RE: difference tones; golden ratio

zHANg wrote,

>I recently acquired a CD by Maryanne Amacher...
>'Sound Characters (making the third ear)' (Tzadik).
>Interesting use of difference tones & psycho-acoustics.

>I'd like to know more about difference tonalities &
>if there are any scales devised to exploit these
>"auditory illusions."

Difference tones can occur in the ear or in poor sound-reinforcing
equipment. They are due to nonlinearities in the amplification function.
They have been studied extensively; see, for example, Reiner Plomp's
_Aspects of Tone Sensation_.

A scale built on the golden ratio (like Chowning's) would be good for
"exploiting" difference tones because the difference tone between a tone and
the golden ratio above is the golden ratio below (only the golden ratio
would work for this).

Paul Erlich answered zHANg:

"A scale built on the golden ratio (like Chowning's) would be good for
"exploiting" difference tones because the difference tone between a tone and
the golden ratio above is the golden ratio below (only the golden ratio would
work for this)."

I came across this behavior a while ago accidentially when comparing the
difference tone pattern of different intervals. I even designed an
experimental scale around this fascinating phenomenon but never found the
time for a realization. Anyway, I can dig it up and put it on the Web in a
quiet minute, possibly next weekend. I'll let you know the URL.
I do not know Chowning's scale; can you provide a source, please?

Heinz Bohlen

>Paul Erlich answered zHANg:

>"A scale built on the golden ratio (like Chowning's) would be good for
>"exploiting" difference tones because the difference tone between a tone
and
>the golden ratio above is the golden ratio below (only the golden ratio
would
>work for this)."

>I came across this behavior a while ago accidentially when comparing the
>difference tone pattern of different intervals. I even designed an
>experimental scale around this fascinating phenomenon but never found the
>time for a realization. Anyway, I can dig it up and put it on the Web in a
>quiet minute, possibly next weekend. I'll let you know the URL.
>I do not know Chowning's scale; can you provide a source, please?

>Heinz Bohlen

From the microtonal discography
(ftp://ella.mills.edu/ccm/tuning/papers/discs.html):

*John Chowning: "Stria" (1977). 13-tone/octave slightly stretched (6 cents
off) or you can think of it as the Golden Section divided into 9 equal
parts. On "John Chowning: Music with Computers", Wergo, 1988. WER 2012-50