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

Tue Dec 22 16:31:17 EST 2009

Greetings,
I am not sure that I understand the confusion with the sonographic image,
Roads 2.2 page 60

> 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.
>

If one looks first @ the sonogram and the lowest left hand corner, noting
where the lines indicating the binding constraints are, there is a portion
of the FFT that is within these confines. From here one can compare this
with the numerical and graphical representations in the top 2 graphs. It is
the same data represented in different fashions.  While the description
describes this in the reverse order, it says virtually the same. I fail to
see the error.

Cheers~
Christohpher

2009/12/22 Randal Davis <randal_davis at operamail.com>

> 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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>
> >
>
>
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