Miracle extensions

The basic 7-limit miracle temperament has various extensions to the 11 and 13 limits.

Tuning Spectra

Spectrum of Miraculous Tunings by Eigenmonzos

Gencom: [2 15/14; 105/104 144/143 196/195 275/273]

Gencom map: [<1 1 3 3 2 4|, <0 6 -7 -2 15 -3|]

Eigenmonzo	Secor
16/15	111.731
13/10	113.553
8/7	115.587
11/9	115.803
3\31	116.129
5/4	116.241
15/11	116.441
7/5	116.502
10\103	116.505
17\175	116.571
|0 -27 25 5>	116.573 (7 limit least squares)
|0 -19 20>	116.578 (5 limit least squares)
6/5	116.588 (5 and 7 limit minimax)
11/10	116.591
12/11	116.596
14/11	116.617
POTE11	116.633
7/6	116.641
7\72	116.667
|0 17 -11 -6 11>	116.672 (11 limit least squares)
POTE5	116.673
POTE7	116.675
10/9	116.716 (9, 11 and 13 limit minimax)
|0 117 -44 -19>	116.721 (9 limit least squares)
POTE13	116.747
11/8	116.755
9/7	116.792
11\113	116.814
|0 127 -84 -36 100 -44>	116.820 (15 limit least squares)
|0 141 -70 -35 84 -42>	116.846 (13 limit least squares)
4/3	116.993 (15 limit minimax)
4\41	117.073
13/11	117.266
18/13	117.559
13/12	117.936
15/14	119.443
16/13	119.824
15/13	123.871
14/13	128.298

Spectrum of Benediction Tunings by Eigenmonzos

Gencom: [2 15/14; 225/224 243/242 351/350 441/440]

Gencom map: [<1 1 3 3 2 7|, <0 6 -7 -2 15 -34|]

Eigenmonzo	Secor
16/15	111.731
8/7	115.587
11/9	115.803
3\31	116.129
5/4	116.241
15/11	116.441
16/13	116.455
7/5	116.502
10\103	116.505
14/13	116.509
13/10	116.511
13/12	116.536
13/11	116.547
|0 -234 39 4 -115 228>	116.56309 (13 limit least squares)
|0 -251 22 5 -131 261>	116.56348 (15 limit least squares)
17\175	116.571
|0 -27 25 5>	116.573 (7 limit least squares)
POTE13	116.574
|0 -19 20>	116.578 (5 limit least squares)
6/5	116.588 (5, 7 and 15 limit minimax)
11/10	116.591
18/13	116.595 (13 limit minimax)
12/11	116.596
15/13	116.598
14/11	116.617
POTE11	116.633
7/6	116.641
7\72	116.667
|0 17 -11 -6 11>	116.672 (11 limit least squares)
POTE5	116.673
POTE7	116.675
10/9	116.716 (9 and 11 limit minimax)
|0 117 -44 -19>	116.721 (9 limit least squares)
11/8	116.755
9/7	116.792
11\113	116.814
4/3	116.993
4\41	117.073
15/14	119.443

Spectrum of Manna Tunings by Eigenmonzos

Gencom: [2 15/14; 225/224 243/242 325/324 385/384]

Gencom map: [<1 1 3 3 2 0|, <0 6 -7 -2 15 38|]

Eigenmonzo	Secor
16/15	111.731
8/7	115.587
11/9	115.803
3\31	116.129
5/4	116.241
15/11	116.441
7/5	116.502
10\103	116.505
17\175	116.571
|0 -27 25 5>	116.573 (7 limit least squares)
|0 -19 20>	116.578 (5 limit least squares)
6/5	116.588 (5 and 7 limit minimax)
11/10	116.591
12/11	116.596
14/11	116.617
POTE11	116.633
7/6	116.641
7\72	116.667
|0 17 -11 -6 11>	116.672 (11 limit least squares)
POTE5	116.673
POTE7	116.675
10/9	116.716 (9 and 11 limit minimax)
|0 117 -44 -19>	116.721 (9 limit least squares)
15/13	116.725 (15 limit minimax)
POTE13	116.739
11/8	116.755
13/10	116.760 (13 limit minimax)
|0 -37 -166 -77 59 243>	116.764 (15 limit least squares)
|0 18 -111 -76 43 204>	116.780 (13 limit least squares)
9/7	116.792
14/13	116.79254
18/13	116.79299
11\113	116.814
13/12	116.830
16/13	116.856
13/11	116.922
4/3	116.993
4\41	117.073
15/14	119.443

Spectrum of Revelation Tunings by Eigenmonzos

Gencom: [2 15/14; 66/65 99/98 105/104 1001/1000]

Gencom map: [<1 1 3 3 5 4|, <0 6 -7 -2 -16 -3|]

Eigenmonzo	Secor
16/15	111.731
13/10	113.553
13/11	114.555
11/10	115.000
14/11	115.536
11/8	115.543
8/7	115.587
15/11	115.797
12/11	115.938
3\31	116.129
11/9	116.164 (11, 13 and 15 limit minimax)
|0 -195 35 5 89>	116.198 (11 limit least squares)
|0 -251 22 5 117 13>	116.229 (15 limit least squares)
5/4	116.241
|0 -234 39 4 102 11>	116.249 (13 limit least squares)
POTE13	116.268
POTE11	116.277
7/5	116.502
10\103	116.505
17\175	116.571
|0 -27 25 5>	116.573 (7 limit least squares)
|0 -19 20>	116.578 (5 limit least squares)
6/5	116.588 (5 and 7 limit minimax)
7/6	116.641
7\72	116.667
POTE5	116.673
POTE7	116.675
10/9	116.716 (9 limit minimax)
|0 117 -44 -19>	116.721 (9 limit least squares)
9/7	116.792
11\113	116.814
4/3	116.993
4\41	117.073
18/13	117.559
13/12	117.936
15/14	119.443
16/13	119.824
15/13	123.871
14/13	128.298