Non-octave periodicity blocks

(Sent to both Tuning and Tuning-math; please ignore it in whichever
group it doesn't belong -- I can't figure it out.)

Can anyone point me to any work done on periodicity blocks on
non-octave lattices, particularly the (5/3, 7/3) lattice?

I know about these:

<http://members.aol.com/bpsite/BPlattice.html>

<http://www.kees.cc/tuning/perbl.html>

However, neither seems actually to explore any periodicity blocks
beyond those giving the Bohlen-Pierce 13-note "chromatic" and 9-note
"diatonic" scales.

- Rich Holmes

Maybe you missed the link from my page to here:

http://www.kees.cc/tuning/s357.html

That's a list of unison vectors and resulting ETs on that lattice.

(I admit the format is a bit obscure)

--- In tuning-math@yahoogroups.com, Rich Holmes<rsholmes@...> wrote:
>
> (Sent to both Tuning and Tuning-math; please ignore it in whichever
> group it doesn't belong -- I can't figure it out.)
>
> Can anyone point me to any work done on periodicity blocks on
> non-octave lattices, particularly the (5/3, 7/3) lattice?
>
> I know about these:
>
> <http://members.aol.com/bpsite/BPlattice.html>
>
> <http://www.kees.cc/tuning/perbl.html>
>
> However, neither seems actually to explore any periodicity blocks
> beyond those giving the Bohlen-Pierce 13-note "chromatic" and 9-note
> "diatonic" scales.
>
> - Rich Holmes
>

--- In tuning-math@yahoogroups.com, Rich Holmes<rsholmes@...> wrote:
>
> (Sent to both Tuning and Tuning-math; please ignore it in whichever
> group it doesn't belong -- I can't figure it out.)
>
> Can anyone point me to any work done on periodicity blocks on
> non-octave lattices, particularly the (5/3, 7/3) lattice?

5/3 and 7/3 define a group with two generators, hence the situation is
analogous to the 3-limit. Periodicity blocks are one-dimensional, and
can be found by using semiconvergents of continued fractions. Hence,
for example, taking the semiconvergent 13/8 for log(7/3)/log(5/3), we
see that 13 notes with a period of 7/3 and 5/3 generators, or 8 notes
with a period of 5/3, with 7/3 generators, will give such a scale.