Re: the One-footed Bride

>It is worth getting hold of Sethares' book to get the details and examples. > Are you the one in South Wales? If you feel like popping over the >bridge, I could lend it to you.

Thank you Graham, but I haven't been in Wales for nearly three years;
I'm in Texas now---and trying to get out! I read Sethares's book when
it came out, but I don't recall a detailed algorithm for estimating dissonance
in it. Has he ever published his method?

Paul says:
>Again, Sethares, working with me, was unable to ascertain exactly how to >use his formula. And his formula fails pretty badly for chords of three or >more notes, where it fails to reproduce our observations that otonal chords >are more consonant than utonal chords.

>The problem Sethares and I were finding was that, depending on the decibel >level you assumed (yes, by "amplitude" Sethares really means "decibel >level"), you can get a wildly different dissonance curve.

This is not too surprising, since non-linear effects in the ear would
create more complex (percieved) spectra---of course, so does playing
acoustic instruments loudly.

>This is a subjective process, and so may be a problem with these automatic >adaptive tuners people have in mind.

It seems like it shouldn't be too dificult to come up with an algorithm
which takes these masking effects into account. I wonder if anyone has
done any work on this?

-m
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In-Reply-To: <F87dgjvM9KfYDovvQ0P0001646f@hotmail.com>
Michael Saunders wrote:

> >It is worth getting hold of Sethares' book to get the details and
> examples. Are you the one in South Wales? If you feel like popping
> > over the >bridge, I could lend it to you.
>
> Thank you Graham, but I haven't been in Wales for nearly three years;
> I'm in Texas now---and trying to get out! I read Sethares's book when
> it came out, but I don't recall a detailed algorithm for estimating
> dissonance
> in it. Has he ever published his method?

Texas, that's quite a swim, huh?

The algorithm for drawing dissonance curves is in an appendix, in Basic
and Matlab code. The only ambiguous thing is what "amplitude" means.

> Paul says:
> >Again, Sethares, working with me, was unable to ascertain exactly how
> to >use his formula. And his formula fails pretty badly for chords of
> three or >more notes, where it fails to reproduce our observations that
> otonal chords >are more consonant than utonal chords.

Oh, to answer this. The methods Plomp&Levelt, Kameoka&Kuriyagawa(sp?) and
Sethares use are all dualistic, so there's no distinction between otonal
and utonal. That's mathematically provable: they're all a sum over all
pairs of partials. It follows from the original experiments using pairs
of sine waves. So if you don't believe in dualism, they can't be a
complete description of consonance (but hey, what's new?)

Graham

--- In tuning@y..., "Michael Saunders" <michaelsaunders7@h...> wrote:

> >The problem Sethares and I were finding was that, depending on the
decibel
> >level you assumed (yes, by "amplitude" Sethares really
means "decibel
> >level"), you can get a wildly different dissonance curve.
>
> This is not too surprising, since non-linear effects in the ear
would
> create more complex (percieved) spectra---of course, so does playing
> acoustic instruments loudly.

Ironically, though, Sethares's formula does _not_ take these non-
linear effects into account -- and the non-linear effects in question
are completely at odds with Sethares's results when comparing otonal
and utonal chords.