# Hyperbolic paraboloid and Xenakis



## RamonC (Jun 7, 2018)

Hello.

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:


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https://soundcloud.com/ramon-capsada-blanch%2Fhyperbolic-paraboloid-and-xenakis

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:








Hyperbolic Paraboloid - Full ScoreHD.pdf


Shared with Dropbox




www.dropbox.com





Information about the life and work of Xenakis:


https://en.wikipedia.org/wiki/Iannis_Xenakis



To listen to Xenakis music:








Iannis Xenakis: most famous pieces


Discover and listen the most famous pieces of Iannis Xenakis. The ones you know or you must know, like: Metastaseis, Pithoprakta... and more. For you, the best of Xenakis, the most objective selection of his main compositions.




soclassiq.com






*Happy Centenary Xenakis !!*


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## NoCoPilot (Nov 9, 2020)

I like the saddle shape to the music which get denser and louder toward the middle, then gradually tapers off again. This reminds me a great deal of "Gmeeoorh" for organ that Xenakis wrote, perhaps not coincidentally? Well done, RamonC.


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## RamonC (Jun 7, 2018)

It is very well to use the expression saddle-shaped to refer to the hyperbolic paraboloid since its form is really a seat fastened on the back of a horse.

Undoubtedly Gmeeoorh is a reference work by Xenakis, there are even doctoral theses written about it, and it is true that in the passages of great sound density, with great musical mass, they bear a certain resemblance to those of my piece, although he, without doubt, goes much further.

Modestly, with a fairly rational approach I have tried to introduce some characteristics of Xenakis's music but filtered through my personal sieve, and prioritizing that the result make musical sense and could be motivating for the (a little specialized) audience. . .

Thank you for listening to my music and for making this kind comment.


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## Prodromides (Mar 18, 2012)

RamonC said:


> *Happy Centenary Xenakis !!*


Greetings, RamonC.

Thank you for your devotion to applied mathematics in music ... and to Xenakis.
Our globe can benefit from more individuals such as yourself.

I hope, though, that your zest for X does not obscure appreciation for other composers.
You know there has been more than one composer born in 1922. Centenaries for Iain Hamilton or Irwin Bazelon (to cite merely 2) should not be marginalized simply because they weren't Xenakis. 

... but I acknowledge how each of us has our own personal favo(u)rites (how can we not?) which occupy our minds more so than music by those we rank as lesser priorities.

Indulge my curiosity, if you don't mind, by offering feedback on conductor Arturo Tamayo who recorded volumes of Xenakis orchestral music for Timpani records over 20 years ago.


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## RamonC (Jun 7, 2018)

Hello Prodromides.

I like it and I appreciate that you have remembered that there are several composers who were born in 1922 besides Xenakis. As you say, the list is long. In addition to Iannis Xenakis, Iain Hamilton and Irwin Bazelon, the Wikipedia page for the list of personalities born during the year 1922 includes 23 more composers (there are bound to be omissions). It is useful to write this list explicitly as our little tribute to all of them: Henri Thévenin, Ester Mägi, Jeanine Rueff, Manuel Oltra (Spanish and Catalan), Felix Werder, Ali Akbar Khan, Sadao Bekku, John Veale, George Walker, Gérard Calvi, Andrzej Koszewski, Ron Grainer, Lazar Nikolov, Robert Dauber, Svend Westergaard, Agnelle Bundervoet, Gilberto Mendes, Luiz Bonfá, Camillo Togni, Lars Edlund, Fikret Amirov, Ilja Hurník, Heinz Alt.

I am not a extreme follower of Xenakis, what I do is that I have studied him a bit because he is one of the forerunners of the application of mathematics and computer science in musical composition, which are areas of interest to me, in addition to his great uniqueness. And when I found out that it was his centenary, I wanted to compose something based on his style.

You show that you have a good musical culture when you meet the Spanish director Arturo Tamayo.
Tamayo (currently 75 years old) was trained as a composer and conductor in Madrid, but completed his training outside of Spain in Basel with Pierre Boulez and in Vienna with Witold Rowicki.
Since the end of the 1970s he maintained an intense conducting activity, directing important European orchestras such as the Bavarian Radio Symphony, Berlin, Cologne, Baden-Baden and the BBC Symphony and London Philharmonic. He specialized in 20th and 21st century music composers, with some of whom he had a very good personal relationship: Pierre Boulez, Stockhausen, Iannis Xenakis, John Cage, Giacinto Scelsi, Klaus Huber, Jose Luis de Las, Brian Ferneyhough, Wolfgang Rihm, Maurice Ohana, Sylvano Bussotti, Niccolò Castiglioni, Luigi Nono, Witold Lutoslawski, Morton Feldmann, Helmut Lachenmann, Salvatore Sciarrino, . . .

He had a great relationship with Xenakis, when Tamayo was still a student he asked him for an interview which very kindly granted, they also had many hours of work, many conversations to prepare the direction of his works. According to Tamayo told in an interview, Xenakis was a really very warm and friendly person. Tamayo also directed the concert-tribute to Xenakis in Paris for his 70th birthday.


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