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m Merge tuning table with the larger one in magic extensions, as there's no need for them to be separate pages.
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* [[Paulsmagic]]
* [[Paulsmagic]]


== Spectrum of magic tunings by eigenmonzos ==
=Tuning Spectra=


{| class="wikitable center-all left-3"
==Spectrum of Magic Tunings by Eigenmonzos==
 
Gencom: [2 5/4; 100/99 105/104 144/143 196/195]
 
Gencom map: [<1 0 2 -1 6 -2|, <0 5 1 12 -8 18|]
 
{| class="wikitable"
|-
! | Eigenmonzo
! | Major Third
|-
| | 14/13
| | 378.617
|-
| | 6/5
| | 378.910
|-
| | 6\19
| | 378.947
|-
| | 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>
| | 380.377 (13 limit least squares)
|-
| | |0 36 -23 32>
| | 380.384 (9 limit least squares)
|-
| | |0 58 -29 52 -108 100>
| | 380.389 (15 limit least squares)
|-
| | 4/3
| | 380.391 (5, 7 and 9 limit minimax)
|-
| | 13\41
| | 380.488
|-
| | |0 1 -7 15>
| | 380.506 (7 limit least squares)
|-
| | 11/9
| | 380.700 (11 limit minimax)
|-
| | |0 85 -14 52 -68>
| | 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==
 
Gencom: [2 5/4; 100/99 225/224 245/243 275/273]
 
Gencom map: [<1 0 2 -1 6 11|, <0 5 1 12 -8 -23|]
 
{| class="wikitable"
|-
! | 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>
| | 380.384 (9 limit least squares)
|-
| | 4/3
| | 380.391 (5, 7 and 9 limit minimax)
|-
| | 13\41
| | 380.488
|-
| | |0 1 -7 15>
| | 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>
| | 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>
| | 380.785 (13 limit least squares)
|-
| | 14/13
| | 380.809
|-
| | |0 -222 -53 -93 67 187>
| | 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
|}
 
==Spectrum of Sorcery Tunings by Eigenmonzos==
 
Gencom: [2 5/4; 65/64 78/77 91/90 100/99]
 
Gencom map: [<1 0 2 -1 6 4|, <0 5 1 12 -8 -1|]
 
{| class="wikitable"
|-
! | Eigenmonzo
! | Major Third
|-
| | 16/13
| | 359.472
|-
| | 13/10
| | 372.893
|-
| | 13/12
| | 376.905
|-
| | 15/13
| | 378.249
|-
| | 18/13
| | 378.489
|-
| | 6/5
| | 378.910
|-
| | 6\19
| | 378.947
|-
| | 14/13
| | 379.100
|-
| | 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>
| | 380.384 (9 limit least squares)
|-
| | 4/3
| | 380.391 (5, 7 and 9 limit minimax)
|-
| | |0 -113 12 -65 75 26>
| | 380.427 (13 limit least squares)
|-
| | |0 134 9 71 -89 -33>
| | 380.457 (15 limit least squares)
|-
| | 13\41
| | 380.488
|-
| | |0 1 -7 15>
| | 380.506 (7 limit least squares)
|-
| | 11/9
| | 380.700 (11, 13 and 15 limit minimax)
|-
| | |0 85 -14 52 -68>
| | 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
|-
| | 13/11
| | 384.173
|-
| | 5/4
| | 386.314
|}
 
==Spectrum of Telepathy Tunings by Eigenmonzos==
 
Gencom: [2 5/4; 55/54 65/64 91/90 99/98]
 
Gencom map: [<1 0 2 -1 -1 4|, <0 5 1 12 14 -1|]
 
{| class="wikitable"
|-
! | Eigenmonzo
! | Major Third
|-
| | 16/13
| | 359.472
|-
| | 13/10
| | 372.893
|-
| | 13/12
| | 376.905
|-
| | 15/13
| | 378.249
|-
| | 18/13
| | 378.489
|-
| | 6/5
| | 378.910
|-
| | 6\19
| | 378.947
|-
| | 14/13
| | 379.100
|-
| | 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>
| | 380.384 (9 limit least squares)
|-
| | 4/3
| | 380.391 (5, 7 and 9 limit minimax)
|-
| | 13\41
| | 380.488
|-
| | |0 1 -7 15>
| | 380.506 (7 limit least squares)
|-
| | |0 47 -34 43 57 -48>
| | 380.676 (13 limit least squares)
|-
| | |0 46 -35 49 65 -55>
| | 380.691 (15 limit least squares)
|-
| | 13/11
| | 380.719 (13 and 15 limit minimax)
|-
| | 8/7
| | 380.735
|-
| | 33\104
| | 380.769
|-
| | 20\63
| | 380.952
|-
| | 7/6
| | 380.982
|-
| | 16/15
| | 381.378
|-
| | |0 19 -36 30 42>
| | 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
|}
 
==Spectrum of Witchcraft Tunings by Eigenmonzos==
 
Gencom: [2 5/4; 105/104 196/195 245/243 275/273]
 
Gencom map: [<1 0 2 -1 -7 -2|, <0 5 1 12 33 18|]
 
{| class="wikitable"
|-
! | Eigenmonzo
! | Major Third
|-
| | 14/13
| | 378.617
|-
| | 6/5
| | 378.910
|-
| | 6\19
| | 378.947
|-
| | 15/13
| | 379.355
|-
| | 18/13
| | 379.577
|-
| | 13/10
| | 379.660
|-
| | 10/9
| | 379.733
|-
| | 27/20
| | 379.968 (5 limit least squares)
|-
| | 13/12
| | 379.890
|-
| | 19\60
| | 380.000
|-
| | 16/13
| | 380.029
|-
| | 15/14
| | 380.093
|-
| | 15/11
| | 380.113 (15 limit minimax)
|-
| | 14/11
| | 380.119 (13 limit minimax)
|-
| | 11/10
| | 380.156
|-
| | |0 -106 -111 11 179 59>
| | 380.193 (15 limit least squares)
|-
| | 32\101
| | 380.198
|-
| | |0 -67 -72 5 152 47>
| | 380.218 (13 limit least squares)
|-
| | 7/5
| | 380.228
|-
| | |0 -38 -55 11 137>
| | 380.278 (11 limit least squares)
|-
| | 11/9
| | 380.322
|-
| | 12/11
| | 380.334
|-
| | 11/8
| | 380.343 (11 limit minimax)
|-
| | |0 36 -23 32>
| | 380.384 (9 limit least squares)
|-
| | 4/3
| | 380.391 (5, 7 and 9 limit minimax)
|-
| | 13\41
| | 380.488
|-
| | 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
|}
 
==Spectrum of Muggles Tunings by Eigenmonzos==
 
Gencom: [2 5/4; 45/44 65/64 78/77 126/125]
 
Gencom map: [<1 0 2 5 0 4|, <0 5 1 -7 11 -1|]
 
{| class="wikitable"
|-
! | Eigenmonzo
! | Major Third
|-
| | 11/9
| | 347.408
|-
| | 16/13
| | 359.472
|-
| | 15/11
| | 372.610
|-
| | 13/10
| | 372.893
|-
| | 12/11
| | 374.894
|-
| | 8/7
| | 375.882
|-
| | 13/11
| | 375.899
|-
| | 11/10
| | 376.500
|-
| | 14/11
| | 376.805
|-
| | 13/12
| | 376.905
|-
| | 7/5
| | 377.186
|-
| | 11/8
| | 377.393 (11, 13 and 15 limit minimax)
|-
| | |0 113 -12 -68 58 -26>
| | 377.630 (13 limit least squares)
|-
| | |0 -21 -5 27>
| | 377.640 (7 limit least squares)
|-
| | |0 134 9 -81 63 -33>
| | 377.718 (15 limit least squares)
|-
| | |0 85 -14 -62 46>
| | 377.758 (11 limit least squares)
|-
| | 7/6
| | 377.761 (7 limit minimax)
|-
| | 15/13
| | 378.249
|-
| | 15/14
| | 378.419
|-
| | 18/13
| | 378.489
|-
| | 9/7
| | 378.534 (9 limit minimax)
|-
| | |0 93 -4 -44>
| | 378.554 (9 limit least squares)
|-
|-
! Eigenmonzo
| | 14/13
! Major Third
| | 378.617
! Comments
|-
|-
| 6/5
| | 6/5
| 378.910
| | 378.910
|
|-
|-
| 10/9
| | 6\19
| 379.733
| | 378.947
|
|-
|-
| 7/5
| | 10/9
| 380.228
| | 379.733
|
|-
|-
| 4/3
| | 27/20
| 380.391
| | 379.968 (5 limit least squares)
| 5-, 7- and 9-odd-limit minimax
|-
|-
| 11/9
| | 19\60
| 380.700
| | 380.000
| 11-odd-limit minimax
|-
|-
| 8/7
| | 32\101
| 380.735
| | 380.198
|
|-
|-
| 12/11
| | 4/3
| 380.818
| | 380.391 (5 limit minimax)
|
|-
|-
| 14/11
| | 13\41
| 380.875
| | 380.488
|
|-
|-
| 7/6
| | 33\104
| 380.982
| | 380.769
|
|-
|-
| 11/8
| | 20\63
| 381.085
| | 380.952
|
|-
|-
| 11/10
| | 16/15
| 381.666
| | 381.378
|
|-
|-
| 9/7
| | 7\22
| 382.458
| | 381.818
|
|-
|-
| 5/4
| | 5/4
| 386.314
| | 386.314
|
|}
|}


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