My Little Grundgestalts

Here I describe the algorithmic music I call "Grundgestalts" and other compositions

This is “Sextant”, by Eidon (Eidon@tutanota.com). Music and pictures by and © Eidon — All rights reserved.

“Sextant” is an original composition for piano, double bass, timpani, and percussions. I wrote it on June 23 and 24, 2021.

The essence of the piece is given by the ostinato on bass, coupled with a reassembling of piano “blocks” of a partitioned leading theme, which cyclically repeats itself.

Such a series of 7/8 music quantums is followed by a second theme, in 6/8. Said theme is first played by piano and percussions; then, again, slightly variated, by contrabass, piano, and percussions.

Then, the first theme enters again, with a new reassembling, which then drives the track to its conclusion.

“Sextant” is available on Bandcamp, here.

A video is available on youtube:

The video features pictures that I took at the St. Hubert's Galleries in Brussels and at the Hortus Botanicus Lovaniensis (the Botanical Garden of Leuven), Belgium.

If you like this music, and if you would like to support me, then follow me on Bandcamp or download my compositions from it.

Best, Eidon.

Sextant, on Open.Tube

“Illyeen” is an original spelling for “عِلِّيِّين”, which is a Quranic name for girls (see other spellings and more info here)

“Illyeen” is also my latest #Grundgestalt. If you like, you can download it from my #Bandcamp

Oh, yes, “Illyeen” is also an anagram of “Ley Line”.

And “Ley Lines”... is my latest album:

Also on Bandcamp yeah

The video has been done with txt2srt, a simple tool to orchestrate the execution of other tools on a sequence of pictures.


Illyeen is by Eidon, and is © Eidon (Eidon at tutanota dot com). All rights are reserved.

Pictures in the video are by Eidon. They are licensed under a Creative Commons Attribution 4.0 International License.

Lately I’ve been tinkering again with my Little Grundgestalts. I have given a lecture about my “method”, and I have written a paper that I submitted to The Journal of New Music Research. Moreover, I have started collaborating with a great Chilean researcher who introduced me to the wonderful “modelling language” of Chemical Organization Theory. I expect to tell more here about this wonderful new journey soon.

Something else recently happened too — regrettably, something very saddening. Humberto Maturana, the great Chilean scientist, passed away.

Apart from his concept of autopoiesis, I know really too little about Maturana’s work — I will start studying soon. Before doing that, though, today I felt the urge to experiment again with my Little Grundgestalts. This post reports about this little experiment of mine.

My starting point

I first asked my algorithm to tell me the sound of the string “Maturana”. In other words, I fed string “Maturana” into my Beggar-my-Neighboursimulator, produced a set of orbits, and converted them into music. The result was this fragment:

First fragment of “Maturana”

I liked this very first output; I said to myself, “this element should appear twice, and have a little conclusion.” So I tried with the string “Maturana Maturana Varela”. The result was much better!

Second fragment of “Maturana”

This motivated me to continue with it.

New elements

I took a very simple direction: I launched the following script:

randperm -i Maturana -n 40 -x

and collected fourty random permutations of string “Maturana”. Then I added at the beginning and at the end the string “Maturana Maturana Varela”. And once again I fed the result into my Beggar-my-neighbour simulator.

The result was quite interesting; though it was the single voices that caught my attention. When played by a piano, they all seemed to me quite interesting. So I decided to… play with them, a little bit. Let me call those voices M1, M2, and M3.

I took M1 and played it. Then I used the second fragment as if it were a second voice of a canon, starting around 5s171ms. The result was surprisingly convincing. I then overlapped the whole M1 again, starting around 9s146ms. I also applied M1, though played by timpani.

At the same time I applied a fragment from M2. The whole M2 was then overlapped at 55s632ms, and M3 at 1m24s630ms.

The three voices (with M3 this time, played by a clarinet) are then overlapped around 1m51s330ms. M1 is also played by timpani here.

This screenshot summarizes how the voices of “Maturana” were combined together.

Conclusive remarks

In this post I wanted to describe in more detail the “compositional” process that I adopt when creating my little Grundgestalts. The example I took is “Maturana”, a track from my album “Ley Lines”:

The track is by Eidon, and it is © Eidon (Eidon at tutanota.com). All rights are reserved.

eARTh is my latest work: a Grundgestalt generated by seeds that are random permutations of the strings “eARTh” and “mousiketekne”.

Genotypical selection led to the following strings:

collect.sh	\
		AheTR  AheTR TeRAh  ReTAh  TRAhe  \
		eTRhA  hTARe  RAhTe  eTARh  AehRT  heART hRTeA \
		\
		ketmeosknuie  ueitmkeoekns  kteoenkmueis  mskntukeeoei  teioukmeknse  uikmktnseeeo  motkuekieesn  uteskoniemek \
		\
		ehART  eRAhT  heATR  eTRAh  RThAe  eRThA  hReAT  ARhTe \
		\
		hRTeA  ThRAe  ARheT  eARhT  ehRTA  TeARh  RAheT  ehATR  hATeR  eRThA  ATheR  ATeRh  \
		ueitmkeoekns  kteoenkmueis  mskntukeeoei  teioukmeknse  uikmktnseeeo  motkuekieesn  uteskoniemek  \
		\
		AheTR  AheTR TeRAh  ReTAh  TRAhe  \
		eTRhA  hTARe  RAhTe  eTARh  AehRT  heART hRTeA \
		\
		ketmeosknuie  ueitmkeoekns  kteoenkmueis  mskntukeeoei  teioukmeknse  uikmktnseeeo  motkuekieesn  uteskoniemek 

The resulting midi file was elaborated with the Evanessence2 soundfonts and with samples of a 1958 Otto Rubner acoustic double bass.

The picture is a G'MIC elaboration of the string “eARTh,” rendered with the Chilanka and Ani font types.

Both music and picture have been created by Eidon and are © Eidon (Eidon@tutanota.com). All rights are reserved.

eARTh is part of my album “ii”, available as 24bit FLAC audio files on Bandcamp. It was created on April 10, 2021.

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:


Addendum – Zappa's Big Note:

“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)

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

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

I compose alternative, progressive, and math rock music. The latter is based on algorithmic procedures that I devised, such as this one.

I talk about my compositions here and (in Italian) here.

I have recently formed a metal duo with the Japanese composer @Guresuke@niu.moe: Mathemorphosis. Check out our first songs, “Long Winter”, “Bygone Days”, “Nightfall”, and “Dread Dagon”.

The American author Howard Bloom, music publicist for singers and bands such as Prince, Billy Joel, and Styx, praised my music.

Roel Vergauwen — programmer for the Rock Werchter festival, recently selected me as an interesting possible candidate to participate to their world-renowned festival:

“Eidon is een solo artiest uit Leuven die zijn muziek bestempelt als progressive rock, wat in deze tijden al bijzonder is. Maar hij put ook uit mathrock, minimal music, jazz, etnische muziek,... Hij zou perfect passen als support van Gogo Penguin, Battles of Dijf Sanders en kan op termijn misschien wel een plaats veroveren op zowel Rock Werchter als Gent Jazz of Couleur Café. Benieuwd hoe hij dit live brengt.”

Roel Vergauwen – Rock Werchter programmer chooses Eidon because ...

“Eidon is a solo artist from Leuven who describes his music as progressive rock, which is already special these days. But he also draws from math rock, minimal music, jazz, ethnic music, ... He would be a perfect support for Gogo Penguin, Battles, or Dijf Sanders, and may eventually be able to conquer a place at both Rock Werchter and Gent Jazz or Couleur Café. Curious how he brings this live. “

More information on Mr. Vergauwen's kind statements is available here, while here you can listen to an interview for Studio Brussel in which Vergauwen talks about me. During that interview, my song FediDance has been broadcast.

As you may know, Fred Hoyle co-wrote a beautiful novel called “A for Andromeda”, in which a very special message coming from the cosmos is received through a radiotelescope leading to a number of surprising events. I have often been thinking about that book because of my current experience with algorithmic music. In short, I'm cuurently experiencing a puzzling variant of a Turing test, in which I know that my interlocutor is artificial and I have to tell whether their messages may be considered, to some extent, “more than artificial.”

I'm talking of tracks such as the ones I called Kwaidan, Mantra, ReLIFE, and several others. These tracks were produced by very simple seeds, interpreted as pack of cards that simulate a game. All the notes are actually the states of the game as it is played. What emerges from those so simple seeds is a truly unexpected complexity — a complexity that is making me reflect on my limited way of understanding intelligence and evolution. I see now more clearly — or I should better say I hear — that the infinite variety of random and not-so-random combinations occasionally result in something that is smart-by-pure-chance; something that, because of its superior “smartness,” is naturally propelled to the next stages of the evolutionary path. All this makes me think of biological evolution in a different way: as an algorithmic, living composition.

Herewith I invite you to perform the above mentioned Turing test variant yourself, and listen to those messages — messages that come not from the cosmos, as in Hoyle's book, but rather from the domain of mathematical ideas...

Here they are!