Negri extensions

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Negri temperament has various extensions to the 11 limit.

Tuning Spectra

Spectrum of Negri Tunings by Eigenmonzos

Gencom: [2 15/14; 45/44 49/48 56/55 78/77]

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

Eigenmonzo Supersecor
16/15 111.731
8/7 115.587
11/9 115.803
15/14 119.443
16/13 119.824
1\10 120.000
7/5 123.498
15/13 123.871
3\29 124.138
13/10 124.298
4/3 124.511 (7 and 9 limit minimax)
5\48 125.000
30517578125/26795786661 125.469 (7 limit least squares)
|0 63 -26 -1> 125.579 (9 limit least squares)
10/9 125.673
11337408/9765625 126.238 (5 limit least squares)
2\19 126.316
6/5 126.337 (5 limit minimax)
|0 79 -40 -5 16 2> 126.445 (13 limit least squares)
|0 34 -17 -2 7> 126.511 (11 limit least squares)
|0 73 -46 -4 20 4> 126.619 (15 limit least squares)
18/13 127.324
9/7 127.486 (11, 13 and 15 limit minimax)
5\47 127.660
14/13 128.298
3\28 128.571
5/4 128.771
11/10 129.374
11/8 129.736
7/6 133.435
15/11 134.238
13/12 138.573
14/11 139.169
13/11 144.605
12/11 150.637

Spectrum of Negril Tunings by Eigenmonzos

Gencom: [2 15/14; 49/48 65/64 91/90 875/858]

Gencom map: [<1 2 2 3 2 4|, <0 -4 3 -2 14 -3|]

Eigenmonzo Supersecor
16/15 111.731
8/7 115.587
15/14 119.443
16/13 119.824
1\10 120.000
7/5 123.498
15/13 123.871
14/11 123.906
11/10 124.091
3\29 124.138
13/11 124.164
15/11 124.203
13/10 124.298
4/3 124.511 (7, 9, 11, 13 and 15 limit minimax)
|0 -149 8 -15 113 -23> 124.700 (15 limit least squares)
|0 -136 21 -14 98 -21> 124.764 (13 limit least squares)
|0 -125 15 -15 81> 124.854 (11 limit least squares)
11/9 124.882
12/11 124.965
5\48 125.000
11/8 125.094
30517578125/26795786661 125.469 (7 limit least squares)
|0 63 -26 -1> 125.579 (9 limit least squares)
10/9 125.673
11337408/9765625 126.238 (5 limit least squares)
2\19 126.316
6/5 126.337 (5 limit minimax)
18/13 127.324
9/7 127.486
5\47 127.660
14/13 128.298
3\28 128.571
5/4 128.771
7/6 133.435
13/12 138.573

Spectrum of Negric Tunings by Eigenmonzos

Gencom: [2 15/14; 33/32 49/48 65/64 91/90]

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

Eigenmonzo Supersecor
16/15 111.731
8/7 115.587
15/14 119.443
16/13 119.824
1\10 120.000
7/5 123.498
15/13 123.871
3\29 124.138
13/10 124.298
4/3 124.511 (7 and 9 limit minimax)
5\48 125.000
30517578125/26795786661 125.469 (7 limit least squares)
|0 63 -26 -1> 125.579 (9 limit least squares)
10/9 125.673
11337408/9765625 126.238 (5 limit least squares)
2\19 126.316
6/5 126.337 (5 limit minimax)
18/13 127.324
9/7 127.486
|0 106 -31 4 -38 11> 127.602 (13 limit least squares)
5\47 127.660
|0 -95 25 -5 31> 127.706 (11 limit least squares)
|0 109 -28 5 -43 13> 127.718 (15 limit least squares)
14/13 128.298
3\28 128.571
5/4 128.771
11/9 128.951 (11, 13 and 15 limit minimax)
13/11 130.113
14/11 130.415
12/11 131.170
15/11 132.610
7/6 133.435
11/8 137.829
13/12 138.573
11/10 165.004

Spectrum of Negroni Tunings by Eigenmonzos

Gencom: [2 15/14; 49/48 55/54 65/64 91/90]

Gencom map: [<1 2 2 3 5 4|, <0 -4 3 -2 -15 -3|]

Eigenmonzo Supersecor
16/15 111.731
8/7 115.587
15/14 119.443
16/13 119.824
1\10 120.000
11/9 121.799 (11, 13 and 15 limit minimax)
12/11 122.785
11/8 123.245
7/5 123.498
15/13 123.871
15/11 124.068
13/11 124.101
3\29 124.138
11/10 124.166
|0 19 -22 -7 32> 124.180 (11 limit least squares)
|0 33 -66 -14 90 -6> 124.186 (15 limit least squares)
|0 49 -50 -15 76 -8> 124.215 (13 limit least squares)
13/10 124.298
14/11 124.424
4/3 124.511 (7 and 9 limit minimx)
5\48 125.000
30517578125/26795786661 125.469 (7 limit least squares)
|0 63 -26 -1> 125.579 (9 limit least squares)
10/9 125.673
11337408/9765625 126.238 (5 limit least squares)
6/5 126.337 (5 limit minimax)
18/13 127.324
9/7 127.486
5\47 127.660
14/13 128.298
3\28 128.571
5/4 128.771
7/6 133.435
13/12 138.573