Orwell extensions
Orwell temperament has various extensions to the 13 limit.
Tuning Spectra
These spectra suggest possible tuning choices. For 13-limit orwell, the 5-limit minimax tuning featuring pure 6/5 eigenmonzos seems like an excellent choice, as it's right in the middle of the least squares range and very close to 13-limit least squares. Pure 13s, using the 16/13 eigenmonzo, might also please some people. For blair, pure 5/4s using the 5/4 eigenmonzo tuning is very close to 15-limit least squares and in general in the middle of the action. For winston, sticking with the 11/9 eigenmonzo minimax tuning seems reasonable.
Tuning spectrum
Gencom: [2 7/6; 99/98 121/120 176/175 275/273]
Gencom mapping: [<1 0 3 1 3 8|, <0 7 -3 8 2 -19|]
ET generator |
eigenmonzo (unchanged-interval) |
subminor third (¢) |
comments |
---|---|---|---|
7/6 | 266.871 | ||
15/11 | 268.475 | ||
14/11 | 269.585 | ||
12/11 | 270.127 | ||
15/14 | 270.139 | ||
7\31 | 270.968 | ||
11/9 | 271.049 | ||
8/7 | 271.103 | ||
7/5 | 271.137 | ||
5/4 | 271.229 | ||
1361367/1000000 | 271.326 | 7 limit least squares | |
14/13 | 271.418 | 13 and 15 limit minimax | |
19\84 | 271.429 | ||
[0 119 -46 20 -16⟩ | 271.445 | 11 limit least squares | |
[math]x^{10} + 2x^3 = 8[/math] | 271.508 | equal beating | |
16/13 | 271.551 | ||
[0 90 -41 14⟩ | 271.561 | 9 limit least squares | |
6/5 | 271.564 | 5 limit minimax | |
[0 -211 30 -47 -5 142⟩ | 271.567 | 13 limit least squares | |
[0 -236 5 -51 -3 165⟩ | 271.570 | 15 limit least squares | |
1220703125/1033121304 | 271.590 | 5 limit least squares | |
13/12 | 271.593 | ||
13/10 | 271.612 | ||
18/13 | 271.618 | ||
10/9 | 271.623 | 9 limit minimax | |
15/13 | 271.641 | ||
12\53 | 271.698 | ||
4/3 | 271.708 | ||
13/11 | 271.942 | ||
16/15 | 272.067 | ||
9/7 | 272.514 | ||
5\22 | 272.727 | ||
11/10 | 273.001 | ||
11/8 | 275.659 |
Tuning Spectrum for Winston
Gencom: [2 7/6; 66/65 99/98 105/104 121/120]
Gencom mapping: [⟨1 0 3 1 3 1], ⟨0 7 -3 8 2 12]]
ET generator |
eigenmonzo (unchanged-interval) |
subminor third (¢) |
comments |
---|---|---|---|
7/6 | 266.871 | ||
13/12 | 267.715 | ||
14/13 | 267.925 | ||
15/11 | 268.475 | ||
13/11 | 268.921 | ||
15/13 | 269.032 | ||
14/11 | 269.585 | ||
16/13 | 270.044 | ||
12/11 | 270.127 | ||
15/14 | 270.139 | ||
13/10 | 270.281 | ||
[0 112 -67 20 -28 52⟩ | 270.860 | 15 limit least squares | |
[0 118 -61 16 -26 44⟩ | 270.933 | 13 limit least squares | |
7\31 | 270.968 | ||
11/9 | 271.049 | 13 and 15 limit minimax | |
8/7 | 271.103 | ||
7/5 | 271.137 | ||
5/4 | 271.229 | ||
1361367/1000000 | 271.326 | 7 limit least squares | |
19\84 | 271.429 | ||
[0 119 -46 20 -16⟩ | 271.445 | 11 limit least squares | |
[math]x^{10} + 2x^3 = 8[/math] | 271.508 | equal beating | |
[0 90 -41 14⟩ | 271.561 | 9 limit least squares | |
6/5 | 271.564 | 5 limit minimax | |
1220703125/1033121304 | 271.590 | 5 limit least squares | |
10/9 | 271.623 | 9 limit minimax | |
12\53 | 271.698 | ||
4/3 | 271.708 | ||
16/15 | 272.067 | ||
9/7 | 272.514 | ||
5\22 | 272.727 | ||
11/10 | 273.001 | ||
11/8 | 275.659 | ||
18/13 | 281.691 |
Tuning spectrum for Blair
Gencom: [2 7/6; 65/64 78/77 91/90 99/98]
Gencom mapping: [<1 0 3 1 3 3|, <0 7 -3 8 2 3|]
eigenmonzo (unchanged-interval) |
subminor third (¢) |
---|---|
15/13 | 247.741 |
13/12 | 265.357 |
14/13 | 265.660 |
7/6 | 266.871 |
15/11 | 268.475 |
18/13 | 269.398 |
14/11 | 269.585 |
12/11 | 270.127 |
15/14 | 270.139 |
7\31 | 270.968 |
11/9 | 271.049 |
8/7 | 271.103 |
7/5 | 271.137 (7, 11, 13 and 15 limit minimax) |
5/4 | 271.229 |
|0 148 -49 29 -19 -11> | 271.231 (15 limit least squares) |
|0 145 -52 25 -17 -10> | 271.261 (13 limit least squares) |
1361367/1000000 | 271.326 (7 limit least squares) |
19\84 | 271.429 |
|0 119 -46 20 -16> | 271.445 (11 limit least squares) |
x^10 + 2x^3 = 8 | 271.508 (equal beating) |
|0 90 -41 14> | 271.561 (9 limit least squares) |
6/5 | 271.564 (5 limit minimax) |
1220703125/1033121304 | 271.590 (5 limit least squares) |
10/9 | 271.623 (9 limit minimax) |
12\53 | 271.698 |
4/3 | 271.708 |
16/15 | 272.067 |
9/7 | 272.514 |
5\22 | 272.727 |
11/10 | 273.001 |
11/8 | 275.659 |
13/10 | 275.702 |
16/13 | 280.176 |
13/11 | 289.210 |