Arnold Schoenberg
In Schoenberg's Variations for Orchestra, Op. 31 tone row form P1's second half has the same notes, in a different order, as the first half of I10: "Thus it is possible to employ P1 and I10 simultaneously and in parallel motion without causing note doubling" (Leeuw 2005, 154–55).  Play (help·info) Featuring hexachordal combinatoriality between its primary forms, P1 and I6, Schoenberg's Piano Piece, Op. 33a tone row  Play (help·info) contains three perfect fifths, which is the relation between P1 and I6, and a source of contrast between, "accumulations of 5ths", and, "generally more complex simultaneity" (Leeuw 2005, 155–57). For example group A consists of B♭-F-C-B♮ while the, "more blended", group B consists of A-F♯-C♯-D♯ Schoenberg's significant compositions in the repertory of modern art music extend over a period of more than 50 years. Traditionally they are divided into three periods though this division is arguably arbitrary as the music in each of these periods is considerably varied. The idea that his twelve-tone period "represents a stylistically unified body of works is simply not supported by the musical evidence" (Haimo 1990, 4), and important musical characteristics—especially those related to motivic development—transcend these boundaries completely. The first of these periods, 1894–1907, is identified in the legacy of the high-Romantic composers of the late nineteenth century, as well as with "expressionist" movements in poetry and art. The second, 1908–1922, is typified by the abandonment of key centers, a move often described (though not by Schoenberg) as "free atonality". The third, from 1923 onward, commences with Schoenberg's invention of dodecaphonic, or "twelve-tone" compositional method. Schoenberg's most well-known students Hanns Eisler, Alban Berg, and Anton Webern, followed Schoenberg faithfully through each of these intellectual and aesthetic transitions, though not without considerable experimentation and variety of approach. First period: Late Romanticism[edit] Beginning with songs and string quartets written around the turn of the century, Schoenberg's concerns as a composer positioned him uniquely among his peers, in that his procedures exhibited characteristics of both Brahms and Wagner, who for most contemporary listeners, were considered polar opposites, representing mutually exclusive directions in the legacy of German music. Schoenberg's Six Songs, Op. 3 (1899–1903), for example, exhibit a conservative clarity of tonal organization typical of Brahms and Mahler, reflecting an interest in balanced phrases and an undisturbed hierarchy of key relationships. However, the songs also explore unusually bold incidental chromaticism, and seem to aspire to a Wagnerian "representational" approach to motivic identity. The synthesis of these approaches reaches an apex in his Verklärte Nacht, Op. 4 (1899), a programmatic work for string sextet that develops several distinctive "leitmotif"-like themes, each one eclipsing and subordinating the last. The only motivic elements that persist throughout the work are those that are perpetually dissolved, varied, and re-combined, in a technique, identified primarily in Brahms's music, that Schoenberg called "developing variation". Schoenberg's procedures in the work are organized in two ways simultaneously; at once suggesting a Wagnerian narrative of motivic ideas, as well as a Brahmsian approach to motivic development and tonal cohesion. Second period: Free atonality[edit] Schoenberg's music from 1908 onward experiments in a variety of ways with the absence of traditional keys or tonal centers. His first explicitly atonal piece was the second string quartet, Op. 10, with soprano. The last movement of this piece has no key signature, marking Schoenberg's formal divorce from diatonic harmonies. Other important works of the era include his song cycle Das Buch der Hängenden Gärten, Op. 15 (1908–1909), his Five Orchestral Pieces, Op. 16 (1909), the disturbing Pierrot Lunaire, Op. 21 (1912), as well as his dramatic Erwartung, Op. 17 (1909). The urgency of musical constructions lacking in tonal centers, or traditional dissonance-consonance relationships, however, can be traced as far back as his Chamber Symphony No. 1, Op. 9 (1906), a work remarkable for its tonal development of whole-tone and quartal harmony, and its initiation of dynamic and unusual ensemble relationships, involving dramatic interruption and unpredictable instrumental allegiances; many of these features would typify the timbre-oriented chamber music aesthetic of the coming century. Third period: Twelve-tone and tonal works[edit] In the early 1920s he worked at evolving a means of order which would enable his musical texture to become simpler and clearer, and this resulted in the "method of composing with twelve tones which are related only with one another" (Schoenberg 1984, 218), in which the twelve pitches of the octave (unrealized compositionally) are regarded