Magic extensions

Magic has various competing extensions to the 11- and 13-limit.

Tuning spectra

Magic

Edo generator	Eigenmonzo (unchanged-interval)	Generator (¢)	Comments
	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

Necromancy

Edo generator	Eigenmonzo (unchanged-interval)	Generator (¢)	Comments
	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

Sorcery

Edo generator	Eigenmonzo (unchanged-interval)	Generator (¢)	Comments
	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

Telepathy

Edo generator	Eigenmonzo (unchanged-interval)	Generator (¢)	Comments
	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

Witchcraft

Edo generator	Eigenmonzo (unchanged-interval)	Generator (¢)	Comments
	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

Muggles

Edo generator	Eigenmonzo (unchanged-interval)	Generator (¢)	Comments
	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