Igor Stravinsky

Igor Fyodorovitch Stravinsky (Russian: Игорь Фёдорович Стравинский) (June 17, 1882 – April 6, 1971) was a Russian-American composer of modern classical music. He composed in the neo-classical and serialist styles, but he is best known for two works from his earlier, Russian period: Le sacre du printemps (The Rite of Spring) and L'oiseau de feu (The Firebird). For some, these ballets practically reinvented the genre. Stravinsky also wrote in a broad spectrum of ensemble combinations and classical forms. His oeuvre included everything from symphonies to piano miniatures.

Stravinsky is shown here conducting the Columbia Symphony Orchestra in Petrushka.

Stravinsky also achieved fame as a pianist and conductor, often at the premieres of his own works. He was also a writer. With the help of Alexis Roland-Manuel, Stravinsky composed a theoretical work entitled Poetics of Music. In it, he famously claimed that music was incapable of "expressing anything but itself". Robert Craft transcribed several interviews with the composer, which were published as Conversations with Stravinsky.

A quintessentially cosmopolitan Russian, Stravinsky was one of the most authoritative composers in 20th century music, both in the West and in his native land. He was named by Time magazine as one of the most influential people of the century.

Biography

Stravinsky was born in Oranienbaum (now Lomonosov), near St. Petersburg, Russia. Brought up in an apartment in St. Petersburg and dominated by his father and elder brother, Stravinsky's early childhood was a mix of experience that hinted little at the cosmopolitan artist he was to become. Though his father was a bass singer at the Mariinsky Theater in St. Petersburg, Stravinsky originally studied to be a lawyer. Composition came later. In 1902, at the age of 20, Stravinsky became the pupil of Nikolai Rimsky-Korsakov, probably the leading Russian composer of the time.

Stravinsky left Russia for the first time in 1910, going to Paris to attend the premiere of his ballet L'oiseau de feu (The Firebird). During his stay in the city, he composed three major works for the Ballets Russes—L'oiseau de feu, Petrushka (1911), and Le sacre du printemps (The Rite of Spring) (1913). The ballets trace his stylistic development: from the L'oiseau de feu, whose style draws largely on Rimsky-Korsakov, to Petrushka's emphasis on bitonality, and finally to the savage polyphonic dissonance of Le sacre du printemps. As he himself said, with these premieres his intention was "[to send] them all to hell". (He succeeded: the 1913 première of Le sacre du printemps turned into a riot.)

Stravinsky displayed an inexhaustible desire to learn and explore art, literature, and life. This desire manifested itself in several of his Paris collaborations. Not only was he the principal composer for Sergei Diaghilev's Ballet Russes, but Stravinsky also collaborated with Pablo Picasso (Pulcinella, 1920), Jean Cocteau (Oedipus Rex, 1927) and George Balanchine (Apollon Musagete, 1928).

Stravinsky and Pablo Picasso collaborated on Pulcinella in 1920. Picasso took the opportunity to make several sketches of the composer.

Relatively short of stature and not conventionally handsome, Stravinsky was nevertheless photogenic, as many pictures show. Although a notorious philanderer (even rumoured to have affairs with high-class partners such as Coco Chanel) Stravinsky was also a family man who devoted considerable amounts of his time and expenditure to his sons and daughters. He was still young when he married his cousin Katerina Nossenko, who he had known since early childhood, on 23 January 1906. Their marriage endured for 33 years, but the true love of his life, and partner until his death, was his second wife Vera de Bosset (1888-1982).

When Stravinsky met Vera in the early 1920s she was married to the painter and stage designer Serge Sudeikin, but they soon began an affair which led to her leaving her husband. From then until the death of Katerina in 1939 Stravinsky led a deft double-life, spending some of his time with his first family and the rest with Vera. Katerina soon learned of the relationship and accepted it as inevitable and permanent. After her death Stravinsky and Vera were married in New York where they had gone from France to escape the war in 1940.

Patronage too was never far away. In the early 1920s Leopold Stokowski was able to give Stravinsky regular support through a pseudonymous "benefactor". The composer was also able to attract commissions: most of his work from The Firebird onwards was written for specific occasions and paid for generously.

Stravinsky proved adept at playing the part of "man of the world", acquiring a keen instinct for business matters and appearing relaxed and comfortable in many of the world's major cities. Paris, Venice, Berlin, London and New York all hosted successful appearances as pianist and conductor. Most people who knew him through dealings connected with performances spoke of him as polite, courteous and helpful. For example, Otto Klemperer, who knew Schoenberg well, said that he always found Stravinsky much more co-operative and easy to deal with. At the same time he had a disregard of his social inferiors: Robert Craft was embarrassed by his habit of tapping a glass with a fork and loudly demanding attention in restaurants.

Eventually Stravinsky's music was noticed by Serge Diaghilev, the director of the Ballets Russes in Paris. He commissioned Stravinsky to write a ballet for his theater; so in 1911, Stravinsky traveled to Paris. That ballet ended up being the famous L'Oiseau de Feu. However, because of World War I and the October Revolution in Russia he moved to Switzerland in 1914. He returned to Paris in 1920 to write more ballets as well as many other works. He moved to the United States in 1939 and became a naturalized citizen in 1945. He continued to live in the United States until his death in 1971, unsuccessfully writing music for films. Stravinsky had adapted to life in France, but moving to America aged 58 was a very different prospect. For a time he preserved a ring of emigré Russian friends and contacts, but eventually realised that this would not sustain his intellectual and professional life in the USA. When he planned to write an opera with W. H. Auden, the need to acquire more familiarity with the English-speaking world coincided with his meeting the conductor and musicologist Robert Craft. Craft lived with Stravinsky until his death, acting as interpreter, chronicler, assistant conductor and factotum for countless musical and social tasks.

The graves of Igor and Vera Stravinsky on San Michele

Stravinsky's taste in literature was wide and reflected his constant desire for new discoveries. The texts and literary sources for his work began with a period of interest in Russian folklore, progressed to classical authors and the Latin liturgy, and moved on to contemporary France (André Gide, in Persephone) and eventually English literature: Auden, Eliot, and medieval English verse. At the end of his life he was even setting Hebrew scripture in Abraham and Isaac.

In 1962 he accepted an invitation to return to Russia for a series of concerts, but remained an émigré firmly based in the West.

He died in New York City on April 6, 1971 at the age of 88 and was buried in Venice on the cemetery island of San Michele. His grave is close to the tomb of his long-time collaborator Diaghilev. Stravinsky's life had encompassed most of the 20th Century, including many of its modern classical music styles, and he influenced composers both during and after his lifetime. He has a Star on the Hollywood Walk of Fame at 6340 Hollywood Boulevard.

Stylistic periods

Stravinsky's career largely falls into three distinct stylistic periods. Most of his compositions can be placed in one of the three.

The Primitive, or Russian, Period

The first of Stravinsky's major stylistic periods (excluding some early minor works) was inaugurated by the three ballets he composed for Diaghilev. The ballets have several shared characteristics: they are scored for extremely large orchestras; they use Russian folk themes and motifs; and they bear the mark of Rimsky-Korsakov's imaginative scoring and instrumentation.

The first of the ballets, L'oiseau de feu, is notable for its unusual introduction (triplets in the low basses) and sweeping orchestration. Petrushka, too, is distinctively scored and the first of Stravinsky's ballets to draw on folk mythology. But it is the third ballet, The Rite of Spring, that is generally considered the apotheosis of Stravinsky's "Russian Period". Here, the composer draws on the brutalism of pagan Russia, reflecting these sentiments in roughly-drawn, stinging motifs that appear throughout the work. There are several famous passages in the work, but two are of particular note: the opening theme played on a bassoon with notes at the very top of its register, almost out of range; and the thumping, off kilter eighth-note motif played by strings and accented by French horns on off-rhythms (See Le sacre du printemps (The Rite of Spring) for a more detailed account of this work).

Other pieces from this period include: Renard (1916), Histoire du soldat (A Soldier's Tale) (1918), and Les Noces (The Wedding) (1923).

The Neo-Classical Period

The next phase of Stravinsky's compositional style, slightly overlapping the first, is marked by two works: Pulcinella 1920 and the Octet (1923) for wind instruments. Both of these works feature what was to become a hallmark of this period; that is, Stravinsky's return, or "looking back", to the classical music of Mozart and Bach and their contemporaries. This "neo-classical" style involved the abandonment of the large orchestras demanded by the ballets. In these new works, written roughly between 1920 and 1950, Stravinsky turns largely to wind instruments, the piano, and choral and chamber works.

Other works such as Oedipus Rex (1927), Apollon Musagete (1928) and the Dumbarton Oaks concerto continue this trend.

Some larger works from this period are the three symphonies: the Symphonie des Psaumes (Symphony of Psalms) (1930), Symphony in C (1940) and Symphony in Three Movements (1945). Apollon, Persephone (1933) and Orpheus (1947) also mark Stravinsky's concern, during this period, of not only returning to "Classic" music but also returning to "Classic" themes: in these instances, the mythology of the ancient Greeks.

The pinnacle of this period is the opera The Rake's Progress completed in 1951. This opera, written to a libretto by Auden and based on the etchings of Hogarth, encapsulates everything that Stravinsky had perfected in the previous 20 years of his neo-classic period. The music is direct but quirky; it borrows from classic tonal harmony but also interjects surprising dissonances; it features Stravinsky's trademark off-rhythms; and it harkens back to the operas and themes of Monteverdi, Gluck and Mozart.

After the opera's completion Stravinsky never wrote another "neo-classic" work and instead began writing the music that came to define his final stylistic change.

The Serialist, or Twelve Tone Period

Only after the death of Arnold Schoenberg, the inventor of the twelve tone system, in 1951 did Stravinsky begin making use of the technique in his own works. No doubt, Stravinsky was aided in his understanding of, or even conversion to, the twelve tone method by his confidant and helper Robert Craft, who had long been advocating the change. Regardless, the next fifteen years were spent writing the works in this style.

Stravinsky first began to dabble in the twelve tone technique in smaller vocal works such as the Cantata (1952), Three Songs from Shakespeare (1953) and In Memoriam Dylan Thomas (1954), as if he were testing the system. He later began expanding his use of the technique in works often based on biblical texts, such as Threni (1958), A Sermon, a Narrative, and a Prayer (1961), and The Flood (1962).

An important transitional work of this period in Stravinsky's work, was a return to the ballet: Agon, a work for twelve dancers written from 1954 to 1957. Some numbers of Agon recollect the "white-note" tonality of the neo-classic period, while others (the Bransle Gay, e.g.) display his unique re-interpretation of serial method. The ballet is thus a sort of miniature encyclopedia of Stravinsky, containing many of the signatures to be found throughout his compositions, whether primitivist, neo-classic, or serial: rhythmic quirkiness and experimentation, harmonic ingenuity, and a deft ear for masterful orchestration. Indeed, these characteristics are what make Stravinsky's output so unique when compared with the work of contemporaneous serial composers.

Influence and innovation

Stravinsky's work embraced multiple compositional styles, revolutionised orchestration, spanned several genres, practically reinvented ballet form and incorporated multiple cultures, languages and literatures. As a consequence, his influence on composers both during his lifetime and after his death was, and remains, considerable.

Compositional innovations

Stravinsky began re-thinking his use of the motif and ostinato as early as The Firebird ballet, but his use of these elements reached its full flowering in The Rite of Spring.

Motivic development, that is using a distinct musical phrase that is subsequently altered and developed throughout a piece of music, has its roots in the sonata form of Mozart's age. The first great innovator in this method was Beethoven; the famous "fate motif" which opens Fifth Symphony and reappears throughout the work in surprising and refreshing permutations is a classic example. However, Stravinsky's use of motivic development was unique in the way he permutated his motifs. In the "Rite of Spring" he introduces additive permutations, that is, subtracting or adding a note to a motif without regard to changes in meter.

The same ballet is also notable for its relentless use of ostinati. The most famous passage, as noted above, is the eighth note ostinato of the strings accented by eight french horns that occurs in the section Auguries of Spring (Dances of the Young Girls). This is perhaps the first instance in music of extended ostinato which is neither used for variation nor for accompaniment of melody. At various other times in the work Stravinsky also pits several ostinati against one another without regard to harmony or tempo, creating a pastiche, a sort of musical equivalent of a Cubist painting. These passages are notable not only for this pastiche-quality but also for their length: Stravinsky treats them as whole and complete musical sections.

Such techniques foreshadowed by several decades the minimalist works of composers such as Terry Riley and Steve Reich.

Neoclassicism

Stravinsky was the greatest, if not the first, practitioner of the "neoclassic" style, a style that would be later adopted by composers as diverse as Darius Milhaud and Aaron Copland. Sergei Prokofiev once chided Stravinsky for his neo-classical mannerisms, though sympathetically, as Prokofiev had broken similar musical ground in his Symphony No. 1, "Classical" of 1916-17.

Stravinsky announced his new style in 1923 with the stripped-down and delicately scored Octet for winds. The clear harmonies, looking back to the Classical music era of Mozart and Bach, and the simpler combinations of rhythm and melody were a direct response to the complexities of the Second Viennese School. Stravinsky may have been preceded in these devices by earlier composers such as Erik Satie, but no doubt when Copland was composing his Appalachian Spring ballet he was taking Stravinsky as his model.

Certainly by the late 1920s and 1930s, Neoclassicism as an accepted modern genre was prevalent throughout art music circles around the world. Ironically, it was Stravinsky himself who announced the death of Neoclassicism, at least in his own work if not for the world, with the completion of his opera The Rake's Progress in 1951. A sort of final statement for the style, the opera was largely ridiculed as too "backward looking" even by those who had lauded the new style only three decades earlier.

Quotation and pastiche

Stravinsky used the now very postmodern technique of direct musical quotation and pastiche as early as 1920 in his work Pulcinella. Here he uses the music of Pergolesi as source material, sometimes directly quoting it and other times simply reinventing it, to create a new and refreshing work. He used the same technique in the ballet The Fairy's Kiss of 1928. Here it is the music of Tchaikovsky, specifically Swan Lake, that Stravinsky uses as his source. Such compositional "borrowing" would come into vogue in the 1960s, as in the work Sinfonia by Luciano Berio.

Use of folk material

There were other composers in the early 20th century who collected and augmented their native folk music and used these themes in their work. Two notable examples are Béla Bartók and Zoltán Kodály. Yet in Le Sacre du Printemps we see Stravinsky again innovating in his use of folk themes. He strips these themes to their most basic outline, melody alone, and often contorts them beyond recognition with additive notes, inversions, diminutions, and other techniques. He did this so well, in fact, that only in recent scholarship, such as in Richard Taruskin's Stravinsky and the Russian Traditions: A Biography of the Works Through Mavra [1], have analysts uncovered the original source material for some of the music in The Rite.

Orchestral innovations

The late 19th century and early 20th century was a time ripe with orchestral innovation. Composers such as Anton Bruckner and Gustav Mahler were well regarded for their skill at writing for the medium. They, in turn, were influenced by the expansion of the traditional classical orchestra by Richard Wagner through his use of large forces and unusual instruments.

Stravinsky continued this Romantic trend of writing for huge orchestral forces, especially in the early ballets. But it is when he started to turn away from this tendency that he began to innovate by introducing unique combinations of instruments. For example, in L'Histoire du Soldat (A Soldier's Tale) the forces used are clarinet, bassoon, tenor and bass trombone, double bass, cornet, violin and percussion, a very striking combination for its time (1918). This combining of distinct timbres would become almost a cliche in post-World War II classical music.

Another notable innovation of orchestral technique that can be partially attributed to Stravinsky is the exploitation of the extreme ranges of instruments. The most famous passage is the opening of the Rite of Spring where Stravsinky uses the extreme reaches of the bassoon to simulate the symbolic "awakening" of a spring morning.

It must also be noted that composers such as Anton Webern, Alban Berg and Arnold Schoenberg were also exploring some of these orchestral and instrumental techniques in the early 20th century. Yet their influence on succeeding generations of composers was equalled if not exceeded by that of Stravinsky.

Criticism

"The music of Le Sacre du Printemps baffles verbal description. To say that much of it is hideous as sound is a mild description. There is certainly an impelling rhythm traceable. Practically it has no relation to music at all as most of us understand the word." Musical Times, London, August 1, 1913 (Slonimsky, 1953)

"All the signs indicate a strong reaction against the nightmare of noise and eccentricity that was one of the legacies of the war.... What has become of the works that made up the program of the Stravinsky concert which created such a stir a few years ago? Practically the whole lot are already on the shelf, and they will remain there until a few jaded neurotics once more feel a desire to eat ashes and fill their belly with the east wind." Musical Times, London, October 1923 (ibid.)

Composer Constant Lambert (1936) described pieces such as L'Histoire du Soldat (A Soldier's Tale) as containing, "essentially cold-blooded abstraction". Further, the "melodic fragments in L'Histoire du Soldat are completely meaningless themselves. They are merely successions of notes that can conveniently be divided into groups of three, five, and seven and set against other mathematical groups", and the cadenza for solo drums is, "musical purity...achieved by a species of musical castration". He compares Stravinsky's choice of, "the drabbest and least significant phrases", to Gertrude Stein's: "Everday they were gay there, they were regularly gay there everyday" ("Helen Furr and Georgine Skeene", 1922), "whose effect would be equally appreciated by someone with no knowledge of English whatsoever".

In his book Philosophy of Modern Music (1948) Theodor Adorno calls Stravinsky an acrobat, a civil servant, a tailor's dummy, hebephrenic, psychotic, infantile, fascist, and devoted to making money. Part of the composer's error, in Adorno's view, was his neo-classicism, but more important was his music's "pseudomorphism of painting", playing off of le temps éspace (space) rather than le temps durée (duration) of Henri Bergson. "One trick characterizes all of Stravinsky's formal endeavors: the effort of his music to portray time as in a circus tableau and to present time complexes as though they were spatial. This trick, however, soon exhausts itself." (1948)

List of works

Ballets

  • L'oiseau de feu (The Firebird) for orchestra (1910)
  • Petrushka for orchestra (1911)
  • Le sacre du printemps (The Rite of Spring) for orchestra (1913)
  • Renard (1916)
  • Pulcinella for chamber orchestra and soloists (1920)
  • Apollon Musagète for string orchestra (1928)
  • Le baiser de la fée (The Fairy's Kiss) for orchestra (1928)
  • Perséphone for speaker, soloists, chorus and orchestra (1933)
  • Jeu de cartes for orchestra (1936)
  • Orpheus for chamber orchestra (1947)
  • Agon for chamber orchestra (1957)

Orchestral works

  • Symphony in E-Flat Major (1907)
  • Scherzo fantastique (1908)
  • Feu d'artifice (Fireworks) (1908)
  • Le chant du rossignol (Song of the Nightingale) (1917)
  • Quatre études for orchestra (1918)
  • Symphonies of Wind Instruments (1920)
  • Suite from Pulcinella for orchestra (1920)
  • Suite No.2 for chamber orchestra (1921)
  • Suite No.1 for chamber orchestra (1925)
  • Concerto for Piano and Wind Instruments (1925)
  • Capriccio for Piano and Orchestra (1929)
  • Concerto in D for violin and orchestra (1931)
  • Divertimento for orchestra (Suite from Le Baiser du Fee, 1934)
  • Preludium for jazz band (1937)
  • Concerto in E-flat (Dumbarton Oaks) for Chamber Orchestra (1938)
  • Symphony in C (1940)
  • Circus Polka for orchestra (1942)
  • Danses Concertantes for chamber orchestra (1942)
  • Four Norwegian Moods for orchestra (1942)
  • Ode for orchestra (1943)
  • Scherzo a la Russe for orchestra (1944)
  • Symphony in Three Movements (1945)
  • Ebony Concerto for clarinet and jazz band (1945)
  • Concerto in D for string orchestra (1946)
  • Tango for chamber orchestra (1940/1953)
  • Greeting Prelude for orchestra (1955)
  • Movements for Piano and Orchestra (1958–[[1959])
  • 8 Instrumental miniatures for 15 Players (1963, orchestration of Les Cinq Doigts)
  • Variations (Aldous Huxley in Memoriam) for orchestra (1963–1964)

Piano works

  • Tarantella for piano (1898)
  • Scherzo for piano (1902)
  • Sonata in F-Sharp Minor for piano (1904)
  • Quatre Etudes for piano Op.7 (1908)
  • Le Sacre du Printemps for two pianos (1913)
  • Valse des fleurs for two pianos (1914)
  • Trois piéces faciles for two pianos (1915)
  • Souvenir d'une Marche Boche for piano (1915)
  • Cinq piéces faciles for two pianos (1917)
  • Valse pour les Enfants for piano (1917)
  • Piano Rag Music for piano (1919)
  • Chorale for piano (1920)
  • Les Cinq Doigts for piano (1921)
  • Sonata for piano (1924)
  • Serenade for piano (1925)
  • Concerto for Two Pianos (1935)
  • Tango for piano (1940)
  • Sonata for Two Pianos (1943)
  • Two Sketches for a Sonata for piano (1967)

Chamber works

  • Three Pieces for string quartet (1914)
  • Pour Pablo Picasso, Piece for clarinet (1917)
  • Canon for two horns (1917)
  • Duet for two bassoons (1918)
  • Suite from Histoire du Soldat for violin, clarinet and piano (1919)
  • Three Pieces for Clarinet (1919)
  • Concertino for string quartet (1920)
  • Octet for wind instruments (1923)
  • Duo Concertant for violin and piano (1932)
  • Pastorale for violin and piano (1933)
  • Suite Italienne (from Pulcinella) for violin or cello and piano (1933/34)
  • Elegy for solo viola (1944)
  • Septet (1953)
  • Epitaphium for flute, clarinet and harp (1959)
  • Double Canon for string quartet 'Raoul Dufy in Memoriam' (1959)
  • Monumentum Pro Gesualdo Di Venosa (arrangement) for chamber ensemble (1960)
  • Fanfare for a New Theatre for two trumpets (1964)

Choral works

  • Le roi des étoiles (The King of the Stars) for Men's Choir and Orchestra (1912)
  • Pater Noster (1926)
  • Symphonie des Psaumes (Symphony of Psalms) for chorus and orchestra (1930)
  • Mass (1948)
  • Cantata for soprano, tenor, female voices, 2 flutes, oboe, English horn, cello (1953-1954)
  • Canticum Sacrum (1955)
  • Threni (1958)
  • A Sermon, a Narrative and a Prayer (1961)
  • Abraham and Isaac (1963)
  • Introitus (1965)
  • Requiem Canticles (1966)

Opera/Theater

  • Le rossignol (The Nightingale) (1914)
  • Burleske for 4 Pantomimes and Chamber Orchestra (1916)
  • Histoire du soldat (A Soldier's Tale) (1918)
  • Mavra (1922)
  • Les Noces (The Wedding) (1923)
  • Oedipus Rex (1927)
  • Babel (1944)
  • The Rake's Progress (1951)
  • The Flood (1962)

Vocal works

  • Romance for Voice and Piano (1902)
  • Faun and Shepherdess for mezzo-soprano and orchestra Op. 2 (1907)
  • Pastorale wordless soprano and piano (1907)
  • Two Melodies for mezzo-soprano and piano Op.6 (1908)
  • Deux poèmes de Paul Verlaine for bariton and piano or orchestra Op.9 (1910/1951)
  • Two Poems of K. Balmont for voice and piano or small orchestra (1911/1954)
  • Trois poésies de la lyrique japonaise for voice and piano or chamber orchestra (1913)
  • Trois petites chansons voice and piano (or small orchestra) (1913/1930)
  • Pribaoutki for voice, flute, oboe, clarinet, bassoon, vln, vla, vc, double bass (1914)
  • Berceuses du Chat for contralto and three clarinets (1916)
  • Three Tales for Children for voice and piano (1917)
  • Four Russian Peasant Songs for female voice unaccompanied (1917)
  • Berceuse for voice and piano (1918)
  • Quatre chants russes Quatre chants russes for voice and piano (1918/1919)
  • Petit ramusianum harmonique single voice or voices (1938)
  • Three Songs from William Shakespeare for mezzo-soprano, flute, clarinet, and viola (1953)
  • Four Russian Songs for mezzo-soprano, flute, harp and guitar (1954, versions from Quatre chants russes and Three Tales for Children)
  • In Memoriam Dylan Thomas (Dirge Canons and Song) (1954)
  • Elegy for J.F.K. for baritone and three clarinets (1964)
  • The Owl and the Pussy Cat for soprano and piano (1966)

See Also

  • Category:Compositions by Igor Stravinsky

References

  • Lambert, Constant (1936). Music Ho! A Study of Music in Decline, p.94–94 and 101–105. New York: Charles Scribner's Sons.
  • Robert Craft. Stravinsky: Glimpses of a Life, St Martins Press, 1993
  • Robert Craft. Stravinsky: Chronicle of a Friendship, Vanderbilt University Press, 1997
  • Slonimsky, Nicolas (1953). Lexicon of Musical Invective: Critical Assaults on Composers Since Beethoven's Time. Seattle: University of Washington Press. ISBN 0295785799.

Further reading

  • Igor Stravinsky, Poetics of Music, ISBN 674678559. Ghostwritten by Alexis Roland-Manuel.
  • Igor Stravinsky and Robert Craft, Conversations with Stravinsky, ISBN 0520040406 .
  • Igor Stravinsky, An Autobiography, ISBN 0393318567. Ghostwritten by Walter Nouvel.
  • Eric Walter White, Stravinsky. The composer and his works, ISBN 0571049230
  • Milan Kundera, Testaments Betrayed: An Essay in Nine Parts, ISBN 0060927518

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This trick, however, soon exhausts itself." (1948). [1][2]. "One trick characterizes all of Stravinsky's formal endeavors: the effort of his music to portray time as in a circus tableau and to present time complexes as though they were spatial. Despite this minor fiasco, the judge, who was apparently a very patient person, still awarded Gödel his citizenship. Part of the composer's error, in Adorno's view, was his neo-classicism, but more important was his music's "pseudomorphism of painting", playing off of le temps éspace (space) rather than le temps durée (duration) of Henri Bergson. An amusing anecdote relating to Gödel relates that he apparently informed the presiding judge at his citizenship hearing, against the pleadings of Einstein, that he had discovered a way in which a dictatorship could be legally installed in the United States. In his book Philosophy of Modern Music (1948) Theodor Adorno calls Stravinsky an acrobat, a civil servant, a tailor's dummy, hebephrenic, psychotic, infantile, fascist, and devoted to making money. It is an international organization for the promotion of research in the areas of logic, philosophy, and the history of mathematics.

He compares Stravinsky's choice of, "the drabbest and least significant phrases", to Gertrude Stein's: "Everday they were gay there, they were regularly gay there everyday" ("Helen Furr and Georgine Skeene", 1922), "whose effect would be equally appreciated by someone with no knowledge of English whatsoever". The Kurt Gödel Society (founded in 1987) was named in his honor. They are merely successions of notes that can conveniently be divided into groups of three, five, and seven and set against other mathematical groups", and the cadenza for solo drums is, "musical purity...achieved by a species of musical castration". He had no children. Further, the "melodic fragments in L'Histoire du Soldat are completely meaningless themselves. Kurt Gödel died of starvation on January 14, 1978, in Princeton, New Jersey, USA. Composer Constant Lambert (1936) described pieces such as L'Histoire du Soldat (A Soldier's Tale) as containing, "essentially cold-blooded abstraction". Due to his paranoia this meant that Gödel refused to eat any food at all.

What has become of the works that made up the program of the Stravinsky concert which created such a stir a few years ago? Practically the whole lot are already on the shelf, and they will remain there until a few jaded neurotics once more feel a desire to eat ashes and fill their belly with the east wind." Musical Times, London, October 1923 (ibid.). Not only was this a cause of deep sorrow for Gödel, it also meant that his wife could no longer cook for him. "All the signs indicate a strong reaction against the nightmare of noise and eccentricity that was one of the legacies of the war... Shortly before Gödel's death, his wife had become extremely ill and was consequently incapacitated in a hospital bed. Practically it has no relation to music at all as most of us understand the word." Musical Times, London, August 1, 1913 (Slonimsky, 1953). As mentioned, Gödel suffered from paranoid psychological disorder. There is certainly an impelling rhythm traceable. There is an ironically titled biography of the great mathematician called, "Gödel: A Life of Logic.".

To say that much of it is hideous as sound is a mild description. For this reason Gödel would only eat his wife's cooking, refusing to even eat his own cooking for fear of being poisoned; this, in particular, would turn out to be fatal for the great logician. "The music of Le Sacre du Printemps baffles verbal description. Amongst his paranoias was the contention that unknown villains were trying to kill him by poisoning his food. Yet their influence on succeeding generations of composers was equalled if not exceeded by that of Stravinsky. All this caused Gödel to suffer further physical illness. It must also be noted that composers such as Anton Webern, Alban Berg and Arnold Schoenberg were also exploring some of these orchestral and instrumental techniques in the early 20th century. The eccentric mathematician was a somewhat sickly man and was prescribed specific diets and medical regimens by doctors, but being as opinionated as he was, Gödel would often do the opposite of what his doctor would prescribe.

The most famous passage is the opening of the Rite of Spring where Stravsinky uses the extreme reaches of the bassoon to simulate the symbolic "awakening" of a spring morning. The great logician was a highly opinionated man, having a strong opinion on just about everything including his diet and his medical prescriptions. Another notable innovation of orchestral technique that can be partially attributed to Stravinsky is the exploitation of the extreme ranges of instruments. He left the windows of his house constantly open because he believed that unknown villains were trying to kill him by pouring poison gas into his house. This combining of distinct timbres would become almost a cliche in post-World War II classical music. In the middle of winter, Gödel would leave all of the windows open in his home, causing it to freeze. For example, in L'Histoire du Soldat (A Soldier's Tale) the forces used are clarinet, bassoon, tenor and bass trombone, double bass, cornet, violin and percussion, a very striking combination for its time (1918). The great mathematician would wear warm, winter clothing in the middle of summer.

But it is when he started to turn away from this tendency that he began to innovate by introducing unique combinations of instruments. Gödel was a shy, withdrawn and eccentric person, and suffered from paranoid schizophrenia. Stravinsky continued this Romantic trend of writing for huge orchestral forces, especially in the early ballets. This is now known as Gödel's ontological proof. They, in turn, were influenced by the expansion of the traditional classical orchestra by Richard Wagner through his use of large forces and unusual instruments. In the early seventies, Gödel, who was deeply religious, circulated among his friends an elaboration on Gottfried Leibniz' ontological proof of God's existence. Composers such as Anton Bruckner and Gustav Mahler were well regarded for their skill at writing for the medium. Gödel was awarded (with Julian Schwinger) the first Einstein Award, in 1951, and was also awarded the National Medal of Science, in 1974.

The late 19th century and early 20th century was a time ripe with orchestral innovation. He became a full professor at the institute in 1953 and an emeritus professor in 1976. He did this so well, in fact, that only in recent scholarship, such as in Richard Taruskin's Stravinsky and the Russian Traditions: A Biography of the Works Through Mavra [1], have analysts uncovered the original source material for some of the music in The Rite. citizen. He strips these themes to their most basic outline, melody alone, and often contorts them beyond recognition with additive notes, inversions, diminutions, and other techniques. He became a permanent member of the IAS in 1946 and in 1948 he was naturalized as an U.S. Yet in Le Sacre du Printemps we see Stravinsky again innovating in his use of folk themes. These "rotating universes" would allow time travel and caused Einstein to have doubts about his own theory.

Two notable examples are Béla Bartók and Zoltán Kodály. In the late 1940s he demonstrated the existence of paradoxical solutions to Albert Einstein's field equations in general relativity. There were other composers in the early 20th century who collected and augmented their native folk music and used these themes in their work. Gödel showed that both the axiom of choice and the generalized continuum hypothesis are true in the constructible universe, and therefore must be consistent. Such compositional "borrowing" would come into vogue in the 1960s, as in the work Sinfonia by Luciano Berio. In that work he introduced the constructible universe, a model of set theory in which the only sets which exist are those that can be constructed from simpler sets. Here it is the music of Tchaikovsky, specifically Swan Lake, that Stravinsky uses as his source. He also continued to work on logic and in 1940 he published his work Consistency of the axiom of choice and of the generalized continuum-hypothesis with the axioms of set theory which is a classic of modern mathematics.

He used the same technique in the ballet The Fairy's Kiss of 1928. He studied the works of Gottfried Leibniz in detail and, to a lesser extent, those of Kant and Edmund Husserl. Here he uses the music of Pergolesi as source material, sometimes directly quoting it and other times simply reinventing it, to create a new and refreshing work. At the Institute, Gödel's interests turned to philosophy and physics. Stravinsky used the now very postmodern technique of direct musical quotation and pastiche as early as 1920 in his work Pulcinella. After they arrived in San Francisco on March 4, 1940, Kurt and Adele took a train to Princeton, where he resumed his membership in the IAS. A sort of final statement for the style, the opera was largely ridiculed as too "backward looking" even by those who had lauded the new style only three decades earlier. In January 1940 he and his wife left Europe via the trans-Siberian railway and traveled via Russia and Japan to the USA.

Ironically, it was Stravinsky himself who announced the death of Neoclassicism, at least in his own work if not for the world, with the completion of his opera The Rake's Progress in 1951. Since Germany had abolished the title of Privatdozent Gödel would now have to fear conscription into the Nazi army. Certainly by the late 1920s and 1930s, Neoclassicism as an accepted modern genre was prevalent throughout art music circles around the world. After the Anschluss in 1938 Austria had become a part of Nazi Germany. Stravinsky may have been preceded in these devices by earlier composers such as Erik Satie, but no doubt when Copland was composing his Appalachian Spring ballet he was taking Stravinsky as his model. After this he visited the USA once more in the spring of 1939 at the University of Notre Dame. The clear harmonies, looking back to the Classical music era of Mozart and Bach, and the simpler combinations of rhythm and melody were a direct response to the complexities of the Second Viennese School. In the autumn of 1938 he visited the IAS again.

Stravinsky announced his new style in 1923 with the stripped-down and delicately scored Octet for winds. He married Adele on September 20, 1938. 1, "Classical" of 1916-17. He returned to teaching in 1937 and during this time he worked on the proof of consistency of the continuum hypothesis; he would go on to show that this hypothesis cannot be disproved from the common system of axioms of set theory. Sergei Prokofiev once chided Stravinsky for his neo-classical mannerisms, though sympathetically, as Prokofiev had broken similar musical ground in his Symphony No. The travelling and the hard work had exhausted him and the next year he had to recover from a depression. Stravinsky was the greatest, if not the first, practitioner of the "neoclassic" style, a style that would be later adopted by composers as diverse as Darius Milhaud and Aaron Copland. Gödel would visit the IAS again in the autumn of 1935.

Such techniques foreshadowed by several decades the minimalist works of composers such as Terry Riley and Steve Reich. at Princeton, took notes of these lectures which have been subsequently published. These passages are notable not only for this pastiche-quality but also for their length: Stravinsky treats them as whole and complete musical sections. Stephen Kleene, who had just completed his Ph.D. At various other times in the work Stravinsky also pits several ostinati against one another without regard to harmony or tempo, creating a pastiche, a sort of musical equivalent of a Cubist painting. In 1934 Gödel gave a series of lectures at the Institute for Advanced Study (IAS) in Princeton entitled On undecidable propositions of formal mathematical systems. This is perhaps the first instance in music of extended ostinato which is neither used for variation nor for accompaniment of melody. This work was developed in number theory, using the construction of the Gödel numbers.

The most famous passage, as noted above, is the eighth note ostinato of the strings accented by eight french horns that occurs in the section Auguries of Spring (Dances of the Young Girls). During this year he also developed the ideas of computability and recursive functions to the point where he delivered a lecture on general recursive functions and the concept of truth. The same ballet is also notable for its relentless use of ostinati. He delivered an address to the annual meeting of the American Mathematical Society. In the "Rite of Spring" he introduces additive permutations, that is, subtracting or adding a note to a motif without regard to changes in meter. In this year he took his first trip to the USA, during which he met Albert Einstein who would become a good friend. However, Stravinsky's use of motivic development was unique in the way he permutated his motifs. However after Schlick, whose seminar had aroused Gödel's interest in logic, was murdered by a National Socialist student, Gödel was much affected and had his first nervous breakdown.

The first great innovator in this method was Beethoven; the famous "fate motif" which opens Fifth Symphony and reappears throughout the work in surprising and refreshing permutations is a classic example. Hitler's rise to power in 1933, in Germany had little effect on Gödel's life in Vienna since he did not have much interest in politics. Motivic development, that is using a distinct musical phrase that is subsequently altered and developed throughout a piece of music, has its roots in the sonata form of Mozart's age. Gödel earned his Habilitation at the UV in 1932 and in 1933 he became a Privatdozent (unpaid lecturer) there. Stravinsky began re-thinking his use of the motif and ostinato as early as The Firebird ballet, but his use of these elements reached its full flowering in The Rite of Spring. He did this using a process known as Gödel numbering. As a consequence, his influence on composers both during his lifetime and after his death was, and remains, considerable. To make this precise, however, Gödel needed to solve several technical issues, such as encoding proofs and the very concept of provability within integer numbers.

Stravinsky's work embraced multiple compositional styles, revolutionised orchestration, spanned several genres, practically reinvented ballet form and incorporated multiple cultures, languages and literatures. That is, a formula which obtains in arithmetic, but which is not provable from any humanly constructible set of axioms for arithmetic. Indeed, these characteristics are what make Stravinsky's output so unique when compared with the work of contemporaneous serial composers. Thus there will always be at least one true but unprovable statement. The ballet is thus a sort of miniature encyclopedia of Stravinsky, containing many of the signatures to be found throughout his compositions, whether primitivist, neo-classic, or serial: rhythmic quirkiness and experimentation, harmonic ingenuity, and a deft ear for masterful orchestration. If it were provable it would be false, which contradicts the fact that provable statements are always true. Some numbers of Agon recollect the "white-note" tonality of the neo-classic period, while others (the Bransle Gay, e.g.) display his unique re-interpretation of serial method. Gödel essentially constructed a formula that claims that it is unprovable in a given formal system.

An important transitional work of this period in Stravinsky's work, was a return to the ballet: Agon, a work for twelve dancers written from 1954 to 1957. In hindsight, the basic idea of the incompleteness theorem is rather simple. He later began expanding his use of the technique in works often based on biblical texts, such as Threni (1958), A Sermon, a Narrative, and a Prayer (1961), and The Flood (1962). It also implies that not all mathematical questions are computable. Stravinsky first began to dabble in the twelve tone technique in smaller vocal works such as the Cantata (1952), Three Songs from Shakespeare (1953) and In Memoriam Dylan Thomas (1954), as if he were testing the system. These theorems ended a hundred years of attempts to establish a definitive set of axioms to put the whole of mathematics on an axiomatic basis such as in the Principia Mathematica and Hilbert's formalism. Regardless, the next fifteen years were spent writing the works in this style. In this article he proved that for any computable axiomatic system that is powerful enough to describe arithmetic on the natural numbers (e.g. the Peano axioms or ZFC) it holds that:.

No doubt, Stravinsky was aided in his understanding of, or even conversion to, the twelve tone method by his confidant and helper Robert Craft, who had long been advocating the change. In 1931 he published his famous incompleteness theorems in Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme. Only after the death of Arnold Schoenberg, the inventor of the twelve tone system, in 1951 did Stravinsky begin making use of the technique in his own works. He added a combinatorial version to his completeness result, which was published by the Vienna Academy of Sciences. After the opera's completion Stravinsky never wrote another "neo-classic" work and instead began writing the music that came to define his final stylistic change. In 1930 a doctorate in Philosophy was granted to Gödel. The music is direct but quirky; it borrows from classic tonal harmony but also interjects surprising dissonances; it features Stravinsky's trademark off-rhythms; and it harkens back to the operas and themes of Monteverdi, Gluck and Mozart. In this dissertation he established the completeness of the first-order predicate calculus (also known as Gödel's completeness theorem).

This opera, written to a libretto by Auden and based on the etchings of Hogarth, encapsulates everything that Stravinsky had perfected in the previous 20 years of his neo-classic period. In 1929 Gödel became an Austrian citizen and later that year he completed his doctoral dissertation under Hans Hahn's supervision. The pinnacle of this period is the opera The Rake's Progress completed in 1951. He started to publish papers on logic and attended a lecture by David Hilbert in Bologna on completeness and consistency of mathematical systems. Apollon, Persephone (1933) and Orpheus (1947) also mark Stravinsky's concern, during this period, of not only returning to "Classic" music but also returning to "Classic" themes: in these instances, the mythology of the ancient Greeks. While at UV Kurt met his future wife Adele Nimbursky (née Porkert). Some larger works from this period are the three symphonies: the Symphonie des Psaumes (Symphony of Psalms) (1930), Symphony in C (1940) and Symphony in Three Movements (1945). Kurt then studied number theory, but when he took part in a seminar run by Moritz Schlick which studied Bertrand Russell's book Introduction to mathematical philosophy he became interested in mathematical logic.

Other works such as Oedipus Rex (1927), Apollon Musagete (1928) and the Dumbarton Oaks concerto continue this trend. He read Kant's Metaphysische Anfangsgründe der Naturwissenschaft, and participated in the Vienna Circle with Moritz Schlick, Hans Hahn, and Rudolf Carnap. In these new works, written roughly between 1920 and 1950, Stravinsky turns largely to wind instruments, the piano, and choral and chamber works. During this time he adopted ideas of mathematical realism. This "neo-classical" style involved the abandonment of the large orchestras demanded by the ballets. Although initially intending to study theoretical physics he also attended courses on mathematics and philosophy. Both of these works feature what was to become a hallmark of this period; that is, Stravinsky's return, or "looking back", to the classical music of Mozart and Bach and their contemporaries. By that time he had already mastered university-level mathematics.

The next phase of Stravinsky's compositional style, slightly overlapping the first, is marked by two works: Pulcinella 1920 and the Octet (1923) for wind instruments. At the age of 18 Kurt joined his brother Rudolf in Vienna and entered the UV. Other pieces from this period include: Renard (1916), Histoire du soldat (A Soldier's Tale) (1918), and Les Noces (The Wedding) (1923). Already during his teens Kurt studied Gabelsberger shorthand, Goethe's Theory of Colours and criticisms of Isaac Newton, and the writings of Kant. There are several famous passages in the work, but two are of particular note: the opening theme played on a bassoon with notes at the very top of its register, almost out of range; and the thumping, off kilter eighth-note motif played by strings and accented by French horns on off-rhythms (See Le sacre du printemps (The Rite of Spring) for a more detailed account of this work). His interest in mathematics increased when in 1920 his older brother Rudolf (born 1902) left for Vienna to go to Medical School at the University of Vienna (UV). Here, the composer draws on the brutalism of pagan Russia, reflecting these sentiments in roughly-drawn, stinging motifs that appear throughout the work. Although Kurt had first excelled in languages he later became more interested in history and mathematics.

But it is the third ballet, The Rite of Spring, that is generally considered the apotheosis of Stravinsky's "Russian Period". He attended German-language primary and secondary school in Brno and completed them with honors in 1923. Petrushka, too, is distinctively scored and the first of Stravinsky's ballets to draw on folk mythology. In his German-speaking family young Kurt was known as Der Herr Warum (Mr Why). The first of the ballets, L'oiseau de feu, is notable for its unusual introduction (triplets in the low basses) and sweeping orchestration. Kurt Gödel was born April 28, 1906, in Brünn (now Brno), Moravia, Austria-Hungary (now the Czech Republic) to Rudolf Gödel, the manager of a textile factory, and Marianne Gödel (née Handschuh). The ballets have several shared characteristics: they are scored for extremely large orchestras; they use Russian folk themes and motifs; and they bear the mark of Rimsky-Korsakov's imaginative scoring and instrumentation. .

The first of Stravinsky's major stylistic periods (excluding some early minor works) was inaugurated by the three ballets he composed for Diaghilev. He published his most important result in 1931 at age of twenty-five when he worked at Vienna University, Austria. Most of his compositions can be placed in one of the three. Kurt Gödel was perhaps the greatest logician of the 20th century and one of the three greatest logicians of all time with Aristotle and Frege. Stravinsky's career largely falls into three distinct stylistic periods. Gödel made important contributions to proof theory; he clarified the connections between classical logic, intuitionistic logic and modal logic by defining translations between them. He has a Star on the Hollywood Walk of Fame at 6340 Hollywood Boulevard. He also produced celebrated work on the continuum hypothesis, showing that it cannot be disproven from the accepted set theory axioms, assuming that those axioms are consistent.

Stravinsky's life had encompassed most of the 20th Century, including many of its modern classical music styles, and he influenced composers both during and after his lifetime. To prove this theorem, Gödel developed a technique now known as Gödel numbering, which codes formal expressions into arithmetic. His grave is close to the tomb of his long-time collaborator Diaghilev. Gödel's most famous works were his incompleteness theorems, the most famous of which states that any self-consistent recursive axiomatic system powerful enough to describe integer arithmetic will allow for "true" propositions about integers that can not be proven from the axioms. He died in New York City on April 6, 1971 at the age of 88 and was buried in Venice on the cemetery island of San Michele. After World War II, at the age of 42, he obtained US citizenship. In 1962 he accepted an invitation to return to Russia for a series of concerts, but remained an émigré firmly based in the West. When Hitler annexed Austria, Gödel automatically became a German citizen at age 32.

At the end of his life he was even setting Hebrew scripture in Abraham and Isaac. He was born in Brünn in Moravia, Austria-Hungary (now Brno in the Czech Republic), became a Czechoslovak citizen at age 12 when the Austro-Hungarian empire was broken up, and an Austrian citizen at age 23. The texts and literary sources for his work began with a period of interest in Russian folklore, progressed to classical authors and the Latin liturgy, and moved on to contemporary France (André Gide, in Persephone) and eventually English literature: Auden, Eliot, and medieval English verse. Kurt Gödel [kurt gøːdl], (April 28, 1906 – January 14, 1978) was a logician, mathematician, and philosopher of mathematics. Stravinsky's taste in literature was wide and reflected his constant desire for new discoveries. (ISBN 0812694082). Craft lived with Stravinsky until his death, acting as interpreter, chronicler, assistant conductor and factotum for countless musical and social tasks. Gödel Meets Einstein: Time Travel in the Gödel Universe. Open Court.

Auden, the need to acquire more familiarity with the English-speaking world coincided with his meeting the conductor and musicologist Robert Craft. Yourgrau, Palle (1999). H. (ISBN 0465092934). When he planned to write an opera with W. A World Without Time: The Forgotten Legacy of Gödel and Einstein. Basic Books. For a time he preserved a ring of emigré Russian friends and contacts, but eventually realised that this would not sustain his intellectual and professional life in the USA. Yourgrau, Palle (2004).

Stravinsky had adapted to life in France, but moving to America aged 58 was a very different prospect. A logical journey: From Gödel to philosophy. Cambridge, MA: MIT Press. He continued to live in the United States until his death in 1971, unsuccessfully writing music for films. Wang, Hao (1996). He moved to the United States in 1939 and became a naturalized citizen in 1945. (ISBN 0-8147-5816-9). He returned to Paris in 1920 to write more ballets as well as many other works. Nagel, Ernst, & Newman, James R..Gödel's Proof. New York University Press.

However, because of World War I and the October Revolution in Russia he moved to Switzerland in 1914. Gödel, Escher, Bach (ISBN 0465026567). That ballet ended up being the famous L'Oiseau de Feu. Hofstadter, Douglas. He commissioned Stravinsky to write a ballet for his theater; so in 1911, Stravinsky traveled to Paris. (ISBN 0534575951). Eventually Stravinsky's music was noticed by Serge Diaghilev, the director of the Ballets Russes in Paris. On Gödel. Wadsworth.

At the same time he had a disregard of his social inferiors: Robert Craft was embarrassed by his habit of tapping a glass with a fork and loudly demanding attention in restaurants. Hintikka, Jaakko (2000). For example, Otto Klemperer, who knew Schoenberg well, said that he always found Stravinsky much more co-operative and easy to deal with. (ISBN 0393051692). Most people who knew him through dealings connected with performances spoke of him as polite, courteous and helpful. Norton & Company. Paris, Venice, Berlin, London and New York all hosted successful appearances as pianist and conductor. W.

Stravinsky proved adept at playing the part of "man of the world", acquiring a keen instinct for business matters and appearing relaxed and comfortable in many of the world's major cities. Incompleteness: The Proof and Paradox of Kurt Godel (Great Discoveries). W. The composer was also able to attract commissions: most of his work from The Firebird onwards was written for specific occasions and paid for generously. Goldstein, Rebecca (2005). In the early 1920s Leopold Stokowski was able to give Stravinsky regular support through a pseudonymous "benefactor". (ISBN 0738205184). Patronage too was never far away. Gödel: A life of logic. Perseus.

After her death Stravinsky and Vera were married in New York where they had gone from France to escape the war in 1940. Depauli-Schimanovich, Werner, & Casti, John L. Katerina soon learned of the relationship and accepted it as inevitable and permanent. (ISBN 1568810253). From then until the death of Katerina in 1939 Stravinsky led a deft double-life, spending some of his time with his first family and the rest with Vera. Logical dilemmas: The life and work of Kurt Gödel. A K Peters. When Stravinsky met Vera in the early 1920s she was married to the painter and stage designer Serge Sudeikin, but they soon began an affair which led to her leaving her husband. Dawson, John W.

Their marriage endured for 33 years, but the true love of his life, and partner until his death, was his second wife Vera de Bosset (1888-1982). (1940). He was still young when he married his cousin Katerina Nossenko, who he had known since early childhood, on 23 January 1906. The Consistency of the Axiom of Choice and of the Generalized Continuum Hypothesis with the Axioms of Set Theory. Princeton University Press, Princeton, NJ. Although a notorious philanderer (even rumoured to have affairs with high-class partners such as Coco Chanel) Stravinsky was also a family man who devoted considerable amounts of his time and expenditure to his sons and daughters. (Available in English at http://home.ddc.net/ygg/etext/godel/ ). Relatively short of stature and not conventionally handsome, Stravinsky was nevertheless photogenic, as many pictures show. 38 (1931).

Not only was he the principal composer for Sergei Diaghilev's Ballet Russes, but Stravinsky also collaborated with Pablo Picasso (Pulcinella, 1920), Jean Cocteau (Oedipus Rex, 1927) and George Balanchine (Apollon Musagete, 1928). Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme, Monatshefte für Mathematik und Physik, vol. This desire manifested itself in several of his Paris collaborations. If the system is consistent, then the consistency of the axioms cannot be proved within the system. Stravinsky displayed an inexhaustible desire to learn and explore art, literature, and life. (It is this theorem that is generally known as the incompleteness theorem.). (He succeeded: the 1913 première of Le sacre du printemps turned into a riot.). The system cannot be both consistent and complete.

As he himself said, with these premieres his intention was "[to send] them all to hell". The ballets trace his stylistic development: from the L'oiseau de feu, whose style draws largely on Rimsky-Korsakov, to Petrushka's emphasis on bitonality, and finally to the savage polyphonic dissonance of Le sacre du printemps. During his stay in the city, he composed three major works for the Ballets Russes—L'oiseau de feu, Petrushka (1911), and Le sacre du printemps (The Rite of Spring) (1913). Stravinsky left Russia for the first time in 1910, going to Paris to attend the premiere of his ballet L'oiseau de feu (The Firebird).

In 1902, at the age of 20, Stravinsky became the pupil of Nikolai Rimsky-Korsakov, probably the leading Russian composer of the time. Composition came later. Petersburg, Stravinsky originally studied to be a lawyer. Though his father was a bass singer at the Mariinsky Theater in St.

Petersburg and dominated by his father and elder brother, Stravinsky's early childhood was a mix of experience that hinted little at the cosmopolitan artist he was to become. Brought up in an apartment in St. Petersburg, Russia. Stravinsky was born in Oranienbaum (now Lomonosov), near St.

. He was named by Time magazine as one of the most influential people of the century. A quintessentially cosmopolitan Russian, Stravinsky was one of the most authoritative composers in 20th century music, both in the West and in his native land. Robert Craft transcribed several interviews with the composer, which were published as Conversations with Stravinsky.

In it, he famously claimed that music was incapable of "expressing anything but itself". With the help of Alexis Roland-Manuel, Stravinsky composed a theoretical work entitled Poetics of Music. He was also a writer. Stravinsky also achieved fame as a pianist and conductor, often at the premieres of his own works.

His oeuvre included everything from symphonies to piano miniatures. Stravinsky also wrote in a broad spectrum of ensemble combinations and classical forms. For some, these ballets practically reinvented the genre. He composed in the neo-classical and serialist styles, but he is best known for two works from his earlier, Russian period: Le sacre du printemps (The Rite of Spring) and L'oiseau de feu (The Firebird).

Igor Fyodorovitch Stravinsky (Russian: Игорь Фёдорович Стравинский) (June 17, 1882 – April 6, 1971) was a Russian-American composer of modern classical music. Milan Kundera, Testaments Betrayed: An Essay in Nine Parts, ISBN 0060927518. The composer and his works, ISBN 0571049230. Eric Walter White, Stravinsky.

Ghostwritten by Walter Nouvel. Igor Stravinsky, An Autobiography, ISBN 0393318567. Igor Stravinsky and Robert Craft, Conversations with Stravinsky, ISBN 0520040406 . Ghostwritten by Alexis Roland-Manuel.

Igor Stravinsky, Poetics of Music, ISBN 674678559. ISBN 0295785799. Seattle: University of Washington Press. Lexicon of Musical Invective: Critical Assaults on Composers Since Beethoven's Time.

Slonimsky, Nicolas (1953). Stravinsky: Chronicle of a Friendship, Vanderbilt University Press, 1997. Robert Craft. Stravinsky: Glimpses of a Life, St Martins Press, 1993.

Robert Craft. New York: Charles Scribner's Sons. Music Ho! A Study of Music in Decline, p.94–94 and 101–105. Lambert, Constant (1936).

Category:Compositions by Igor Stravinsky. The Owl and the Pussy Cat for soprano and piano (1966). Elegy for J.F.K. for baritone and three clarinets (1964). In Memoriam Dylan Thomas (Dirge Canons and Song) (1954).

Four Russian Songs for mezzo-soprano, flute, harp and guitar (1954, versions from Quatre chants russes and Three Tales for Children). Three Songs from William Shakespeare for mezzo-soprano, flute, clarinet, and viola (1953). Petit ramusianum harmonique single voice or voices (1938). Quatre chants russes Quatre chants russes for voice and piano (1918/1919).

Berceuse for voice and piano (1918). Four Russian Peasant Songs for female voice unaccompanied (1917). Three Tales for Children for voice and piano (1917). Berceuses du Chat for contralto and three clarinets (1916).

Pribaoutki for voice, flute, oboe, clarinet, bassoon, vln, vla, vc, double bass (1914). Trois petites chansons voice and piano (or small orchestra) (1913/1930). Trois poésies de la lyrique japonaise for voice and piano or chamber orchestra (1913). Balmont for voice and piano or small orchestra (1911/1954).

Two Poems of K. Deux poèmes de Paul Verlaine for bariton and piano or orchestra Op.9 (1910/1951). Two Melodies for mezzo-soprano and piano Op.6 (1908). Pastorale wordless soprano and piano (1907).

2 (1907). Faun and Shepherdess for mezzo-soprano and orchestra Op. Romance for Voice and Piano (1902). The Flood (1962).

The Rake's Progress (1951). Babel (1944). Oedipus Rex (1927). Les Noces (The Wedding) (1923).

Mavra (1922). Histoire du soldat (A Soldier's Tale) (1918). Burleske for 4 Pantomimes and Chamber Orchestra (1916). Le rossignol (The Nightingale) (1914).

Requiem Canticles (1966). Introitus (1965). Abraham and Isaac (1963). A Sermon, a Narrative and a Prayer (1961).

Threni (1958). Canticum Sacrum (1955). Cantata for soprano, tenor, female voices, 2 flutes, oboe, English horn, cello (1953-1954). Mass (1948).

Symphonie des Psaumes (Symphony of Psalms) for chorus and orchestra (1930). Pater Noster (1926). Le roi des étoiles (The King of the Stars) for Men's Choir and Orchestra (1912). Fanfare for a New Theatre for two trumpets (1964).

Monumentum Pro Gesualdo Di Venosa (arrangement) for chamber ensemble (1960). Double Canon for string quartet 'Raoul Dufy in Memoriam' (1959). Epitaphium for flute, clarinet and harp (1959). Septet (1953).

Elegy for solo viola (1944). Suite Italienne (from Pulcinella) for violin or cello and piano (1933/34). Pastorale for violin and piano (1933). Duo Concertant for violin and piano (1932).

Octet for wind instruments (1923). Concertino for string quartet (1920). Three Pieces for Clarinet (1919). Suite from Histoire du Soldat for violin, clarinet and piano (1919).

Duet for two bassoons (1918). Canon for two horns (1917). Pour Pablo Picasso, Piece for clarinet (1917). Three Pieces for string quartet (1914).

Two Sketches for a Sonata for piano (1967). Sonata for Two Pianos (1943). Tango for piano (1940). Concerto for Two Pianos (1935).

Serenade for piano (1925). Sonata for piano (1924). Les Cinq Doigts for piano (1921). Chorale for piano (1920).

Piano Rag Music for piano (1919). Valse pour les Enfants for piano (1917). Cinq piéces faciles for two pianos (1917). Souvenir d'une Marche Boche for piano (1915).

Trois piéces faciles for two pianos (1915). Valse des fleurs for two pianos (1914). Le Sacre du Printemps for two pianos (1913). Quatre Etudes for piano Op.7 (1908).

Sonata in F-Sharp Minor for piano (1904). Scherzo for piano (1902). Tarantella for piano (1898). Variations (Aldous Huxley in Memoriam) for orchestra (1963–1964).

8 Instrumental miniatures for 15 Players (1963, orchestration of Les Cinq Doigts). Movements for Piano and Orchestra (1958–[[1959]). Greeting Prelude for orchestra (1955). Tango for chamber orchestra (1940/1953).

Concerto in D for string orchestra (1946). Ebony Concerto for clarinet and jazz band (1945). Symphony in Three Movements (1945). Scherzo a la Russe for orchestra (1944).

Ode for orchestra (1943). Four Norwegian Moods for orchestra (1942). Danses Concertantes for chamber orchestra (1942). Circus Polka for orchestra (1942).

Symphony in C (1940). Concerto in E-flat (Dumbarton Oaks) for Chamber Orchestra (1938). Preludium for jazz band (1937). Divertimento for orchestra (Suite from Le Baiser du Fee, 1934).

Concerto in D for violin and orchestra (1931). Capriccio for Piano and Orchestra (1929). Concerto for Piano and Wind Instruments (1925). Suite No.1 for chamber orchestra (1925).

Suite No.2 for chamber orchestra (1921). Suite from Pulcinella for orchestra (1920). Symphonies of Wind Instruments (1920). Quatre études for orchestra (1918).

Le chant du rossignol (Song of the Nightingale) (1917). Feu d'artifice (Fireworks) (1908). Scherzo fantastique (1908). Symphony in E-Flat Major (1907).

Agon for chamber orchestra (1957). Orpheus for chamber orchestra (1947). Jeu de cartes for orchestra (1936). Perséphone for speaker, soloists, chorus and orchestra (1933).

Le baiser de la fée (The Fairy's Kiss) for orchestra (1928). Apollon Musagète for string orchestra (1928). Pulcinella for chamber orchestra and soloists (1920). Renard (1916).

Le sacre du printemps (The Rite of Spring) for orchestra (1913). Petrushka for orchestra (1911). L'oiseau de feu (The Firebird) for orchestra (1910).

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