the One-footed Bride (+ sacrilege)

>Which brings up an interesting question: what timbres
>was Partch listening to when he was drawing these curves?
>From the look of the curve, clearly something with many
>strong harmonics... maybe his reed organ?

That's what I always thought, since it's the easiest
of his instruments to experiment with (the only one
with sustained, fixed pitches, I think). I had the
impression that he plotted the points on the consonance
axis just by judging them, expressing his opinion
as a consonance value (more important relative to the
others rather than absolutely), and eyeballed a spline
through the points.

Finding the harmonic spectrum best suited to his
curve is interesting, but it might be more interesting
to find a scale optimized for the actual spectra of
his (inharmonic) instruments. If analogies can be drawn
with the levels of consonance of his 43 on the
chromelodeon, you might be able to call it "Partch's
implied" scale. I think it would be interesting in
any case, and I wonder what recasting his music in
that tuning would sound like.

-m

--- In tuning@y..., michaelsaunders7@h... wrote:

> That's what I always thought, since it's the easiest
> of his instruments to experiment with (the only one
> with sustained, fixed pitches, I think). I had the
> impression that he plotted the points on the consonance
> axis just by judging them, expressing his opinion
> as a consonance value (more important relative to the
> others rather than absolutely), and eyeballed a spline
> through the points.

A monotonic spline. But there's more to it. Partch constructed the
entire graph mathematically. As you can verify with a straightedge,
there are only eight consonance levels between the splines. They are:

1/1
2/1
Ratios of 3
Ratios of 5
Ratios of 7
Ratios of 9
Ratios of 11
Secondary Ratios

That's it. But clearly Partch's text suggests that the splines are
not to be taken at face value -- at all! See my posts from yesterday.