This piece is inspired by the music of the composer Iannis Xenakis, since precisely in this year 2022 the centenary of his birth is celebrated.

You can listen to it on my SoundCloud page:


To make it easier for you to read, although it is also on the SoundCloud page, I include below the presentation of the work in which I explain the details:



Hyperbolic Paraboloid and Xenakis.

For 47 acoustic timbre instruments interpretable only electronically.


When I knew that in this year 2022 the centenary of the birth of the composer Iannis Xenakis is being celebrated, I got the impulse of composing a piece inspired by his music. My motivation is given by the fact that the work of this composer can be considered among the most innovative and influential of those emerged in the second half of the 20th century and more particularly for being considered the most important pioneer in the use of mathematics and also of the computer in the musical composition, and that these are precisely my favourite fields of study and application in the creation of my musical pieces.

The characteristics of Iannis Xenakis music are very wide, very original and cover very diverse fields. Then I highlight those that I have taken into account in the composition of my musical piece and also explain how I have applied them.

1. Orchestral music and electroacoustic music. Xenakis was interested in the two types of music and has great works in the two fields. He is considered a precursor in various areas of creation with electronic means.

My idea has been to try to present a mixture of these two types of music, but not proposing a simple addition of instruments of the two types in a single set but choosing to use instruments with acoustic timbre but electronically emulated and, what is more Important, doing an interpretation that is only possible electronically: speeds, ranges, timbres unification. . ., which are impossible in real acoustic instruments and executions. Thus the audition of the music of this piece is born and dies in its electronic production.

Specifically I used a total of 47 instruments: 29 string instruments with unified range and 18 piano lines. The score that I have written (in the end attached its link) is not to be used in an orchestral interpretation, but as a basis for electronic production and also for its subsequent analysis. In the elaboration of this score I have applied a slightly artificial graphic distribution and a impression large size to enhance its visual character and thus help understand the geometric content of the work.

2. Great and dense musical masses. Although Xenaquis, as he advanced in his compositional production, he became increasingly interested in the small ensembles and soloists writing for them true masterpieces, in the works of his early stages he frequently uses large sound masses, what he calls large clouds of point-notes inspired by the musicality of natural mass phenomena: "The sing of cicadas in summer, the hail against hard surfaces"; or social: "a political crowd of dozens or hundreds of thousands of people."

In my case I have tried to obtain a continuous gradation between passages of low sound density and among others of high density where they would simultaneously sound the 47 instruments, but never in unison but using a total divisi, in such a way each of the 47 instruments have a melodic line different, but, nevertheless trying to achieve, sometimes, the effect of a unique melody with a lot of power, in reality two melodies, the string and the piano. Sometimes, due to the intersection of a large number of different string melodies, an auditory synthesis is achieved and appearing new timbres.

3. Musical space as a sound architecture. The fact that Xenakis was an architect greatly influenced his music. The Philips Pavilion, designed for Expo 1958 in Brussels by the office of Le Corbusier, and also, much later in 1977, the transportable structure called Le Diatope, to houses the multimedia show based on his work La Légende d'Eer, they have a clear relationship with some of their musical works. He had a special interest in the geometric figure in three dimensions called hyperbolic paraboloid that used it both in these architectural constructions as well as in the composition of passages of his works, for example in the generation the sections of glissandos of his work Metastaseis.

This hyperbolic paraboloid (which shows a drawing in the image that accompanies my piece on the Soundcloud page) has been the base where I have built the bulk of the melodic and harmonic materials of my composition. It has been a different use than Xenakis in the aforementioned glissandos since he did it using the property that the paraboloid is a ruled surface, that is, it can be generated by a straight line when moving; The different straight lines that compose it were precisely violin glissados. In my case I have used its most internal structure when considering the different sections that originate by cutting it by parallel planes, generating two sets of parabolas, some that begin by growing and the others that begin by decreasing. In this way I can transform the continuum of this figure in a discrete collection of parabolic lines.

4. Using mathematics. As I have already commented, due to his technical formation he had good knowledge of mathematics and used them in the musical composition. The composer Olivier Messiaen, refers to him as follows: «… You are lucky to be Greek, to be an architect and have studied special mathematics. Take advantage of them! Use them in your music ”. And he obeyed him.

Two have been the main mathematical tools that I have used in my composition. The first, the definition of the mathematical functions that allow to generate the parabolic lines in a three -dimensional space and that make up the hyperbolic paraboloid. Each of the three dimensions (x, y, z) of the points that form the parabolas have a musical meaning. The x corresponds to time, the y corresponds to the pitch of the note and the z to each of the different voices or musical lines. As the paraboloid is rotated on an axis, different views of the disposition of the parables corresponding to the different delays of the musical voices are obtained in the corresponding counterpoints.

The second mathematical tool has been statistical analysis. Xenakis created the concept of Stochastic Music. He used different probability distributions to control some of the parameters of his musical masses. One of the most prominent is the parameter of the sound density that generally imposed that it followed the Poisson's probability distribution. In my case I have also wanted to control the sound density of my piece, analyzing the distribution of frequencies of the different densities and retouching the amount of musical lines that appear in the different musical units so that it will adjust more to the theoretical probability distribution.


I finish attaching some links:


Score of my piece:



Information about the life and work of Xenakis:



To listen to Xenakis music:




Happy Centenary Xenakis !!


You need to be a member of Composers' Forum to add comments!

Join Composers' Forum

Email me when people reply –


  • Aloha, Ramon!

    I thoroughly enjoyed your Hyperbolic Parabaloid and Xenakis, both the music and the text. Not being familiar with Xenakis until now, I had many pleasant surprises. The use of mathematics to create music is wonderful – each melodic line one straight line describing the parabola, creating a rich polyphonic “sound mass.” This is something Nature also does, as you say, with crickets or rain on a tin roof. The effect on the listener is sound overload which is a classic tool for entering a trance state.

    You then flex this sound density so it keeps changing, which becomes a large part of the musical architecture, at least for the casual listener like myself. And you make this statement, which I heartily second: “Sometimes, due to the intersection of a large number of different string melodies, an auditory synthesis is achieved.” This synthesis becomes the bones of the musical architecture.

    I use the same phenomenon in a much cruder form, by overdubbing guitar improvisations. The first improv sets the chord progression. Then I jam over that, and again over the duet. Because nothing is planned ahead, the result is that the intersection of melodic lines creates an auditory synthesis strong enough to hold the whole piece together. I call these “improvisitions,” and again they can sometimes have the effect of auditory overload, inducing a sort of listening trance. I recently posted a gentle acoustic guitar trio improvisition called Plastic Jesus Variations, and an electric guitar trio improvisition with orchestral cyber-instrument backup, called Dances with Dragons.

    Keep composing!

    • Hola Dr Matthew.

      How nice it is to see that the work done, makes the listener enjoy, as you indicate that you have done, also taking into account that this piece is not easy to get into. Thank you very much for taking the time to read my long explanations and for reflecting on my music.

      Regarding the use of the parabolic line strictly as a basis in the definition of the melodic material, I applied it to achieve more clarity in the musical construction of the geometric figure of the paraboloid and to avoid possible amorphousness. However, this drastic reduction of basic melodic motifs was in danger of provoking excessive repetition of a simplistic nature; problem that I have tried to solve by increasing the variation in the other musical parameters (tonality, rhythm, polyphony, sound density, . . .), variations that also correspond to different arrangements of the geometric set.

      I have listened to your two pieces that you have indicated in your comment. Although "Dances with Dragons" has greater timbre richness (and also the magic of the small Hawaiian lizards), I found the Plastic Jesus Variations more interesting. I have left a comment on its Discussion.




  • Most fascinating. From the little I remember of Xenakis it fits. (I rarely read the prose commentaries. I was a follower of Die Reihe while it was about and found all too often the commentary was miles more interesting than the composition! but here we have some beautiful music. Your use and development of the thematic material is superb. The ethos is laudable ("is not to be used in an orchestral interpretation, but as a basis for electronic production and also for its subsequent analysis." Although I'm happy enough to accept your particular interpretation as one of possibly many possibilities)).

    In short, it can stand as a piece of music, an instance. There's no point in analytic comment here about reception - you change the approach to the material most noticeably around 3'12" and thereafter. And the fade down at the close is easily in keeping - it could have gone on but needn't have.

    I'm fairly averse to "mechanical" processes underlying the construction of a musical result but in this case the result IS musical. Thank you for giving a chance to listen to your work once again.

    (And thank you for offering a work of a duration that won't take half a morning to listen to and comment on!!)



    • Thank you Dane for your excellent and kind comments.

      You are right that the important thing is the music more than the possible literature that can accompany it. The musical work must be the only protagonist. Although I must confess that I like to accompany my works with a fairly complete explanation, but my intention is none other than to explain the context, mainly theoretical, in which the work was created in order to reduce the wide indeterminacy that suppose listening to music and thus help its possible assimilation. But if the music is bad, there is no prose to save it.

      The piece has two very different parts and the change occurs, as you have rightly observed, around 3:12. It is like starting over, the sound density is again minimal and will progress, for the second time, to the maximum. It is a start over but now with more speed and tension. Speed ​​that will be maintained until the end, but in the passage that closes the work the tension gradually decreases. I would have liked this break point (3:12) to have happened a little later, specifically about 22” later, in this way the duration of the two parts would have been in the golden ratio (1.618) which is the famous ratio in the art history and was also used by Xenakis.. However, I dismissed it since I couldn't find any musical or formal reason to justify it, on the contrary, it implied a shorter second part that didn't fit.

      It's true that try to be careful with "mechanical processes" since they can lead to results that are too crude and schematic. I think that algorithmic procedures can only be used if they are subordinated and controlled by the composer's decisions that respond to criteria of an aesthetic nature and of musical significance.

      And about the length of the piece, it may be difficult for you to believe it, but whenever I check the length of the work I am composing, I get worried when I see that it exceeds 6 minutes because I remember the comment that you made in this forum some time ago in the sense that 6 minutes was the maximum time that you recommended so that a piece would not become tedious. . . Although the works of Xenakis are very long, but they were other contexts, other times and other interests.

  • I enjoyed listening to your tribute to Xenakis here. The sound cloud densities were like a hugh flock of migrating birds to me. You could view the shape of the flock from afar or put yourself inside the flock and hear some of the individual birds or sub-nodes within the flock. When the density thinned out, it was delightful to hear the indidvual instruments emerging from the cloud. 

    Thanks for sharing this with us.


    • Marty, I'm glad you enjoyed listening to my piece of music.

      Certainly, Xenakis explained that his use of sound masses in his musical compositions was inspired by the musicality of natural mass phenomena. It is wonderful that when you have listened to the music it has evoked for you the evolutions of a flock of migratory birds. This may indicate that the musical result that I have obtained fits quite well with some of Xenakis's musical approaches.

      I really appreciate your comments.



    • I have no interest in Xenakis or his theories (although I occasionality do hear a work of his which does something for me) and yet your description of this piece seems very apt. I've listened to this several times and find it curiously compelling even without having more than the slightest inkling of what it's about. There is something about the changing textures indeed which gets to me.

      • I sincerely thank you that, despite not being the type of music that interests you, you have listened (several times) to my composition and have read its explanations. I am also pleased that you found it convincing. Perhaps it is because there are common logical structures between musical concepts and geometric spaces. . .

        • as an unreformable Romantic who tries to compose what I would perhaps call humanist works, a mathematical concept of musical composition is indeed rather alien to me though naturally I respect the right of every composer to develop whatever theories he or she sees fit. In the end, it's the results that matter to me and I do find what you have done here somehow compelling.


          • I love listening to music from the romantic period !

This reply was deleted.