projecting high-dimension down to 3-D

i'm welcoming suggestions on the best ways
to project higher-dimensional lattices into
3-D space.

are any particular polyhedra favored for
particular dimensionalities, etc?

responses should probably go to tuning-math.
(this list has many more members, that's why
i asked here.)

-monz

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
>
> i'm welcoming suggestions on the best ways
> to project higher-dimensional lattices into
> 3-D space.
>
> are any particular polyhedra favored for
> particular dimensionalities, etc?

Pojecting the lattice down so that the commas of some temperament
vanish is one way to do it.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> --- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> >
> > i'm welcoming suggestions on the best ways
> > to project higher-dimensional lattices into
> > 3-D space.
> >
> > are any particular polyhedra favored for
> > particular dimensionalities, etc?
>
> Pojecting the lattice down so that the commas of some
> temperament vanish is one way to do it.

Musica already does that for temperaments, resulting
in the warped helical or toroidal lattices.

but what about JI? if someone wants to create a
fairly simple (4-D) 11-limit JI tuning, what's the best
way to project that in 3-D space?, which is the highest
dimensionality we can get visually.

and what about 5-D, 6-D, and 7-D?

i'm guessing that certain polyhedra are good for
certain dimensionalities.

anyone who's interested in this thread will be fascinated
to read the website by Mr. Polytope himself, George Olshevsky.

http://members.aol.com/Polycell/next.html

George lives right here near my neighborhood and i met
him for coffee a couple of years ago, but can't seem to
be able to contact him now.

-monz

-monz

> i'm welcoming suggestions on the best ways
> to project higher-dimensional lattices into
> 3-D space.
>
> are any particular polyhedra favored for
> particular dimensionalities, etc?
>
> responses should probably go to tuning-math.
> (this list has many more members, that's why
> i asked here.)

Speaking of questions Dave is perfectly suited
to answer! He had to do this, with the help
of KEENAN PEPPER, to render the 3-D dekany.

There was also a thread involving Paul and an
off-list mathematician, which I reposted last
year, which culminated in a table giving
polytopes for various CPS.....

It was in fact in January of this year:

/tuning/topicId_51540.html#51560

-Carl

>> > i'm welcoming suggestions on the best ways
>> > to project higher-dimensional lattices into
>> > 3-D space.
//
>> Pojecting the lattice down so that the commas of some
>> temperament vanish is one way to do it.
>
>Musica already does that for temperaments, resulting
>in the warped helical or toroidal lattices.
>
>but what about JI? if someone wants to create a
>fairly simple (4-D) 11-limit JI tuning, what's the best
>way to project that in 3-D space?, which is the highest
>dimensionality we can get visually.
>
>and what about 5-D, 6-D, and 7-D?
>
>i'm guessing that certain polyhedra are good for
>certain dimensionalities.

Amazing! I just replied to this! And unlike Gene,
I amazingly knew what you were asking.

>anyone who's interested in this thread will be fascinated
>to read the website by Mr. Polytope himself, George
>Olshevsky.

Amazingly, I mention Mr. Olshevsky!

-Carl