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

Tue Dec 22 16:49:36 EST 2009

http://teneolupum.blogspot.com/

2009/12/22 christopher jette <christopherjette at gmail.com>

> 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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