Negri

Negri, 19 & 29, is a 5-limit temperament that splits 4/3 into four sharp 16/15's. It enables the following comma loop progression (19edo notation):

F C F A
A C E (F -> A: 5/4 up)
E B E G# (A -> E: 4/3 down)
G# B D# (E -> G#: 5/4 up)
D# A# D# Fx (G# -> D#: 4/3 down)
Fx A# Cx = Gb Bbb Db (D# -> Fx: 5/4 up)
Db Ab Db F (Gb -> Db: 4/3 down)
F C F A (Db -> F: 5/4 up)

Extensions

Negri has an endoparticular extension to 2.3.5.7.13 via tempering out 49/48 and 676/675. It also has a weak 7-limit extension Semibuzzard which tempers out the Buzzard comma instead.

List of patent vals

The following patent vals support 5-limit Negri, not including vals contorted in the 5-limit.

1, 9, 10, 19, 28, 29, 47, 48