MATHS  ET  MUSIQUE

DOCUMENT : Faculté  des  Sciences  de  Luminy  

                                                            VOIR  FICHIER   P D F                                                                                        

L' ANALYSE  MUSICALE.
  

                                                                                                                                
L'analyse  musicale  est  essentiellement  destinée   aux  candidats  préparant  des  examens ( BAC , CAPES , AGREGATION ...) , ainsi  qu'aux  élèves  désirant  étudier  la  COMPOSITION .
L' ANALYSE  MUSICALE  commence  par  l'étude  des  oeuvres  du  XIIeme  siècle ( chant  grégorien , monophonie , ARS  NOVA )  et  se  poursuit  par  l'étude  des  oeuvres  du  XXeme   siecle.
Les  périodes  comprises  entre  ces  deux  pôles  sont  toutes  étudiées :

- LA  RENAISSANCE

- LA  PERIODE  BAROQUE

- LA  PERIODE  CLASSIQUE

- LA  PERIODE  ROMANTIQUE

- LA  PERIODE  IMPRESSIONNISTE

- LA  PERIODE  MODERNE

- LA  PERIODE  CONTEMPORAINE

Iannis Xenakis est né en 1922 (ou 1921), à Braïla (Roumanie), au sein d’une famille grecque. Il passe sa jeunesse à Athènes, où il achève des études d’ingénieur civil et s’engage d’abord contre l’occupation allemande, puis contre l’occupation britannique (guerre civile). En 1947, après une terrible blessure et une période de clandestinité, il fuit la Grèce et s’installe en France, où il travaille pendant douze ans avec Le Corbusier, en tant qu’ingénieur, puis en tant qu’architecte (Couvent de la Tourette, Pavillon Philips de l’Expo universelle de Bruxelles de 1958 – où fut donné le Poème électronique de Varèse – célèbre pour ses paraboloïdes hyperboliques).
En musique, il suit l’enseignement d’Olivier Messiaen et, dans un premier temps, emprunte une voie bartókienne qui tente de combiner le ressourcement dans la musique populaire avec les conquêtes de l’avant-garde (les Anastenaria, 1953). Puis, il décide de rompre avec cette voie et d’emprunter le chemin de l’« abstraction » qui combine deux éléments : d’une part, des références à la physique et aux mathématiques ; d’autre part, un art de la plastique sonore. Les scandales de Metastaseis (1953-1954) et de Pithoprakta (1955-1956), qui renouvellent l’univers de la musique orchestrale, le hissent au niveau d’alternative possible à la composition sérielle, grâce à l’introduction des notions de masse et de probabilité, ainsi que de sonorités faites de sons glissés, tenus ou ponctuels. C’est également l’époque de ses premières expériences de musique concrète ou, entre autres, il ouvre la voie du granulaire (Concret PH, 1958). Son premier livre, Musiques formelles (1963), analyse ses applications scientifiques – qui vont des probabilités (Pithoprakta, Achorripsis, 1956-1957) à la théorie des ensembles (Herma, 1960-1961) en passant par la théorie des jeux (Duel, 1959) – ainsi que ses premières utilisations de l’ordinateur (programme ST, 1962).
Durant les années soixante, la formalisation prend de plus en plus l’allure d’une tentative de fonder la musique (au sens de la crise des fondements en mathématiques), notamment avec l’utilisation de la théorie des groupes (Nomos alpha, 1965-1966) ou encore la distinction théorique « en-temps/hors-temps » (article « Vers une métamusique », 1965-1967) – on pourrait trouver un équivalent architectural de la question des fondements dans le projet de la Ville cosmique (1965). En revanche, avec Eonta (1963-1964), c’est le modèle du son qui est parachevé. Ce sont des œuvres (libres) telles que Nuits (1967), qui lui font acquérir une très large audience, en même temps que les pièces spatialisées (Terretektorh, 1965-1966, Persephassa, 1969) : le public découvre que la formalisation et l’abstraction vont de pair avec un aspect dionysiaque prononcé, où la musique se conçoit comme phénomène énergétique. La décennie suivante est marquée par l’envolée utopique des Polytopes (Polytope de Cluny, 1972-1974, Diatope, 1977), prémices d’un art multimédia technologique caractérisé par des expériences d’immersion. Avec les « arborescences » (Erikhthon, 1974) et les mouvements browniens (Mikka, 1971), Xenakis renoue avec la méthode graphique qui lui avait fait imaginer les glissandi de Metastaseis, méthode qu’il utilise également dans l’UPIC, premier synthétiseur graphique, avec lequel il compose Mycènes alpha (1978). Les années soixante-dix se concluent avec l’utilisation extensive de la théorie des cribles (échelles). Ceux-ci, appliqués aux rythmes, assurent un renouveau de l’écriture pour percussions (Psappha, 1975). En tant qu’échelles de hauteurs, ils témoignent, durant cette époque, de la quête d’universalité de Xenakis (le début de Jonchaies, 1977, utilise une échelle qui évoque le pelog javanais).

Le début des années quatre-vingt voit la création d’Aïs (1981), où, comme dans l’Orestie (1965-1966), le texte, en grec ancien, est source d’inspiration, mais, cette fois, avec des réflexions autour de la mort. Durant les années quatre-vingt, l’esthétique xenakienne s’infléchit progressivement. Encore marquée par les débordements énergétiques (Shaar, 1982, Rebonds, 1987-1988) ou les recherches formelles (cribles dans pratiquement toutes les œuvres, automates cellulaires dans Horos, 1986), elle devient de plus en plus sombre (Kyania, 1990). Ses dernières œuvres (Ergma, 1994, Sea-Change, 1997) évoluent dans un univers sonore très épuré et dépouillé. La dernière, composée en 1997, s’intitule d’après la dernière lettre de l’alphabet grec (O-Mega). Xenakis est mort le 4 février 2001.

© Ircam-Centre Pompidou, 2007

DOCUMENT      brahms.ircam.fr      LIEN

A guide to Iannis Xenakis's music

It sounds like something out of a film script. A Greek man in his early 20s fights for his homeland as part of the Communist resistance at the end of the second world war. Shrapnel from a blast from a British tank causes a horrendous facial injury that means the permanent loss of sight in one eye. He is sentenced to death after his exile to Paris (a sentence that was later commuted to a prison term, with his conviction finally quashed with the end of the junta in 1974). By the time he returns, he has become one of the leading creative figures of the century: an architect who trained, worked, and often transcended the inspiration of his mentor and boss, Le Corbusier; an intellectual whose physical and mathematical understanding of the way individual particles interact with each other and create a larger mass - atoms, birds, people, and musical notes - would produce one of the most fertile and prophetic aesthetic explorations in musical history; and above all a composer, whose craggily, joyously elemental music turned collections of pitches and rhythms and instruments into a force of nature, releasing a power that previous composers had only suggested metaphorically but which he would realise with arguably greater clarity, ferocity, intensity than any musician, before or since. This is the music of Iannis Xenakis.
When you hear Xenakis's music – any piece of what we recognise as his mature work, starting with 1954's Metastasis, onwards – you're confronted with an aesthetic that seems unprecedented according to any of the frames of reference that musical works usually relate to. You won't hear vestiges of things like familiar forms, or shapes, or languages. Even the furthest-out reaches of early 1950s serialism sound resolutely conventional next to Xenakis's works of the same period. It's music whose sheer, scintillating physicality creates its own territory in every piece, whether it's for solo cello or huge orchestra. As Ben Watson has put it, Xenakis's work is "an alien shard, glimmering in the heart of the West". When Xenakis approached Olivier Messiaen in Paris for composition lessons, Messiaen turned him down, because, "I think one should study harmony and counterpoint. But this was a man so much out of the ordinary that I said… 'No, you are almost 30, you have the good fortune of being Greek, of being an architect and having studied special mathematics. Take advantage of these things. Do them in your music'."

And that's exactly what Xenakis would do, and was already doing - which is both one explanation of his music's shocking otherness (it was heard as "alien" even by the hipsters of the early 1950s; the 1955 premiere of Metastasis at the Donaueschingen Festival was one of the scandals of postwar music) and a revelation of this music's deep, primal rootedness in richer and older phenomena even than musical history: the physics and patterning of the natural world, of the stars, of gas molecules, and the proliferating possibilities of mathematical principles. Xenakis resisted the label of being a mere mathematician in music just as surely as he refused the idea of his music's political or social message, and it was of course how he used those scientific principles (outlined in his book, Formalized Music) to create pieces of shattering visceral power.

His architectural output offers ways into his music's imaginative world. Take the Philips Pavilion that Xenakis designed for the Brussels World's Fair in 1958 and for which he and Edgard Varèse wrote electronic music to animate its still gorgeously futuristic-looking parabolas, swoops, curves. The maths underlying its construction, and the shapes it makes, have a direct correlation in the way Xenakis uses the instruments of the orchestra in Metastasis, organising the entries of the instruments, and the pitches they play, according to the working-out of mathematical and statistical formulae, translating the space of architectural planes into musical time. (Take a look at his near-contemporary design for a "Cosmic City", a gloriously sci-fi vision of the metropolis of the future - and what happens when Dan Dare meets curvy brutalism.) Xenakis also designed what he called "polytopes", high-art son-et-lumière installations that involved his lighting designs, his sets, his music, and his sound projection to create vivid multi-media experiences, in places from Canada to Iran to Greece. And he designed a system for the conversion of graphic stimuli into sound, a programme he called UPIC and which has now morphed into more sophisticated computer software like IanniX. (More than a decade before Boulez founded IRCAM, Xenakis had set up his own institute for music-technological research in Paris called EMAMu, which now exists as CCMIX.)
Those are some clues to the elemental concerns of his music. But what happens when you hear his music goes beyond even the sensation of teeming natural phenomena or landscapes transmuted into music. Listen to this piece - Synaphaï - for piano and orchestra. You'll hear a piano part of mind-bending complexity, which has the unique distinction, as far as I'm aware, of having a separate stave for each finger. You did read that right: Xenakis uses 10 staves in this piece. You'll hear clouds of minutely detailed orchestral sonority wrap around the solo part, like flocks of small birds mobbing an avaricious raptor; and you'll hear a near-continuous rhythmic intensity and textural violence that takes your breath away. Hearing this piece is as awesome an experience as watching some life-changing natural spectacle. Synaphaï has all the teeming unpredictable power of a glacier, the thrilling complexity of shape and movement of a mass animal migration.
But there's something else as well. This music is expressive: not in a conventionally emotional way, perhaps, but it has an ecstatic, cathartic power. Xenakis's music – and its preternaturally brilliant performers - allows its listeners to witness seismic events close at hand, to be at the middle of a musical happening of cosmic intensity. (That's literally true in Terratektorh, in which the orchestra perform from within the audience – it would have been fun to be part of this performance conducted by Matthias Pintscher…) Xenakis has said that his war-time experience informed his desire to create his new kind of sound-experience. (He described the play of sirens, gunfire, and spotlights in Athens in the 1940s as like a "large-scale spectacle") Yet his music sounds, to me at least, to be purged – or perhaps to be a purging - of the sort of existential darkness that György Ligeti's music, say, never escapes. (Among the closest Xenakis comes to a direct emotional utterance is in his Nuits for chorus; music that sounds like a primordial cry, an impassioned scream.)
There's a huge amount to discover in Xenakis's music, and much of his vast output is out there on YouTube. Some highlights: the non-stop dynamism of Keqrops for piano and ensemble, the epic scale of the 75-minute long Kraanerg for ensemble and tape; the dagger-like pointillism of Khoai for solo harpsichord; or the devastating virtuosity of Tetras for string quartet. The piece that converted me, though, was Jonchaies for orchestra, composed in 1977, and quite simply one of the most exciting experiences you can have in music. Listen to it as loud as you can and convert all your neighbours to Xenakis too.

Jonchaies embodies the elemental truth about all of Xenakis's music. Beethoven described nature in the Pastoral Symphony, Sibelius was terrified by it in Tapiola, but it took Xenakis for music to become nature. On holiday in Corsica, Xenakis would pilot his canoe into the teeth of the biggest storm he and his paddle could manage. When you're listening to his music, you also go out there into the eye of a musical storm that will invigorate, inspire, and awe. See you out there…

DOCUMENT          theguardian.com         LIEN