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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
The basic 7-limit [[Miracle|miracle]] temperament has various extensions to the 11 and 13 limits.
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>2014-12-26 18:27:02 UTC</tt>.<br>
: The original revision id was <tt>535923234</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>
<h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">The basic 7-limit [[miracle]] temperament has various extensions to the 11 and 13 limits.


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


Gencom: [2 15/14; 105/104 144/143 196/195 275/273]
Gencom: [2 15/14; 105/104 144/143 196/195 275/273]
Gencom map: [&lt;1 1 3 3 2 4|, &lt;0 6 -7 -2 15 -3|]
Gencom map: [&lt;1 1 3 3 2 4|, &lt;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&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 ||
|| 12/11 || 116.596 ||
|| 14/11 || 116.617 ||
|| POTE11 || 116.633 ||
|| 7/6 || 116.641 ||
|| 7\72 || 116.667 ||
|| |0 17 -11 -6 11&gt; || 116.672 (11 limit least squares) ||
|| POTE5 || 116.673 ||
|| POTE7 || 116.675 ||
|| 10/9 || 116.716 (9, 11 and 13 limit minimax) ||
|| |0 117 -44 -19&gt; || 116.721 (9 limit least squares) ||
|| POTE13 || 116.747 ||
|| 11/8 || 116.755 ||
|| 9/7 || 116.792 ||
|| 11\113 || 116.814 ||
|| |0 127 -84 -36 100 -44&gt; || 116.820 (15 limit least squares) ||
|| |0 141 -70 -35 84 -42&gt; || 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==  
{| class="wikitable"
|-
! | 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&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
|-
| | 12/11
| | 116.596
|-
| | 14/11
| | 116.617
|-
| | POTE11
| | 116.633
|-
| | 7/6
| | 116.641
|-
| | 7\72
| | 116.667
|-
| | |0 17 -11 -6 11&gt;
| | 116.672 (11 limit least squares)
|-
| | POTE5
| | 116.673
|-
| | POTE7
| | 116.675
|-
| | 10/9
| | 116.716 (9, 11 and 13 limit minimax)
|-
| | |0 117 -44 -19&gt;
| | 116.721 (9 limit least squares)
|-
| | POTE13
| | 116.747
|-
| | 11/8
| | 116.755
|-
| | 9/7
| | 116.792
|-
| | 11\113
| | 116.814
|-
| | |0 127 -84 -36 100 -44&gt;
| | 116.820 (15 limit least squares)
|-
| | |0 141 -70 -35 84 -42&gt;
| | 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: [2 15/14; 225/224 243/242 351/350 441/440]
Gencom map: [&lt;1 1 3 3 2 7|, &lt;0 6 -7 -2 15 -34|]
Gencom map: [&lt;1 1 3 3 2 7|, &lt;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&gt; || 116.56309 (13 limit least squares) ||
|| |0 -251 22 5 -131 261&gt; || 116.56348 (15 limit least squares) ||
|| 17\175 || 116.571 ||
|| |0 -27 25 5&gt; || 116.573 (7 limit least squares) ||
|| POTE13 || 116.574 ||
|| |0 -19 20&gt; || 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 ||
|| POTE11 || 116.633 ||
|| 7/6 || 116.641 ||
|| 7\72 || 116.667 ||
|| |0 17 -11 -6 11&gt; || 116.672 (11 limit least squares) ||
|| POTE5 || 116.673 ||
|| POTE7 || 116.675 ||
|| 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 ||
|| 11\113 || 116.814 ||
|| 4/3 || 116.993 ||
|| 4\41 || 117.073 ||
|| 15/14 || 119.443 ||


==Spectrum of Manna Tunings by Eigenmonzos==  
{| class="wikitable"
|-
! | 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&gt;
| | 116.56309 (13 limit least squares)
|-
| | |0 -251 22 5 -131 261&gt;
| | 116.56348 (15 limit least squares)
|-
| | 17\175
| | 116.571
|-
| | |0 -27 25 5&gt;
| | 116.573 (7 limit least squares)
|-
| | POTE13
| | 116.574
|-
| | |0 -19 20&gt;
| | 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
|-
| | POTE11
| | 116.633
|-
| | 7/6
| | 116.641
|-
| | 7\72
| | 116.667
|-
| | |0 17 -11 -6 11&gt;
| | 116.672 (11 limit least squares)
|-
| | POTE5
| | 116.673
|-
| | POTE7
| | 116.675
|-
| | 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
|-
| | 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: [2 15/14; 225/224 243/242 325/324 385/384]
Gencom map: [&lt;1 1 3 3 2 0|, &lt;0 6 -7 -2 15 38|]
Gencom map: [&lt;1 1 3 3 2 0|, &lt;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&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 ||
|| 12/11 || 116.596 ||
|| 14/11 || 116.617 ||
|| POTE11 || 116.633 ||
|| 7/6 || 116.641 ||
|| 7\72 || 116.667 ||
|| |0 17 -11 -6 11&gt; || 116.672 (11 limit least squares) ||
|| POTE5 || 116.673 ||
|| POTE7 || 116.675 ||
|| 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) ||
|| POTE13 || 116.739 ||
|| 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 || 116.79254 ||
|| 18/13 || 116.79299 ||
|| 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==  
{| class="wikitable"
|-
! | 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&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
|-
| | 12/11
| | 116.596
|-
| | 14/11
| | 116.617
|-
| | POTE11
| | 116.633
|-
| | 7/6
| | 116.641
|-
| | 7\72
| | 116.667
|-
| | |0 17 -11 -6 11&gt;
| | 116.672 (11 limit least squares)
|-
| | POTE5
| | 116.673
|-
| | POTE7
| | 116.675
|-
| | 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)
|-
| | POTE13
| | 116.739
|-
| | 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
| | 116.79254
|-
| | 18/13
| | 116.79299
|-
| | 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: [2 15/14; 66/65 99/98 105/104 1001/1000]
Gencom map: [&lt;1 1 3 3 5 4|, &lt;0 6 -7 -2 -16 -3|]
Gencom map: [&lt;1 1 3 3 5 4|, &lt;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&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) ||
|| POTE13 || 116.268 ||
|| POTE11 || 116.277 ||
|| 7/5 || 116.502 ||
|| 10\103 || 116.505 ||
|| 17\175 || 116.571 ||
|| |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 ||
|| 7\72 || 116.667 ||
|| POTE5 || 116.673 ||
|| POTE7 || 116.675 ||
|| 10/9 || 116.716 (9 limit minimax) ||
|| |0 117 -44 -19&gt; || 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 ||</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;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Tuning Spectra"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Tuning Spectra&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Tuning Spectra-Spectrum of Miraculous Tunings by Eigenmonzos"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Spectrum of Miraculous Tunings by Eigenmonzos&lt;/h2&gt;
&lt;br /&gt;
Gencom: [2 15/14; 105/104 144/143 196/195 275/273]&lt;br /&gt;
Gencom map: [&amp;lt;1 1 3 3 2 4|, &amp;lt;0 6 -7 -2 15 -3|]&lt;br /&gt;
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;th&gt;Eigenmonzo&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Secor&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;111.731&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;113.553&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;115.587&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;115.803&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3\31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.129&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.241&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.441&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.502&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10\103&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.505&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;17\175&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.571&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;
    &lt;tr&gt;
        &lt;td&gt;6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.588 (5 and 7 limit minimax)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.591&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;12/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.596&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.617&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;POTE11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.633&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7/6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.641&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7\72&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.667&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;
    &lt;tr&gt;
        &lt;td&gt;POTE5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.673&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;POTE7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.675&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.716 (9, 11 and 13 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;
    &lt;tr&gt;
        &lt;td&gt;POTE13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.747&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.755&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.792&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11\113&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.814&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;|0 127 -84 -36 100 -44&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.820 (15 limit least squares)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;|0 141 -70 -35 84 -42&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.846 (13 limit least squares)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.993 (15 limit minimax)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4\41&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;117.073&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;117.266&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;18/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;117.559&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13/12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;117.936&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;119.443&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;119.824&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;123.871&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;128.298&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Tuning Spectra-Spectrum of Benediction Tunings by Eigenmonzos"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Spectrum of Benediction Tunings by Eigenmonzos&lt;/h2&gt;
&lt;br /&gt;
Gencom: [2 15/14; 225/224 243/242 351/350 441/440]&lt;br /&gt;
Gencom map: [&amp;lt;1 1 3 3 2 7|, &amp;lt;0 6 -7 -2 15 -34|]&lt;br /&gt;
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;th&gt;Eigenmonzo&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Secor&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;111.731&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;115.587&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;115.803&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3\31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.129&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.241&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.441&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.455&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.502&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10\103&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.505&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.509&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.511&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13/12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.536&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13/11&lt;br /&gt;
&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;17\175&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.571&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;POTE13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.574&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;
    &lt;tr&gt;
        &lt;td&gt;6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.588 (5, 7 and 15 limit minimax)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.591&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;18/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.595 (13 limit minimax)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;12/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.596&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.598&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.617&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;POTE11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.633&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7/6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.641&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7\72&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.667&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;
    &lt;tr&gt;
        &lt;td&gt;POTE5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.673&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;POTE7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.675&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10/9&lt;br /&gt;
&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;
    &lt;tr&gt;
        &lt;td&gt;11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.755&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.792&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11\113&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.814&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.993&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4\41&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;117.073&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;119.443&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Tuning Spectra-Spectrum of Manna Tunings by Eigenmonzos"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Spectrum of Manna Tunings by Eigenmonzos&lt;/h2&gt;
&lt;br /&gt;
Gencom: [2 15/14; 225/224 243/242 325/324 385/384]&lt;br /&gt;
Gencom map: [&amp;lt;1 1 3 3 2 0|, &amp;lt;0 6 -7 -2 15 38|]&lt;br /&gt;
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;th&gt;Eigenmonzo&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Secor&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;111.731&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;115.587&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;115.803&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3\31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.129&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.241&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.441&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.502&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10\103&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.505&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;17\175&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.571&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;
    &lt;tr&gt;
        &lt;td&gt;6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.588 (5 and 7 limit minimax)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.591&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;12/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.596&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.617&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;POTE11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.633&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7/6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.641&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7\72&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.667&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;
    &lt;tr&gt;
        &lt;td&gt;POTE5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.673&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;POTE7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.675&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10/9&lt;br /&gt;
&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;
    &lt;tr&gt;
        &lt;td&gt;15/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.725 (15 limit minimax)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;POTE13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.739&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.755&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13/10&lt;br /&gt;
&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;
    &lt;tr&gt;
        &lt;td&gt;9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.792&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.79254&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;18/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.79299&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11\113&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.814&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13/12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.830&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.856&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.922&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.993&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4\41&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;117.073&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;119.443&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Tuning Spectra-Spectrum of Revelation Tunings by Eigenmonzos"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Spectrum of Revelation Tunings by Eigenmonzos&lt;/h2&gt;
&lt;br /&gt;
Gencom: [2 15/14; 66/65 99/98 105/104 1001/1000]&lt;br /&gt;
Gencom map: [&amp;lt;1 1 3 3 5 4|, &amp;lt;0 6 -7 -2 -16 -3|]&lt;br /&gt;
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;th&gt;Eigenmonzo&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Secor&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;111.731&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;113.553&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;114.555&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;115.000&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;115.536&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;115.543&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;115.587&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;115.797&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;12/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;115.938&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3\31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.129&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11/9&lt;br /&gt;
&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;
    &lt;tr&gt;
        &lt;td&gt;5/4&lt;br /&gt;
&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;
    &lt;tr&gt;
        &lt;td&gt;POTE13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.268&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;POTE11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.277&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.502&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10\103&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.505&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;17\175&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.571&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;
    &lt;tr&gt;
        &lt;td&gt;6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.588 (5 and 7 limit minimax)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7/6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.641&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7\72&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.667&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;POTE5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.673&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;POTE7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.675&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10/9&lt;br /&gt;
&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;
    &lt;tr&gt;
        &lt;td&gt;9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.792&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11\113&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.814&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.993&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4\41&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;117.073&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;18/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;117.559&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13/12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;117.936&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;119.443&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;119.824&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;123.871&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;128.298&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
{| class="wikitable"
|-
! | 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&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)
|-
| | POTE13
| | 116.268
|-
| | POTE11
| | 116.277
|-
| | 7/5
| | 116.502
|-
| | 10\103
| | 116.505
|-
| | 17\175
| | 116.571
|-
| | |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
|-
| | 7\72
| | 116.667
|-
| | POTE5
| | 116.673
|-
| | POTE7
| | 116.675
|-
| | 10/9
| | 116.716 (9 limit minimax)
|-
| | |0 117 -44 -19&gt;
| | 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
|}
[[Category:benediction]]
[[Category:eigenmonzo]]
[[Category:manna]]
[[Category:miracle]]
[[Category:miraculous]]
[[Category:revelation]]
[[Category:spectrum]]

Revision as of 00:00, 17 July 2018

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
POTE11 116.633
7/6 116.641
7\72 116.667
|0 17 -11 -6 11> 116.672 (11 limit least squares)
POTE5 116.673
POTE7 116.675
10/9 116.716 (9, 11 and 13 limit minimax)
|0 117 -44 -19> 116.721 (9 limit least squares)
POTE13 116.747
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)
POTE13 116.574
|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
POTE11 116.633
7/6 116.641
7\72 116.667
|0 17 -11 -6 11> 116.672 (11 limit least squares)
POTE5 116.673
POTE7 116.675
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
POTE11 116.633
7/6 116.641
7\72 116.667
|0 17 -11 -6 11> 116.672 (11 limit least squares)
POTE5 116.673
POTE7 116.675
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)
POTE13 116.739
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
14/13 116.79254
18/13 116.79299
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)
POTE13 116.268
POTE11 116.277
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
POTE5 116.673
POTE7 116.675
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
Retrieved from "https://en.xen.wiki/index.php?title=Miracle_extensions&oldid=2690"