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Sieve Analysis and Construction: Theory and Implementation
Get PDFSieve Theory was used in order to construct symmetries at a desired degree of complexity. This was achieved by the combination of two or more modules, where each module is notated as an ordered pair (M, I) that indicates a modulus (period) and a residue (an integer between zero and M-1) within that modulus. The abstract image of a sieve is that of a selection of points on a straight line; according to Xenakis “Every well-ordered set can be represented as points on a line, if it is given a reference point for the origin and a length u for the unit distance, and this is a sieve” (Xenakis 1992, 268). Modules are combined by the set-theoretical operations of union, intersection and complementation. Given the possibility of multiple notations of the same sieve, the use of each logical operation depends on both the type of formula we choose and on the type of sieve in question. This paper is based on typology of both the different types of sieves as well as the available formulae types for a given sieve. We categorise sieves according to their symmetry and periodicity. Xenakis refers to these two notions as two distinct levels of identity: in the opening of his article on sieves he talks about “spatial identities” and “identities in time”, correspondingly; he then refers to these levels as being internal and external to the sieve (Xenakis 1992, 268). Symmetry is evident in the sieve's intervallic structure and periodicity in its periodic nature
Aspects of compositional realization in Xenakis's pre-stochastic and early stochastic music
No full textIn the preface to the score of Metastaseis (1953-54), Xenakis indicates that certain of the work’s features prefigured aspects of stochastic composition, the approach that he would adopt in Pithoprakta (1955-56) and subsequent works. While there are good reasons to contrast the serial procedures that underlie certain passages in Metastaseis with the stochastic approach taken in later works, there are also significant points of contact between Xenakis’s compositional realization of both approaches. These points of contact include harmonic contexts, both within a given work and between works, and specific techniques for managing the flow of musical events in the rhythmic domain. Throughout this brief inquiry, emphasis is placed on the musical effectiveness of Xenakis’s solutions to the compositional problems posed by the non-serial atonal, serial, and stochastic approaches that followed one another in close proximity in his early works. While his pioneering efforts in the development of stochastic composition remain a source of fascination in themselves, along with his particular syntheses of ideas from both architecture and music, there appear to be eminently practical musical reasons for some of the compositional choices that Xenakis made in his early music. This presentation hopes to uncover a few of these practical reasons as a stimulus toward further thought about the immediacy of the impact produced by Xenakis’s music, as well as about its enduring effectiveness
Chance between passivity and control: The post-humanist ethics of Xenakis, Cage, & Lyotard
No full textThough much has already been written on the relationship between Iannis Xenakis and John Cage, in this paper I contribute to this discussion by arguing that their parallel adoptions of chance—whether Zen-cum-“anarchical” as in Cage, or mediated and controlled through the scientific method as in Xenakis—represent a response to a common intellectual phenomenon. This is the apparent exhaustion of humanistic ethics and all of its attendant notions: subject-object dualism, the primacy of the ego and dialectics, and anthropocentrism. A fundamental dissatisfaction with humanistic subjectivity was also the essential preoccupation of philosopher Jean-François Lyotard, a thinker noted for producing some of the most incisive commentaries on contemporary music in recent years. Particularly pertinent in this context is Lyotard’s longstanding focus on the ethical realm, which he saw as more important than ever given recent anti-humanistic philosophy’s rejection of foundationalism. I demonstrate that Cage and Xenakis were unique among composers of their generation in also refusing to lose sight of this same concern. Yet while both composers go very far in dissolving subjectivity and the self-propriety of reason by following what is akin to a Lyotardian aesthetics/ethics of the sublime, each also makes compromises on the extent to which they ask their listeners to passively submit to an Other of reason. From a humanistic perspective, such a move appears little more than “enslavement” to an amorphous, ungovernable “nature”. Lyotard, however, follows Emmanuel Levinas by arguing that this is actually a fundamentally ethical act insofar as it requires an obligation prior to any post facto rationalization. Though Xenakis and Cage both reject traditional political praxis, they remain partially unsatisfied with this extreme “ethical” alternative and its apparent dangers, and in spite of themselves, they ultimately admit of some of the reflective politics which they appear to disdain
Proceedings of the Xenakis International Symposium
No full textProceedings of the Xenakis International Symposium. Goldsmiths University of London in association with Southbank Centre, London, 1-3 April 2011
"Xenakis Alive!": Explorations and extensions of Xenakis' electroacoustic thought by selected artists
No full textThis is a presentation of selected artists who extend Xenakis’ electroacoustic thinking. I concentrate on four aspects which I think are still radiating, or in some way only start to become virulent in our days: UPIC, GENDYN, Emergence, and Immersion. With this paper, I'd like to spread the virus a bit more
"Music is not a language...": Listening to Xenakis's electroacoustic music
No full textWhen Iannis Xenakis wrote, in the Diatope presentation: “Music is not a language. Every musical piece is like a complex rock, formed by ridges and designs engraved within and without, that can be interpreted in a thousand different ways without a single one being the best or the most true. By virtue of this multiple exegesis, music inspires all sorts of fantastic imaginings, like a Crystal catalyst” (Xenakis 2006, 261), he asserts an important change in music conception, which has little by little gained ground during the twentieth-century. Here, Iannis Xenakis probably criticises the idea that music can only be structured—and conceived—depending on a temporal and chronological axis. When we are listening to Iannis Xenakis’s electroacoustic music, we have to take into account this important assertion. Listener cannot consider Iannis Xenakis’s music like a succession of entities, of well-delimited phenomena. The listener doesn’t perceive a static musical structure composed of elements set in time, but he perceives a dynamical space. Thus, we have to analyse the particular confrontation between the different dynamical spaces and the listening..
Stochastic analysis of Stravinsky's varied ostinati
No full textAn analogy is drawn between the varied ostinato, a common musical device in Stravinsky’s music, and Xenakis’ stochastically generated soundmasses. The analogy is constructed as follows: Stravinsky’s varied ostinati are made up of cellular melodies; these cells can be represented as Markov chains, as can the sequence of cells themselves; the Markov chain for an sequence of cells has the property of ergodicity; this ergodicity allows two stochastic variables, the mean and variance of cell density in a sequence, to uniquely determine the chain. The irregularity of Stravinsky’s melodic repetition, in the past considered largely inscrutable, is perhaps accessible to musical analysis in terms of these stochastic variables. An example of computer-generated output that uses these variables to simulate Stravinsky’s style is given
Physicality as a performer-specific perspectival point to I. Xenakis's piano work: Case study Mists
No full textThe current paper is attempting a hands-on approach to Xenakian piano performance practice, using Mists as a case study, while also reflecting upon the problematic status of performative physicality in current Xenakian scholarship. Starting off with S. Kanach's Performing Xenakis, I detect two poles (the body as obstacle versus the body as transparent object) in the keyboard performers' references to physicality. Subsequently, I rethink a list of the most common challenges (physical effort, non-linear keyboard, complex rhythm, form and detail) against a historically informed background, including: a reading of G. Sandor's On piano playing (pre-Xenakis) under the light of ideas on embodied and extended cognition, as presented by M. Rowlands in his The New Science of the Mind; plus insights and remarks gained from New Complexity theorization (post-Xenakis). The emerging notion of corporeal navigation, demonstrated through multi-layered tablatures, is hopefully a useful tool towards the demystification of difficulty in Xenakian performance, as well as an original contribution in the construction of a much needed performer-specific discourse for complex music, focusing on physicality and non-serial learning
Pithoprakta: The historical measures 52-59: New evidence in glissando speed formalization Theory & theoretical applications
No full textAssimilating glissandos to monatomic gas molecular movements and considering that molecular speeds are proportional to molecular mean kinetic energy (temperature), Xenakis seeks for normal distributions of sound speeds (glissandos) via Gauss equation. He uses a two-variable form of the equation (bi-dimensional domains) and then a three-variable one (three-dimensional domains). Through correlation he proves that speed distributions provided by both forms of Gauss equation are practically equivalent. Thus, temperature might be resulting from glissando execution limitations, i.e. speed limits. Since mean speed value becomes an invariable, temperature is meant to be a logically designated magnitude. Consequently, the introduction of speed as a scientific notion in composition is justified. Given that glissando directions are not stochastically preset, probabilistic determinism controls the interior of the sound mass, meas. 52-59, but not its overall evolving form. After having set all required parameters, Xenakis draws a general probability table that leads to 33 analytical sub-tables; 1168 theoretical and 1221 effective speeds are provided and virtually distributed to bowed instruments. Yet, both numbers remain theoretical as the majority of speeds are too quick for execution. A more realistic eventual maximum speed is applied then. Depending on speed, temperature is now close to “temperature proportional to α=35” stated in Musiques formelles. Pre-compositional applications are completed by a set of three very detailed graphic tables, through which a wider range of speeds is assigned anew to individual instruments. Due to the composer’s musical intentions, a number of theoretical data are revised. Anticipating the graphic score, creative theoretical reasoning that leads to speed distributions constitutes the scientific matrix of the work, which is bridged with the musical matrix by the application of theoretical results. Xenakis’s theoretical reasoning might be regarded as pure creation proportionally equivalent to composition itself
A Theory of Music Analysis: On Segmentation and Associative Organization by Dora A. Hanninen (review)
Get PDFIn lieu of an abstract, here is a brief excerpt of the content:
Comprising research spanning over a decade, A Theory of Music Analysis constitutes a comprehensive account and a culmination of Dora A. Hanninen’s work to date. To the extent that no theory of music is independent of analysis, this work is indispensable as a theory of analysis. The main (philosophical) concern of the book is how to create a precise analytical language, one that can secure a credible interpretation; intertwined with this is a (practical) concern with how to employ this language in a way that reflects the individual analyst’s flair. Analytical applications are not set against theory as singular instances of ready-made methods; on the contrary, by negating the usual rhetoric of theory and analysis, Hanninen sets out to provide a kind of metatheory, independent of the particular existing music-theoretic tools that it aims to encompass. This level of interaction between Hanninen’s overarching metatheory (or simply “theory”) and particular, or what she calls orienting theories is, I think, most intriguing and—although at times not easy to ascertain—promising.
From the outset, the author wishes to safeguard the “interpretive autonomy and imagination of the individual analysts” who use the theory (p. 4). In this spirit, the book addresses music theorists, analysts, and musicologists. It is ideal for a postgraduate and academic readership and it could serve as a main reference item in analysis courses. Analysis scholars will appreciate its focus on segmentation. From atonal-theoretic to semiotic methods, segmentation relies on interpretation of the music score. Hanninen endeavors to formalize segmentation protocols by constructing three basic types of criteria; although she provides comprehensive lists for the three types, these lists are left open-ended.
The book encompasses a wide range of Western music traditions from the baroque onward. This feature is one among its several qualities of methodological flexibility, afforded precisely by the relation between metatheory and orienting theory. From Bach to Brahms and from Varèse to Babbitt, the first half of the book abounds in examples and indicative applications of analytical tools and concepts. The second half comprises a set of six detailed analyses of mostly piano-based music, two European (Beethoven and Debussy), and four American (Nancarrow, Riley, Feldman, and Morris). Analytically, the book employs, and thus presupposes, a firm knowledge of common-practice tonality, serial systems, atonal theory, and Schenkerian analysis. These four approaches suffice to cover the repertoire with which Hanninen engages. Having said that, the flexibility just mentioned should provide enough space for one to apply new orienting theories to analysis (e.g., the often-idiosyncratic approaches by Iannis Xenakis, who is mentioned briefly).
Orientations and criteria for segmentation form the theory’s conceptual part, while associative sets and organization lie on the objective end, segments being the interface. The schematic of the theory is a synoptic representation of these five levels, which interact within three domains: sonic (psychoacoustic), contextual (associative), structural (theoretical). Thus, orientations refer respectively to disjunction, association, theory; and criteria can be sonic, contextual, structural, or linked as structural–sonic, structural–contextual.
Any analyst of the post-tonal repertoire will appreciate the difficulties around segmentation strategies. Allen Forte’s distinction between primary and composite segments, or the practice of imbrication, can be useful, but his reference to contextual criteria for segmentation was left un-systematized. In practice, this was counter-balanced by a refining of the segmentation process according to both those contextual criteria and set relations (The Structure of Atonal Music [New Haven, CT: Yale University Press, 1973], 91). Such practices point to a conundrum of theory and analysis: to what extent should we allow (the orienting) theory to affect our interpretation? Such problematics are usually confronted in analysis classes, where students are required to provide a convincing (as opposed to convenient) segmentation. The three types of criteria that Hanninen’s theory provides refer to disjunction (bottom-up feature extraction; sonic), association (by some kind of repetition; contextual), and specific orienting theory (compositional/analytical strategies; structural). The interaction between these three provides a sufficiently rigorous (albeit at times demanding) framework for segmentation. Following this rigorously allows one to mitigate the tension between theory and “the music.
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