INTRO - MATEMATICA E MUSICA CONTEMPORANEA. Con questo studio sui rapporti tra serialismo e il superamento strutturalista, tra matematica e musica, arriviamo al centro di una complessissima relazione tra metodi, tecnologia ed estetica. Un percorso andato dalla crisi del sistema tonale e gli sviluppi seriali post-weberniani alla 'neue musik' di Darmstadt, fino cioè alla nuova accezione di musica contemporanea d'avanguardia; congiungendosi quindi alle sperimentazioni elettroacustiche della musique concréte/ tape music . Come già nei precedenti post, il tutto è esposto alla luce di una fondamentale (forse personale) convinzione: la centralità of twelve-tone serial method and Webern in these developments, leading to the "rediscovery" of the relationship in this century mathematics and music, brought to prominence by his twelve-tone method and the integral serialism and then continued with the electronic music avant-garde - up to drifts of combinatorial ' acousmatic-. This report has ancient roots in history as the studies that have focused on structural investigations of the composition and calculation reports in it. Leaving aside the fact ancient oriental studies in the West is with the Pythagorean school that is beginning to weave the first theories and to draw the first compositional systems (Pythagorean temperament or diatonic scale, etc). In addition to the equations of physical acoustics, the basic fractions math used to describe the rhythmic division, analysis of noise through the decomposition of waves and the analysis of harmonic sine waves mathematically-expressed with the Fourier transform algorithm - is in the appearance of composition that the relationship between mathematics and music finds its most interesting and complex implications, with the distribution of sounds in different heights, time intervals, the polyphony, the different 'voices' of the performers, etc.. It is clear, however, that the implications of complex developments have found the best contemporary music in the music-and beyond electronically, through academic circles, the first studies of phonology and electroacoustic music and the work of certain musicians, all Iannis Xenakis, Pierre Boulez and Philip Glass (the latter two both graduates in mathematics; Philip Glass is also known for the contamination of his music, leading to collaborations outside the niches avant-garde, with characters such as Richard D. James / AFX). This part then is just an introduction to the work of Xenakis and connections with the structural programs and at the same time direct continuation of the studies on twelve-tone method, neue Musik in Darmstadt, integral serialism and the avant garde post-Webern Topics covered in-post: pantonal, twelve-tone technique, serialism full. towards a time when the electronic music Expressionist. , 'Neue Musik' and post-Webern serialism. Constructivism serial contenutivi between impulse and formal discipline. and TW Adorno, "Neue Musik", Protocols & popular atonal music. The role of the vanguard in representing the Invisible.
THE STRUCTURAL 'logocentrism' composition. trying not to lose his speech with the influence of structuralism in cultural, philosophical and scientific, that are here are interested in investigating the real possibility that the structuralist program has in influencing the artistic domain. In fact, the analysis made by Iannis Xenakis in "Musique formelles" comes down to the concepts evoked by the definitions of structuralism proposed by Jean Piaget and Gilles Deleuze , pushing for a continuity between the efforts obtained in linguistics, anthropology and human sciences, and the search for systems operating within the object under investigation in an attempt to bring out the set of elements that constitute, through their reports, a total autonomy . In this sense, the scope of the arts-painting, literature and music- can be considered as an object to find and create structures or private persons and formalized that make up the work only through their relations, emphasizing the experimental nature of the art form, in its becoming a field architecture. According to Roland Barthes and structuralism represents the will of systematic construction, structural art is "activities whose sole purpose is to rebuild an object in order to manifest the operation" (Roland Barthes, "L'activité structural", in "Lettres Nouvelles , 1963). The contribution highly theoretical research in the music of composers such as Xenakis, Boulez, Schaffer, corresponds to a desire to systematize the practice of composition which, organized around the thesis of Darmstadt, moves towards the search for a total autonomy of the work, focusing on the absolute priority, and formal outlining a specific tendency to compositions in a closed logocentrism perfect: in the vision defined "constructivist" or, indeed, "structuralist." "These my research about the composition were carried out in different directions. The effort to reduce certain sensations of sound, to understand their causes logic, domination, and use it for construction desired, the attempt to materialize the movement of thought through sound, test them in composition, and the desire to better understand the works of the past, trying to emphasize a deeper unity which is the scientific thought of our time, the effort of making art through a geometric process, that is, giving a more certain support logical impulse of the moment, and yet more serious, more deserving of the fierce struggle that human intelligence does in all other domains. All these efforts should lead to a kind of abstraction and formalization of the musical composition. "(Iannis Xenakis," Musiques formelles " preface). Fabien Lévy, French composer and teacher at the University of Paris IV-Sorbonne, confirms this influence of the structural method in the art world. In 1949, Olivier Messiaen composes "Modes de valeur et d'intensity" , generalizing to all parameters the serial principle, after Pierre Boulez composed "Polyphonie X" (1950-51) and "The Structures pour deux pianos " (1952), Stockhausen Karlaheinz instead " Kreuzspiel, Formel, Spiel, Kontrapunkt-Punkte " and " Klavierstücke I / IV ": during the fifties integral serialism and mathematical models of Xenakis, and Philippot Barbaud, are appropriate responses to the influence of structuralist thinking about music. "These compositional techniques prove to be formalized in fact, made autonomous in relation to the object (the work). They are self-regulated for, and are processed and semi-whole." Lévy in "De la perception par la industrial structure déduits aux processus de la perception" found in the musical expressions of the first 'Ferienkurse' Darmstadt a notion of structure that responds to the characters cited in Deleuze and Piaget. Pierre Boulez in "Penser la musique aujourd'hui" (1963) , as a theorist and composer, says that music can not be considered simply a mezzo di espressione, ma innanzitutto un oggetto cui applicare una riflessione sistematica.
MATEMATICA, ARCHITETTURA E MUSICA STOCASTICA MARKOVIANA. L'opera di Xenakis può essere sintetizzata nel binomio delle sue passioni: matematica e architettura. Denominatore comune di questo binomio è lo spazio; uno spazio in cui Xenakis ha espresso la sua necessità di strutturare forme condivisibili, unità formali analizzabili alla luce delle connessioni e delle relazioni reciproche. Nel 1948 Xenakis, stabilitosi a Parigi, comincia a lavorare come architetto nello studio del famoso Le Corbusier, architetto e padre dell'urbanistica contemporanea, maestro del Movimento Modern (even antithetical is the starting point of Deconstructivism and its formal exercise) of Functionalism and architecture on a human scale. At the same time pursuing his studies in music, but does not find its size within the rigid schemes of counterpoint and harmony. But everything changed in 1951 and began his career thanks to a meeting at the Paris Conservatoire with Olivier Messiaen, who pushes him to pursue the path of an interdisciplinary research that can be expressed in music. In particular, the mathematics becomes a way of exploring the world, discovery of form and regularity, but also how to describe the chaos and entropy. Jobs al rapporto musica-matematica sia da un punto di vista pragmatico sia teorico, "costruendo" complesse strutture compositive partendo da strumenti quali il calcolo della probabilità e la teoria degli insiemi, apportando nuovi elementi teorici attraverso il concetto di 'musica stocastica' , 'musica simbolica' e 'masse musicali' . Tra il 1953 e il 1954 compone il suo capolavoro d'esordio "Metastaseis" , una ricerca di corrispondenze fra elementi geometrici dello spazio e suoni, è storicamente la prima volta che una composizione musicale viene interamente dedotta da regole e processi matematici. Nella composizione c'è infatti una relazione diretta tra musica e architettura , combinazione sicuramente inedita ma che sembra essere la cosa più naturale per l'assistente di Le Corbusier. Con "Pithoprakta" , 1955-1956, fa la sua comparsa lo strumento probabilistico, che attraverso il calcolo delle probabilità esplora la logica dell'incerto, dove gli addensamenti di suoni sono l'espressione della ricerca sulle leggi che regolano i grandi numeri. Xenakis generalizza lo strumento probabilistico con "Achorripsis" (1956-1957), "Analogique A et B" (1958-1959) e i brani intitolati "ST" (1956-1962)-later will use it to calculate probabilities of particular passages in later works, but from a purely exploited, that is without the ambition of the formalization. " In "Achorripsis" there is a quest to make physically perceptible stochastic laws, which become tools for forecasting, division asymmetry and the randomness of the real, structuring of new forms on the probabilistic distribution of sounds, "until the emergence of a true drama of note" .
PERCEPTIONS AND SPACE '. definition - 'Music stochastic: random music, whose structure è decisa sulla base di funzioni matematiche probabilistiche'-----. Xenakis compie un avanzata ricerca nel campo della commistione fra elettronica e strumenti acustici, assemblando composizioni per nastro magnetico, impiegando l'informatica ed il calcolatore ("Orient-Occident", 1960, "La Légende D'Eer", 1977, etc) e giungendo ad elaborare il termine "musica stocastica markoviana" . Nel 1956 infatti, pubblica una teoria della musica stocastica che, come superamento dell'alea -tipica di compositori quali John Cage-, tende ad un processo globale totalmente "prevedibile", il quale, pur contenendo avvenimenti aleatori, riflette di un preciso calcolo della probabilità, It thus attempts a phenomenological approach to the processes of its own, organic and natural living world. The first electronic pieces based on stochastic structures date back to 1957, and for the first time, with "Diamorphoses" his theories stochastic Markovian had the benefit of technological support through an IBM computer . It was also the first work written in the GRM (Groupe de recherches musicales), research and production of electronic music in Paris founded by Pierre Schaeffer . Xenakis also works with key works media, opening up a whole new way with "Polytopes" and then the "Diatòpe" , sound installations, sound design environments that contribute to the achievement of which several elements: architecture, lights, laser beams, projected images and the very nature of the place, real audio-visual shows, fount of integration between music and architecture, new technology and visual projections, which show the spirit of research in science, dealing with percettologia ( proprioception), investigating the sensitive features of the brain in the perception of reality and application perceptual functions of these trials, the position of the listener and the use of space in listening to the sounds. I "Polytopes" (creati per il padiglione francese dell'Esposizione di Montréal [1967], per lo spettacolo Persepolis [Iran, 1971] e ha realizzato il Polytpope di Cluny [Parigi, 1972], il Polytope di Micene [1978]) ed il "Diatope" (realizzato all'inaugurazione del Centre Pompidou di Parigi nel 1978) riprendono infatti il concetto di dimensioni architettoniche/spaziali e strutture sonore, tentativo di riunire le arti visive con le esperienze e gli studi legati alla percezione del suono, lasciando erompere, "come uno scoppio fragoroso dopo il silenzio, una visione drammatica della realtà sospesa nell'intervallo fra il passato remoto e il futuro estremo, il tempo per il dipanarsi della human history "[stochastic-it]. Xenakis took the experiences of combinatorics used in music, to synthesize the same rules of construction for the design of the Philips Pavilion for the Universal Exhibition in Brussels in 1958. In practice, this design structure that was inspired by the animated his musical score "Metastasis", and inside the pavilion within the future multimedia show staged by Le Corbusier, will be disseminated works of Edgard Varèse (Poème électronique ") and Xenakis (" Concret PH ") through speakers set up in the tree. The strong connection between music and architecture, which has space as a common denominator, is also expressed in many other architectural works of Xenakis, such as the Dominican monastery near Lyon St. Marie de la Tourette, for which he was commissioned to design the facades and where it took the glass, inspired by the musical concept of polyphony, getting those Le Corbusier called "glass screen musical" . Xenakis was then among the first to experiment with compositional techniques and algorithmic work on digital synthesis ** (build and change in the waveform), using electronics and computer science to explore the "structure" sound, as autonomous units of events and 'inter-connections', showing highly expressive potential. He founded two hundred research: in 1965 the CEMAMU (Centre de Mathématique and Automatique Musicales) in Paris and in 1967 the CMAM (Center for Mathematical and Automated Music) at Indiana University.
** Xenakis and granular synthesis. The first experiments were nastromagnetico Xenakis on the basis of future granular synthesis. Been known by any electronic music player, is a basic method of synthesis, implementation through elementary acoustic elements such microsounds or grains. The method of granular synthesis is basically a construction of complex sounds from simple sounds of a certain amount: the result is not a single sound, but a set of sounds handled quite differently from any other synthesis method, to manage parameters such as envelope , length, waveform, spatial location and density of the grains can generate a huge amount of different sounds, including the production of effects that can be produced, such as amplitude modulation, timestretching and morphing. Granular synthesis has been developed through different stages, different research and different personalities: Dennis Gabor explored the area of \u200b\u200bcommunication and human perception ("considered the sound as a sum of Gaussian functions is shifted into the domain of elementary that time-domain frequency . These basic functions were called acoustic much and used as the basis for the creation of a sound "[Wiki]) , Curtis Roads is considered the first person that implements a digital granular synthesis, Barry Truax was one of the first hand to implement a real-time version of This summary, Iannis Xenakis has always claimed the invention of granular synthesis and development from his early experiments su nastro magnetico come esigenza dettata dalla lacuna di varietà timbrica e sonora da poter manipolare unicamente attraverso oscillatori e filtri. "In questo contesto si ottenevano suoni in maniera dinamica ritagliando parti di nastri e riassemblando il tutto assieme. Da qui si sviluppò la sua tecnica che consisteva nello specificare la durata e la velocità (frequenza) di riproduzione di ogni singolo grano". "La sintesi granulare, al pari di quella additiva, utilizza più suoni elementari per costruirne uno complesso. Questo è dato da una successione di suoni di breve durata (qualche centesimo di secondo) chiamati grani. Tale tecnica ricorda il processo cinematografico in cui il movimento è dato da una rapida successione of static images. The grains can be pieces of abstract sounds or sampled acoustic sounds generated by algorithmic. Also highlighted is the synchronous granular synthesis with the period of the sound from that used to generate asynchronous sound textures "[" Computer Music and Music Theory. "Chapter 1/2.3].
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