271.326 (7 limit least squares) ||
|| |0 119 -46 20 -16> || 271.445 (11 limit least squares) ||
|| |0 90 -41 14> || 271.561 (9 limit least squares) ||
|| 6/5 || 271.564 (5 limit minimax) ||
|| 1220703125/1033121304 || 271.590 (5 limit least squares) ||
|| 10/9 || 271.623 (9 limit minimax) ||
|| 4/3 || 271.708 ||
|| 16/15 || 272.067 ||
|| 9/7 || 272.514 ||
|| 11/10 || 273.001 ||
|| 11/8 || 275.659 ||
|| 13/10 || 275.702 ||
|| 16/13 || 280.176 ||
|| 13/11 || 289.210 ||

Original HTML content:

<html><head><title>Orwell extensions</title></head><body><a class="wiki_link" href="/Orwell">Orwell</a> temperament has various extensions to the 13 limit.<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 Orwell Tunings by Eigenmonzos"></a><!-- ws:end:WikiTextHeadingRule:2 -->Spectrum of Orwell Tunings by Eigenmonzos</h2>
 <br />
Gencom: [2 7/6; 99/98 121/120 176/175 275/273]<br />
Gencom map: [&lt;1 0 3 1 3 8|, &lt;0 7 -3 8 2 -19|]<br />


<table class="wiki_table">
    <tr>
        <th>Eigenmonzo<br />
</th>
        <th>Subminor Third<br />
</th>
    </tr>
    <tr>
        <td>7/6<br />
</td>
        <td>266.871<br />
</td>
    </tr>
    <tr>
        <td>15/11<br />
</td>
        <td>268.475<br />
</td>
    </tr>
    <tr>
        <td>14/11<br />
</td>
        <td>269.585<br />
</td>
    </tr>
    <tr>
        <td>12/11<br />
</td>
        <td>270.127<br />
</td>
    </tr>
    <tr>
        <td>15/14<br />
</td>
        <td>270.139<br />
</td>
    </tr>
    <tr>
        <td>11/9<br />
</td>
        <td>271.049<br />
</td>
    </tr>
    <tr>
        <td>8/7<br />
</td>
        <td>271.103<br />
</td>
    </tr>
    <tr>
        <td>7/5<br />
</td>
        <td>271.137<br />
</td>
    </tr>
    <tr>
        <td>5/4<br />
</td>
        <td>271.229<br />
</td>
    </tr>
    <tr>
        <td>1361367/1000000<br />
</td>
        <td>271.326 (7 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>|0 119 -46 20 -16&gt;<br />
</td>
        <td>271.445 (11 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>|0 90 -41 14&gt;<br />
</td>
        <td>271.561 (9 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>6/5<br />
</td>
        <td>271.564 (5 limit minimax)<br />
</td>
    </tr>
    <tr>
        <td>|0 -211 30 -47 -5 142&gt;<br />
</td>
        <td>271.567 13 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>|0 -236 5 -51 -3 165&gt;<br />
</td>
        <td>271.570 (15 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>1220703125/1033121304<br />
</td>
        <td>271.590 (5 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>10/9<br />
</td>
        <td>271.623 (9 limit minimax)<br />
</td>
    </tr>
    <tr>
        <td>14/13<br />
</td>
        <td>271.418 (13 and 15 limit minimax)<br />
</td>
    </tr>
    <tr>
        <td>16/13<br />
</td>
        <td>271.551<br />
</td>
    </tr>
    <tr>
        <td>6/5<br />
</td>
        <td>271.564<br />
</td>
    </tr>
    <tr>
        <td>13/12<br />
</td>
        <td>271.593<br />
</td>
    </tr>
    <tr>
        <td>13/10<br />
</td>
        <td>271.612<br />
</td>
    </tr>
    <tr>
        <td>18/13<br />
</td>
        <td>271.618<br />
</td>
    </tr>
    <tr>
        <td>10/9<br />
</td>
        <td>271.623<br />
</td>
    </tr>
    <tr>
        <td>15/13<br />
</td>
        <td>271.641<br />
</td>
    </tr>
    <tr>
        <td>4/3<br />
</td>
        <td>271.708<br />
</td>
    </tr>
    <tr>
        <td>13/11<br />
</td>
        <td>271.942<br />
</td>
    </tr>
    <tr>
        <td>16/15<br />
</td>
        <td>272.067<br />
</td>
    </tr>
    <tr>
        <td>9/7<br />
</td>
        <td>272.514<br />
</td>
    </tr>
    <tr>
        <td>11/10<br />
</td>
        <td>273.001<br />
</td>
    </tr>
    <tr>
        <td>11/8<br />
</td>
        <td>275.659<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Tuning Spectra-Spectrum of Winston Tunings by Eigenmonzos"></a><!-- ws:end:WikiTextHeadingRule:4 -->Spectrum of Winston Tunings by Eigenmonzos</h2>
 <br />
Gencom: [2 7/6; 66/65 99/98 105/104 121/120]<br />
Gencom map: [&lt;1 0 3 1 3 1|, &lt;0 7 -3 8 2 12|]<br />


<table class="wiki_table">
    <tr>
        <th>Eigenmonzo<br />
</th>
        <th>Subminor Third<br />
</th>
    </tr>
    <tr>
        <td>7/6<br />
</td>
        <td>266.871<br />
</td>
    </tr>
    <tr>
        <td>13/12<br />
</td>
        <td>267.715<br />
</td>
    </tr>
    <tr>
        <td>14/13<br />
</td>
        <td>267.925<br />
</td>
    </tr>
    <tr>
        <td>15/11<br />
</td>
        <td>268.475<br />
</td>
    </tr>
    <tr>
        <td>13/11<br />
</td>
        <td>268.921<br />
</td>
    </tr>
    <tr>
        <td>15/13<br />
</td>
        <td>269.032<br />
</td>
    </tr>
    <tr>
        <td>14/11<br />
</td>
        <td>269.585<br />
</td>
    </tr>
    <tr>
        <td>16/13<br />
</td>
        <td>270.044<br />
</td>
    </tr>
    <tr>
        <td>12/11<br />
</td>
        <td>270.127<br />
</td>
    </tr>
    <tr>
        <td>15/14<br />
</td>
        <td>270.139<br />
</td>
    </tr>
    <tr>
        <td>13/10<br />
</td>
        <td>270.281<br />
</td>
    </tr>
    <tr>
        <td>|0 112 -67 20 -28 52&gt;<br />
</td>
        <td>270.860 (15 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>|0 118 -61 16 -26 44&gt;<br />
</td>
        <td>270.933 (13 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>11/9<br />
</td>
        <td>271.049 (13 and 15 limit minimax)<br />
</td>
    </tr>
    <tr>
        <td>8/7<br />
</td>
        <td>271.103<br />
</td>
    </tr>
    <tr>
        <td>7/5<br />
</td>
        <td>271.137<br />
</td>
    </tr>
    <tr>
        <td>5/4<br />
</td>
        <td>271.229<br />
</td>
    </tr>
    <tr>
        <td>1361367/1000000<br />
</td>
        <td>271.326 (7 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>|0 119 -46 20 -16&gt;<br />
</td>
        <td>271.445 (11 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>|0 90 -41 14&gt;<br />
</td>
        <td>271.561 (9 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>6/5<br />
</td>
        <td>271.564 (5 limit minimax)<br />
</td>
    </tr>
    <tr>
        <td>1220703125/1033121304<br />
</td>
        <td>271.590 (5 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>10/9<br />
</td>
        <td>271.623 (9 limit minimax)<br />
</td>
    </tr>
    <tr>
        <td>4/3<br />
</td>
        <td>271.708<br />
</td>
    </tr>
    <tr>
        <td>16/15<br />
</td>
        <td>272.067<br />
</td>
    </tr>
    <tr>
        <td>9/7<br />
</td>
        <td>272.514<br />
</td>
    </tr>
    <tr>
        <td>11/10<br />
</td>
        <td>273.001<br />
</td>
    </tr>
    <tr>
        <td>11/8<br />
</td>
        <td>275.659<br />
</td>
    </tr>
    <tr>
        <td>18/13<br />
</td>
        <td>281.691<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Tuning Spectra-Spectrum of Blair Tunings by Eigenmonzos"></a><!-- ws:end:WikiTextHeadingRule:6 -->Spectrum of Blair Tunings by Eigenmonzos</h2>
 <br />
Gencom: [2 7/6; 65/64 78/77 91/90 99/98]<br />
Gencom map: [&lt;1 0 3 1 3 3|, &lt;0 7 -3 8 2 3|]<br />


<table class="wiki_table">
    <tr>
        <th>Eigenmonzo<br />
</th>
        <th>Subminor Third<br />
</th>
    </tr>
    <tr>
        <td>15/13<br />
</td>
        <td>247.741<br />
</td>
    </tr>
    <tr>
        <td>13/12<br />
</td>
        <td>265.357<br />
</td>
    </tr>
    <tr>
        <td>14/13<br />
</td>
        <td>265.660<br />
</td>
    </tr>
    <tr>
        <td>7/6<br />
</td>
        <td>266.871<br />
</td>
    </tr>
    <tr>
        <td>15/11<br />
</td>
        <td>268.475<br />
</td>
    </tr>
    <tr>
        <td>18/13<br />
</td>
        <td>269.398<br />
</td>
    </tr>
    <tr>
        <td>14/11<br />
</td>
        <td>269.585<br />
</td>
    </tr>
    <tr>
        <td>12/11<br />
</td>
        <td>270.127<br />
</td>
    </tr>
    <tr>
        <td>15/14<br />
</td>
        <td>270.139<br />
</td>
    </tr>
    <tr>
        <td>11/9<br />
</td>
        <td>271.049<br />
</td>
    </tr>
    <tr>
        <td>8/7<br />
</td>
        <td>271.103<br />
</td>
    </tr>
    <tr>
        <td>7/5<br />
</td>
        <td>271.137 (7, 11, 13 and 15 limit minimax)<br />
</td>
    </tr>
    <tr>
        <td>5/4<br />
</td>
        <td>271.229<br />
</td>
    </tr>
    <tr>
        <td>|0 148 -49 29 -19 -11&gt;<br />
</td>
        <td>271.231 (15 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>|0 145 -52 25 -17 -10&gt;<br />
</td>
        <td>271.261 (13 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>1361367/1000000<br />
</td>
        <td>271.326 (7 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>|0 119 -46 20 -16&gt;<br />
</td>
        <td>271.445 (11 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>|0 90 -41 14&gt;<br />
</td>
        <td>271.561 (9 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>6/5<br />
</td>
        <td>271.564 (5 limit minimax)<br />
</td>
    </tr>
    <tr>
        <td>1220703125/1033121304<br />
</td>
        <td>271.590 (5 limit least squares)<br />
</td>
    </tr>
    <tr>
        <td>10/9<br />
</td>
        <td>271.623 (9 limit minimax)<br />
</td>
    </tr>
    <tr>
        <td>4/3<br />
</td>
        <td>271.708<br />
</td>
    </tr>
    <tr>
        <td>16/15<br />
</td>
        <td>272.067<br />
</td>
    </tr>
    <tr>
        <td>9/7<br />
</td>
        <td>272.514<br />
</td>
    </tr>
    <tr>
        <td>11/10<br />
</td>
        <td>273.001<br />
</td>
    </tr>
    <tr>
        <td>11/8<br />
</td>
        <td>275.659<br />
</td>
    </tr>
    <tr>
        <td>13/10<br />
</td>
        <td>275.702<br />
</td>
    </tr>
    <tr>
        <td>16/13<br />
</td>
        <td>280.176<br />
</td>
    </tr>
    <tr>
        <td>13/11<br />
</td>
        <td>289.210<br />
</td>
    </tr>
</table>

</body></html>

Orwell extensions: Difference between revisions

Revision as of 10:23, 10 November 2012

IMPORTED REVISION FROM WIKISPACES

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