Xenakis' Duel: Analysis of the Music

Xenakis' Duel is a work, which is pioneering in several aspects. Its variable form based on game theory has attracted the interest of the analysis. Xenakis himself in [4] and Schmidt in [3] analyse the construction of the game matrix, i.e. the rules that determine the macroform of the work. However almost no notice is made about the structure of the 5 pieces which constitute the material out of which the two conductors can make their selections.

In my doctoral thesis ([1]) I analysed the music in two stages. In the first I applied statistical and decrypting techniques in order to determine some constants of the 5th piece, under the assumption, that Xenakis used there methods similar to the stochastic composition of Achorripsis. I concluded based on the density process, that the period length of the 5th piece and this of Achorripsis where almost equal.

Then —in the second stage— I compared the two works and concluded that the whole 5th piece of Duel is completely a jigsaw construction with pieces taken out of Achorripsis. This jigsaw construction features many interesting regularities, which were analysed in my thesis. The same holds for the 4th piece (percussion).

[After discovering this astounding property about the 4th and 5th piece of Duel that not only shows the structure of the work, but of the construction process as well, I summarised the results and sent them to  Perspectives of New Music in May 2009. In June 2010 PNM answered; one of the reviewers did not recommend publication. 🙁 In the article I described the statistical-decrypting analysis and then the comparative analysis, which showed the complete structure of the 4th and 5th piece; at the end I reviewed the results of the mathematical analysis based on the results of the comparative one.]

After sending the article, I discovered that the first 3 pieces are made completely of pieces taken out of Syrmos (Syrmos was also analysed in my thesis). Both works were written in the same period. Would it be possible to conclude that Duel1-3 was made out of Syrmos and not vice vesa by not using any information data based on catalogues or compositional methods? In my thesis I gave some suggestions based on some sings and possible errors of the faksimiles, that point out that the direction was Syrmos / Duel and not vice versa.

Benoît Gibson gives many examples in [2] and mentions the extreme case of  Mosaïques about the self-borrowing technique of Xenakis; however he does not mention Duel, which is a complete jigsaw construction.

I think that the most interesting fact about my results, is not the result itself. Anyone could come to the idea, that Achorripsis and Duel4-5 have some similarities based on the instrumentation, which is identical. The most important thing is that a proper mathematical analysis can reveal many things about the "DNA" of a work which is composed on material based on mathematics. Subsequently one can compare works which share similar DNA, and therefore, avoid overkill comparative analyses.

PS (27/08/2011): The thesis has been published since some months and is available online. Here is its page on the site of the TU.

PS2 (3/12/2011): The thesis (upgraded version) is now available over the SVH Editions. Here is its page.


[1] Droseltis, Alexandros: Zufall und Determination in der westeuropäischen Musik um 1960; Dargestellt an Werken von Iannis Xenakis und Karlheinz Stockhausen, Dissertation, TU Berlin.

[2] Gibson, Benoît: Self-Borrowings in the Instrumental Music of Iannis Xenakis. In: Definitive Proceedings of the “International Symposium Iannis Xenakis”, Athens, May 2005.

[3] Schmidt, Christoph: Komposition und Spiel. Zu Iannis Xenakis, Band 4 der Reihe Berliner Musik Studien. Studio, Verl. Schewe, Köln, 1995.

[4] Xenakis, Iannis: Formalized Music: Thoughts and Mathematics in Composition. Pendragon Press, Stuyvesant New York, 1990.

Leave a Reply

Your email address will not be published. Required fields are marked *