Negri
Negri is a temperament generated by a generator of approximately 125.7549 cents, which can be identified with a tempered 16/15, such that:
- Two of them make a tempered 7/6~8/7~15/13
- Three of them make a tempered 5/4~16/13
- Four of them make a tempered 4/3.
It is most naturally viewed as a 2.3.5.7.13 subgroup temperament, tempering out 49/48, 65/64 and 91/90. This is called negra.
It is an important temperament which is most notable for being in 19edo, where it is generated by the "diatonic half step" of 2\19, but can also be found (albeit not very accurately) in 9edo and 10edo.
It forms 9-note MOS's at 1L 8s, with the mode ssssLssss being particularly useful as it has identical ssss pentachords (analogous to the tetrachords of classical Greek music theory) on the 1/1 and 3/2 , as well as 10-note MOS's at 9L 1s, which is also useful in that it makes 4:5:6 and 10:12:15 share the same "shape" of generic intervals in the scale (as in other rank-2 decatonic scales such as Pajara and Blackwood scales; this is because 5/4 and 6/5 get tempered to the same thing in 10edo).
The 7-limit extension can also be viewed as joining with the Marvel temperament family; the tuning information below is also located there. For the various 11-limit extensions, see negri extensions.
Interval chain
| # | Cents* | Approximate Ratios |
|---|---|---|
| 0 | 0.0 | 1/1 |
| 1 | 125.6 | 16/15, 15/14, 14/13, 13/12 |
| 2 | 251.1 | 8/7, 7/6, 15/13 |
| 3 | 376.7 | 5/4, 16/13 |
| 4 | 502.3 | 4/3 |
| 5 | 627.8 | 10/7, 13/9 |
| 6 | 753.4 | 14/9, 32/21, 20/13 |
| 7 | 879.0 | 5/3 |
| 8 | 1004.5 | 16/9 |
| 9 | 1130.1 | 35/18, 40/21, 52/27 |
| 10 | 55.7 | 25/24, 28/27, 50/49, 64/63 |
* In 2.3.5.7.13 POTE tuning
Temperament data
- 5-limit
- 7-limit
Subgroup: 2.3.5.7
Comma list: 49/48, 225/224
Mapping: [⟨1 2 2 3], ⟨0 -4 3 -2]]
Wedgie: ⟨⟨4 -3 2 -14 -8 13]]
- 2.3.5.7.13 (negra)
Subgroup: 2.3.5.7.13
Comma list: 49/48, 65/64, 91/90
Mapping: [⟨1 2 2 3 4], ⟨0 -4 3 -2 -3]]
Gencom mapping: [⟨1 2 2 3 0 4], ⟨0 -4 3 -2 0 -3]]
Gencom: [2 14/13; 49/48 65/64 91/90]
Examples
- La Mulți Ani (negri[10], 19edo) - play by Sebastian Dumitrescu
- Negri Shmegri [dead link] - play by Gareth Hearne in Negri[9] symmetric mode, 19et tuning
- Negri Comma Pump played by Mike Battaglia
- Negri-9 Modal Fugues (YouTube playlist, 4 of 9 complete) by Ray Perlner