Iannis Xenakis was a prolific composer who accompanied his work with theoretical writings. Also trained as an engineer, he is known for having used mathematical models in his compositions and for developing a formalization of music. This book presents Xenakis's main theories from an analytical perspective without calling for special knowledge of mathematics. It features numerous musical examples and relies on detailed analyses to explain Xenakis's compositional procedures, yielding new insight into the relation between theory and practice in the composer's music. As a comprehensive study, it also reveals for the first time the extent to which Xenakis borrowed from his earlier works. The use of montage is examined as a compositional device, challenging the view that mathematics plays a dominant role in his music. On the whole, this book offers a fresh approach to the music of Xenakis and contributes to a better understanding of his creative thinking. In the year marking the 10th anniversary of his death, it provides a fitting tribute to one of the most original composers of the twentieth century.
December 1, 2012
Whatever the desires of the musicological world, the world of new music has long seemed in desperate need of a book that is able to explain comprehensively the work of Iannis Xenakis and that goes beyond the biographical, but that does not rely—or relies only in part—on the mathematical conceits that dominate Formalized Music. Benoît Gibson’s The Instrumental Music of Iannis Xenakis
is not that book. Indeed, it does not set out to be, and it would be a wholly unfair standard against which to judge it. Yet what this study demonstrates eminently clearly is that such a volume is entirely conceivable and that there is no need for scholars working on Xenakis to feel that understanding the equations of Xenakis’s own theoretical models is a prerequisite for writing. One of the great strengths of Gibson’s approach to Xenakis is that it demonstrates that there are valuable, illuminating strategies to be taken that are not necessarily dominated by the composer’s apparently preferred hermeneutic apparatus.
Gibson is keenly aware of the speciﬁc difficulties of approaching Xenakis’s work, stressing in his introduction the fact that, notwithstanding the formidable appearance and reputation of Formalized Music, on the odd occasions on which he actually allied his theoretical apparatus with a speciﬁc example from his music, he had little concern for whether the theory and the practice truly agreed, suggesting that on some occasions he made errors in writing the score—either “slips of the pen” or “theoretic errors”—or changed the strict results of the theory in the interest of aesthetic considerations. In a gloss worthy of Ferney-hough at his densest, Xenakis summarizes his position thus: “bi-univocal exactness realisation-theory may be sometimes non-absolute” (p. xviii). Far from being put off by the problems, Gibson laudably seizes the absence of any deﬁnitive answers from the composer’s hand, taking the ways in which Xenakis borrowed materials from his own scores in later work as his principal lens. Given the sometimes stark divide between the theoretical frameworks which Xenakis described and the way in which they were deployed in practice, the volume is also subdivided into two large parts, devoted to practice and theory respectively.
The ﬁrst part of the book, then, examines the contexts and ways in which Xenakis reused elements from earlier scores in his later music. Gibson is clear that he is, in the main body of his text, only scratching the surface of the volume of borrowing undertaken by Xenakis; a lengthy appendix gives a fuller picture, showing borrowings across Xenakis’s entire output in tabulated form, from the ﬁrst major example in Duel I (1959) to the latest in Mosaïques (1993), the title in the latter case overtly signaling the presence of borrowed materials within the piece. Nevertheless, the number of examples Gibson provides is striking, from near-enough literal insertions of fragments of one piece into another (as in the recurrence of elements from Nomos Alpha (1965–66) in Antikhthon (1971)), to more complex reuses of material, less obvious at ﬁrst glance, where rhythmic patterns recur with wholly different timbral or pitch characteristics (as in the relationship between Idmen B (1985) and à l’île de Gorée (1986)), or where pitch recurs almost literally, but with other characteristics adapted or transformed—such a situation occurs with Pithoprakta (1955–56) and Aroura (1971). One of the matters here illuminated is the degree to which Xenakis applies similar procedures, described here as micromontage, within individual scores, as for instance in Pithoprakta, Nomos Gamma (1967–68), or Kraanerg (1968–69), to generate textures exhibiting similar characteristics while being distinct from one another at the superﬁcial level. The number of examples of borrowing shown by Gibson is surely enough to convince the reader that there is no coincidence at play here. Yet, despite the proposal that “self-borrowings occur more often when Xenakis is in the process of developing new compositional procedures” (p. 162), the volume might have gone rather further in discussing what these borrowings mean for a listener to his music. Speciﬁcally, some more detailed discussion of how the experience of listening to any one of these pieces might change, after one has gained the knowledge of the other contexts in which its materials had otherwise appeared, would have been very welcome. It is worth noting, too, that in order to use this section of the book to its fullest, the reader ought ideally to have a strong knowledge of Xenakis’s output, both through particular performances or recordings and through the score.
The second part of the volume, the theoretical part, can be discussed more brieﬂy, although it is certainly the more substantial. In essence, it provides an explanation, here with analytical examples from Xenakis’s output, of certain parts of Formalized Music as well as showing theoretical approaches he took that were themselves formalized after its publication. After a brief, though largely extremely lucid discussion of Xenakis’s stochastic approach, Gibson looks at the ways in which he constructs sieves—which is to say principally the procedures via which he determined pitch space—and the way in which sieves can be transformed, often through quite simple operations that nevertheless have rather complex results. In truth, these sections are certainly not wholly without equations, and many who despaired at Formalized Music may be equally dispirited to read that a “modulus signals the repetition of an interval; the subscript index indicates its position in relation to the origin (reference point). A modulus m with an index i constitutes a residue class or elementary sieve” (p. 83). Yet despite brief sections of this sort (and there are certainly more complex bits of mathematics to work through for those so inclined), Gibson provides detailed examples of what is meant at all points such that the practice genuinely illuminates the theory. He is also keen to stress—and does so very successfully—the points at and degree to which what Xenakis actually does may be distant from the theoretical results of his calculations and, indeed, that there may be points where the calculations may not have taken place at all, where the piece was worked on intuitively, in the knowledge of the kinds of results the calculations would be likely to cause. These intuitions are themselves examined in the tree-like, graphic representations— arborescences—that Xenakis began to use in the 1970s. Where previously he had intuitively elaborated upon more-or-less strict theoretical processes, here processes acted upon the broadly intuitive drawing of wavelike shapes in order to transform his graphical resources into notational results.
The major difficulty facing the volume is a structural one. The idea of placing Xenakis’s practice in advance of the theoretical basis upon which is was carried out—however loose the relationship between the two—feels odd in principle and causes some genuine problems. On the second page of the main body of text, Gibson observes that “[i]n Xenakis’ instrumental music, geometric ﬁgures, arborescences or other forms derived from the principles of cellular automata constitute the main objects” (p. 4). Yet, although the part of the book devoted to practice relies strongly on Xenakis’s conception of arborescence, a footnote advises the reader that what is meant by this will not be explained until chapter 8, some 130-plus pages away. Similar problems persist throughout the early stages of the volume: on page ten, the reader is advised both that “[a]t that time, Xenakis’ composition procedures relied heavily on sieves” and that it will be page eighty-one before sieves, Xenakis-style, are explained; likewise, the concept of “sound tapestry” is introduced on page twelve, with its associated exegetical commentary also more than one hundred pages away. This sort of structural uncertainty is also strikingly highlighted in the second chapter, where “sound tapestry” is again referred to, here twice on the same page: both mentions receive a near-identical footnote directing the reader to just those pages to which the original mention of “sound tapestry” made reference. Though the volume is short enough that one can skip forward and backward within the text without too much difficulty, in truth it seems almost as if the overall structure was altered at quite a late stage and that, initially, the theory section preceded the one focusing on practice. The conclusion, too, even though it does point forward to a lengthy, and extremely useful, genealogy of self-borrowings in Xenakis’s output, feels as if it may, at some point in its history, have acted as a hinge between the theoretical and practical parts of the volume: this is most striking in the opening sentence of the last, relatively brief, paragraph: “We shall stress the importance of a genealogy that establishes links between Xenakis’ works” (p. 162; my emphasis). While there is no space to make that stress in the four sentences that follow, arguably that is precisely what the ﬁrst part of the volume seems to attempt.
If it is the case that the volume has been reordered in this way, the scars of the process still seem rather visible. I am certainly sympathetic to the decision to order the text thus: to be sure, the theoretical section of the volume is, if only comparatively and to some extent inevitably, relatively dry; the section devoted to practice is signiﬁcantly more immediately engaging and, as such, is doubtless the right place to begin. Nevertheless, and whatever the reasons for the structural decisions, the stitching together of the two parts of the volume could surely have been achieved more seamlessly.
The volume is also marred by some unfortunate carelessness in proofreading: commas abound a little too freely in the sentence “[t]hat is why, most frequently, Xenakis, borrows them [arborescences] without altering their structure” (p. 8); page 40 yields both “[w]hat is important, the melodic line is ‘thickened’ by the viola, cello and double bass playing a quarter tone apart as a moving cluster” and “long gray automn [sic] days”; the second footnote of the seventh chapter (“Ibid., pp. 155–177”) ostensibly thus refers to the same item as the ﬁrst footnote of that chapter—Xenakis’s score for Akrata (1964– 65)—yet surely is really intended instead to Bálint Varga’s Conversations with Iannis Xenakis. Indeed, there seems to be little consistency regarding when ‘ibid.’ is felt appropriate and when a cited item is simply repeated.
These quibbles should not take away from what is valuable in Gibson’s volume. First, his genealogy of Xenakis’s self-borrowings is comprehensive and he articulates the way in which Xenakis carried out the process extremely clearly, at the same time showing quite how ‘normal’ he is in this respect. That Gibson’s section on practice can be understood with little recourse to the later theoretical section is testament not only to the clarity of his description but also, more importantly, to the possibility of ﬁnding ways to approach Xenakis’s work that stand on their own terms, if one is not put off by his mathematically cerebral reputation. Second—and this, I suspect will be where Gibson ﬁnds his volume most used and most useful—the section dealing with theory does not shy away from the mathematical underpinnings of Formalized Music, but is signiﬁcantly more approachable. In certain senses, this part of Gibson’s volume acts as an exegetical commentary on Formalized Music, and I believe it will make practical sense of sections of Xenakis’s theoretical writing that remain, by and large, impenetrable on their own terms. Thus, though this remains very much a book of two halves—and halves that I’m not wholly convinced are fully reconcilable in the form the volume currently takes—each half does work. This will prove incredibly valuable, certainly for composers, but hopefully for musicologists and listeners too who have, thus far, been put off, principally by mathematics, from coming to terms with Xenakis’s remarkable output.
Martin Iddon, University of Leeds
Notes, Quarterly Journal of the Music Library Association