Fortuin@Winnipeg

Daniel,
Let's try to wind this up.

>I know, for example, that I can hear,
>identify, and reproduce the sine wave complex 500, 600, 750 Hz. I hear it
>distinctly as a "minor" triad and neither as a mistuned harmonic series
>segment where 500Hz = 2^n nor as a harmonic series segment over the
>fundamental of 50Hz.

Okay, well that is different from my experience, and seems different from
any documented psychoacoustic phenomena. But that doesn't mean you're wrong.
How well does this extend up to, say, 11-limit hexads? I've found that
tuning an 11-limit otonal hexad is easy, even with sine waves, while tuning
an 11-limit utonal hexad, without listening to smaller subsets while tuning,
is nearly impossible, unless the tones are unusually rich in harmonic
partials.

>(2) Phase differences can have dramatic effects on pitch perception. With
>long duration sound installations, the relative phase positions are
>apparent in physical space. I recently heard an extraordinary installation
>by Hauke Harder in Copenhagen, where phase relationships were essentially
>the only dynamic element in the work. When phases were locked this entire
>quality disappeared. Young has worked with _drifting_ phases and has made
>some interesting psychoacoustical conjectures. (I have had similar - but
>not precisely so - experiences in recording sine wave complexes from my
>Rayna synthesize onto CD or DAT, where differences in sampling speed all
>but destroyed entire works).

Well, the effect is apparantly specialized enough that most music retains
its character, since the BBE hardware works by reducing peaks through
judicious frequency-dependent phase-shifts. This is what I thought you were
talking about, the relative phases of two different partials in a harmonic
relationship.

>(3) A spacing theory would be a method of analysis and not a theory of
>composition, although the information obtained might be useful to
>composers. Last time I checked, composers were free to proceed with or
>without a theory.

By a theory of composition I meant a method of analyzing compositions, just
as a theory of physics does not cause physical phenomena to occur but merely
explains them.

>(4) I believe your procedure is closely tied to western musical materials
>(I try to be a bit more global in my approach, but the simple matter is
>that the number of repertoires with pitch complexes of three or more
>members is limited; a parallel project of mine involves harmonization
>procedures for repertoires with melodic properties distinctive from the
>German folksongs upon which classical chorale harmonization is based); for
>this reason, a coupling of your algorithm with an approach to chord
>progression is worthwhile if not necessary, since your procedure demands
>parameters only close to those offered by traditional western classical and
>vernacular musics. In this (broadly defined) repertoire, contrast between
>harmonic structures is a (if not THE) defining feature.

Yikes. I don't see where you're getting this, and I should also point out
that a pitch complex of two members is enough.

Look, I'm only trying to explain certain features of the musical experience
here, namely phenomena that are due to what is going on at a given instant
in time. Whether a certain chord is a tension or a relaxation will obviously
depend on what goes on *before* and *after*, but there is a component that
depends on the *during*, and one of the two components of that is related to
the virtual pitch detection process. I feel it is very important to model
and understand this process, becuase it is so strong as to convert all
near-simultaneous near-harmonic sine-wave complexes into single sensations.
To assume it has no impact on the musical effect of harmony would be folly.

>(5) For the Boomsliter and Creel example, I should have said harmonic
>_progressions_, for the choice of 224/128 over 7/4 was aopparently made in
>reference to position in a larger network of relationships, and not to a
>stretching preference (although Linus Liu recently sent me an example of a
>scale for Chinese music - which is primarily melodic - where a sequence of
>just melodic intervals leads to an octave stretched by 81/80).

Ah, well in that case I would agree. (You meant 225/128, since 224/128=7/4.)
Certainly one can follow a relatively long chain of 3/2 relationships, a
relatively short chain of 5/4 or 6/5 relationships, and perhaps only one 7/4
relationship (or not even) in the roots of consecutive chords. This is very
different from the perception of simultaneities.

-Paul


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