Prime, retrograde, inverse, and retrograde-inverse permutations.
The Second Viennese School (German: Zweite Wiener Schule, Neue Wiener Schule) is the group of composers that comprised Arnold Schoenberg and his pupils and close associates in early 20th century Vienna, where he lived and taught, sporadically, between 1903 and 1925. Their music was initially characterized by late-Romantic expanded tonality and later, following Schoenberg's own evolution, a totally chromatic expressionism without firm tonal centre (often referred to as atonality) and later still, Schoenberg's serialtwelve-tone technique. Though this common development took place, it neither followed a common time-line nor a cooperative path. Likewise, it was not a direct result of Schoenberg's teaching—which (as his various published textbooks demonstrate) was highly traditional and conservative. Schoenberg's textbooks also reveal that the Second Viennese School spawned not from the development of his serial method, but rather from the influence of his creative example.
Though the school included highly distinct musical personalities (the styles of Berg and Webern are in fact very different from each other, and from Schoenberg—for example, only the works of Webern conform to the rule stated by Schoenberg that only a single row be used throughout all movements of a composition—while Gerhard and Skalkottas were closely involved with the folk music of their respective countries) the impression of cohesiveness was enhanced by the literary efforts of some of its members. Wellesz wrote the first book on Schoenberg, who was also the subject of several Festschriften put together by his friends and pupils; Rufer and Spinner both wrote books on the technique of twelve-tone composition; and Leibowitz's influential study of Schoenberg, Berg and Webern, Schoenberg et son école, helped to establish the image of a school in the period immediately after World War II in France and abroad. Several of those mentioned (e.g. Jalowetz, Rufer) were also influential as teachers, and others (e.g. Kolisch, Rankl, Stein, Steuermann, Zillig) as performers, in disseminating the ideals, ideas and approved repertoire of the group. Perhaps the culmination of the school took place at Darmstadt almost immediately after WWII, at the Internationale Ferienkurse für Neue Musik, wherein Schoenberg—who was invited but too ill to travel—was ultimately usurped in musical ideology by the music of his pupil, Webern, as composers and performers from the Second Viennese School (e.g. Leibowitz, Rufer, Adorno, Kolisch, Heiss, Stadlen, Stuckenschmidt, Scherchen) converged with the new serialists (e.g. Boulez, Stockhausen, Maderna, Nono, et al.).
German musical literature refers to the grouping as the "Wiener Schule" or "Neue Wiener Schule". The existence of a "First Viennese School" is debatable. The term is often assumed to connote the great Vienna-based masters of the Classical style working in the late 18th and early 19th century, particularly Joseph Haydn, Wolfgang Amadeus Mozart, Ludwig van Beethoven and Franz Schubert. Though Mozart and Schubert did not study with Haydn, Mozart and Haydn were admirers of each other's work and evidence suggests that the two composers fed off the other's compositional craftsmanship. Beethoven, however, did for a time receive lessons from the older master, though he was not a pupil in the sense that Berg and Webern were pupils of Schoenberg.
^Rudolf Stephan, "Wiener Schule", Die Musik in Geschichte und Gegenwart: allgemeine Enzyklopädie der Musik, second, revised edition, edited by Ludwig Finscher, 26 volumes in two parts, (Kassel, Basel, London, [etc.]: Bärenreiter-Verlag; Stuttgart and Weimar: J. B. Metzler, 1998): Part 1 (Sachteil), vol. 9 (Sy–Z): cols. 2034–45. ISBN 9783761811283 (Bärenreiter); ISBN 9783476410252 (Metzler). citation from cols. 2035–36.
^Perle, George. Serial Composition and Atonality: An Introduction to the Music of Schoenberg, Berg, and Webern, p.2n3. Fourth Edition. 1977. Berkeley, Los Angeles, and London: University of California Press. ISBN 0-520-03395-7
René Leibowitz, Schoenberg et son école (Paris, Editeur J B Janin, 1947) translated by Dika Newlin as Schoenberg and His School: The Contemporary Stage of the Language of Music (New York, Philosophical Library, 1949)