--- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning-math@y..., "paulerlich" <paul@s...> wrote:
>
> However, I think the only reality for Schoenberg's
> > system is a tuning where there is ambiguity, as defined by the
kernel
> > <33/32, 64/63, 81/80, 225/224>. BTW, is this Minkowski-reduced?
>
> Nope. The honor belongs to <22/21, 33/32, 36/35, 50/49>.

Awesome. So this suggests a more compact Fokker parallelepiped
as "Schoenberg PB" -- here are the results of placing it in different
positions in the lattice (you should treat the inversions of these as
implied):


0 1 1
84.467 21 20
203.91 9 8
315.64 6 5
386.31 5 4
470.78 21 16
617.49 10 7
701.96 3 2
786.42 63 40
933.13 12 7
968.83 7 4
1088.3 15 8


0 1 1
119.44 15 14
203.91 9 8
315.64 6 5
386.31 5 4
470.78 21 16
617.49 10 7
701.96 3 2
786.42 63 40
933.13 12 7
968.83 7 4
1088.3 15 8


0 1 1
119.44 15 14
155.14 35 32
301.85 25 21
386.31 5 4
470.78 21 16
617.49 10 7
701.96 3 2
772.63 25 16
884.36 5 3
968.83 7 4
1088.3 15 8


0 1 1
84.467 21 20
155.14 35 32
266.87 7 6
386.31 5 4
470.78 21 16
582.51 7 5
701.96 3 2
737.65 49 32
884.36 5 3
968.83 7 4
1053.3 147 80