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Rating: 
Summary: Difficult but profitable
Review: 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}.
Rating: 
Summary: Xenakis is a blowhard and a maniac
Review: 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.
Rating: 
Summary: Sieve Theory
Review: As Mr. Oscar points out, this book is difficult but profitable. For example, the theory of sieve can actually be coded with CommonLisp as follows.
(progn
(defun congruent (divisor remainder i) (= (mod i divisor) remainder))
(defun sieve (a b i)
(or (and (not (congruent a 2 i)) (congruent b 0 i))
(and (not (congruent a 1 i)) (congruent b 1 i))
(and (congruent a 2 i) (congruent b 2 i))
(and (not (congruent a 0 i)) (congruent b 3 i))))
(loop for i from 0 to 24 if (sieve 3 4 i) collect i))
This short program will output the major scale up to two octaves (see p.196). Different moduli could generate different repetitions, which Xenakis tries to combine and to fold by three logical operators. That will represent complicated signals, whose complexity is, however, not phenomenal but potential so that there remain various plasticities of interval combinations. In the actual architecture he uses much more different moduli for dynamically modulating several parameters on all levels of musical structure. It would be this procedure that he calls the "gigantic montage" of harmonia. By the way, Xenakis provides the source code of the sieve program written in C (translated from Basic by Gerard Marino, one of his co-workers at CEMAMu), which is divided into two parts (chapter XII). He originally elaborated it by himself after having studied the ancient Greek Harmonology of Aristoxenus.
A) Generation of points on a straight line from the logical formula of the sieve.
B) Generation of the logical formula of the sieve from a series of points on a straight line.
One can successfully compile these codes, although there are a few trivial misprints. And there is also a tiny problem in the source code of Program A, for it includes "conio.h", which might not be contained in your programming enviroment. In this case the functions getch() and getche() should be replaced by getchar().
Rating:
Summary: Sieve Theory
Review: As Mr. Oscar points out, this book is difficult but profitable. For example, the theory of sieve can actually be coded with CommonLisp as follows. (progn
(defun congruent (divisor remainder index) (= (mod index divisor) remainder))
(defun sieve (a b i)
(or (and (not (congruent a 2 i)) (congruent b 0 i))
(and (not (congruent a 1 i)) (congruent b 1 i))
(and (congruent a 2 i) (congruent b 2 i))
(and (not (congruent a 0 i)) (congruent b 3 i))))
(loop for i from 0 to 24 if (sieve 3 4 i) collect i)) This short program will output the major scale up to two octaves (see, p.196). Different moduli could generate different repetitions, which Xenakis tries to combine and to fold by three logical operators. That will represent the complicated sign-signals, whose complexity is, however, not phenomenal but potential so that there remain various plasticities of interval combinations. In the actual architecture he uses much more different moduli for dynamically modulating several parameters on all levels of musical structure. It is this procedure that he baptizes the "gigantic montage" of Harmonia. By the way, Xenakis provides the source code of the sieve program written in C, which includes two parts (chapter XII). He had designed it by studying togather with Yuji Takahashi the ancient Greek Harmonology of Aristoxenos. A) Generation of points on a straight line from the logical formula of the sieve.
B) Generation of the logical formula of the sieve from a series of points on a straight line. One can successfully compile these codes, although there are a few trivial MISPRINTS. And there is also a tiny problem in the source code of Program A, for it includes "conio.h", which might not be contained in your programing enviroment. In this case the functions getch() and getche() should be replaced by getchar().
Rating:
Summary: Unique theory book for music based on mathematics
Review: 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.
Rating:
Summary: Xenakis and the road not taken
Review: 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" !!
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