Music - Constructivism - Abstract Synthesis

What I'd like to see in music#

Let's think about the history of mathematics. Before around the time of Riemann, mathematics was really just about properties of numbers, about finding roots of certain equations, etc. This for me is profoundly boring so that I wasn't interested in mathematics at all when I hadn't learn abstract algebra and didn't know what topology is. Now we more or less know that mathematics is a general science of structure and mechanism, the most general science of abstract synthesis. It now seemingly has nothing to do with number at all - though factually in the deeper levels they're still connected.

Similarly, music for me is never about sound per se, or about organization of sounds. It's the most general art of abstract synthesis. What this term "art of abstract synthesis" means I don't know, but for me music is very mathematical and mathematics is very musical. Focusing on sound per se, or on the permutations of sounds, for me is like focusing on numbers per se, or on the algebraic equations. The point, for me, is the landscapes of sounds, the general morphology of these landscapes, and the interaction between the landscapes, and more. This all sound extremely abstract, but I don't know whether there's a better way to put it.

Let's start with the most primitive process of abstraction and synthesis (note that synthesis here is not sound synthesis but synthesis in the Kantian sense). For example, the context of additive synthesis is a landscape of sounds. What I want to hear is not a particular synthesized sound, but the very process of additive synthesis, this may be called the "morphology" of the landscape of additive synthesis. Additive synthesis maybe continuously produce individual sounds, and these sounds form a new landscape, the landscape of synthesized sounds. I want to see the morphology of this landscape of synthesized sounds, and I want also to see its morphogenesis - the interaction between the landscape of addtive synthesis and the landscape of synthesized sounds. Once the landscape of synthesized sounds is integrated (or synthesized in the Kantian sense), it might automatically disintegrate, since the structural or "categorical" element can be abstracted from the concrete landscape, and yield something new. I'd like to first get a concrete grasp of this process (a process not in time but in a general logical/conceptual order).

This is very similar to how the study of the natural numbers became the study of algebraic equations, and how the study of algebraic equations became the study of mathematical structures such as group and module.

I think I'll need to elaborate more on this line of thought. First, clarify terms such as "the art of abstract synthesis", and then etc.

PS: Musical truth is synthetic a priori. It has very little to do with perception. I don't think music is about sound at all.

Expansion#

For me music, and abstract plastic forms in painting, are always somehow gestural. Not in the sense of bodily movement, but in its metaphysical sense: the dynamical, life-movement of forms. Growth, mirroring, parallelism, contrast-tension, superposition, overlaying. A breath, a burst, a turn, a spasm, a twist. A bodily movement, a gesture is actually a somatic variant of a movement-form, whose traces can be discerned in the residual of the time-consciousness of the observation of the corresponding gesture. People tend to search for biological or physiological correspondences between dance and music, but it is plain that these are related spiritually or even mathematically: in a Mondrian painting it is possible to discern the same tension-form that enables a spasm/twist to be apprehended in a passage-twist of music or in a sudden change of dance-form.
Also, by the way, I pay almost exclusively my attention not to melody or a passage or a phrase, but to the transitions between different form-sectors in music. The form-sectors themselves are not really interesting, but the way different form-sectors interact is of prime importance, though these interaction-forms are also form-sectors themselves and in, say, Beethoven's late string quartets the most profound thing is the interactions between these interaction-forms. It is as if while for superficial arts objects are the locus of artistic forms, for profound arts the morphisms between the objects, and the morphisms between morphisms, etc., or even functorial principles, are the locus of artistic forms that individuate/characterize the piece.

"the dynamical, life-movement of forms", this just corresponds to integration-disintegration (I don't like this terminology since it reminds me of Deleuze). Music is really about the progression of forms, the mirroring of the internal (syntax) and the external (semantics). How the whole and the atomic determine each other, and to grasp the essence, to identify the essential and exhibit it. To identify the topos, and identify the syntax-semantics interface.

I mean, the point is not to produce interesting sounds, but to musically exhibit, for example, what is it that a sound is additively synthesized. The organization itself should reflect the very process, by integration-disintegration. Just like in the definition of an abelian group the nature of numerical addition and subtraction is presented.

Integration: this corresponds to the definition of natural numbers, +, -, etc. in terms of 0, S(0).
Disintegration: this corresponds to the definition of abelian group, ring.
Of course we can have reintegration: from ring we not only can study the properties of ring itself, but also get algebraic geometry.

The quest is to really comprehend and form a concrete picture of music out of this abstract speculation.

Constructivism#

I like austere sounds, because they are rich.

I don't want sound to be

natural in the sense that
to imitate nature
to represent anything
to simulate anything

I want them to be _constructive_, to be pure, naked, as they are in themselves, which means:

sines, squares, triangles, etc.
affected by impulses, Heaviside steps
be guided by a law of themselves
"objective" and without “subject”

But a philosophical problems is that in a post-Kantian conception of the reality how should I make sure that sound that I conceive of as "objective" is really objective? Some forms which are not really there in the so-called "objective world" are more objective than the "objective world" but at the same time more subjective as in idealism - is set theory objective or subjective? The word "abstract" is misguided and misguiding since I don't want to abstract from anything. I want abstract as they are in themselves.

In spirit it is very similar to the broad idea of constructivism that does away with any representation and imitation of nature, e.g., biomorph (which Xenakis does), or with the use of "natural" "raw" elements out there in the world (which Xenakis also does, say, in Concret PH or Bohor) - musique concrete is bad while it had its own historical significance. But Xenakis is a thinker who needs not only to be heard but also to be read and pondered upon - but not in the techniques that he focuses too much on.

Surprisingly the ONLY musician that I heard that does anything similar to what I want were Ryoji Ikeda and Marco Momi. I don't want richness that is perceptible, I want richness itself, which is not that perceptible, especially for those dumb normies.

I like Alvin Lucier's works a lot though it is too Mondrian-isque in some respect, and Morton Feldman I like. Camilo Mendez, etc. these composers are closer to abstract expressionism which is fine and I like a lot but not what I myself want since I require precision and inherent law ("law" is a bad word) in anything.

Ivan Fedele has a really good sense of form, but he's not a thinker.

I don't want to misinterpreted as advocating for a "Euclidean" concept of sound. I'm not arguing for sines, squares themselves, they are just examples. Neither am I advocating for a complete elucidation of clear, clear-cut forms of sound. What I want is austerity not simplicity. It is absolutely possible for a complex object to be austere, for example the Peano curve is complex but astere. For example E8 polytope is complex but austere - but maybe too symmetric for my taste.

When I say something is "natural" it doesn't mean it is natural in the sense of being present in "Nature", but natural as it is in itself. One of the most natural thing in the world which includes the "abstract Platonic world" is the cumulative hierarchy. There's nothing that is more natural than a continuous-trace algebra. Rieffel induction is one of the most natural "abstract" process that I've seen. (It is very hard for me to express anything if people persist in their understanding of words as they are used in the traditional Romantic and pre-Romantic sense. I've provided abundant context for them to contextualize the words I use; I can't do anymore to help them comprehend what I'm talking about.)

Just a simple, maybe misleading, concordance:

Analysis - sound synthesis/"spectralism"; what Lachenmann is doing is similar to some kind of dumb polynomial decomposition - his taste in his choice of the bases he uses is awfu; such an overrated composer.
Oldschool algebra - harmony, counterpoint
Oldschool Geometry - form
Abstract algebra - serialism, but not post-Bourbaki.
Topology - ?

Music is relatively very old-fashioned, maybe antiquated. It is still in the 19th century, in large.

One enormously difficult class of feelings to express:

the feeling of nature as inexorable laws
the feeling of nature as orderly relationships
the feeling of the intricate structure of the landscape of mathematical objects
the feeling of a theorem/a definition, such as Kolmogorov complexity, such as Chaitin's incompleteness
the feeling of mathematical logic, not in the sense that it is "cold" and "impersonal", but more intricate, more deeply felt.

Grothendieck and those who worked with him possessed an uncanny ability to express his feelings in words. Look at the words he chose for definitions: sheaf, stack, gerbe… And his metaphors, "the rising sea". But his interest was strangely biological and more specifically botanical.

There's a lack of means for anything that pertains to sense perception - conventionally people think art pertains to sense perception, but I may disagree, but let's assume that it is the case - to express/exhibit/convey inner complexity rather than outer complexity.

It is relatively straightforward for a piece of music to have outer complexity. Say Xenakis, say Bach. But for inner complexity it is really hard not to degenerate into minimalism when executed due to the lack of expression of the idea that is to be conveyed.

I don't want spasm, don't want screams, don't want extended techniques. Harsh sounds are okay, but I don't want them to be expressionist.

To be honest I like my writing style when I'm writing serious essays. It is a toil for me to write like that since I occasionally find myself tightly constrained. "Abstract", labyrinthine, but structured, in that every sentence should be in proper places and every clause should be ordered so that not only the semantic but the syntactic structure becomes one that of concordances, of self-mirroring, and a autonomous dynamical unit that operates by the power of "natural" flow of inferences. Complexity should not be imposed or added, it should emerge. Emergent complexities, either are chaotic, or are superficially simple. Of course I don't want chaos. I want emergent, asymmetric, symmetries.
I've seen some artists tries to convey a similar idea by plainly showing the process of emergence. I'm not interested in this. I'm not interested the perceptible phenomena of emergence, I'm interested in the structural necessity that induces emergence.