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
- 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 225/224).
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 1L8s, with the mode ssssLssss being particularly useful as it has 4:5:6's on the 1/1 and 3/2, as well as 10-note MOS's at 9L1s, 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 many decatonic scales such as Pajara scales).
The 7-limit extensions can also be viewed as joining with the Marvel temperament family; the tuning information below is also located there.
5-limit
Commas: 16875/16384
POTE temperament: ~16/15 = 125.7549
Map: [<1 2 2|, <0 -4 3|]
Wedgie: <<4 -3 -14||
7-limit
Commas: 49/48, 225/224
POTE temperament: ~15/14 = 125.608
Map: [<1 2 2 3|, <0 -4 3 -2|]
Wedgie: <<4 -3 2 -14 -8 13||
11-limit
Commas: 45/44, 49/48, 56/55
POTE generator: ~15/14 = 126.474
Map: [<1 2 2 3 4|, <0 -4 3 -2 -5|]
EDOs: 9, 10, 19
Badness: 0.0262
13-limit
Commas: 45/44, 49/48, 56/55, 78/77
POTE generator: ~14/13 = 126.431
Map: [<1 2 2 3 4 4|, <0 -4 3 -2 -5 -3|]
EDOs: 9, 10, 19
Examples
La Mulți Ani (negri[10], 19edo) - play by Sebastian Dumitrescu
Negri Shmegri - play by Gareth Hearne in Negri[9] symmetric mode, 19et tuning
Negri Comma Pump played by Mike Battaglia