[microsound] Gabor's matrix vs. Xenakis' screens

[Randal Davis]

An excellent question, and I'll have a go at its answer[s], in plural.  There are, I think, several different ways of approaching it, all, in their own ways, reasonable. Page references are to both Microsound and Formalized Music.

>From what perspectives do differences between Gabor and Xenakis appear?  As Rafal correctly points out, they are both mathematical formalisms representing a "3-dimensional structure of grain: frequency, time and amplitude."  One could, therefore, reasonably conclude that the differences between them are not significant, if the vehicle of comparison is, say, a Fourier model. 

That is the most general, and simplest, answer to the question; not very illuminating, either.  Evenso, to understand Xenakis' contention that "a book of screens equals the life of a complex sound" (Xenakis, 1971, 51) as opposed to the Fourier model is to understand a very profound distinction in how sound may be conceptualized.  

It's also useful to consider questions of intent.  As Roads points out, "it is important to emphasize the analytical orientation of Gabor's theory" (57).  Gabor was interested in a theory of hearing, arguing that an approach premised on sound quanta was superior to the "Fourier analysis of infinite signals" (58), and hence the Gabor matrix.  While a simplified graphic representation of such a matrix and one of Xenakis' screens might appear visually similar, Xenakis, Roads notes, had interests less purely theoretical, instead aiming toward the "explication of a compositional theory for sound grains" (65).  

Let's not, though, do too much too quickly with this distinction of what looks like "theory" (Gabor) and "practice" (Xenakis).  Look more closely at Xenakis'lemma for Markovian stochastic music:  "All sound, even continuous musical variation, is conceived as an assemblage of a large number of elementary sounds adequately disposed in time.  In the attack, body and decline of a complex sound, thousands of pure sounds appear in a more or less short interval of time delta-t" (Xenakis, 1971 & 1992, 43, and Roads, 65).

Does Xenakis differ from Gabor here?  If so, how?  We could return to our earlier, very general, statement of their congruence, or try and phrase the matter of their difference differently, one might say.  That is, accepting certain similarities in their formalisms, which is the most complete?  Does Gabor "explain" Xenakis better, i.e., more completely, than Xenakis "explains" Gabor?  Look back at Roads' explication of Gabor's sound quanta, specifically the necessity of an "uncertainty relation between time and frequency resolution" (58).  Now reread the lemma, and note the revealing phrase, that the sound grains appear "in a more or less short interval of time."  

That phrase, in my interpretation, is a specific reference to Gabor's uncertainty relation - as the interval of time grows "more or less" longer, the sound may indeed become more "pure" (e.g. pitch-determinant).  However, as the time interval grows shorter, resolution in the pitch domain lessens, and the "pure" sound becomes "fuzzier" or, more precisely, subject only to a more probabilistic representation.  Thus does Roads refer to the "problems with a constant microtime grid" (67-8).  

Xenakis was surely not unaware of this, and it is therefore significant to observe that in his graphic representation of a "book of screens" (Xenakis, 1971, 51 & 53) each cell of the screen is itself something very much like the graphic representation of a Gabor matrix; he also allows that grains may "fluctuate around a mean frequency and intensity" (52).  

It therefore seems to me that Gabor's is the more complete, which is to say the more fundamental, account of the sonic quanta for its premising of an irreducible uncertainty.  At the same time, as noted, one might imagine that most musicians and composers preferring the Xenakis formalism (at least speaking for myself, here) for its more ready conceptualization of the behavior and manipulation of complex sounds. 

The question, too, concerning the sonographic representation (Roads' figure 2.2) also is a good one, as the description and the graphic representation do not seem to me to coincide.  I have nothing more to offer there except this may be an editorial error.

Best wishes to all for 2010.

RD

> ----- Original Message -----
> From: "rafał zapała" <rafal at zapala.com.pl>
> To: microsound at or8.net
> Subject: [microsound] Gabor's matrix vs. Xenakis' screens
> Date: Fri, 18 Dec 2009 15:35:22 +0100
> 
> 
> Hi
> (question about Microsound by Roads) - do you
> understend the difference between Gabor's Mattrix and Xanakis'
> conception of screens - it's completly unclear for me, i can't see any
> progress there? Both represent 3dimentional structure of grain:
> frequency, time and amplitude. According to the figure 2.2 p60 - i don't
> understand the sonogram too.
> 
> 
> +48 506050417
> www.myspace.com/zapalarafal
> www.myspace.com/anarchenewmusicensemble :.
> 
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