Customer Reviews

Formalized Music: Thought and Mathematics in Composition (Harmonologia)

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This is an incredible work, the concentrated expression of Xenakis' philosophy of music, and the category he pioneered, "stochastic music." Of course very few composers have followed Xenakis into this new universe -- Roger Reynolds is perhaps the best and most important, though Xenakis is only one of his key sources.

"Musiques Formelles" was originally published in French in 1963, and the English edition dates from 1971. The potential reader should know that the better part of the book is expressed in mathematics. It therefore provides a working basis for an aspiring stochastic music composer, but not what most of the rest of us consider gripping reading. I found the discussion of the use of "screens" in composition based on Markov chains to be intelligible, but there are pages and pages of equations that I would only read if it would further a goal such as a stochastic composition. There are, however, several powerful passages in chapters I ("Free Stochastic Music") and VIII ("Towards a Philosophy of Music") that are crucial for anyone interested in 20th century music.

It would be a great development if Xenakis was to belatedly replace the minimalists as a major force in "contemporary classical"/"new music" !!

A very difficult book even for experienced musicians, due to complex high mathematics terms and explanations (you will need any degree of math training for understanding some concepts displayed in this book). However, there are several chapters with interesting information and ideas to be applied in your own music or analysis approach. For instance, chapters XI and XII (titled "Sieves" and "Sieves: A User's Guide") have an interesting and clear (the most one of entire book) explanation about a fundamental tool in Xenakis music as is sieve theory, which can be applied to several music parameters such as pitch, duration or intensity, etc. Other chapters as XIII and XIV can be useful if you are interested in synthesis or computer-based synthesis software such as Csound and Common Lisp or another synthesis programming language.
Rather than difficulty of this book, I think the main problem is about how useful can be this book for 70's and 80's Xenakis repertoire. The book is mainly focused and written for mid 50's and 60's Xenakis music (works such as Metastaseis, Pithoprakta, Achorripsis, etc) and can be disappointing if you are interested in 70's Xenakis music (for me, his most interesting period}.

It is Unique theory book for music based on mathematics as I know. Xenakis's musical world is based on modern mathematics. He use statistics, stochastic process, game theory, group theory, etc. in order to formalize macro level musical structure. This book shows how mathematics can be applied to music. He insists that the criterion for aesthetics of music be "intelligence", not beauty. I think that It is historical publication in music theory area.

If you liked Curtis Road's "Microsound", you might like this book. However, be warned that it is not for the faint of heart. You need to be well versed in music theory and mathematics to get the most from it. It has a very academic tone, but has some unique things to say about algorithmic composition that makes it worthwhile. Also be warned that much of it is translated from the original French, so that makes some phrases in the book seem oddly worded. I guess I would best describe it as the "Godel,Escher,Bach" of algorithmic composers. It's rough going, but once you "get" what Xenakis is saying, you will have a perspective on algorithmic composition that is invaluable.
This book includes:
1) six chapters that are the translation of Musiques formelles, including the appendixes.
2) two chapters that are translations, with some additions, of the chapters "Vers une metamusique" and "Vers une philosophie de la musique" from "Musique Architecture".
3) "New Proposals in Microsound Structure", where Xenakis challenges sound synthesis by Fourier analysis and proposes a new synthesis based on probability theories.
4) "Concerning Time, Space and Music", which is similar to the article "Sur le temps" (1988). This paper describes time as intrinsically related to space and then ties this relationship to music.
5) "Sieves" and "Sieves : a User's guide," which constitute the two sections of the article "Sieves" (1990). The first chapter explains in detail the construction of sieves and the second reproduces the computer program that generates this construction. Sieves are integer sequence generators that can help generate pitch scales and rhythm sequences in compositions.
6) "Dynamic Stochastic Synthesis", which involves multiple levels of probabilistic functions that determine the break points in an envelope that in turn describe one cycle in an audio waveform.
7) "More Thorough Stochastic Music" provides the program of dynamic stochastic analysis that was used for the first version of Gendy, which was a computer program written by Xenakis that performed sound synthesis.
8) an annex on "The new UPIC system" based on an article from 1990 written by the engineers at CEMAMU at the time (G. Marino, J.M. Raczinski, M.H. Serra). CEMAMU is an acronym for "Centre d'Etudes de Mathematique et Automatique Musicales". The UPIC console is a direct-input graphics device that allows for one to escape the messy complexities of musical notation in the scoring of complex electronic sounds.
It is hard to find anything on the web written by Xenakis that is not in French, so this book is about the only way for English speakers to enjoy this man's work.

After putting this book down I am not at all sure who Xenakis meant it to be for. He mixes his own vague ideas with incredibly dense math, all with an entirely egotistical slant. There are some pretty drawings and designs, but I found his explanations insufficiently accessible.

He is prone to quoting himself ("To be is not to be"); using made up or Greek words in the text ("Echos metabolae using special signs, the martyrikai phthorai or alternations of the mode initialization"); elaborating his ideas in too-complex mathematical terms; and denigrating alternate methodologies.

His ideas about "stochastic music" are certainly well-respected, but it was very difficult for me to ascertain why. I think I would prefer to read someone else's account of his ideas, because I found his own tone and approach so unpleasant.