My Little Grundgestalts

Here I describe the algorithmic music I call "Grundgestalts"

My latest composition, “Esercizio no. 16” (Exercise no. 16):

Three voices, which I assigned to soundfonts of a Steinway piano, a Otto Rubner double bass from 1958, and percussions.

Video is obtained via https://github.com/Eidonko/Permutation-feed-povray with as input the string “000011112222”.

Resulting Povray file was edited by changing the camera structure as follows:

camera {
   sky <0,0,1>          //Don't change this
   direction <-1,0,0>   //Don't change this  
   right <-4/3,0,0>     //Don't change this
   location  <300+clock*43000,300+clock*clock*43000,300+clock*43000>  //Camera location
   look_at   <-400,0,0>    //Where camera is pointing
   angle 1      //Angle of the view--increase to see more, decrease to see less
 }

The audio is also available on

#funkwhale

and

#peertube

and on mastodon:

Composed on October 18—20, 2020.

Both video and audio are by Eidon and © Eidon (Eidon at tutanota.com). All rights are reserved.

This song is called 金曜日でした, kinyobi deshita. It means “it was a Friday”, which is the literal translation of a phrase from the song I love the most of those written by the Italian band “Matia Bazar”. That song and its counterpoints literally make me crazy :–)

It was a Friday,” Antonella Ruggero sings; “t' was a night of silence and full moon.” It's Matia Bazar's wonderful “Fantasia”!

I called like this for I wanted to celebrate the day I love most, the prelude to the end of the week. The day of gold, as the Japanese say – hence the title. The bass part came to mind on my way home, and I wrote the rest straight away – a kind of desktop improvisation, with no second thoughts. I orchestrated it in simplicity: double bass, then piano; a touch of kalimba and finally a pinch of woodblock. That's all.

I hope you'll enjoy it. Have a great weekend!


On #peertube:

On #funkwhale:

On #mastodon:


And here's my translation of the lyrics of Fantasia:

A room, a house, a city Empty streets and shadows in the darkness. In Berlin, soldiers, tired and ageless, Stand by walls with women near them Premonition – in a little while everything’s going to end In Paris, London and all other cities.

It all happened on a Friday – it was a night of silence and full moon How much tension there was in the city and how much in that room.

On the Seine a solitary barge goes on Champagne in rivers, ammunition and people unaware. In Paris, connivance under unlit lamps Cigarettes and voices for an hour of happiness. Premonition – in a little while everything’s going to end In Paris, London and all other cities.

It all happened on a Friday – it was a night of silence and full moon How much tension there was in the city How much tension there was ...

Hei! Some tolling – of bells now silent Radio London, a message, in the Thames, a wave. Lord and Lady ‘nother whiskey are going to have But those Englishmen in their pubs are no longer standing. Premonition – in a little while everything’s going to end In Paris, London and all other cities.

It all happened on a Friday – it was a night of silence and full moon How much tension there was in the city...


“金曜日でした” was written and orchestrated by Eidon on October 16, 2020. All rights are reserved to the author. © Eidon, Eidon@tutanota.com. All rights reserved.

...Lysardgig is a lysergic, obsessive, psychedelic, minimalist Ostinato. It is based on only two voices, one of which, the bass, is stubbornly repeated. A slow trend, like abandoning oneself, canceling oneself. Written in one go, last night. Yes, a nocturnal piece – a dark blue piece. Lysardgig Yggdrasil.

Here it is on #peertube

as well as on #FunkWhale

On #Bandcamp you may find the song in lossless format and the whole album that I'm writing.

Photo by Josh Sorenson from Pexels


Lysardgig was composed on October 2 2020. © Eidon (Eidon at tutanota.com). All rights reserved.

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.

This is Ordnas, a little “Grundgestalt” generated by the simple theme in this picture:

*Youtube video! The idea of adding subtitles to it was kindly suggested by @GustavinoBevilacqua@mastodon.cisti.org!*

The structure and arrangement are perhaps the things that I like the most in this piece.

  1. The theme is presented by electric guitar followed by tenor sax and clarinet; it's a 4/4 with a “comfortable” pace of 50 beats per minute.

  2. The piece gets in full swing immediately afterwards, with piano, flute, double bass, drums, oboe and bass clarinet joining sax and clarinet, while the guitar leaves the stage.

  3. The drums show a small change in tension: the piece becomes a little tighter here.

  4. Modules 2. and 3. are re-exposed.

  5. At this point, the piece becomes frenetic — the sax exposes a theme that makes me think of the circus, and of tango; as I said to a friend on Bida, Piazzolla is a great love of mine and perhaps his influence is felt more at this point. The battery underlines the new change of trend.

  6. Here, we slowly return to the initial concept; the electric guitar fades in, re-proposing the theme; bass and drums support the musical moment, while the sax prepares for the solo.

  7. Sax, oboe and piano are alone here. The piano plays a simple arpeggio. Tenor sax is the absolute protagonist here. It is “he” that sings here. It exposes a simple theme, very melancholy for me, which then becomes the theme of the electric guitar, with note values that are doubled.

  8. After having exposed the theme of the guitar twice, Element 5 enters again; this time, however, the electric guitar clearly emerges — it makes its voice heard – once again with the initial theme.

  9. Here, the guitar theme becomes more and more central and is re-proposed as in 1., though it is the wind instruments that propose the conclusion – it is they who “close” the guitar theme, providing those notes still missing in the guitar theme; it is they who pronounce the kotodama, the “seed” that generates this piece...

* Images obtained by applying G'mic-Qt filters*


Ordas was composed from 21 to 23 September 2020. © Eidon (Eidon at tutanota.com). All rights reserved.

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.

“The deep mountains of karma” is one of the verses of the Iroha, perhaps the most perfect pangram ever composed: a text that uses each character of an alphabet — in this case, the Japanese syllabary — exactly once. My thanks go to my kind friend Wim who taught me about it.

*”Gently calligraphed in India ink on the two pieces of washi papers. Meiji-Taisho period, early 20th century, Japan. Attached with with acrylic frame. Missing the last phrase of *’e-hi-mo-se-su-n’. Some stains and aging degradation as seen”.*

Also interesting to me is that the Iroha had been initially attributed to Kūkai, the founder of the Shingon Esoteric sect of Buddhism in Japan, whose life and thought I have recently got acquainted to thanks to Massimo Raveri's book Il Pensiero giapponese classico (ISBN 9788806165871).

An absolute must-read: Massimo Raveri's book Il Pensiero giapponese classico.

Wikipedia kindly provides the English translation by Professor Ryuichi Abe:

Although its scent still lingers on the form of a flower has scattered away For whom will the glory of this world remain unchanged? Arriving today at the yonder side of the deep mountains of evanescent existence We shall never allow ourselves to drift away intoxicated, in the world of shallow dreams.

I don't know how it is for you, o Reader, though the above lines evoke in me the verses of “Perhaps One Day” by Eugenio Montale... and that sentence, “the form of a flower”, is it not a magical reference to Umberto Eco's “The Name of the Rose”?


“The deep mountains of karma” is also a Grundgestalt available on

It begins with a piano solo, then enters uduhachi, followed by congas; bass and percussions follow; then baya suwuk, and finally African percussions. The various instrument then exit one by one, as actors in a play, until only the first and the last one remain on stage and conclude the piece. I don't really know why, though rather than a Japanese piéce I'm thinking now of Luigi Pirandello...

Composed on July 26, 2020. ©Eidon (Eidon@tutanota.com). All rights reserved. desrever sgnorw llA

Les Fleurs du Mal is a story that never leaves me — on the contrary, it doesn’t let me go away — une histoire qui ne me délivre pas. Though I don’t think this is bad. I am attracted to those thoughts, to those people …

So I decided to watch Mais ne nous délivrez pas du mal (Don't Deliver us From Evil), which Oshimi explained was an inspiration to his Aku no Hana; a 1970-1971 film by Joël Séria.

At the same time, I created such a slightly obsessive music. After all, obsessions are the main characters of these stories. Obsessions — such as light for the moth, or darkness for those attracted to it.

Or like Aku no Hana to me.

A transitive closure of sources of inspiration! Baudelaire → Mais ne nous délivrez pas du mal → Aku no Hana...

A significant source of inspiration: Les Chants de Maldoror.


Now, I don't want to spoil the experience of the movie or the manga, though there is an event I need to highlight here; the one that closes the first part of Aku no Hana and is at the very end of Mais ne nous délivrez pas du mal (Don't Deliver us From Evil). Yes, the same event takes place, although it concludes very differently. This is the pivotal scene in both works:


Where does fiction end, and where does reality begin? Sometimes the boundaries between those domains are very blurred. Have a look at the Wikipedia page on the real-life event that inspired the movie: the so-called “Parker–Hulme murder case”.


If you want to follow the whole story of Les Fleurs du Mal, it’s here on PeerTube

On FunkWhale it is here:

This frame from Mais ne nous délivrez pas du mal brought my mind to a recent reading, the 20th Century Boys manga


And if you would like to contact me, please do so on Mastodon at @Eidon@octodon.social or @Eidon@mastodon.bida.im.

I recently joined Guresuke (@guresuke@shpposter.club) in a metal project called MATHEMORPHOSIS

Long Winter Our first song, “Long Winter”, was written by Guresuke-san. Its lyrics evoke in me the spirit of recent days of social segregation — the reign of Camus' Absurd. The above link points to song and lyrics.

Bygone Days Our second song, “Bygone Days”, focuses on a different types of absurd — the one that sometimes we face in the course of our daily activities.

The gods had condemned Sisyphus to ceaselessly rolling a rock to the top of a mountain, whence the stone would fall back of its own weight. They had thought with some reason that there is no more dreadful punishment than futile and hopeless labor. (Albert Camus, The Myth of Sysiphus)

Nightfall Here, I want to spend a few words about our latest work, “Nightfall”. It tells of apocalyptic scenarios, of a humanity that has made a mistake too many and is one step away from extinction; at the end of the game, to put it with Beckett. But it’s also a song that tells of hope; of a different relationship between man and the World Ecosystem. Of a new rebirth, a new Humanity — definition and never again oxymoron.

Writing the lyrics for this song was a great experience to me. Guresuke-san offered me a detailed idea of the theme of the song; in a sense, the concept was already written down in music. Also the melodies were there, and I just put the words that I felt would express best that musical concept. A little magic took place when my mind went, by association, to beloved play “Endgame”. I opened again Beckett's book and found there the words that Ham says at the beginning of the play:

All is absolute

Suddenly I realized that those words expressed perfectly and exactly what I wanted to say with the lyrics. And that they matched metrically the chorus of Nightfall... I could not but quote them there...


I always liked early Genesis songs that were structured into parts — “Get 'em Out By Friday”, as an example. This led me to have parts in our latest song: Narrator, the Government, and then the Chorus. The latter plays the same role as in ancient Greek Theatre: “a homogeneous, non-individualised group of performers, who comment with a collective voice on the dramatic action” (wiki).

“Homogeneous, non-individualised” means that the Chorus wore the same mask. The ancient Greek for mask is πρόσωπον (pronounced as “prosopon”), which later became persona, Latin for person, possibly also through the Etruscan phersu. So the person is the mask, the non-person, if they passively accept all decisions without questioning its ethical significance.

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!