Magic extensions

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Tuning Spectra

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|]

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|]

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|]

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|]

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|]

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|]

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)
14/13 378.617
6/5 378.910
6\19 378.947
10/9 379.733
27/20 379.968 (5 limit least squares)
19\60 380.000
32\101 380.198
4/3 380.391 (5 limit minimax)
13\41 380.488
33\104 380.769
20\63 380.952
16/15 381.378
7\22 381.818
5/4 386.314