Fooling around with Scala

I've been testing out Euler genera on Scala. It usually identifies them as weakly epimorphic, but not always. Since I don't know what Scala does, this doesn't tell me there is a counterexample to convex ==> weakly epimoprhic, but it leaves the possibility open.

--- In tuning-math@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> I've been testing out Euler genera on Scala. It usually identifies them as weakly epimorphic, but not always. Since I don't know what Scala does, this doesn't tell me there is a counterexample to convex ==> weakly epimoprhic, but it leaves the possibility open.
>

If someone wants to prove it, I imagine the 6x6 Euler genus, Euler(15^5), provides a counterexample.

On Sun, Mar 4, 2012 at 12:45 PM, genewardsmith <genewardsmith@sbcglobal.net>
wrote:
>
> --- In tuning-math@yahoogroups.com, "genewardsmith" <genewardsmith@...>
> wrote:
> >
> > I've been testing out Euler genera on Scala. It usually identifies them
> > as weakly epimorphic, but not always. Since I don't know what Scala does,
> > this doesn't tell me there is a counterexample to convex ==> weakly
> > epimoprhic, but it leaves the possibility open.
> >
>
> If someone wants to prove it, I imagine the 6x6 Euler genus, Euler(15^5),
> provides a counterexample.

Both Keenan and myself have suggested shapes on the lattice like
circles and triangles as being convex but not epimorphic. Does that
not suffice as a counterexample?

-Mike

--- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> Both Keenan and myself have suggested shapes on the lattice like
> circles and triangles as being convex but not epimorphic. Does that
> not suffice as a counterexample?

Indeed it does, but the 6x6 is a counterexample to a stronger claim, since it is both convex and tiles the lattice of 5-limit pitch classes.

On Mon, Mar 5, 2012 at 3:33 PM, genewardsmith <genewardsmith@sbcglobal.net>
wrote:
>
> --- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...>
> wrote:
>
> > Both Keenan and myself have suggested shapes on the lattice like
> > circles and triangles as being convex but not epimorphic. Does that
> > not suffice as a counterexample?
>
> Indeed it does, but the 6x6 is a counterexample to a stronger claim, since
> it is both convex and tiles the lattice of 5-limit pitch classes.

This is actually a 6x6 square on the 5-limit lattice that isn't epimorphic?

-Mike

--- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> This is actually a 6x6 square on the 5-limit lattice that isn't epimorphic?

Yup. In Scala, go to Euler-Fokker genus under the "New" pull-down menu. Put in 3 and 5 for the primes, and 5 and 5 for the multiplicities, and there's your non-weakly-epimorphic square.