Grundgestalt is a German word meaning *fundamental form*. The fundamental form, in music, is a concept introduced by Schoenberg to indicate the idea that is the foundation of a piece of music. This basic idea, in Schoenberg, is not just the idea from which a piece “starts”; in reality that idea is *the piece itself*, or rather its gene within which the whole piece is already contained and from which the whole piece can be derived through a mechanical, deterministic procedure. The Grundgestalt is therefore the most compact form to express a piece of music; a genotype from which a complex phenotype can automatically be derived, yet all contained in the initial seed. In a sense, it is the most compressed form of a certain musical information — the developed piece. Grundgestalt, in other words, is the *foundational*, basic form of a complex musical idea.

This is expressed by Schoenberg in his 1950 article, in which he states:

“Whatever happens in a piece of music is the endless reshaping of the basic shape … There is nothing in a piece of music but what comes from the theme, springs from it and can be traced back to it; to put it still more severely, nothing but the theme itself.”

So the theme is the Grundgestalt, and it is at the same time the piece of music that a certain algorithm *decompresses*. Or, we could say, *realizes* (makes real), or *gives birth* to. I also like to think of it as an isomorphism that preserves the meaning by passing from a genotypic to a phenotypic domain.

# My little Grundgestalts

I don't know what the Grundgestalt for Schoenberg was in practice. In fact, I just don't understand how he could have created a compositional model like this without the aid of modern computers. But I, who live in a different era, have been able to play with compositional models based on the Schoenberg Principle with relative ease. The idea comes from the definition of *dynamic system*: we have a function *f* and a domain value *x*; we compute *f(x)* and use it again as input to *f* (of course we assume that *f(x)* is still part of the domain of *f*). We end up with a series of values:

*x, f (x), f (f (x)), f (f (f (x)))*, ...

and so on. Dynamical systems mathematics studies the properties of these series as *x* and *f* vary. And this is the mathematics of the Grundgestalt, in which *x* is none other than the theme that Schoenberg was talking about!

Hence it is possible, and now even simple, to create a compositional model that follows Schoenberg's theory. If my function *f* acts on a domain made of musical objects, andthe series of values *x, f (x), f (f (x))*, etc., produces musical compositions. And those musical compositions necessarily derive from the choice of *f* and the choice of *x*. In a sense,

There is nothing in a piece of music but what comes from *x*, springs from *x* and can be traced back to it; to put it still more severely, nothing but the theme *x*.

I like to call *Grundgestalt* those pieces of music that fit this definition — this math. And my pieces are just Grundgestalt. I use two functions *f* (one of which is computed by this program), while my *x* are simple alphanumeric strings. Some results are surprising to my ear, inexplicably so. You can listen to them here and here.

# A small selection of my Grundgestalt ...

... which I will expand little by little:

“Everything in the universe is ... is ... is made of one element, which is a note, a single note. Atoms are really vibrations, you know, which are extensions of THE BIG NOTE ... Everything's one note. Everything, even the ponies. The note, however, is the ultimate power, but see, the pigs don't know that, the ponies don't know that ...”

(*Spider in Very Distraughtening ~ Lumpy Gravy*)

This work is licensed under a Creative Commons Attribution 4.0 International License. Author is Eidon.

Quest'opera è distribuita con Licenza Creative Commons Attribuzione 4.0 Internazionale. Ne è l'autore Eidon.