Orwell extensions: Difference between revisions
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Cmloegcmluin (talk | contribs) →Spectrum of Orwell Tunings by Eigenmonzos: improve and standardize tuning spectra tables |
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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. | 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: [2 7/6; 99/98 121/120 176/175 275/273] | ||
| Line 10: | Line 10: | ||
Gencom map: [<1 0 3 1 3 8|, <0 7 -3 8 2 -19|] | Gencom map: [<1 0 3 1 3 8|, <0 7 -3 8 2 -19|] | ||
{| class="wikitable" | {| class="wikitable center-all" | ||
|- | |- | ||
! | | ! | ET<br>generator | ||
! | | ! | [[eigenmonzo|eigenmonzo<br>(unchanged interval]]) | ||
! | subminor<br>third (¢) | |||
! | comments | |||
|- | |- | ||
| | | |||
| | 7/6 | | | 7/6 | ||
| | 266.871 | | | 266.871 | ||
| | | |||
|- | |- | ||
| | | |||
| | 15/11 | | | 15/11 | ||
| | 268.475 | | | 268.475 | ||
| | | |||
|- | |- | ||
| | | |||
| | 14/11 | | | 14/11 | ||
| | 269.585 | | | 269.585 | ||
| | | |||
|- | |- | ||
| | | |||
| | 12/11 | | | 12/11 | ||
| | 270.127 | | | 270.127 | ||
| | | |||
|- | |- | ||
| | | |||
| | 15/14 | | | 15/14 | ||
| | 270.139 | | | 270.139 | ||
| | | |||
|- | |- | ||
| | 7\31 | | | 7\31 | ||
| | | |||
| | 270.968 | | | 270.968 | ||
| | | |||
|- | |- | ||
| | | |||
| | 11/9 | | | 11/9 | ||
| | 271.049 | | | 271.049 | ||
| | | |||
|- | |- | ||
| | | |||
| | 8/7 | | | 8/7 | ||
| | 271.103 | | | 271.103 | ||
| | | |||
|- | |- | ||
| | | |||
| | 7/5 | | | 7/5 | ||
| | 271.137 | | | 271.137 | ||
| | | |||
|- | |- | ||
| | | |||
| | 5/4 | | | 5/4 | ||
| | 271.229 | | | 271.229 | ||
| | | |||
|- | |- | ||
| | | |||
| | 1361367/1000000 | | | 1361367/1000000 | ||
| | 271.326 | | | 271.326 | ||
| | 7 limit least squares | |||
|- | |- | ||
| | | |||
| | 14/13 | | | 14/13 | ||
| | 271.418 | | | 271.418 | ||
| | 13 and 15 limit minimax | |||
|- | |- | ||
| | 19\84 | | | 19\84 | ||
| | | |||
| | 271.429 | | | 271.429 | ||
| | | |||
|- | |- | ||
| | |0 119 -46 20 -16 | | | | ||
| | 271.445 | | | {{vector|0 119 -46 20 -16}} | ||
| | 271.445 | |||
| | 11 limit least squares | |||
|- | |- | ||
| | x^10 + 2x^3 = 8 | | | | ||
| | 271.508 | | | <math>x^{10} + 2x^3 = 8</math> | ||
| | 271.508 | |||
| | equal beating | |||
|- | |- | ||
| | | |||
| | 16/13 | | | 16/13 | ||
| | 271.551 | | | 271.551 | ||
| | | |||
|- | |- | ||
| | |0 90 -41 14 | | | | ||
| | 271.561 | | | {{vector|0 90 -41 14}} | ||
| | 271.561 | |||
| | 9 limit least squares | |||
|- | |- | ||
| | | |||
| | 6/5 | | | 6/5 | ||
| | 271.564 | | | 271.564 | ||
| | 5 limit minimax | |||
|- | |- | ||
| | |0 -211 30 -47 -5 142 | | | | ||
| | 271.567 | | | {{vector|0 -211 30 -47 -5 142}} | ||
| | 271.567 | |||
| | 13 limit least squares | |||
|- | |- | ||
| | |0 -236 5 -51 -3 165 | | | | ||
| | 271.570 | | | {{vector|0 -236 5 -51 -3 165}} | ||
| | 271.570 | |||
| | 15 limit least squares | |||
|- | |- | ||
| | | |||
| | 1220703125/1033121304 | | | 1220703125/1033121304 | ||
| | 271.590 | | | 271.590 | ||
| | 5 limit least squares | |||
|- | |- | ||
| | | |||
| | 13/12 | | | 13/12 | ||
| | 271.593 | | | 271.593 | ||
| | | |||
|- | |- | ||
| | | |||
| | 13/10 | | | 13/10 | ||
| | 271.612 | | | 271.612 | ||
| | | |||
|- | |- | ||
| | | |||
| | 18/13 | | | 18/13 | ||
| | 271.618 | | | 271.618 | ||
| | | |||
|- | |- | ||
| | | |||
| | 10/9 | | | 10/9 | ||
| | 271.623 | | | 271.623 | ||
| | 9 limit minimax | |||
|- | |- | ||
| | | |||
| | 15/13 | | | 15/13 | ||
| | 271.641 | | | 271.641 | ||
| | | |||
|- | |- | ||
| | 12\53 | | | 12\53 | ||
| | | |||
| | 271.698 | | | 271.698 | ||
| | | |||
|- | |- | ||
| | | |||
| | 4/3 | | | 4/3 | ||
| | 271.708 | | | 271.708 | ||
| | | |||
|- | |- | ||
| | | |||
| | 13/11 | | | 13/11 | ||
| | 271.942 | | | 271.942 | ||
| | | |||
|- | |- | ||
| | | |||
| | 16/15 | | | 16/15 | ||
| | 272.067 | | | 272.067 | ||
| | | |||
|- | |- | ||
| | | |||
| | 9/7 | | | 9/7 | ||
| | 272.514 | | | 272.514 | ||
| | | |||
|- | |- | ||
| | 5\22 | | | 5\22 | ||
| | | |||
| | 272.727 | | | 272.727 | ||
| | | |||
|- | |- | ||
| | | |||
| | 11/10 | | | 11/10 | ||
| | 273.001 | | | 273.001 | ||
| | | |||
|- | |- | ||
| | | |||
| | 11/8 | | | 11/8 | ||
| | 275.659 | | | 275.659 | ||
| | | |||
|} | |} | ||