otonally-weighted lattices (was: from the realms of private correspondence)

hi paul,

> From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
> To: <tuning-math@yahoogroups.com>
> Sent: Friday, November 08, 2002 3:39 PM
> Subject: [tuning-math] Re: from the realms of private correspondence
>
>
> <snip> ... i don't see how one could ever hope to
> embody favoritism for otonal over utonal in a lattice,
> as much as i believe in such favoritism myself.

hmmm ... wow, you really "struck a chord" here
with me!

several years ago, when i had first moved to San Diego
and was setting up the Sonic Arts website, i was
pondering how one might favor otonality in a lattice.

i haven't thought about it since then, and don't really
remember what ideas i had come up with, but i do recall
that i was trying to incorporate Erv Wilson's famous
"harmonic spiral" diagram into my own lattice formula,
whereby the angles and lengths of each prime-axis would
radiate outward from each lattice-point according to
the measurements in Erv's diagram.

any thoughts on that?

-monz

--- In tuning-math@y..., "monz" <monz@a...> wrote:
> > From: "wallyesterpaulrus" <wallyesterpaulrus@y...>

> > <snip> ... i don't see how one could ever hope to
> > embody favoritism for otonal over utonal in a lattice,
> > as much as i believe in such favoritism myself.
>
>
> hmmm ... wow, you really "struck a chord" here
> with me!

The only method which occurs to me is to take the lattice of otonal *chords*, and ignore utonal anything.

--- In tuning-math@y..., "monz" <monz@a...> wrote:
>
> hi paul,
>
>
> > From: "wallyesterpaulrus" <wallyesterpaulrus@y...>
> > To: <tuning-math@y...>
> > Sent: Friday, November 08, 2002 3:39 PM
> > Subject: [tuning-math] Re: from the realms of private
correspondence
> >
> >
> > <snip> ... i don't see how one could ever hope to
> > embody favoritism for otonal over utonal in a lattice,
> > as much as i believe in such favoritism myself.
>
>
> hmmm ... wow, you really "struck a chord" here
> with me!
>
> several years ago, when i had first moved to San Diego
> and was setting up the Sonic Arts website, i was
> pondering how one might favor otonality in a lattice.
>
> i haven't thought about it since then, and don't really
> remember what ideas i had come up with, but i do recall
> that i was trying to incorporate Erv Wilson's famous
> "harmonic spiral" diagram into my own lattice formula,
> whereby the angles and lengths of each prime-axis would
> radiate outward from each lattice-point according to
> the measurements in Erv's diagram.
>
> any thoughts on that?

as far as i can tell, you're already doing the angles that way; as
for the lengths, i'm not sure if erv used a specific formula, but it
looks like a logarithmic spiral, so log(p) would be a good choice for
the lengths.