how come i never saw this before?

http://www.musikwissenschaft.uni-mainz.de/Musikinformatik/schriftenreihe/nr45/scale.pdf btw, what makes much more sense to me is to do multidimensional scaling based on a rationalization of the *interval matrix*, not the pitch matrix -- intervals are the objects of psychoacoustic consonance, not pitches. i've posted such multidimensional scaling results years ago. better yet would be to simply use the harmonic entropies of the intervals, which i think i did in a few posts as well. hmm, i'm getting an idea for a movie . . .

---------------------------------
Do you Yahoo!?
The New Yahoo! Search - Faster. Easier. Bingo.

>http://www.musikwissenschaft.uni-mainz.de/
>Musikinformatik/schriftenreihe/nr45/scale.pdf

You're mentioned, with a link to sonic arts. You didn't know it?

>btw, what makes much more sense to me is to do multidimensional
>scaling based on a rationalization of the *interval matrix*, not
>the pitch matrix

Indeed.

>i've posted such multidimensional scaling results years ago.

You did?

>better yet would be to simply use the harmonic entropies of the
>intervals, which i think i did in a few posts as well.

You're referring to the minimum pairwise entropy posts? Those
were awesome.

Harmonic entropy sort of makes the idea of rationalizing a scale
irrelevant. On the other hand, starting with a *temperament*,
it's useful to have a method for snapping it to the lattice in a
simple way, as in TM reduction. There's sooo much publishable
on tuning-math . . . . .

>hmm, i'm getting an idea for a movie . . .

Cooool.

-C.

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >http://www.musikwissenschaft.uni-mainz.de/
> >Musikinformatik/schriftenreihe/nr45/scale.pdf
>
> You're mentioned, with a link to sonic arts. You didn't know it?
>
> >btw, what makes much more sense to me is to do multidimensional
> >scaling based on a rationalization of the *interval matrix*, not
> >the pitch matrix
>
> Indeed.
>
> >i've posted such multidimensional scaling results years ago.
>
> You did?

yeah, baby, yeah i sure did! back on the mills list, i believe . . .
>
> >better yet would be to simply use the harmonic entropies of the
> >intervals, which i think i did in a few posts as well.
>
> You're referring to the minimum pairwise entropy posts?

no, just multidimensional scaling solutions.

> Harmonic entropy sort of makes the idea of rationalizing a scale
> irrelevant. On the other hand, starting with a *temperament*,
> it's useful to have a method for snapping it to the lattice in a
> simple way, as in TM reduction.

yeah but then you break a lot of the consonant connections. which
makes this whole "rationalization" business look pretty unhealthy to
me.

>> >better yet would be to simply use the harmonic entropies of the
>> >intervals, which i think i did in a few posts as well.
>>
>> You're referring to the minimum pairwise entropy posts?
>
>no, just multidimensional scaling solutions.

How should I go about finding those posts?

>> Harmonic entropy sort of makes the idea of rationalizing a scale
>> irrelevant. On the other hand, starting with a *temperament*,
>> it's useful to have a method for snapping it to the lattice in a
>> simple way, as in TM reduction.
>
>yeah but then you break a lot of the consonant connections. which
>makes this whole "rationalization" business look pretty unhealthy to
>me.

Sure.

-C.

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> >better yet would be to simply use the harmonic entropies of the
> >> >intervals, which i think i did in a few posts as well.
> >>
> >> You're referring to the minimum pairwise entropy posts?
> >
> >no, just multidimensional scaling solutions.
>
> How should I go about finding those posts?

search for "multidimensional scaling" on the tuning list here and in
robert's mills tuning list archive.