Negri extensions
Negri temperament has various competing extensions to the 11-limit. This is evidenced by the fact that its supporting equal temperaments, 10 and 19, do less well in the 11-limit. The extensions are:
- Undecimal negri (10 & 19) – tempering out 45/44, 49/48, and 56/55
- Negril (10e & 19) – tempering out 49/48, 100/99, 225/224
- Negric (10e & 19e) – tempering out 33/32, 49/48, 77/75
- Negroni (10 & 19e) – tempering out 49/48, 55/54, 225/224
Another possible path which relates a sense of compromise is to temper out 121/120, leading to wilsec. This has the effect of slicing the generator in two, and is supported by 20, 29, and 38df.
Tuning spectra
Undecimal negri
| Edo generator |
Eigenmonzo (unchanged-interval) |
Generator (¢) | Comments |
|---|---|---|---|
| 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-odd-limit minimax | |
| 5\48 | 125.000 | ||
| 30517578125/26795786661 | 125.469 | 7-odd-limit least squares | |
| [0 63 -26 -1⟩ | 125.579 | 9-odd-limit least squares | |
| 10/9 | 125.673 | ||
| 11337408/9765625 | 126.238 | 5-odd-limit least squares | |
| 2\19 | 126.316 | ||
| 6/5 | 126.337 | 5-odd-limit minimax | |
| [0 79 -40 -5 16 2⟩ | 126.445 | 13-odd-limit least squares | |
| [0 34 -17 -2 7⟩ | 126.511 | 11-odd-limit least squares | |
| [0 73 -46 -4 20 4⟩ | 126.619 | 15-odd-limit least squares | |
| 18/13 | 127.324 | ||
| 9/7 | 127.486 | 11-, 13- and 15-odd-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 |
Negril
| Edo generator |
Eigenmonzo (unchanged-interval) |
Generator (¢) | Comments |
|---|---|---|---|
| 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-odd-limit minimax | |
| [0 -149 8 -15 113 -23⟩ | 124.700 | 15-odd-limit least squares | |
| [0 -136 21 -14 98 -21⟩ | 124.764 | 13-odd-limit least squares | |
| [0 -125 15 -15 81⟩ | 124.854 | 11-odd-limit least squares | |
| 11/9 | 124.882 | ||
| 12/11 | 124.965 | ||
| 5\48 | 125.000 | ||
| 11/8 | 125.094 | ||
| 30517578125/26795786661 | 125.469 | 7-odd-limit least squares | |
| [0 63 -26 -1⟩ | 125.579 | 9-odd-limit least squares | |
| 10/9 | 125.673 | ||
| 11337408/9765625 | 126.238 | 5-odd-limit least squares | |
| 2\19 | 126.316 | ||
| 6/5 | 126.337 | 5-odd-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 |
Negric
| Edo generator |
Eigenmonzo (unchanged-interval) |
Generator (¢) | Comments |
|---|---|---|---|
| 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-odd-limit minimax | |
| 5\48 | 125.000 | ||
| 30517578125/26795786661 | 125.469 | 7-odd-limit least squares | |
| [0 63 -26 -1⟩ | 125.579 | 9-odd-limit least squares | |
| 10/9 | 125.673 | ||
| 11337408/9765625 | 126.238 | 5-odd-limit least squares | |
| 2\19 | 126.316 | ||
| 6/5 | 126.337 | 5-odd-limit minimax | |
| 18/13 | 127.324 | ||
| 9/7 | 127.486 | ||
| [0 106 -31 4 -38 11⟩ | 127.602 | 13-odd-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-odd-limit least squares | |
| 14/13 | 128.298 | ||
| 3\28 | 128.571 | ||
| 5/4 | 128.771 | ||
| 11/9 | 128.951 | 11-, 13- and 15-odd-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 |
Negroni
| Edo generator |
Eigenmonzo (unchanged-interval) |
Generator (¢) | Comments |
|---|---|---|---|
| 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-odd-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-odd-limit least squares | |
| [0 33 -66 -14 90 -6⟩ | 124.186 | 15-odd-limit least squares | |
| [0 49 -50 -15 76 -8⟩ | 124.215 | 13-odd-limit least squares | |
| 13/10 | 124.298 | ||
| 14/11 | 124.424 | ||
| 4/3 | 124.511 | 7- and 9-odd-limit minimax | |
| 5\48 | 125.000 | ||
| 30517578125/26795786661 | 125.469 | 7-odd-limit least squares | |
| [0 63 -26 -1⟩ | 125.579 | 9-odd-limit least squares | |
| 10/9 | 125.673 | ||
| 11337408/9765625 | 126.238 | 5-odd-limit least squares | |
| 6/5 | 126.337 | 5-odd-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 |