Miracle extensions
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 2012-11-13 20:15:08 UTC.
- The original revision id was 382127624.
- 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:
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 || || 3\31 || 116.129 || || 5/4 || 116.241 || || 15/11 || 116.441 || || 7/5 || 116.502 || || 10\103 || 116.505 || || 17\175 || 116.571 || || |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 || || 7\72 || 116.667 || || |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 || || 11\113 || 116.814 || || |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) || || 4\41 || 117.073 || || 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 || || 3\31 || 116.129 || || 5/4 || 116.241 || || 15/11 || 116.441 || || 16/13 || 116.455 || || 7/5 || 116.502 || || 10\103 || 116.505 || || 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) || || 17\175 || 116.571 || || |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 || || 7\72 || 116.667 || || |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 || || 11\113 || 116.814 || || 4/3 || 116.993 || || 4\41 || 117.073 || || 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 || || 3\31 || 116.129 || || 5/4 || 116.241 || || 15/11 || 116.441 || || 7/5 || 116.502 || || 10\103 || 116.505 || || 17\175 || 116.571 || || |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 || || 7\72 || 116.667 || || |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 || || 11\113 || 116.814 || || 13/12 || 116.830 || || 16/13 || 116.856 || || 13/11 || 116.922 || || 4/3 || 116.993 || || 4\41 || 117.073 || || 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 || || 3\31 || 116.129 || || 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 || || 10\103 || 116.505 || || 17\175 || 116.571 || || |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 || || 7\72 || 116.667 || || 10/9 || 116.716 (9 limit minimax) || || |0 117 -44 -19> || 116.721 (9 limit least squares) || || 9/7 || 116.792 || || 11\113 || 116.814 || || 4/3 || 116.993 || || 4\41 || 117.073 || || 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:<h1> --><h1 id="toc0"><a name="Tuning Spectra"></a><!-- ws:end:WikiTextHeadingRule:0 -->Tuning Spectra</h1>
<!-- ws:start:WikiTextHeadingRule:2:<h2> --><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: [<1 1 3 3 2 4|, <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>3\31<br />
</td>
<td>116.129<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>10\103<br />
</td>
<td>116.505<br />
</td>
</tr>
<tr>
<td>17\175<br />
</td>
<td>116.571<br />
</td>
</tr>
<tr>
<td>|0 -27 25 5><br />
</td>
<td>116.573 (7 limit least squares)<br />
</td>
</tr>
<tr>
<td>|0 -19 20><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>7\72<br />
</td>
<td>116.667<br />
</td>
</tr>
<tr>
<td>|0 17 -11 -6 11><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><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>11\113<br />
</td>
<td>116.814<br />
</td>
</tr>
<tr>
<td>|0 127 -84 -36 100 -44><br />
</td>
<td>116.820 (15 limit least squares)<br />
</td>
</tr>
<tr>
<td>|0 141 -70 -35 84 -42><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>4\41<br />
</td>
<td>117.073<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:<h2> --><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: [<1 1 3 3 2 7|, <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>3\31<br />
</td>
<td>116.129<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>10\103<br />
</td>
<td>116.505<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><br />
</td>
<td>116.56309 (13 limit least squares)<br />
</td>
</tr>
<tr>
<td>|0 -251 22 5 -131 261><br />
</td>
<td>116.56348 (15 limit least squares)<br />
</td>
</tr>
<tr>
<td>17\175<br />
</td>
<td>116.571<br />
</td>
</tr>
<tr>
<td>|0 -27 25 5><br />
</td>
<td>116.573 (7 limit least squares)<br />
</td>
</tr>
<tr>
<td>|0 -19 20><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>7\72<br />
</td>
<td>116.667<br />
</td>
</tr>
<tr>
<td>|0 17 -11 -6 11><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><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>11\113<br />
</td>
<td>116.814<br />
</td>
</tr>
<tr>
<td>4/3<br />
</td>
<td>116.993<br />
</td>
</tr>
<tr>
<td>4\41<br />
</td>
<td>117.073<br />
</td>
</tr>
<tr>
<td>15/14<br />
</td>
<td>119.443<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:6:<h2> --><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: [<1 1 3 3 2 0|, <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>3\31<br />
</td>
<td>116.129<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>10\103<br />
</td>
<td>116.505<br />
</td>
</tr>
<tr>
<td>17\175<br />
</td>
<td>116.571<br />
</td>
</tr>
<tr>
<td>|0 -27 25 5><br />
</td>
<td>116.573 (7 limit least squares)<br />
</td>
</tr>
<tr>
<td>|0 -19 20><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>7\72<br />
</td>
<td>116.667<br />
</td>
</tr>
<tr>
<td>|0 17 -11 -6 11><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><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><br />
</td>
<td>116.764 (15 limit least squares)<br />
</td>
</tr>
<tr>
<td>|0 18 -111 -76 43 204><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>11\113<br />
</td>
<td>116.814<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>4\41<br />
</td>
<td>117.073<br />
</td>
</tr>
<tr>
<td>15/14<br />
</td>
<td>119.443<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:8:<h2> --><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: [<1 1 3 3 5 4|, <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>3\31<br />
</td>
<td>116.129<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><br />
</td>
<td>116.198 (11 limit least squares)<br />
</td>
</tr>
<tr>
<td>|0 -251 22 5 117 13><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><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>10\103<br />
</td>
<td>116.505<br />
</td>
</tr>
<tr>
<td>17\175<br />
</td>
<td>116.571<br />
</td>
</tr>
<tr>
<td>|0 -27 25 5><br />
</td>
<td>116.573 (7 limit least squares)<br />
</td>
</tr>
<tr>
<td>|0 -19 20><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>7\72<br />
</td>
<td>116.667<br />
</td>
</tr>
<tr>
<td>10/9<br />
</td>
<td>116.716 (9 limit minimax)<br />
</td>
</tr>
<tr>
<td>|0 117 -44 -19><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>11\113<br />
</td>
<td>116.814<br />
</td>
</tr>
<tr>
<td>4/3<br />
</td>
<td>116.993<br />
</td>
</tr>
<tr>
<td>4\41<br />
</td>
<td>117.073<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>