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Target tunings
 
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Breadcrumb|Magic}}
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>2012-11-17 11:39:32 UTC</tt>.<br>
: The original revision id was <tt>383550892</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">


=Tuning Spectra=
[[Magic]] has various competing [[extension]]s to the [[11-limit|11-]] and [[13-limit]]. The following temperaments are discussed in this article:
==Spectrum of Magic Tunings by Eigenmonzos==


Gencom: [2 5/4; 100/99 105/104 144/143 196/195]
* '''Tridecimal magic''' ({{nowrap| 19 & 22f }}) – tempering out 100/99, 105/104, 144/143, and 196/195;
Gencom map: [&lt;1 0 2 -1 6 -2|, &lt;0 5 1 12 -8 18|]
* '''Necromancy''' ({{nowrap| 19f & 22 }}) – tempering out 100/99, 225/224, 245/243, and 275/273;
||~ Eigenmonzo ||~ Major Third ||
* '''Witchcraft''' ({{nowrap| 19e & 22ef }}) – tempering out 105/104, 196/195, 245/243, and 275/273;
|| 14/13 || 378.617 ||
* '''Sorcery''' ({{nowrap| 19 & 22 }}) – tempering out 65/64, 78/77, 91/90, and 100/99;  
|| 6/5 || 378.910 ||
* '''Intuition''' ({{nowrap| 19e & 22f }}) – tempering out 55/54, 66/65, 99/98, and 105/104;  
|| 6\19 || 378.947 ||
* '''Telepathy''' ({{nowrap| 19e & 22 }}) – tempering out 55/54, 65/64, 91/90, and 99/98.  
|| 15/13 || 379.355 ||
|| 18/13 || 379.577 ||
|| 13/10 || 379.660 ||
|| 10/9 || 379.733 ||
|| 13/12 || 379.890 ||
|| 27/20 || 379.968 (5 limit least squares) ||
|| 19\60 || 380.000 ||
|| 16/13 || 380.029 ||
|| 15/14 || 380.093 ||
|| 32\101 || 380.198 ||
|| 7/5 || 380.228 ||
|| 13/11 || 380.354 (13 and 15 limit minimax) ||
|| |0 56 -31 46 -94 88&gt; || 380.377 (13 limit least squares) ||
|| |0 36 -23 32&gt; || 380.384 (9 limit least squares) ||
|| |0 58 -29 52 -108 100&gt; || 380.389 (15 limit least squares) ||
|| 4/3 || 380.391 (5, 7 and 9 limit minimax) ||
|| 13\41 || 380.488 ||
|| |0 1 -7 15&gt; || 380.506 (7 limit least squares) ||
|| 11/9 || 380.700 (11 limit minimax) ||
|| |0 85 -14 52 -68&gt; || 380.714 (11 limit least squares) ||
|| 8/7 || 380.735 ||
|| 33\104 || 380.769 ||
|| 12/11 || 380.818 ||
|| 14/11 || 380.875 ||
|| 20\63 || 380.952 ||
|| 7/6 || 380.982 ||
|| 11/8 || 381.085 ||
|| 15/11 || 381.211 ||
|| 16/15 || 381.378 ||
|| 11/10 || 381.666 ||
|| 7\22 || 381.818 ||
|| 9/7 || 382.458 ||
|| 5/4 || 386.314 ||


==Spectrum of Necromancy Tunings by Eigenmonzos==
The most important of these is tridecimal magic, where primes 11 and 13 are mapped such that 10/9 and 11/10 are tempered together and that 14/13 and 16/15 are tempered together. Necromancy takes the same mapping of 11 as magic, but swaps in a more complex mapping for 13, enabling the possibility of a higher-accuracy harmony. Similarly, witchcraft takes the same mapping of 13 as magic, but swaps in a more complex mapping for 11. Necromancy is the {{nowrap| 41 & 63 }} temperament [[support]]ed by [[104edo]], whereas witchcraft is the {{nowrap| 41 & 60e }} temperament supported by [[101edo]] in the 101cd [[val]].


Gencom: [2 5/4; 100/99 225/224 245/243 275/273]
Sorcery swaps in a less complex and less accurate mapping for prime 13, as it finds ~16/13 where magic will find ~26/21, which is of course conflated with ~5/4. Likewise, intuition uses a less complex and less accurate mapping for prime 11. Finally, telepathy adopts the changes of both sorcery and intuition, resulting in a very low-accuracy temperament.  
Gencom map: [&lt;1 0 2 -1 6 11|, &lt;0 5 1 12 -8 -23|]
||~ Eigenmonzo ||~ Major Third ||
|| 6/5 || 378.910 ||
|| 6\19 || 378.947 ||
|| 10/9 || 379.733 ||
|| 27/20 || 379.968 (5 limit least squares) ||
|| 19\60 || 380.000 ||
|| 15/14 || 380.093 ||
|| 32\101 || 380.198 ||
|| 7/5 || 380.228 ||
|| |0 36 -23 32&gt; || 380.384 (9 limit least squares) ||
|| 4/3 || 380.391 (5, 7 and 9 limit minimax) ||
|| 13\41 || 380.488 ||
|| |0 1 -7 15&gt; || 380.506 (7 limit least squares) ||
|| 11/9 || 380.700 (11 limit minimax) ||
|| 18/13 || 380.709 (13 and 15 limit minimax) ||
|| |0 85 -14 52 -68&gt; || 380.714 (11 limit least squares) ||
|| 13/11 || 380.719 ||
|| 8/7 || 380.735 ||
|| 13/12 || 380.765 ||
|| 33\104 || 380.769 ||
|| |0 -179 -10 -87 53 158&gt; || 380.785 (13 limit least squares) ||
|| 14/13 || 380.809 ||
|| |0 -222 -53 -93 67 187&gt; || 380.817 (15 limit least squares) ||
|| 12/11 || 380.818 ||
|| 16/13 || 380.847 ||
|| 14/11 || 380.875 ||
|| 20\63 || 380.952 ||
|| 15/13 || 380.957 ||
|| 7/6 || 380.982 ||
|| 13/10 || 381.074 ||
|| 11/8 || 381.085 ||
|| 15/11 || 381.211 ||
|| 16/15 || 381.378 ||
|| 11/10 || 381.666 ||
|| 7\22 || 381.818 ||
|| 9/7 || 382.458 ||
|| 5/4 || 386.314 ||


See [[Magic family #Magic]], [[Magic family #Necromancy|#Necromany]], [[Magic family #Witchcraft|#Witchcraft]], [[Magic family #Sorcery|#Sorcery]], [[Magic family #Intuition|#Intuition]], and [[Magic family #Telepathy|#Telepathy]] for technical data.


==Spectrum of Sorcery Tunings by Eigenmonzos==  
== Interval chain ==
In the following table, odd harmonics and subharmonics 1–13 are in '''bold'''.


Gencom: [2 5/4; 65/64 78/77 91/90 100/99]
{| class="wikitable center-1 right-2"
Gencom map: [&lt;1 0 2 -1 6 4|, &lt;0 5 1 12 -8 -1|]
|-
||~ Eigenmonzo ||~ Major Third ||
! rowspan="3" | #
|| 16/13 || 359.472 ||
! rowspan="3" | Cents*
|| 13/10 || 372.893 ||
! colspan="7" | Approximate ratios
|| 13/12 || 376.905 ||
|-
|| 15/13 || 378.249 ||
! rowspan="2" | 7-limit
|| 18/13 || 378.489 ||
! colspan="6" | 13-limit extensions
|| 6/5 || 378.910 ||
|-
|| 6\19 || 378.947 ||
! Magic
|| 14/13 || 379.100 ||
! Necromancy
|| 10/9 || 379.733 ||
! Witchcraft
|| 27/20 || 379.968 (5 limit least squares) ||
! Sorcery
|| 19\60 || 380.000 ||
! Intuition
|| 15/14 || 380.093 ||
! Telepathy
|| 32\101 || 380.198 ||
|-
|| 7/5 || 380.228 ||
| 0
|| |0 36 -23 32&gt; || 380.384 (9 limit least squares) ||
| 0.0
|| 4/3 || 380.391 (5, 7 and 9 limit minimax) ||
| '''1/1'''
|| |0 -113 12 -65 75 26&gt; || 380.427 (13 limit least squares) ||
|  
|| |0 134 9 71 -89 -33&gt; || 380.457 (15 limit least squares) ||
|  
|| 13\41 || 380.488 ||
|  
|| |0 1 -7 15&gt; || 380.506 (7 limit least squares) ||
|  
|| 11/9 || 380.700 (11, 13 and 15 limit minimax) ||
|  
|| |0 85 -14 52 -68&gt; || 380.714 (11 limit least squares) ||
|  
|| 8/7 || 380.735 ||
|-
|| 33\104 || 380.769 ||  
| 1
|| 12/11 || 380.818 ||
| 380.4
|| 14/11 || 380.875 ||
| '''5/4'''
|| 20\63 || 380.952 ||
| 26/21
|| 7/6 || 380.982 ||
|  
|| 11/8 || 381.085 ||
| 26/21
|| 15/11 || 381.211 ||
| '''16/13'''
|| 16/15 || 381.378 ||
| 26/21
|| 11/10 || 381.666 ||
| '''16/13'''
|| 7\22 || 381.818 ||
|-
|| 9/7 || 382.458 ||
| 2
|| 13/11 || 384.173 ||
| 760.9
|| 5/4 || 386.314 ||
| 14/9
|  
|  
|  
| 20/13
| 11/7
| 11/7, 20/13
|-
| 3
| 1141.4
| 27/14
| 52/27, 64/33
| 64/33
| 52/27
| 64/33
| 21/11, 52/27
| 21/11
|-
| 4
| 321.8
| 6/5
| 40/33
| 40/33
|  
| 40/33
| 11/9, 13/11
| 11/9
|-
| 5
| 702.3
| '''3/2'''
|  
|  
|  
|
|  
|  
|-
| 6
| 1082.7
| 15/8, 28/15
| 13/7
|  
| 13/7
| 24/13
| 13/7
| 24/13
|-
| 7
| 263.2
| 7/6
|  
|  
|  
| 13/11
|  
|  
|-
| 8
| 643.7
| 35/24
| 13/9, '''16/11'''
| '''16/11'''
| 13/9
| '''16/11'''
| 13/9, 22/15
| 22/15
|-
| 9
| 1024.1
| 9/5
| 20/11
| 20/11
|  
| 20/11
| 11/6
| 11/6
|-
| 10
| 204.6
| '''9/8'''
|  
|  
|  
|  
|  
|  
|-
| 11
| 585.0
| 7/5
|  
|  
|  
| 18/13
|  
| 18/13
|-
| 12
| 965.5
| '''7/4'''
| 26/15
|  
| 26/15
|  
| 26/15
|  
|-
| 13
| 146.0
| 35/32
| 12/11, 13/12
| 12/11
| 13/12
| 12/11, 14/13
| 11/10, 13/12
| 11/10, 14/13
|-
| 14
| 526.4
| 27/20
| 15/11
| 15/11
|  
| 15/11
| '''11/8'''
| '''11/8'''
|-
| 15
| 906.9
| 27/16, 42/25
|  
| 22/13
| 22/13
|
|  
| 22/13
|-
| 16
| 87.3
| 21/20
|  
|  
| 22/21
| 27/26
|  
| 27/26
|-
| 17
| 467.8
| 21/16
| 13/10
|  
| 13/10
|  
| 13/10
|  
|-
| 18
| 848.2
| 49/30
| '''13/8''', 18/11
| 18/11
| '''13/8'''
| 18/11, 21/13
| '''13/8'''
| 21/13
|-
| 19
| 28.7
| 49/48, 81/80, 126/125
| 45/44
| 45/44
|  
| 45/44
| 33/32
| 33/32
|-
| 20
| 409.2
| 63/50
| 14/11
| 14/11
|  
| 14/11
|  
|  
|-
| 21
| 789.6
| 63/40
|  
|  
| 11/7
|  
|  
|  
|-
| 22
| 1170.1
| 49/25, 63/32
| 39/20
|  
| 39/20
|  
| 39/20
|  
|}
<nowiki/>* In 7-limit [[CWE tuning]]


== Tunings ==
=== Target tunings ===
{| class="wikitable center-all left-5 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Target tunings (magic)
|-
! rowspan="2" | Target
! colspan="2" | Minimax
! colspan="2" | Least squares
|-
! Generator
! Eigenmonzo*
! Generator
! Eigenmonzo*
|-
| 11-odd-limit
| ~5/4 = 380.700{{c}}
| 11/9
| ~5/4 = 380.714{{c}}
| {{Monzo| 0 85 -14 52 -68 }}
|-
| 13-odd-limit
| ~5/4 = 380.354{{c}}
| 13/11
| ~5/4 = 380.377{{c}}
| {{Monzo| 0 56 -31 46 -94 88 }}
|-
| 15-odd-limit
| ~5/4 = 380.354{{c}}
| 13/11
| ~5/4 = 380.389{{c}}
| {{Monzo| 0 58 -29 52 -108 100 }}
|}


==Spectrum of Telepathy Tunings by Eigenmonzos==  
{| class="wikitable center-all left-5 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Target tunings (necromancy)
|-
! rowspan="2" | Target
! colspan="2" | Minimax
! colspan="2" | Least squares
|-
! Generator
! Eigenmonzo*
! Generator
! Eigenmonzo*
|-
| 13-odd-limit
| ~5/4 = 380.709{{c}}
| 13/9
| ~5/4 = 380.705{{c}}
| {{Monzo| 0 -179 -10 -87 53 158 }}
|-
| 15-odd-limit
| ~5/4 = 380.709{{c}}
| 13/9
| ~5/4 = 380.817{{c}}
| {{Monzo| 0 -222 -53 -93 67 187 }}
|}


Gencom: [2 5/4; 55/54 65/64 91/90 99/98]
{| class="wikitable center-all left-5 mw-collapsible mw-collapsed"
Gencom map: [&lt;1 0 2 -1 -1 4|, &lt;0 5 1 12 14 -1|]
|+ style="white-space: nowrap;" | Target tunings (witchcraft)
||~ Eigenmonzo ||~ Major Third ||
|-
|| 16/13 || 359.472 ||
! rowspan="2" | Target
|| 13/10 || 372.893 ||
! colspan="2" | Minimax
|| 13/12 || 376.905 ||
! colspan="2" | Least squares
|| 15/13 || 378.249 ||
|-
|| 18/13 || 378.489 ||
! Generator
|| 6/5 || 378.910 ||
! Eigenmonzo*
|| 6\19 || 378.947 ||
! Generator
|| 14/13 || 379.100 ||
! Eigenmonzo*
|| 10/9 || 379.733 ||
|-
|| 27/20 || 379.968 (5 limit least squares) ||
| 11-odd-limit
|| 19\60 || 380.000 ||
| ~5/4 = 380.343{{c}}
|| 15/14 || 380.093 ||
| 11/8
|| 32\101 || 380.198 ||
| ~5/4 = 380.278{{c}}
|| 7/5 || 380.228 ||
| {{Monzo| 0 -38 -55 11 137 }}
|| |0 36 -23 32&gt; || 380.384 (9 limit least squares) ||
|-
|| 4/3 || 380.391 (5, 7 and 9 limit minimax) ||
| 13-odd-limit
|| 13\41 || 380.488 ||
| ~5/4 = 380.119{{c}}
|| |0 1 -7 15&gt; || 380.506 (7 limit least squares) ||
| 11/7
|| |0 47 -34 43 57 -48&gt; || 380.676 (13 limit least squares) ||
| ~5/4 = 380.218{{c}}
|| |0 46 -35 49 65 -55&gt; || 380.691 (15 limit least squares) ||
| {{Monzo| 0 -67 -72 5 152 47 }}
|| 13/11 || 380.719 (13 and 15 limit minimax) ||
|-
|| 8/7 || 380.735 ||
| 15-odd-limit
|| 33\104 || 380.769 ||
| ~5/4 = 380.113{{c}}
|| 20\63 || 380.952 ||
| 15/11
|| 7/6 || 380.982 ||
| ~5/4 = 380.193{{c}}
|| 16/15 || 381.378 ||
| {{Monzo| 0 -106 -111 11 179 59 }}
|| |0 19 -36 30 42&gt; || 381.380 (11 limit least squares) ||
|}
|| 7\22 || 381.818 ||
|| 11/10 || 381.923 (11 limit minimax) ||
|| 11/8 || 382.237 ||
|| 9/7 || 382.458 ||
|| 15/11 || 382.881 ||
|| 12/11 || 383.263 ||
|| 5/4 || 386.314 ||
|| 11/9 || 386.852 ||
|| 14/11 || 391.246 ||


{| class="wikitable center-all left-5 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Target tunings (sorcery)
|-
! rowspan="2" | Target
! colspan="2" | Minimax
! colspan="2" | Least squares
|-
! Generator
! Eigenmonzo*
! Generator
! Eigenmonzo*
|-
| 13-odd-limit
| ~5/4 = 380.700{{c}}
| 11/9
| ~5/4 = 380.427{{c}}
| {{Monzo| 0 -113 12 -65 75 26 }}
|-
| 15-odd-limit
| ~5/4 = 380.700{{c}}
| 11/9
| ~5/4 = 380.457{{c}}
| {{Monzo| 0 134 9 71 -89 -33 }}
|}


==Spectrum of Witchcraft Tunings by Eigenmonzos==  
{| class="wikitable center-all left-5 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Target tunings (intuition)
|-
! rowspan="2" | Target
! colspan="2" | Minimax
! colspan="2" | Least squares
|-
! Generator
! Eigenmonzo*
! Generator
! Eigenmonzo*
|-
| 13-odd-limit
| ~5/4 = 380.029{{c}}
| 13/8
| ~5/4 = 380.568{{c}}
| {{Monzo| 0 -10 -53 24 38 66 }}
|-
| 15-odd-limit
| ~5/4 = 380.029{{c}}
| 13/8
| ~5/4 = 380.562{{c}}
| {{Monzo| 0 -30 -73 30 46 78 }}
|}


Gencom: [2 5/4; 105/104 196/195 245/243 275/273]
{| class="wikitable center-all left-5 mw-collapsible mw-collapsed"
Gencom map: [&lt;1 0 2 -1 -7 -2|, &lt;0 5 1 12 33 18|]
|+ style="white-space: nowrap;" | Target tunings (telepathy)
||~ Eigenmonzo ||~ Major Third ||
|-
|| 14/13 || 378.617 ||
! rowspan="2" | Target
|| 6/5 || 378.910 ||
! colspan="2" | Minimax
|| 6\19 || 378.947 ||
! colspan="2" | Least squares
|| 15/13 || 379.355 ||
|-
|| 18/13 || 379.577 ||
! Generator
|| 13/10 || 379.660 ||
! Eigenmonzo*
|| 10/9 || 379.733 ||
! Generator
|| 27/20 || 379.968 (5 limit least squares) ||
! Eigenmonzo*
|| 13/12 || 379.890 ||
|-
|| 19\60 || 380.000 ||
| 11-odd-limit
|| 16/13 || 380.029 ||
| ~5/4 = 381.923{{c}}
|| 15/14 || 380.093 ||
| 11/10
|| 15/11 || 380.113 (15 limit minimax) ||
| ~5/4 = 381.380{{c}}
|| 14/11 || 380.119 (13 limit minimax) ||
| {{Monzo| 0 19 -36 30 42 }}
|| 11/10 || 380.156 ||
|-
|| |0 -106 -111 11 179 59&gt; || 380.193 (15 limit least squares) ||
| 13-odd-limit
|| 32\101 || 380.198 ||
| ~5/4 = 380.719{{c}}
|| |0 -67 -72 5 152 47&gt; || 380.218 (13 limit least squares) ||
| 13/11
|| 7/5 || 380.228 ||
| ~5/4 = 380.676{{c}}
|| |0 -38 -55 11 137&gt; || 380.278 (11 limit least squares) ||
| {{Monzo| 0 47 -34 43 57 -48 }}
|| 11/9 || 380.322 ||
|-
|| 12/11 || 380.334 ||
| 15-odd-limit
|| 11/8 || 380.343 (11 limit minimax) ||
| ~5/4 = 380.719{{c}}
|| |0 36 -23 32&gt; || 380.384 (9 limit least squares) ||
| 13/11
|| 4/3 || 380.391 (5, 7 and 9 limit minimax) ||
| ~5/4 = 380.691{{c}}
|| 13\41 || 380.488 ||
| {{Monzo| 0 46 -35 49 65 -55 }}
|| 13/11 || 380.719 ||
|}
|| 8/7 || 380.735 ||
|| 33\104 || 380.769 ||
|| 20\63 || 380.952 ||
|| 7/6 || 380.982 ||
|| 16/15 || 381.378 ||
|| 7\22 || 381.818 ||
|| 9/7 || 382.458 ||
|| 5/4 || 386.314 ||


=== Tuning spectra ===
==== Magic ====
{| class="wikitable center-all left-4"
|-
! Edo<br>generator
! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]
! Generator (¢)
! Comments
|-
|
| 21/13
| 369.747
|
|-
|
| 13/7
| 378.617
|
|-
|
| 5/3
| 378.910
|
|-
| 6\19
|
| 378.947
| Lower bound of 9- to 15-odd-limit diamond monotone
|-
|
| 15/13
| 379.355
|
|-
|
| 13/9
| 379.577
|
|-
|
| 13/10
| 379.660
|
|-
|
| 9/5
| 379.733
|
|-
|
| 13/12
| 379.890
|
|-
| 19\60
|
| 380.000
|
|-
|
| 13/8
| 380.029
|
|-
|
| 15/14
| 380.093
|
|-
| 32\101
|
| 380.198
| 101cde val
|-
|
| 7/5
| 380.228
|
|-
|
| 21/20
| 380.279
|
|-
|
| 13/11
| 380.354
| 13- and 15-odd-limit minimax
|-
|
| 3/2
| 380.391
| 5-, 7- and 9-odd-limit minimax
|-
| 13\41
|
| 380.488
|
|-
|
| 21/16
| 380.634
|
|-
|
| 11/9
| 380.700
| 11-odd-limit minimax
|-
|
| 7/4
| 380.735
|
|-
| 33\104
|
| 380.769
| 104ff val
|-
|
| 21/11
| 380.779
|
|-
|
| 11/6
| 380.818
|
|-
|
| 11/7
| 380.875
|
|-
| 20\63
|
| 380.952
| 63f val
|-
|
| 7/6
| 380.982
|
|-
|
| 11/8
| 381.085
|
|-
|
| 15/11
| 381.211
|
|-
|
| 15/8
| 381.378
|
|-
|
| 11/10
| 381.666
|
|-
| 7\22
|
| 381.818
| 22f val, upper bound of 9- to 15-odd-limit diamond monotone
|-
|
| 9/7
| 382.458
|
|-
|
| 5/4
| 386.314
|
|}


==Spectrum of Muggles Tunings by Eigenmonzos==  
==== Necromancy ====
{| class="wikitable center-all left-4"
|-
! Edo<br>generator
! Unchanged interval<br>(eigenmonzo)
! Generator (¢)
! Comments
|-
|
| 5/3
| 378.910
|
|-
| 6\19
|
| 378.947
| 19f val, lower bound of 9- and 11-odd-limit diamond monotone
|-
|
| 9/5
| 379.733
|
|-
| 19\60
|
| 380.000
| 60f val
|-
|
| 15/14
| 380.093
|
|-
| 32\101
|
| 380.198
| 101cdeff val
|-
|
| 7/5
| 380.228
|
|-
|
| 21/20
| 380.279
|
|-
|
| 3/2
| 380.391
| 5-, 7- and 9-odd-limit minimax
|-
| 13\41
|
| 380.488
| Lower bound of 13- and 15-odd-limit diamond monotone
|-
|
| 21/16
| 380.634
|
|-
|
| 11/9
| 380.700
| 11-odd-limit minimax
|-
|
| 13/9
| 380.709
| 13- and 15-odd-limit minimax
|-
|
| 13/11
| 380.719
|
|-
|
| 7/4
| 380.735
|
|-
|
| 21/13
| 380.756
|
|-
|
| 13/12
| 380.765
|
|-
| 33\104
|
| 380.769
|
|-
|
| 21/11
| 380.779
|
|-
|
| 13/7
| 380.809
|
|-
|
| 11/6
| 380.818
|
|-
|
| 13/8
| 380.847
|
|-
|
| 11/7
| 380.875
|
|-
| 20\63
|
| 380.952
| Upper bound of 13- and 15-odd-limit diamond monotone
|-
|
| 15/13
| 380.957
|
|-
|
| 7/6
| 380.982
|
|-
|
| 13/10
| 381.074
|
|-
|
| 11/8
| 381.085
|
|-
|
| 15/11
| 381.211
|
|-
|
| 15/8
| 381.378
|
|-
|
| 11/10
| 381.666
|
|-
| 7\22
|
| 381.818
| Upper bound of 9- and 11-odd-limit diamond monotone
|-
|
| 9/7
| 382.458
|
|-
|
| 5/4
| 386.314
|
|}


Gencom: [2 5/4; 45/44 65/64 78/77 126/125]
==== Witchcraft ====
Gencom map: [&lt;1 0 2 5 0 4|, &lt;0 5 1 -7 11 -1|]
{| class="wikitable center-all left-4"
||~ Eigenmonzo ||~ Major Third ||
|-
|| 11/9 || 347.408 ||
! Edo<br>generator
|| 16/13 || 359.472 ||
! Unchanged interval<br>(eigenmonzo)
|| 15/11 || 372.610 ||
! Generator (¢)
|| 13/10 || 372.893 ||
! Comments
|| 12/11 || 374.894 ||
|-
|| 8/7 || 375.882 ||
|  
|| 13/11 || 375.899 ||
| 21/13
|| 11/10 || 376.500 ||
| 369.747
|| 14/11 || 376.805 ||
|  
|| 13/12 || 376.905 ||
|-
|| 7/5 || 377.186 ||
|  
|| 11/8 || 377.393 (11, 13 and 15 limit minimax) ||
| 13/7
|| |0 113 -12 -68 58 -26&gt; || 377.630 (13 limit least squares) ||
| 378.617
|| |0 -21 -5 27&gt; || 377.640 (7 limit least squares) ||
|  
|| |0 134 9 -81 63 -33&gt; || 377.718 (15 limit least squares) ||
|-
|| |0 85 -14 -62 46&gt; || 377.758 (11 limit least squares) ||
|  
|| 7/6 || 377.761 (7 limit minimax) ||
| 5/3
|| 15/13 || 378.249 ||
| 378.910
|| 15/14 || 378.419 ||
|  
|| 18/13 || 378.489 ||
|-
|| 9/7 || 378.534 (9 limit minimax) ||
| 6\19
|| |0 93 -4 -44&gt; || 378.554 (9 limit least squares) ||
|  
|| 14/13 || 378.617 ||
| 378.947
|| 6/5 || 378.910 ||
| 19e val, lower bound of 9-odd-limit diamond monotone
|| 6\19 || 378.947 ||
|-
|| 10/9 || 379.733 ||
|  
|| 27/20 || 379.968 (5 limit least squares) ||
| 15/13
|| 19\60 || 380.000 ||
| 379.355
|| 32\101 || 380.198 ||
|  
|| 4/3 || 380.391 (5 limit minimax) ||
|-
|| 13\41 || 380.488 ||
|  
|| 33\104 || 380.769 ||  
| 13/9
|| 20\63 || 380.952 ||
| 379.577
|| 16/15 || 381.378 ||
|  
|| 7\22 || 381.818 ||
|-
|| 5/4 || 386.314 ||</pre></div>
|  
<h4>Original HTML content:</h4>
| 13/10
<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;Magic extensions&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;br /&gt;
| 379.660
&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 Magic Tunings by Eigenmonzos"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Spectrum of Magic Tunings by Eigenmonzos&lt;/h2&gt;
|  
&lt;br /&gt;
| 9/5
Gencom: [2 5/4; 100/99 105/104 144/143 196/195]&lt;br /&gt;
| 379.733
Gencom map: [&amp;lt;1 0 2 -1 6 -2|, &amp;lt;0 5 1 12 -8 18|]&lt;br /&gt;
|  
|-
|  
| 13/12
| 379.890
|  
|-
| 19\60
|  
| 380.000
| 60e val, lower bound of 11- to 15-odd-limit diamond monotone
|-
|  
| 13/8
| 380.029
|  
|-
|  
| 21/11
| 380.034
|  
|-
|  
| 15/14
| 380.093
|  
|-
|  
| 15/11
| 380.113
| 15-odd-limit minimax
|-
|  
| 11/7
| 380.119
| 13-odd-limit minimax
|-
|  
| 11/10
| 380.156
|  
|-
| 32\101
|  
| 380.198
| 101cd val
|-
|  
| 7/5
| 380.228
|  
|-
|  
| 21/20
| 380.279
|  
|-
|  
| 11/9
| 380.322
|  
|-
|  
| 11/6
| 380.334
|  
|-
|  
| 11/8
| 380.343
| 11-odd-limit minimax
|-
|  
| 3/2
| 380.391
| 5-, 7- and 9-odd-limit minimax
|-
| 13\41
|  
| 380.488
| Upper bound of 11- to 15-odd-limit diamond monotone
|-
|  
| 21/16
| 380.634
|  
|-
|  
| 13/11
| 380.719
|  
|-
|  
| 7/4
| 380.735
|  
|-
| 33\104
|  
| 380.769
| 104eeff val
|-
| 20\63
|  
| 380.952
| 63eef val
|-
|  
| 7/6
| 380.982
|
|-
|
| 15/8
| 381.378
|  
|-
| 7\22
|  
| 381.818
| 22ef val, upper bound of 9-odd-limit diamond monotone
|-
|  
| 9/7
| 382.458
|  
|-
|
| 5/4
| 386.314
|
|}


==== Sorcery ====
{| class="wikitable center-all left-4"
|-
! Edo<br>generator
! Unchanged interval<br>(eigenmonzo)
! Generator (¢)
! Comments
|-
|
| 13/8
| 359.472
|
|-
|
| 13/10
| 372.893
|
|-
|
| 13/12
| 376.905
|
|-
|
| 15/13
| 378.249
|
|-
|
| 13/9
| 378.489
|
|-
|
| 5/3
| 378.910
|
|-
| 6\19
|
| 378.947
| Lower bound of 9- and 11-odd-limit diamond monotone<br>13- and 15-odd-limit diamond monotone (singleton)
|-
|
| 13/7
| 379.100
|
|-
|
| 21/13
| 379.459
|
|-
|
| 9/5
| 379.733
|
|-
| 19\60
|
| 380.000
| 60ff val
|-
|
| 15/14
| 380.093
|
|-
| 32\101
|
| 380.198
| 101cdefff val
|-
|
| 7/5
| 380.228
|
|-
|
| 21/20
| 380.279
|
|-
|
| 3/2
| 380.391
| 5-, 7- and 9-odd-limit minimax
|-
| 13\41
|
| 380.488
| 41f val
|-
|
| 21/16
| 380.634
|
|-
|
| 11/9
| 380.700
| 11-, 13- and 15-odd-limit minimax
|-
|
| 7/4
| 380.735
|
|-
| 33\104
|
| 380.769
| 104fff val
|-
|
| 21/11
| 380.779
|
|-
|
| 11/6
| 380.818
|
|-
|
| 11/7
| 380.875
|
|-
| 20\63
|
| 380.952
| 63ff val
|-
|
| 7/6
| 380.982
|
|-
|
| 11/8
| 381.085
|
|-
|
| 15/11
| 381.211
|
|-
|
| 15/8
| 381.378
|
|-
|
| 11/10
| 381.666
|
|-
| 7\22
|
| 381.818
| Upper bound of 9- and 11-odd-limit diamond monotone
|-
|
| 9/7
| 382.458
|
|-
|
| 13/11
| 384.173
|
|-
|
| 5/4
| 386.314
|
|}


&lt;table class="wiki_table"&gt;
==== Intuition ====
    &lt;tr&gt;
{| class="wikitable center-all left-4"
        &lt;th&gt;Eigenmonzo&lt;br /&gt;
|-
&lt;/th&gt;
! Edo<br>generator
        &lt;th&gt;Major Third&lt;br /&gt;
! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]
&lt;/th&gt;
! Generator (¢)
    &lt;/tr&gt;
! Comments
    &lt;tr&gt;
|-
        &lt;td&gt;14/13&lt;br /&gt;
|
&lt;/td&gt;
| 21/13
        &lt;td&gt;378.617&lt;br /&gt;
| 369.747
&lt;/td&gt;
|
    &lt;/tr&gt;
|-
    &lt;tr&gt;
|
        &lt;td&gt;6/5&lt;br /&gt;
| 13/11
&lt;/td&gt;
| 372.302
        &lt;td&gt;378.910&lt;br /&gt;
|
&lt;/td&gt;
|-
    &lt;/tr&gt;
|
    &lt;tr&gt;
| 21/11
        &lt;td&gt;6\19&lt;br /&gt;
| 373.154
&lt;/td&gt;
|
        &lt;td&gt;378.947&lt;br /&gt;
|-
&lt;/td&gt;
|
    &lt;/tr&gt;
| 13/7
    &lt;tr&gt;
| 378.617
        &lt;td&gt;15/13&lt;br /&gt;
|
&lt;/td&gt;
|-
        &lt;td&gt;379.355&lt;br /&gt;
|
&lt;/td&gt;
| 5/3
    &lt;/tr&gt;
| 378.910
    &lt;tr&gt;
|
        &lt;td&gt;18/13&lt;br /&gt;
|-
&lt;/td&gt;
| 6\19
        &lt;td&gt;379.577&lt;br /&gt;
|
&lt;/td&gt;
| 378.947
    &lt;/tr&gt;
| 19e val, lower bound of 9-odd-limit diamond monotone
    &lt;tr&gt;
|-
        &lt;td&gt;13/10&lt;br /&gt;
|
&lt;/td&gt;
| 15/13
        &lt;td&gt;379.660&lt;br /&gt;
| 379.355
&lt;/td&gt;
|
    &lt;/tr&gt;
|-
    &lt;tr&gt;
|
        &lt;td&gt;10/9&lt;br /&gt;
| 13/9
&lt;/td&gt;
| 379.577
        &lt;td&gt;379.733&lt;br /&gt;
|
&lt;/td&gt;
|-
    &lt;/tr&gt;
|
    &lt;tr&gt;
| 13/10
        &lt;td&gt;13/12&lt;br /&gt;
| 379.660
&lt;/td&gt;
|
        &lt;td&gt;379.890&lt;br /&gt;
|-
&lt;/td&gt;
|
    &lt;/tr&gt;
| 9/5
    &lt;tr&gt;
| 379.733
        &lt;td&gt;27/20&lt;br /&gt;
|
&lt;/td&gt;
|-
        &lt;td&gt;379.968 (5 limit least squares)&lt;br /&gt;
|
&lt;/td&gt;
| 13/12
    &lt;/tr&gt;
| 379.890
    &lt;tr&gt;
|
        &lt;td&gt;19\60&lt;br /&gt;
|-
&lt;/td&gt;
| 19\60
        &lt;td&gt;380.000&lt;br /&gt;
|
&lt;/td&gt;
| 380.000
    &lt;/tr&gt;
| 60eee val
    &lt;tr&gt;
|-
        &lt;td&gt;16/13&lt;br /&gt;
|
&lt;/td&gt;
| 13/8
        &lt;td&gt;380.029&lt;br /&gt;
| 380.029
&lt;/td&gt;
| 13- and 15-odd-limit minimax
    &lt;/tr&gt;
|-
    &lt;tr&gt;
|
        &lt;td&gt;15/14&lt;br /&gt;
| 15/14
&lt;/td&gt;
| 380.093
        &lt;td&gt;380.093&lt;br /&gt;
|
&lt;/td&gt;
|-
    &lt;/tr&gt;
| 32\101
    &lt;tr&gt;
|
        &lt;td&gt;32\101&lt;br /&gt;
| 380.198
&lt;/td&gt;
| 101cdeeee val
        &lt;td&gt;380.198&lt;br /&gt;
|-
&lt;/td&gt;
|
    &lt;/tr&gt;
| 7/5
    &lt;tr&gt;
| 380.228
        &lt;td&gt;7/5&lt;br /&gt;
|
&lt;/td&gt;
|-
        &lt;td&gt;380.228&lt;br /&gt;
|
&lt;/td&gt;
| 21/20
    &lt;/tr&gt;
| 380.279
    &lt;tr&gt;
|
        &lt;td&gt;13/11&lt;br /&gt;
|-
&lt;/td&gt;
|
        &lt;td&gt;380.354 (13 and 15 limit minimax)&lt;br /&gt;
| 3/2
&lt;/td&gt;
| 380.391
    &lt;/tr&gt;
| 5-, 7- and 9-odd-limit minimax
    &lt;tr&gt;
|-
        &lt;td&gt;|0 56 -31 46 -94 88&amp;gt;&lt;br /&gt;
| 13\41
&lt;/td&gt;
|
        &lt;td&gt;380.377 (13 limit least squares)&lt;br /&gt;
| 380.488
&lt;/td&gt;
| 41e val
    &lt;/tr&gt;
|-
    &lt;tr&gt;
|
        &lt;td&gt;|0 36 -23 32&amp;gt;&lt;br /&gt;
| 21/16
&lt;/td&gt;
| 380.634
        &lt;td&gt;380.384 (9 limit least squares)&lt;br /&gt;
|
&lt;/td&gt;
|-
    &lt;/tr&gt;
|
    &lt;tr&gt;
| 7/4
        &lt;td&gt;|0 58 -29 52 -108 100&amp;gt;&lt;br /&gt;
| 380.735
&lt;/td&gt;
|
        &lt;td&gt;380.389 (15 limit least squares)&lt;br /&gt;
|-
&lt;/td&gt;
| 33\104
    &lt;/tr&gt;
|
    &lt;tr&gt;
| 380.769
        &lt;td&gt;4/3&lt;br /&gt;
| 104eeeff val
&lt;/td&gt;
|-
        &lt;td&gt;380.391 (5, 7 and 9 limit minimax)&lt;br /&gt;
| 20\63
&lt;/td&gt;
|
    &lt;/tr&gt;
| 380.952
    &lt;tr&gt;
| 63ef val
        &lt;td&gt;13\41&lt;br /&gt;
|-
&lt;/td&gt;
|
        &lt;td&gt;380.488&lt;br /&gt;
| 7/6
&lt;/td&gt;
| 380.982
    &lt;/tr&gt;
|
    &lt;tr&gt;
|-
        &lt;td&gt;|0 1 -7 15&amp;gt;&lt;br /&gt;
|
&lt;/td&gt;
| 15/8
        &lt;td&gt;380.506 (7 limit least squares)&lt;br /&gt;
| 381.378
&lt;/td&gt;
|
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| 7\22
        &lt;td&gt;11/9&lt;br /&gt;
|
&lt;/td&gt;
| 381.818
        &lt;td&gt;380.700 (11 limit minimax)&lt;br /&gt;
| 22f val, upper bound of 9-odd-limit diamond monotone<br>11- to 15-odd-limit diamond monotone (singleton)
&lt;/td&gt;
|-
    &lt;/tr&gt;
|
    &lt;tr&gt;
| 11/10
        &lt;td&gt;|0 85 -14 52 -68&amp;gt;&lt;br /&gt;
| 381.923
&lt;/td&gt;
| 11-odd-limit minimax
        &lt;td&gt;380.714 (11 limit least squares)&lt;br /&gt;
|-
&lt;/td&gt;
|
    &lt;/tr&gt;
| 11/8
    &lt;tr&gt;
| 382.237
        &lt;td&gt;8/7&lt;br /&gt;
|
&lt;/td&gt;
|-
        &lt;td&gt;380.735&lt;br /&gt;
|
&lt;/td&gt;
| 9/7
    &lt;/tr&gt;
| 382.458
    &lt;tr&gt;
|
        &lt;td&gt;33\104&lt;br /&gt;
|-
&lt;/td&gt;
|
        &lt;td&gt;380.769&lt;br /&gt;
| 15/11
&lt;/td&gt;
| 382.881
        &lt;td&gt;&lt;br /&gt;
|
&lt;/td&gt;
|-
        &lt;td&gt;12/11&lt;br /&gt;
|
&lt;/td&gt;
| 11/6
        &lt;td&gt;380.818&lt;br /&gt;
| 383.263
&lt;/td&gt;
|
    &lt;/tr&gt;
|-
    &lt;tr&gt;
|
        &lt;td&gt;14/11&lt;br /&gt;
| 5/4
&lt;/td&gt;
| 386.314
        &lt;td&gt;380.875&lt;br /&gt;
|
&lt;/td&gt;
|-
    &lt;/tr&gt;
|
    &lt;tr&gt;
| 11/9
        &lt;td&gt;20\63&lt;br /&gt;
| 386.852
&lt;/td&gt;
|
        &lt;td&gt;380.952&lt;br /&gt;
|-
&lt;/td&gt;
|
    &lt;/tr&gt;
| 11/7
    &lt;tr&gt;
| 391.246
        &lt;td&gt;7/6&lt;br /&gt;
|
&lt;/td&gt;
|}
        &lt;td&gt;380.982&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;381.085&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;381.211&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;381.378&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;381.666&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7\22&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;381.818&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;382.458&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;386.314&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
==== Telepathy ====
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Tuning Spectra-Spectrum of Necromancy Tunings by Eigenmonzos"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Spectrum of Necromancy Tunings by Eigenmonzos&lt;/h2&gt;
{| class="wikitable center-all left-4"
&lt;br /&gt;
|-
Gencom: [2 5/4; 100/99 225/224 245/243 275/273]&lt;br /&gt;
! Edo<br>generator
Gencom map: [&amp;lt;1 0 2 -1 6 11|, &amp;lt;0 5 1 12 -8 -23|]&lt;br /&gt;
! Unchanged interval<br>(eigenmonzo)
! Generator (¢)
! Comments
|-
|
| 13/8
| 359.472
|
|-
|
| 13/10
| 372.893
|
|-
|
| 21/11
| 373.154
|
|-
|
| 13/12
| 376.905
|
|-
|
| 15/13
| 378.249
|
|-
|
| 13/9
| 378.489
|
|-
|
| 5/3
| 378.910
|
|-
| 6\19
|
| 378.947
| 19e val, lower bound of 9-odd-limit diamond monotone<br>2.3.5.7.13-subgroup 13-odd-limit diamond monotone (singleton)
|-
|
| 13/7
| 379.100
|
|-
|
| 21/13
| 379.459
|
|-
|
| 9/5
| 379.733
|
|-
| 19\60
|
| 380.000
| 60eeeff val
|-
|
| 15/14
| 380.093
|
|-
| 32\101
|
| 380.198
| 101cdeeeefff val
|-
|
| 7/5
| 380.228
|
|-
|
| 21/20
| 380.279
|
|-
|
| 3/2
| 380.391
| 5-, 7- and 9-odd-limit minimax
|-
| 13\41
|
| 380.488
| 41ef val
|-
|
| 21/16
| 380.634
|
|-
|
| 13/11
| 380.719
| 13- and 15-odd-limit minimax
|-
|
| 7/4
| 380.735
|
|-
| 33\104
|
| 380.769
| 104eeefff val
|-
| 20\63
|
| 380.952
| 63eff val
|-
|
| 7/6
| 380.982
|
|-
|
| 15/8
| 381.378
|
|-
| 7\22
|
| 381.818
| Upper bound of 9-odd-limit diamond monotone<br>11-odd-limit diamond monotone (singleton)
|-
|
| 11/10
| 381.923
| 11-odd-limit minimax
|-
|
| 11/8
| 382.237
|
|-
|
| 9/7
| 382.458
|
|-
|
| 15/11
| 382.881
|
|-
|
| 11/6
| 383.263
|
|-
|
| 5/4
| 386.314
|
|-
|
| 11/9
| 386.852
|
|-
|  
| 11/7
| 391.246
|
|}


 
[[Category:Magic]]
&lt;table class="wiki_table"&gt;
[[Category:Temperament extensions]]
    &lt;tr&gt;
[[Category:Rank-2 temperaments]]
        &lt;th&gt;Eigenmonzo&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Major Third&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;378.910&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6\19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;378.947&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;379.733&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;27/20&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;379.968 (5 limit least squares)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;19\60&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.000&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;380.093&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;32\101&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.198&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;380.228&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;|0 36 -23 32&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.384 (9 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;380.391 (5, 7 and 9 limit minimax)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13\41&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.488&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;|0 1 -7 15&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.506 (7 limit least squares)&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;380.700 (11 limit minimax)&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;380.709 (13 and 15 limit minimax)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;|0 85 -14 52 -68&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.714 (11 limit least squares)&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;380.719&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;380.735&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;380.765&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;33\104&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.769&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|0 -179 -10 -87 53 158&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.785 (13 limit least squares)&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;380.809&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;|0 -222 -53 -93 67 187&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.817 (15 limit least squares)&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;380.818&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;380.847&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;380.875&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;20\63&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.952&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;380.957&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;380.982&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;381.074&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;381.085&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;381.211&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;381.378&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;381.666&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7\22&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;381.818&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;382.458&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;386.314&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&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 Sorcery Tunings by Eigenmonzos"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Spectrum of Sorcery Tunings by Eigenmonzos&lt;/h2&gt;
&lt;br /&gt;
Gencom: [2 5/4; 65/64 78/77 91/90 100/99]&lt;br /&gt;
Gencom map: [&amp;lt;1 0 2 -1 6 4|, &amp;lt;0 5 1 12 -8 -1|]&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;Major Third&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;359.472&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;372.893&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;376.905&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;378.249&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;378.489&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;378.910&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6\19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;378.947&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;379.100&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;379.733&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;27/20&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;379.968 (5 limit least squares)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;19\60&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.000&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;380.093&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;32\101&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.198&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;380.228&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;|0 36 -23 32&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.384 (9 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;380.391 (5, 7 and 9 limit minimax)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;|0 -113 12 -65 75 26&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.427 (13 limit least squares)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;|0 134 9 71 -89 -33&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.457 (15 limit least squares)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13\41&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.488&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;|0 1 -7 15&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.506 (7 limit least squares)&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;380.700 (11, 13 and 15 limit minimax)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;|0 85 -14 52 -68&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.714 (11 limit least squares)&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;380.735&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;33\104&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.769&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.818&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;380.875&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;20\63&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.952&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;380.982&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;381.085&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;381.211&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;381.378&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;381.666&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7\22&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;381.818&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;382.458&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;384.173&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;386.314&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&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 Telepathy Tunings by Eigenmonzos"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Spectrum of Telepathy Tunings by Eigenmonzos&lt;/h2&gt;
&lt;br /&gt;
Gencom: [2 5/4; 55/54 65/64 91/90 99/98]&lt;br /&gt;
Gencom map: [&amp;lt;1 0 2 -1 -1 4|, &amp;lt;0 5 1 12 14 -1|]&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;Major Third&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;359.472&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;372.893&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;376.905&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;378.249&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;378.489&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;378.910&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6\19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;378.947&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;379.100&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;379.733&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;27/20&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;379.968 (5 limit least squares)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;19\60&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.000&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;380.093&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;32\101&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.198&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;380.228&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;|0 36 -23 32&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.384 (9 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;380.391 (5, 7 and 9 limit minimax)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13\41&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.488&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;|0 1 -7 15&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.506 (7 limit least squares)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;|0 47 -34 43 57 -48&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.676 (13 limit least squares)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;|0 46 -35 49 65 -55&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.691 (15 limit least squares)&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;380.719 (13 and 15 limit minimax)&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;380.735&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;33\104&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.769&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;20\63&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.952&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;380.982&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;381.378&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;|0 19 -36 30 42&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;381.380 (11 limit least squares)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7\22&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;381.818&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;381.923 (11 limit minimax)&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;382.237&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;382.458&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;382.881&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;383.263&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;386.314&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;386.852&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;391.246&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Tuning Spectra-Spectrum of Witchcraft Tunings by Eigenmonzos"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Spectrum of Witchcraft Tunings by Eigenmonzos&lt;/h2&gt;
&lt;br /&gt;
Gencom: [2 5/4; 105/104 196/195 245/243 275/273]&lt;br /&gt;
Gencom map: [&amp;lt;1 0 2 -1 -7 -2|, &amp;lt;0 5 1 12 33 18|]&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;Major Third&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;378.617&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;378.910&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6\19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;378.947&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;379.355&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;379.577&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;379.660&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;379.733&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;27/20&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;379.968 (5 limit least squares)&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;379.890&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;19\60&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.000&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;380.029&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;380.093&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;380.113 (15 limit minimax)&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;380.119 (13 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;380.156&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;|0 -106 -111 11 179 59&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.193 (15 limit least squares)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;32\101&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.198&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;|0 -67 -72 5 152 47&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.218 (13 limit least squares)&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;380.228&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;|0 -38 -55 11 137&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.278 (11 limit least squares)&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;380.322&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;380.334&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;380.343 (11 limit minimax)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;|0 36 -23 32&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.384 (9 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;380.391 (5, 7 and 9 limit minimax)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13\41&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.488&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;380.719&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;380.735&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;33\104&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.769&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;20\63&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.952&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;380.982&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;381.378&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7\22&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;381.818&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;382.458&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;386.314&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Tuning Spectra-Spectrum of Muggles Tunings by Eigenmonzos"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Spectrum of Muggles Tunings by Eigenmonzos&lt;/h2&gt;
&lt;br /&gt;
Gencom: [2 5/4; 45/44 65/64 78/77 126/125]&lt;br /&gt;
Gencom map: [&amp;lt;1 0 2 5 0 4|, &amp;lt;0 5 1 -7 11 -1|]&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;Major Third&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;347.408&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;359.472&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;372.610&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;372.893&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;374.894&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;375.882&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;375.899&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;376.500&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;376.805&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;376.905&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;377.186&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;377.393 (11, 13 and 15 limit minimax)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;|0 113 -12 -68 58 -26&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;377.630 (13 limit least squares)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;|0 -21 -5 27&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;377.640 (7 limit least squares)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;|0 134 9 -81 63 -33&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;377.718 (15 limit least squares)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;|0 85 -14 -62 46&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;377.758 (11 limit least squares)&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;377.761 (7 limit minimax)&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;378.249&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;378.419&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;378.489&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;378.534 (9 limit minimax)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;|0 93 -4 -44&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;378.554 (9 limit least squares)&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;378.617&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;378.910&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6\19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;378.947&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;379.733&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;27/20&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;379.968 (5 limit least squares)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;19\60&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.000&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;32\101&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.198&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;380.391 (5 limit minimax)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13\41&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.488&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;33\104&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.769&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;20\63&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.952&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;381.378&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7\22&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;381.818&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;386.314&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/body&gt;&lt;/html&gt;</pre></div>
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