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Saturday, June 25, 2016

Continuums and saturated spaces

My parents took me to the square often. It was more like a park for me, because of it's size. Going through it involved pebbly curved paths. For some reason I keep that memory: me, walking with my dad, thinking exactly how many little stones would there be. Then, some other questions came like how big can a little stone be without being a regular stone, or how little can be before being just sand.

This memory came back to me trying to think about some ideas related to sound, of the composer Antoine Beuger. The text I will refer to is translated to English as Fundamental Decisions1. I will just take some of its initial issues related to some concepts of my own.

Beuger starts his text with two categorical questions: the first one about the material of music ("what is it made of?") and the second one about its form ("how is it made?"). His answer to the first question is that the material of music is "the ubiquitous noise of the world; i.e.: everything that sounds". The second question is answered saying that music is a cutout, an extract of this "noise". Form is "the fragment that music cuts of this infinite diversity".

In relation to the first concept ("the ubiquitous noise of the world"), the key would be to think of an infinite, continuous and monotonous matter. The concept is of wholeness: it's not only everything that sounds, but all this is included in a set that brings it together: everything that sounds, simultaneously. This is easily referable to the idea of white noise, chaotic, messy. But there is a subtle but fundamental difference with this expression of sound that will give place to other ideas. White noise is a chaotic evolution of sound, an "unpredictable" evolution. What is chaotic there is the organization in time and spectrum of sound. But as the sound continuum proposed by Beuger includes everything that sounds, it also includes every possible evolution of sound. I.e.: every possible duration, every possible time. For our perception, one thing cannot have more than one duration. That's why Beuger will say that this object (the sound continuum) as a result of a speculation is mute, inexpressible.

Sound is only expressed as something that is extracted from there, as physical actions that reproduce a possible part of the whole. Beuger emphasizes that the qualities of sound are given by the cut that is made. That is equal to say that on the physical level, sound is form. The nature of the continuum is also given within the limits of sound shape: the last one is made of a lot of frequencies in its spectrum and if we consider its evolution it's also made of an infinity of different moments².

I see this continuum as a saturated set. In other context, making reference to this idea, Beuger will say that in the sound continuum there are no spaces3, there is no way to identify discrete elements. This is equal to silence. A presence so vast and complete that cannot be anything but nothing: so full that every space and duration is occupied, so much that there is no possible change, no possible movement. This concept is even more definitive if we think in a saturated topological space, where every element is related to the others at the same level and with the same hierarchy among all. Not only including a new element is impossible, but including a new relation between elements is also impossible. But then, deleting a relation is to make a cut. What I try to say is that composing is to think of elements in relation within a topological level4. And this is achieved by selecting part of the available relations in the sound whole, i.e. cutting it.

How is this different from what we were discussing? Well, in his text Beuger goes from the sound continuum directly to the form5 and does not talk about the procedure that this passage takes or better, he does not consider the procedure as a different level in this scheme. I'll say that as we have seen when sound is sounding is form, when sound is thought it is structure. With structure I refer again to the topological level, to the structure mounted as relations between elements. The difference here is that when we think in sounds as topological elements we are thinking them as points. That is to say that composition goes through a state of discrete organization (separate elements) that will not be translated intact to the sound reality: the fact that a sound is made of many elements makes it highly unlikely, if not ontologically impossible, that an identical sound exists. But this doesn't prevent us from thinking a sound appearing more than once, from the structural point of view, having the same relations with the rest of the elements. A topological form (written note) carried out (played note) in has infinite possibilities of being. "Pure differentiality of what exists. No need to worry about the differences. They do not need us to find their own. They do not need us to recognize them: they already are. They are what exists. Each sound is different. There is no repetition6."

Moreover, Beuger opposes to the idea of music as a construction of minimum units that build larger ones. It's clear that in a structural level this can be thought this way or not. For Beuger, however the composition is organized, the result is a cutout from a continuum that also embraces aesthetics, geographies, archaeologies and histories of sound and music. Similarly, I consider that the structural level is in the end analytical, and does not make music by its own, but its scaffolding, thought either before or after the piece realization. The saturated topological space would be identical to Beuger's sound continuum, but the first will now represent all paths and structural relations of aesthetics, geographies, etc.

Now I'm thinking you can reduce the category "little stones" to only one element if you can answer the questions of the first paragraph. Like a single little stone that includes in its properties "being all the little stones in the world existing in this moment". Let's put a number if we want it to be more spectacular. But I think I like it more the other way around: thinking that all the little stones are attracting each other, however immutable, beating on a dark backround that unites them.

1 Beuger, A. Grundsätzliche Entscheidungen. 1997. Wandelweiser Editions. http://www.timescraper.de/_antoine-beuger/texts.html#Antoine_Beuger__

2 Sinze the Fourier Theorem, any periodic waveform can be decomposed in many sine waves. See for example Roederer, J. Acústica y Psicoacústica de la Música. Melos (Ricordi Americana). Buenos Aires, 1997.

3 Saunders, J. Antoine Beuger. The Ashgate Research Companion to Experimental Music. pp. 231–241. Farnham: Ashgate, 2009. http://www.james-saunders.com/interview-with-antoine-beuger/

4 Topology is the branch of mathematics that studies the properties of figures regardless of their size or shape.

5 Surely this is for clarity on the concept that is intended to express and because his interest would rather be to talk about the matter and form in the procedures that apply to them. 

6 Beuger, A. op. cit.

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