hair raising timbres

A while ago, Jon wrote to me about one of the pieces on Exomusicology:

>Well, maybe at some point we could put up an illustrative clip, but
first
>off: what is it about "Intersecting Spheres"? The intonation/tuning
on that
>one, certainly before the percussion comes in, is a perfect example of a
>tuning phenomenon where I feel like the hairs are standing up on end,
>either in my ears, or at least on the back of my neck!

>There must be some reason - is it the tuning, or the timbres in
combination
>with the tuning, or... ?

I think the effect here is caused by all the (almost inaudibly) high
frequency stuff. Here's a rundown on the creation of the sounds used
in "Intersecting Spheres".

The basic timbre is harmonic, restricted to all
multiples of 50 Hz. So, for instance, some notes contain
all multiples of 100 Hz, and others contain all multiples
of 150 Hz, etc. The tuning is an additive "overtone" scale
consisting of all multiples of 50 Hz - though only a small
subset of the all the possibilities are actually used.

When I started crafting the timbres for this piece, I was
basically doing additive-style synthesis (using "metasynth"),
and then passing the result through various nonlinearities
(in metasynth and Matlab). When you pass a signal through
nonlinearities, you get all sorts new overtones, and these
typically are at ever higher frequencies... until you
hit the Nyquist rate (22050 for normal CD recording),
at which point they "fold over" and start descending again.

Here's the interesting part: because 22050 is divisible by
50, when the partials fold back, they still lie on the same
50 Hz lattice - they just augment (or decrease) the amplitude
of the partials. So no matter how many nonlinearities you apply,
you still have the same basic "harmonic" template, but with
differing amplitudes. Of course, many of these didnt sound good,
and I later went back and removed (with a low pass filter) many
of the highest frequency things from others.

So, I think much of the character (the "hair-raising on end")
of the timbres is due to this unorthodox method of making
the sounds, and in particular, to having so much high frequency
energy...

--Bill Sethares