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.

Spectrum of Orwell Tunings by Eigenmonzos

Gencom: [2 7/6; 99/98 121/120 176/175 275/273]

Gencom map: [<1 0 3 1 3 8|, <0 7 -3 8 2 -19|]

Eigenmonzo	Subminor Third
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)
x^10 + 2x^3 = 8	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

Spectrum of Winston Tunings by Eigenmonzos

Gencom: [2 7/6; 66/65 99/98 105/104 121/120]

Gencom map: [<1 0 3 1 3 1|, <0 7 -3 8 2 12|]

Eigenmonzo	Subminor Third
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)
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
18/13	281.691

Spectrum of Blair Tunings by Eigenmonzos

Gencom: [2 7/6; 65/64 78/77 91/90 99/98]

Gencom map: [<1 0 3 1 3 3|, <0 7 -3 8 2 3|]

Eigenmonzo	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