Softcover, 2006, ISBN-10 3-7643-7745-3, 245 pages, US$ 39.95, illustrated, bibliography; available from Birkhäuser Verlag, P.O. Box 133, CH-4010 Basel, Switzerland; Web www.birkhauser.ch/.

Reviewed by Charles Turner
New York, New York, USA

Best known for his commanding contribution to music theory, The Topos of Music (2002), Guerino Mazzola has produced a very interesting textbook on Music Informatics in collaboration with Roland Bärtschi and Stefan Göller. This textbook provides an Internet link to the music examples used, but for those of us in the United States used to crutches, it has none of the “instructor resource manuals” or “testing CD-ROMs” that commonly accompany offerings from publishers such as McGraw-Hill or Thompson. Based on the subject matter explored, a teacher contemplating using this book would want students to have access to a computer that could run the author’s RUBATO software, and also have Apple's Logic sequencer and Cycling '74's Max/MSP software installed. Although Elemente describes the features of these specific programs, the FLOSS (Free/Libre/Open Source Software) equivalents, Rosegarden, Pure Data, or others, could certainly be substituted. The full text of Elemente der Musikinformatik can be accessed online at www.encyclospace.org/Musikinformatik_1/index.html. This review provoked a very amiable email exchange with Dr. Mazzola upon which some of this review is based.

Elemente is the manifestation of a pedagogy based on Mr. Mazzola's philosophical and mathematical theory of music elucidated in Topos. This pedagogical approach has found a home at the Institut de Recherche et Coordination Acoustique/Musique (IRCAM), Technische Universität Berlin, Brock University, Canada, and courtesy of the author’s recently-established presence there, the University of Minnesota. Elemente would be suitable as an undergraduate introduction to Music Informatics for a semester course, unless the teacher supplemented the presentations with projects or more detailed readings keyed to the individual chapters. Music Informatics (or Musikinformatik) may be a familiar discipline in Europe, but here in the USA, it merits discussion. From my admittedly not-extensive familiarity with university offerings nationwide, I would propose that departments offering instruction in the history, theory, and performance of music most often integrate computation at the level of technology. There, computers offer no more than a kind of word-processing power for the tasks of composition or writing papers. The kind of revolution experienced in the next building over, where students are “doing science” on their laptop computers is a largely foreign experience. On the other hand, computer science departments don't seem to have responded to audio in the same way they did with graphics. There is no sonic equivalent of the Association for Computing Machinery SIGGRAPH (Special Interest Group on Graphics and Interactive Techniques) to exert a horizontal pull across a wide swath of sub-disciplines. Music Informatics, at least as I understand it from Mr. Mazzola's work, implies something more than “computer-based musicology” or “music CS.” Elemente instructs a theoretical foundation for the artistic use of sounds. This foundation proposes to be valuable not only in the humanities, but also in scientific disciplines such as music information retrieval, music perception, and others.

Elemente's chapters are grouped in two major sections: “Theory” and “Technology.” Mr. Mazzola opens his consideration of theory with a chapter on the interaction of composition and technology that constructs an historical arc from the Pythagorean tetractys and Athanasius Kirchner's music machines to Iannis Xenakis's UPIC (Unité Polygogique Informatique CeMAMu) system and the performance art of Stelarc. His chapter “Musiksemiotische Grundlagen” presents the three-dimensional coordinate space of musical knowledge familiar from Topos. The dimension of Reality involves physical, psychological, and mental layers. A phenomenon located in one layer can correspond to a phenomenon in another layer, but its reality is not reduced as a result. The dimension of Communication follows Jean Molino's tripartite scheme of a creator's production (poiesis) and a listener's reception (esthesis) converging on the work, or neutral niveau. The final Semiotic dimension is developed in more detail, in part because it introduces the author’s presentation of coding schemes for musical objects. His discussion of the Semiotic layer follows a structuralist leaning, which in music is exemplified by Molino's student Jean-Jacques Nattiez. The presentation of Saussurian dichotomies is accompanied by useful examples. This is true also of the section on the Hjelmslev-Schema, which establishes relations between sign systems as recursive in the manner of Russian dolls. The examples here are a useful compliment to Mr. Mazzola's parallel discussion in Topos, as they clarify the character of the recursive relation, depending on whether it is found at the significant, signification, or significate layer. (Interested readers might wish to consult Mr. Mazzola's “Semiotic Aspects of Musicology: Semiotics of Music,” which can be downloaded from his personal Web page at www.ifi.unizh.ch.) This coordinate space constitutes the topos of music: a musical object can take a place within these three dimensions of Reality, Communication, and Semiosis.

The remainder of the “Theory” section of Elemente discusses the representation of a variety of musical objects that can be placed in this coordinate system. Sound events are described in terms of their waveform and amplitude envelope, and later, Fourier's theory of the overtone series begins a section on synthesis with accompanying descriptions of frequency modulation techniques, wavelets, and physical modeling. The presentation here emphasizes how these techniques and objects describe sound, and is not a tutorial on the practice of synthesis. Mr. Mazzola breaks down note information into pitch, intensity, onset time, and duration parameters. He discusses how notes can be located in Euler space, and further grouped as chords, motives, or melodies, as well as rhythmically or contrapuntally related. Performance notation is also presented as another type of musical sign. The musical representation of several software systems are compared: Max Mathews' Music-N languages, Mr. Mazzola's own presto and RUBATO software, and a number of efforts based on the Lambda Calculus such as Yann Orlarey's work and Paul Hudak's Haskore. The author also offers enlarged explanations of the MIDI data format, the FFT algorithm, and the coding of MP3 audio streams.

The presentation of the fundamental objects of Mr. Mazzola's topos theory, his “universal concept formats,” spans the division between Elemente's “Theory” and “Technology” sections. Here he begins with the concept of the encyclopedia, an approach to the organization of knowledge whose properties are unity, discursivity, and completeness. Toward the end of Elemente, the author returns to the encyclopedia in the presentation of his Encyclospace project, a global distributed collaboratory and concept management system. He argues in Topos that the historical sciences are likely to be absorbed by a type of dynamical knowledge management, and Encyclospace is his conceptual and technical framework to support such an effort. The Encyclospace's data format for musical objects is the Denotator, a recursive formalism composed of a “substance-point” in its own “form-space.” Building on the concepts developed with other encoding schemes, Mr. Mazzola demonstrates the generality of the Denotator by explaining how it could be used to encode note information, or a simple FM-synthesis object. With Denotators as a basic building block, he expands their consideration to the construction of a database specification. Examination of this denoteX format, actually an ASCII interchange format, demonstrates how complex musical representations can be built up from Denotators.

Once the data formats have been presented, Mr. Mazzola provides an extensive tour of his music software, RUBATO. Its architecture as a distributed knowledge tool is described, and the author gives an extensive operational example of the use of the MetroRUBETTE plug-in in music analysis. This is followed by shorter presentations of the Melo-, Harmo- and PerformanceRUBETTEs. Although these presentations are complete, they do not dwell on operational issues, so actually duplicating the results with an installed copy of RUBATO is not so easy. (RUBATO is available for free download at www.rubato.org.) Making intelligent use of the software would require a fairly detailed knowledge of Mr. Mazzola's theories, necessarily gained from a study of The Topos of Music, or some simple operational examples that would enable “learning by doing.” This is addressed in part by Gérard Milmeister's dissertation, “The RUBATO Composer Music Software: Component-Based Implementation of a Functorial Concept Architecture,” available on the RUBATO Web site. In spite of its imposing title, Mr. Milmeister includes a very readable tutorial on the use of RUBATO. Apparently a “RUBATO Bible” is in the works for release sometime in 2008. Elemente's consideration of music software concludes with a look at three very different types of applications: Logic, Max/MSP and Mr. Mazzola's own presto composition application. In keeping with the goals of the book, these applications are discussed in terms of the way they represent and enable certain actions in musical space, and less so on operational or functional aspects.

Returning to the discussion of Encyclospace mentioned above, Mr. Mazzola concludes his text with a consideration of the iPod and its social impact on the consumption of music. This linkage of technology and cultural form is a fitting place to end his introduction to representation in music. Elemente der Musikinformatik is yet another facet of the author’s extensive contribution to contemporary music theory and musicology. In many ways, it is best read as a manifesto of the social value of his theoretical work, that is, how the topos of music can change the way we practice music composition, performance, and history. In my brief encounter (so far) with Mr. Mazzola's thinking, I am unclear whether he considers the topos a universal or general theory; whether it is happy to coexist with other approaches, or be “cherry-picked” for what people find useful in it. Milton Babbit, it might be remembered, postulated that any self-consistent system has its own limited applicability. But given the collaborative nature of Mr. Mazzola's adventure so far, well captured in his evocation of Galileo's method in the beginning of Topos, I would expect his ideas to have a long and widespread significance.