Miracle extensions

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

Tuning spectra

Miraculous

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

Gencom mapping: [1 1 3 3 2 4], 0 6 -7 -2 15 -3]]

ET
generator
eigenmonzo
(unchanged interval
)
secor
(¢)
comments
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
116.633 POTE11
7/6 116.641
7\72 116.667
[0 17 -11 -6 11 116.672 11 limit least squares
116.673 POTE5
116.675 POTE7
10/9 116.716 9, 11 and 13 limit minimax
[0 117 -44 -19 116.721 9 limit least squares
116.747 POTE13
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

Benediction

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

Gencom mapping: [1 1 3 3 2 7], 0 6 -7 -2 15 -34]]

ET
generator
eigenmonzo
(unchanged interval)
secor
(¢)
comments
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
116.574 POTE13
[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
116.633 POTE11
7/6 116.641
7\72 116.667
[0 17 -11 -6 11 116.672 11 limit least squares
116.673 POTE5
116.675 POTE7
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

Manna

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

Gencom mapping: [1 1 3 3 2 0], 0 6 -7 -2 15 38]]

ET
generator
eigenmonzo
(unchanged interval)
secor
(¢)
comments
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
116.633 POTE11
7/6 116.641
7\72 116.667
[0 17 -11 -6 11 116.672 11 limit least squares
116.673 POTE5
116.675 POTE7
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
116.739 POTE13
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

Revelation

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

Gencom mapping: [1 1 3 3 5 4], 0 6 -7 -2 -16 -3]]

ET
generator
eigenmonzo
(unchanged interval)
secor
(¢)
comments
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
116.268 POTE13
116.277 POTE11
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
116.673 POTE5
116.675 POTE7
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