Iannis Xenakis

ЯНИС КСЕНАКИС
ヤニス·クセナキス

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Iannis Xenakis  Strategie

source: theguardian

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…
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source: furious

The 1950’s marked an extraordinary era of music experimentation and development in the current of emerging European composers. Amongst these, Iannis Xenakis would begin to compose his first mature works. He would reject the avant-garde trend of serialism and build his own aesthetic principles founded in the world of abstract mathematics, which, amongst other things, applied a unique philosophy of ‘chance’ to music. The style of music which arose from these principles he labeled ‘stochastic music,’ and the first two works which arose in this style, “Metastaseis” and “Pithoprakta,” set the foundation of his aesthetic principles that he would go on to develop and experiment with for the rest of his musical career. In assessing how Xenakis came to use aesthetics grounded in abstract mathematics one must examine his early life prior to mature music composition. This involves examining his childhood, education, influences and experiences with the Second World War.
From an early age it seems Xenakis had been mapping out his intelligence and capabilities as though for his benefit alone. He recalls, in a 1987 article, that at around twelve or thirteen years of age he would be practising piano, reading about astronomy for hours on end and studying mathematics and archaeology. He confidently disdained schoolwork in favour of his own personal reading, and left school at the age of sixteen without any distinguishable academic record. It was at this time, in 1938, that he enrolled in the Athens Polytechnic to study engineering, where he undertook courses in mathematics, physics, law and ancient literature. He also took up studying harmony and counterpoint with Aristotle Kondourov “who impressed upon Xenakis the necessity of absolute rigour and discipline in the pursuit of composition.” Therefore the assimilation of interests that shaped his aesthetic principles in music, namely those of mathematics, physics, astronomy and ancient literature6 can be traced back to his early years of education, and his highly disciplined approach to formalizing music can also be traced back to his first formal music lessons with Kondourov in these years.

Study at the Polytechnic was to be abandoned in 1940 with the Second World War affecting Greece. It would take Xenakis another seven years to finally graduate with his diploma of engineering. During these years, Xenakis would mostly involve himself as a Communist resistance fighter against the Germans, who had occupied Greece, and he was frequently involved in mass resistance demonstrations, often finding himself in prison as a result. At the end of those seven years, in November 1947, Xenakis illegally fled to Paris where his diploma of engineering landed him work with the famous French architect Le Corbusier. In an interview Xenakis spoke of Le Corbusier’s influence on his creative thought:

It was the first time I had ever met a man with such spiritual force, such a constant questioning of things normally taken for granted. I knew a good deal about the ancient architecture and that had been enough for me; he, on the other hand, opened my eyes to a new kind of architecture I had never thought of. This was a most important revelation because quite suddenly, instead of boring myself with mere calculations, I discovered points of common interest with music, which remained, in spite of all, my sole aim. Up to then my architectural and engineering work had been done to gain a crust, but thanks to Le Corbusier I had now found a fresh interest in architecture.
Evidently, Le Corbusier and the influence of architectural work gave Xenakis impetus to apply a visual approach to music by applying the technical facilities inherent in architectural design to the same plateau as music design.
This technical grounding was further encouraged by Messiaen, composer and then lecturer in musical analysis at the Paris Conservatoire, with of whom it was suggested by Le Corbusier that a meeting should take place between the two. At that point, Xenakis was becoming disillusioned by other teachers of composition, namely Milhaud and Honegger, who assessed Xenakis’ compositions with complete stubbornness. Not until he approached Messiaen after an analysis class did Xenakis finally attain a clear directed response of the path in which he should take. Xenakis basically asked Messiaen whether he should wipe his slate clean and begin studying harmony and counterpoint again, but Messiaen surprised Xenakis, as Messiaen himself recounts:

I did something horrible which I should do with no other student, for 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 thirty, 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.
Although Messiaen and Le Corbusier acted as final catalysts in assuring Xenakis’ mature compositional style to be born, the impact of the war definitely marked itself on him, as it did with all composers at that time. As Elisabet Sahtouris wrote, in her 1998 article “The Biology of Globalization,” “some of the greatest catastrophes in our planet’s life history have spawned the greatest creativity”; this would hold true as a result of the highly experimental compositional climate that came about in Europe during the 1950’s. The Second World War definitely impressed itself on European composers of this period.
It was more than an emotional and psychological upheaval, living through the war. Everyone had recollections, images, experiences and impressions involving the different senses, but especially recollections of extraordinary sounds heard during air raids, sirens, explosions, bombing. A person suffering from shock is often more acutely disturbed by sound than sight. Several composers, among them Stockhausen, Berio, Xenakis, report detailed accounts of aural phenomena which have remained with them twenty years after the experience. The war had accustomed them to a sound world which had never seemed possible before and each one had to adjust to it in his own way. This assimilation took many forms, it explains why, for instance, musique concréte was so quickly accepted by this generation as a perfectly natural extension of the sound continuum they had perceived, and secondly, the violence, anger and horror of the war could be transformed into a music which was openly aggressive, brutal and violent.
The war experience was to leave a profound effect upon Xenakis’ music and intertwining creative thought. He illustrates this in a passage from his 1971 book Formalized Music which explains the sonic events of a demonstration march where rhythmic, uniform shouting of slogans graduates to chaotic screaming as the enemy opens fire:
Everyone has observed the sonic phenomena of a political crowd of dozens or hundreds of thousands of people. The human river shouts a slogan in a uniform rhythm. Then another slogan springs from the head of the demonstration; it spreads towards the tail replacing the first. A wave of transition thus passes from the head to the tail. The clamour fills the city, and the inhibiting force of voice and rhythm reaches a climax. It is an event of great power and beauty in its ferocity. Then the impact between the demonstrators and the enemy occurs. The perfect rhythm of the last slogan breaks up in a huge cluster of chaotic shouts, which also spreads to the tail. Imagine, in addition the reports of dozens of machine guns and the whistle of bullets adding their punctuations to this total disorder. The crowd is then rapidly dispersed, and after sonic and visual hell follows a detonating calm, full of despair, dust and death. The statistical laws of these events, separated from their political or moral context… are the laws of the passage from complete order to total disorder in a continuous or explosive manner. They are stochastic laws.
The mathematical makeup of these ‘stochastic laws’ were to become principal features in the compositional development of Xenakis’ first mature works, “Metastaseis” (1953-54) and “Pithoprakta” (1955-56). In Formalized Music, Xenakis labels this music ‘Free Stochastic Music’ where the movements of microscopic parts (in orchestration a ‘microscopic part’ is represented by a single instrument) are subservient to the macroscopic whole which governs the microscopic parts through deterministic tendencies. Peter Hoffmann, on the other hand, labels this music ‘Macroscopic Stochastic Music’ which illustrates this point more clearly than Xenakis’ label.
The mass ‘sonic phenomena’ demonstrated in the social disorder of the demonstration rallies definitely created a large impetus of creative inspiration which led to the creation of ‘stochastic music,’ and which led to many sounds and effects that Xenakis would demand in his musical compositions; however it represents one of a few other crossroads which sufficed this train of thought for him, for immediately prior to the passage about the sonic phenomena of the demonstration crowd Xenakis wrote of ‘natural events’ that also follow stochastic laws, these being

the collision of hail or rain with hard surfaces, or the song of cicadas in a summer field. These sonic events are made out of thousands of isolated sounds; this multitude of sounds, seen as a totality, is a new sonic event. This mass event is articulated and forms a plastic mould of time, which itself follows aleatory and stochastic laws.
All the sonic phenomena explained in terms of stochastic laws thus far are examples of ‘noise’, which is a key sonic feature in most of Xenakis’ compositions (all of them in the 1950’s) and also a feature many composers in Europe were exploring at the same time (one that Edgar Varèse pioneered in terms of traditional instrumental writing). However, the formal methods for ordering the sonic state of ‘noise’ between Xenakis and his European contemporaries were highly different. Where a trend amongst European composers was taking serialism to its most extreme manifestation in a total serialization of a number of the musical elements, this was attacked by Xenakis in his 1954 article “The Crisis of Serial Music.” In this he commented that in serial music “linear polyphony destroys itself by its very complexity” producing “nothing but a mass of notes in different registers” and also noted the contradiction between the “deterministic causality” of serial methods and the actual effect of “an irrational and fortuitous dispersion of sounds over the whole extent of the sonic spectrum.” This article, however, was not so much an attack on serial music as much as it was a boost for his own compositional aesthetics. As he wrote in Formalized Music, “this article served as a bridge to my introduction of mathematics in music.”
As much as his rejection of serialism as unsuitable for his compositional objectives, Xenakis also rejected the John Cagean manifestation of chance music as he remarked in an interview, “for myself this attitude is an abuse of language and is an abrogation of a composer’s function.” John Cage first applied the fundamental philosophical principle of chance to music, that is, “to remove from music any reference to tradition or any trace of subjectivity.” In his lecture Indeterminacy, Cage stipulates this point very precisely:

Finally I said the purpose of this purposeless music would be achieved if people learned to listen; that when they listened they might discover that they preferred the sounds of everyday life to the ones they would presently hear in the musical program; that that was alright as far as I was concerned.
When an interviewer asked Xenakis why he avoids using fortuitous sounds in his compositions, Xenakis promptly answered, “we all have fortuitous sounds in our daily lives. They are completely banal and boring. I’m not interested in reproducing banalities.” He went on to attack the various forms of chance music that he was aquainted with, each originating from the Cagean frame of mind:
The assumption that removing certain constraints from a performing situation frees the player and audience from learned responses and habits was rejected by Xenakis who asserted that on the contrary the player was likely to fall back on his habitual conditioned behaviour or merely oppose it in the most superficial way under pressure of performance. To equate chance with the suspension of responsibility by the composer in the name of freedom was illusory. He also noted that composers never relinquished their authorship over performances despite claims made in the name of chance which smacked to him not only of inconsistency, but piracy.
It was nothing new to encounter chance in a different way from John Cage amongst European composers in this period. Contemporaries like Boulez and Stockhausen also explored chance differently from Cage in this decade, “where the performer is placed in a position to make spontaneous or rehearsed decisions about the ordering of the music.” Xenakis’ fundamental approach to chance, however, differed in that it applied reason and order to ‘controlling’ chance the most progressively it possibly could with the knowledge available at that time in the field of science and mathematics. This is stated in Formalized Music:
Since antiquity concepts of chance, disorder and disorganization were considered the opposite and negation of reason, order and organization. It is only recently that knowledge has been able to penetrate chance and has discovered how to separate its degrees – in other words to rationalize it progressively, without, however, succeeding in a definitive and total explanation of the problem of ‘pure chance’.

Therefore Xenakis’ eagerness to embrace chance and chaos and try to understand what role these concepts play in our world led to what role they could play in the creation of his music.

In “Metastaseis,” Xenakis confronted most of the fundamental musical problems and in effect “Metastaseis” presents the foundation for the style and aesthetics he would follow through for a good deal of his musical career with the concept of textural sound composition. In his 1954 article “Les Metastaseis,” Xenakis describes this concept: “the sonorities of the orchestra are building materials, like brick, stone and wood… the subtle structures of orchestral sound masses represent a reality that promises much.” Le Corbusier’s influence and architectural work was prominently realized in “Metastaseis” as the original plotting of the massed glissandi were done on the same graph paper that was used for plotting building structures. This reflects Xenakis’ idea of a musical ‘space-time’, where pitch is represented on the y-axis and time on the x-axis. “A two-dimensional space is created where potentially time-independent musical structures can be contained in a temporal setting.” He later used plotting of string glissandi in “Metastaseis” as the curvature for the walls in the Philips Pavilion (constructed for the 1958 Brussels World Fair).

The massed moving formations of string glissandi and ‘brass in total disorder’, as Xenakis describes, that occur in “Metastaseis” and later in “Pithoprakta” relate to the kinetic theory of gases. This theory states that “the temperature of a gas derives from the independent movement of its molecules.”

Xenakis drew an analogy between the movement of a gas molecule through space and that of a string instrument through its pitch range. To construct the seething movement of the piece, he governed the ‘molecules’ according to a coherent sequence of imaginary temperatures and pressures. The result is a music in which separate ‘voices’ cannot be determined, but the shape of the sound mass they generate is clear.
While in “Metastaseis” Xenakis applied the kinetic theory of gases to organize musical materials, the materials themselves, such as pitch, were acquired via a dodecaphonic row set with time (at the opening) ordered by the Fibonacci series (both common sources for organization amongst European composers at the time), which is why some critics argue that “Pithoprakta” is Xenakis’ first truly mature musical composition in a style that acquires all its musical elements through mathematical theories and principles. The concept of ‘sound masses’ and the textural use of the orchestra (for example glissandi, pizzicati) remain similar in “Pithoprakta”, however the musical materials were undertaken purely by using Probability theory (“Pithoprakta” literally means ‘actions through probabilities’). In the case of “Pithoprakta,” this relates to Jacque Bernoulli’s law of large numbers which states that as the number of occurrences of a chance event increases, the more the average outcome approaches ‘a determinate end’. Xenakis would still apply other theories and principles in creating the music, such as the theory of gases and Poisson’s law of sparse events, which dictates the sparse textures late in the work, but the importance of Probability theory was, according to Christopher Butchers, of vast importance in the blending of science and art. Butchers wrote that “Xenakis is, to my knowledge, the first in any artistic field both to invoke the notion of chance and to use it in a way which is acceptable rigorously to modern logic.” This application of chance to ‘modern logic’ that Butchers assigns comes from a statement made earlier in the article that:
it is the central importance of probability which principally differentiates the science of the twentieth century from that of the past; in that we have moved from the belief that science consists of an ever more exact measurement of ever more precise entities to the belief that knowledge is as valid and comprehensive when it embraces an appreciation of the general characteristics of entities on a macrocosmic plane, the precise properties of those micro-components being irrelevant.

The composer’s graph plotting paths of glissandi in “Pithoprakta,” bars 52-60. Each line represents a string instrument named on the vertical axis, starting with the lowest register at the bottom to the highest at the top while the horizontal axis represents time.
Therefore, the style of ‘stochastic music’ that Xenakis created amidst a wilderness of other experimental trends was to stand out as his own unique entity. Inspired by ‘noisy’ and/or violent sonic phenomena such as demonstration rallies in the Second World War or the song of cicadas in a summer field, Xenakis applied mathematical theories and principles in assembling the makeup of this music that grounded its sonic principle as textural sound composition. The influence of architecture, where Xenakis also used abstract mathematics as his aesthetic foundation, grounded a means of technical facility whereby Xenakis was able to visualize music graphically from an ‘externally-relative’ position. Aesthetically, theories such as the kinetic theory of gases and Probability theory became two major standpoints in organizing the musical materials in his first two works “Metastaseis” and “Pithoprakta.” These works had assembled the aesthetic means of a mathematically formalized organization of music and acted as the foundation for a myriad of works which were to develop and experiment with these aesthetic means for the rest of his career.
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source: ciencia-arteblogspot

En 1971, Iannis Xenakis compuso una obra llamada Antikhthon. Encargada por Balanchine para el Ballet de la Ciudad de Nueva York, esta abrumadora composición hace referencia a un planeta hipotético, propuesto en el siglo V a.c. por el filósofo pitagórico Filolao.

Iannis Xenakis (1922 – 2001) en su estudio. A su espalda hay un pizarrón garabateado con curvas. Vemos además varias imágenes de planetas, escuadras y reglas colgando de un soporte, y estantes doblados por el peso de multitud de libros. Si no supiéramos quien es, y nos pidieran adivinar su profesión en base a lo que vemos en esta foto, seguramente imaginaríamos que se trata de un astrónomo o un físico. Nunca pensaríamos que esa foto corresponde a uno de los músicos más reconocidos y, al mismo tiempo, controvertidos de siglo XX.

La música y el método musical de Xenakis han despertado muchas discusiones y controversias. Es evidente que su libro Formalized Music es intencionalmente oscuro, aún para un lector con amplios conocimientos de matemática. Mucho se ha discutido también sobre que tan estricto fue el mismo Xenakis en aplicar sus desarrollos matemáticos a sus propias composiciones. Se me ocurre que podríamos volver sobre este punto en alguna entrada futura. Y podríamos hacerlo usando como ejemplo la tercera obra importante compuesta en 1956-7 por Xenakis, llamada Achorripsis (palabra griega que significa “chorros de sonido”), para 21 instrumentos. ¿Por qué elegiría esta obra en particular? Debido a fue estrenada nada menos que en el Teatro Colón de Buenos Aires el 20 de Julio de 1958, con dirección de Herman Scherchen.

Y finalmente llegamos a Antikhthon, la obra a la que quería referirme en esta entrada. Es una composición de 19 minutos de duración para una orquesta de 86 o 60 músicos. Fue encargada por Balanchine en 1971 para el Ballet de la Ciudad de Nueva York y estrenada en el Festival Xenakis de Bonn el 21 de Setiembre de 1974, con dirección de Michel Tabachnik. Se trata de un abrumador asalto a los sentidos, aunque no tan concentrado como Tracées. De hecho, la nube sonora se aclara de tanto en tanto, revelando detalles de algún instrumento en particular. Pero sólo son pausas breves.

Ahora, ¿de dónde viene el nombre de esta obra, “Antikhthon”? ¿A qué se refiere Xenakis?

Una posibilidad sería la siguiente: En el siglo I, Pomponio Mela, geógrafos romano posiblemente contemporáneo de Claudio, propuso que en una Tierra esférica la materia debería estar distribuida de manera tal que cada continente fuese balanceado por otro similar en sus antípodas. Llamó Antikhthones a esas masas de Tierra que darían balance a Europa, Asia y Africa. En la imagen vemos un mapamundi de la edición de Wechel de 1536 de “De situ Orbis” (Descripción del Mundo) de Pomponius Mela, donde se muestra este continente oculto. Por supuesto que la Iglesia, bajo la idea de que todos descendemos de un único Adán, negó la posibilidad de que este continente, oculto al sur del Ecuador, pudiese estar habitado.

Pero seguramente Xenakis no estaba pensando en esta idea de Antikhthon, sino en un concepto cosmológico desarrollado por los griegos muchos siglos antes. Para informarnos sobre este tema podemos recurrir al libro Dante and the Early Astronomers publicado en 1913 por la astrónoma Mary Acworth Orr. Allí leemos lo siguiente:

“Antichthon” es el nombre que los Griegos dieron a un objeto celeste hipotético, la Contra-Tierra, ubicado entre la Tierra y el centro del Universo para impedir al hombre mirar directamente a Zeus, que allí tenía su trono.

En el siglo V a.c. el filósofo pitagórico Filolao de Crotona propuso a Antikhthon como parte de su cosmología no geocéntrica, donde todos los objetos del universo, incluidos el Sol, los planetas y la Tierra, giran en torno a un fuego central. Sin embargo, puesto que la Tierra no está compuesta de materia etérea sino de elementos densos como tierra y agua, su rotación produciría un desequilibrio. Para contrarrestarlo, Filolao imaginó una segunda Tierra que llamó Antikhthon, ubicada al otro lado del fuego central, y que actuaría como contrapeso. Tanto la Tierra como su contra-Tierra serían planas, con la superficie habitada opuesta al fuego central, y girarían alrededor del mismo con un período de 24 horas. En las figuras vemos la ubicación que tendrían la Tierra, la contra-Tierra y el Sol, tanto de noche de noche (izquierda) y de día (derecha).

El el capítulo V de Il Convito, Dante Alighieri nos dice que:
Questo mondo volle Pittagora e li suoi seguaci dicere che fosse una delle stelle, e che un´ altra a lei fosse opposita così fatta: e chiavama quella Antíctona: e dicea ch’ erano ambedue in una spera che si volgea da oriente in occidente, e per questa revoluzione si giraba il sole intorno a noi, e ora si vedea e ora non si vedea; e dicea que ´l fuoco era nel mezzo di queste, ponendo quello essere più nobile corpo che l´acqua e che la terra, e ponendo il mezzo nobilissimo in tra li luoghi delli quattro corpi simplici; e però dicea che ´l fuoco, quando parea salire, secondo in vero al mezzo discendea.
Tal vez resulte sorprendente, pero a fines del siglo XVIII, el matemático y astrónomo Joseph Louis Lagrange (1736 – 1813) demostró que esta Contra-Tierra podría existir, tanto si estuviese entre la Tierra y el Sol o al otro lado de este. Y más aún, mostró que podría haber hasta cinco cuerpos semejantes en distintas ubicaciones del sistema solar. Y si esos objetos no existiesen, podríamos crearlos artificialmente. ¿Suena de Ciencia Ficción? Pues, no. Tal como veremos en una próxima entrada, ya lo hemos hecho…
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source: publicopt

O compositor francês de origem grega Iannis Xenakis faleceu ontem de manhã, na sua residência em Paris, aos 78 anos, na sequência de uma doença prolongada. Matemático e arquitecto de profissão – algumas das suas peças foram concebidas como versões sonoras de formas arquitectónicas -, foi uma das figuras cruciais da música do século XX e personagem isolada no contexto da vanguarda europeia. Será lembrado como um dos compositores que melhor exemplifica a relação estreita
entre a música e a ciência no nosso tempo, mas também por uma obra de grande força telúrica e como infatigável militante da liberdade.

Xenakis nasceu em Braila (Roménia), a 29 de Maio de 1922, no seio de uma família de armadores gregos. Viveu nessa região até aos dez anos, familiarizando-se com o rico folclore do vale do Danúbio e com a música bizantina do rito ortodoxo.
Em 1932, a sua família regressou à Grécia e foi enviado para um colégio particular, na ilha de Spetsai, onde concluiu os estudos secundários. Estudava engenharia civil no Instituto Politécnico de Atenas quando deflagrou a Segunda Guerra Mundial e a Grécia foi invadida pelas tropas de Mussolini. Juntou-se à resistência comunista em 1941 e, em 1945, sofre um acidente com a deflagração de uma bomba, que lhe deixa para sempre uma cicatriz na cara e o faz perder a visão do olho esquerdo.
Foi capturado e condenado à morte, mas escapou para França em 1947, onde permaneceu como refugiado político até 1965, altura em adquiriu a nacionalidade francesa. Em 1953 casou com Françoise, prolífica escritora e jornalista, de quem teve uma filha, Makhi, que é hoje pintora e escultora.
Até chegar a França, Xenakis tinha sido um músico autodidacta, mas a capital francesa permitiu-lhe o contacto com Honegger, Milhaud e Messiaen, com quem estuda composição. Este último mostra-se especialmente impressionado com a sua originalidade e aconselha-o a
permanecer “ingénuo e livre”.
É também nesta época que conhece o célebre arquitecto Le Corbusier, que o contrata como colaborador. Xenakis é envolvido nos estudos de projectos importantes como o Convento de La Tourette, a Assembleia de Chandigarh ou o Estádio de Baghdad, mas o fruto mais marcante desta colaboração é o original Pavilhão Philips da Exposição de Bruxelas de 1958 (baseado em superfícies derivadas de uma mesma linha parabólica), que serviria de palco à apresentação da obra electroacústica de Varèse “Poème Electronique”.
Esta revolução arquitectónica encontra um equivalente na revolução musical patente na sua primeira obra publicada, “Metastasis”. Estreada no Festival de Donaueschingen, em 1955, provoca um verdadeiro escândalo. Xenakis não vê nenhuma divisão entre as teorias que desenvolve na arquitectura e na música. A problemática do som liga-se permanentemente à sua obsessão pelo espaço.
Com o advento da tecnologia, Xenakis passou a aplicar as suas teorias a programas informáticos. Foi um dos primeiros a recorrer ao computador na composição musical, mais especificamente a um IBM 7090, que usa para conceber “ST48″ (1962) e, para estimular a investigação, fundou, em 1966, o Centre d’Études de Mathematique et Automatique Musicales (CEMAMu). Nas décadas subsequentes, viajou por todo o mundo, acompanhando as apresentações das suas obras, proferindo conferências e orientando cursos de composição e estética. Leccionou na City University, em Londres, na Universidade de Indiana e na Sorbonne em Paris (1972-89).
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source: buscabiografias

Nació el 29 de mayo de 1922 en Braila, Rumania, de padres griegos.

Vivió con su familia en Grecia desde 1932 y se graduó en el Instituto de Tecnología de Atenas. Durante la II Guerra Mundial formó parte de la resistencia, y perdió un ojo. Tras la guerra escapa a Francia a causa de sus actividades políticas. En 1965 adoptó la nacionalidad francesa.

Cursó estudios con los compositores franceses Arthur Honegger, Darius Milhaud y Olivier Messiaen y entre 1948 y 1960 fue ayudante del arquitecto francés Le Corbusier. Diseñó el pabellón Philips de la Exposición mundial de Bruselas de 1958. Le Corbusier -dijo Xenakis- me abrió los ojos para la arquitectura moderna. Para mí, después del Partenón, no había otra cosa. Lo que era admirable en él era su espíritu de búsqueda perpetua, su facultad de ver las cosas desde ángulos diferentes, su doble tendencia hacia lo abstracto y hacia lo funcional”. La fachada del Convento de dominicanos de La Tourette, cerca de Lyon, fue otra significativa contribución de Xenakis a la arquitectura moderna.

Sus composiciones musicales interaccionan la física, la arquitectura y las matemáticas. Su idea de música estocástica (música compuesta con la ayuda de los ordenadores y basada en sistemas matemáticos de probabilidad) se basa en la teoría de conjuntos, la lógica simbólica y la teoría de probabilidades unidas a un concepto de stochos o evolución hacia un estado estable. En vez de la visión atomizada y puntillista de la música serial, Xenakis se interesó por las grandes masas de sonidos. “Es necesario cambiar la plataforma del observador -escribió el músico-, sea compositor o simplemente oyente, y encontrar el medio de controlar los vastos conjuntos de sonidos. Los métodos basados en cálculos de posibilidades que se utilizan con todo éxito forman un instrumento capaz de transformar la visión de la música y, por lo tanto, de la composición”.

En el año 1966 funda la Escuela de Música Matemática y Automática. Es autor de las composiciones Oresteia (1966), Medea (1967) y Persépolis (1971).

Iannis Xenakis falleció el 4 de febrero de 2001 en París.
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source: brahmsircamfr

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.
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source: ololofm

Французский композитор-модернист, занимавшийся также архитектурой, математикой, теорией музыки, грек по происхождению, Янис Ксенакис (Jannis Xenakis), родился 29 мая 1922 в румынском городе Браила, в обеспеченной семье. Отец его, Клихос Ксенакис, был выходцем с острова Наксос, работал представителем английской экспортной компании. Был также большим любителем оперы. Мать Яниса, Фотини Павлу, родилась на острове Лемнос, была прекрасной пианисткой. В 1932 Ксенакис с семьей переезжает в Грецию (о-в Спетсес, до 1938). Там Ксенакис берет первые уроки музыки – гармонии и игры на фортепиано. В 1940 Ксенакис поступил в политехнический университет в Афинах, где получил инженерное образование; закончил ун-т в 1946. В то же время не прекращал заниматься музыкой, изучал музыкальную композицию и контрапункт. В годы второй мировой войны молодой инженер Янис Ксенакис воевал в партизанском отряде с фашистами, а потом – с освободителями англичанами. В результате тяжёлого ранения и контузии потерял глаз. Ксенакис был мобилизован в регулярную греческую армию, но скрылся, был объявлен государственным преступником и приговорён к смертной казни. Ему удалось бежать, сначала в Италию, затем во Францию (1948).

По приезде во Францию Ксенакис поступил на работу в мастерскую известного французского архитектора, представителя авангарда, Ле Корбюзье в Париже. Участвовал в разработке многих его проектов, как например, Жилая Единица в Марселе (1949), здание Парламента в г.Чандигарх, Индия (1951), монастырь Ла Туретт (1953) и другие. В 1956 Ле Корбюзье получил заказ на проектирование павильона Филипс (от известного голландского концерна) для всемирной выставки ЭКСПО-58 в Брюсселе. Разработку этого проекта, который был назван «Электронная поэма», Корбюзье доверил Ксенакису. Моделирование сложных и весьма необычных форм павильона производилось математическим методом построения фигур 2-го и 3-го порядка (гиперболоид вращения). Его основная конструкция, вантовая в основе, с туго натянутыми металлическими растяжками, напоминает архаический струнный музыкальный инструмент, что-то вроде арфы. Внешний вид готового павильона в целом смахивал на абстрактную скульптуру экспрессивных форм. Исполнявшаяся внутри павильона аудио-визуальная программа под названием «Электронная поэма», – плод коллективного творчества. Аудиоряд «поэмы» был создан и записан Ксенакисом и Варезом. Это трёхминутный, беспрерывно повторяющийся опус под названием «Concret PH». Автором архитектуры павильона Филипс долгое время считался Ле Корбюзье, поскольку проект павильона создавался в рамках его мастерской, да и сама концепция «Электронной поэмы» также вырабатывалась под его началом. Конструкция павильона Филипс, созданная Ксенакисом, новаторская и, по сути, не имеющая прецедентов, предвосхитила появление целого направления в строительстве павильонов (например, вантовые перекрытия Олимпийского комплекса в Токио, арх. Кендзо Танге). Корбюзье и Ксенакиса, этих двух разных, и по возрасту и по основным увлечениям людей, сближал не только общий интерес к математике (Корбюзье как раз в это время создал свой знаменитый «Модулор», математический ряд пропорций). И тому, и другому были свойственны стремление к новаторскому поиску, пытливый склад ума, свой собственный, незаемный взгляд на вещи. В мастерской Корбюзье Янис Ксенакис проработал в общей сложности двенадцать лет – с 1948 по 1960.

В Париже Ксенакис возобновил свои музыкальные занятия, брал уроки у композиторов A.Онеггера и Д. Мийо (1948—1950), изучал композицию в Парижской консерватории у О. Мессиана (1950—1953). В ранних своих произведениях он сочетает традиционные формы с современными тенденциями, вплетая нередко национальные греческие мотивы. В это время им написаны «Весенняя Симфония» (1949-50), «Zygia» (для скрипки и виолончели, (1951), «Zygia kathisto» (фортепьяно в 4 руки, 1952), «Трио» (1952), «Anastenaria» и «Шествие к ясным водам» (1953), «Голубь мира» (август 1953). Известность Ксенакису принесла его написанная для оркестра пьеса «Metastaseis» (Метастазы, 1954), премьера которой состоялась в октябре 1955 на фестивале Donaueschingen в Германии, а также его статьи, в которых он критиковал доктрину сериализма, популярную тогда среди авнгардистов музыкальную теорию. Пьеса была отвергнута не только консерваторами, но и такими известными музыкантами авангарда, как Штокхаузен и Булез. Статьи Ксенакиса, направленные против сериализма, были изданы его пылким поклонником, дирижером Германом Шерхеном (Hermann Scherchen), и вызвали негативное отношение к Ксенакису всего музыкального авангарда. Впоследствии Шерхен представил публике несколько композиций Ксенакиса: «Pithoprakta» (оркестр, 1955-56), «Achorripsis» (1956-57), «Полла Таа Дхина» (оркестр и детский хор, 1962), «Terretektorh» (1966).

В начале 60-х годов Ксенакис начал использовать, наряду с обычными музыкальными инструментами, звучания, сгенерированные c помощью ЭВМ, компьютерной техники тех времен, и специальных программ на языке Fortran.

Он выработал свою собственную систему композиции, которая строится на математических принципах, использует необычные звучания, созданные электроникой. Ему принадлежит приоритет во введении в технику музыкальной композиции методов точных наук – теории вероятности, в частности.

Всемирную известность Ксенакису принесли его балеты, а также произведения для оркестра «Действительность», «Персеполис», «Сапфо». Он выступил инициатором спектаклей «свето-музыки», – концертов симфонического оркестра и хора, исполнявшихся в ночное время под открытым небом, обычно в романтическом окружении древней архитектуры, в сопровождении специальных световых эффектов (им же самим и спрограммированных). В 1983 году он был принят в члены французской Академии изящных искусств. Музыкальное творчество Ксенакиса отличается изощренной сложностью, – и в отношении письма, и в отношении исполнения. Тем не менее, и сегодня Янис Ксенакис – исполняемый композитор, признанный классик музыкального авангарда, один из создателей самобытной ветви модернизма в музыке.

Цитата: « На первый взгляд, в музыке Ксенакиса ничего не изменилось. Она сохраняет ту же жесткость, терпкость, категоричную ясность рисунка; ей присуща выразительность стальной конструкции, и в то же время радость грубого осязания живых тканей, сложно устроенных текстур. Как никто другой из авангардистов, за исключением разве что Вареза, Ксенакис смог привнести в звуковую область ощущения плотности и тяжести, тепла и холода, трения и рикошета. Он изобрел большую часть ставших теперь типовыми приемов авангардной инструментальной игры. Рассчитывая на ЭВМ «стохастическую» структуру своих опусов, Ксенакис разбудил в музыке дыхание доисторической природы и сделал мир ненасытно прожорливым к звуку; его творчество явило собой альтернативу музыке пауз, тишины, среды и атмосферы». (ПЕТР ПОСПЕЛОВ)