Magic extensions

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