The Darmstadt School is less a stylistic label than the name of a network. Its centre is the Internationale Ferienkurse für Neue Musik, an annual two-week summer course held in Darmstadt, Germany, since 1946. In its formative period (1949-58) it was where the postwar generation of European composers met, exchanged ideas, and premièred each other's work. The initial phase, 1951 to about 1958, produced total serialism — extending Schoenberg's row-based organisation from pitch to duration, dynamics, and timbre. Stockhausen's Kreuzspiel (1951), Boulez's Polyphonie X (1951) and Structures I (1952), and Nono's Variazioni canoniche (1950) established the technique; Boulez's Le Marteau sans maître (1955), Nono's Il canto sospeso (1956), and Stockhausen's Gruppen (1957) marked its peak. John Cage's 1958 Darmstadt lecture then reoriented the school toward chance, indeterminacy, and open form (Stockhausen's Klavierstück XI, Boulez's Piano Sonata No. 3). Electronic music developed in parallel at the WDR studio in Cologne (Stockhausen, from 1953) and Studio di fonologia in Milan (Berio and Maderna, from 1955), both institutionally part of the Darmstadt network. From 1968 a political turn — Nono's Como una ola de fuerza y luz (1972) — and from the 1970s further branching (Lachenmann's musique concrète instrumentale, Rihm's Neue Einfachheit, Ferneyhough's New Complexity) fanned the school out.

The Ferienkurse was set up by the musicologist Wolfgang Steinecke (1910-61) in 1946, as part of the American occupation's Umerziehung (re-education) programme aimed at recovering the modernist repertoire the Nazis had suppressed. In 1949 René Leibowitz — a French conductor and composer, and Schoenberg's disciple — gave lectures on the twelve-tone technique that lit the fuse. The 25-year-old Nono, 29-year-old Maderna, 24-year-old Boulez and 21-year-old Stockhausen were in the audience. Within two years they had extended Schoenberg's method into total serialism. In 1952, Nono married Nuria Schoenberg, Arnold's daughter, physically linking the Second Viennese School to what was becoming its Darmstadt continuation. Cage arrived in 1958. Political radicalisation followed the 1968 unrest, especially in Nono's work. The Ferienkurse continues to this day (as of 2024, in its 78th year).

First, the density of total serialism. In Boulez's Le Marteau sans maître (1955) or Stockhausen's Gruppen for three orchestras (1957), the pulse is not shared: different sections move at independent tempi, producing time that does not flow uniformly. Second, the electronic-music time-sense. In Stockhausen's Gesang der Jünglinge (1956), boys' voices on tape blend with electronic tones in five-channel space; continuous timbral transformation, impossible for acoustic instruments, becomes the compositional subject. Third, notation for chance. Stockhausen's Klavierstück XI (1956) is a single large sheet of nineteen fragments; the pianist's gaze picks the order. Each performance is a different length. Fourth, political music. Nono's Il canto sospeso (1956, on the letters of executed anti-Nazi resistance fighters) and Como una ola de fuerza y luz (1972, elegy for the Chilean militant Luciano Cruz) show that at least one branch of the Darmstadt project was inseparable from left-wing political commitment.

Start with Boulez's Le Marteau sans maître (1955) — the total-serialism peak. Boulez conducting Ensemble intercontemporain (1985, Deutsche Grammophon) is the reference. Then Stockhausen's Gruppen (1957, three-orchestra piece) in the Rattle / Berlin Philharmonic recording. For depth: Nono's Il canto sospeso (1956), Berio's Sinfonia (1968-69, Boulez / New York Philharmonic première recording), Cage's Concert for Piano and Orchestra (1958), Lachenmann's Pression (1969). On the Japanese side, Yuasa Jōji's Interpenetration (1963) and Takemitsu's Textures (1968).

In 1952 Nono, then 28, married Nuria Schoenberg (1932-2016), the composer's daughter, in Los Angeles. Schoenberg had died the previous year and did not see it. Through the marriage the Second Viennese School and the Darmstadt School became literally family-connected; Nuria later ran the Schoenberg Estate and managed her father's manuscripts. Second: Cage's 1958 Darmstadt lecture was a shock to a whole generation. Stockhausen and Boulez, then the standard-bearers of European serial rigour, were shaken by his advocacy of chance. Stockhausen absorbed it within a few years; Boulez resisted longer and only partially accepted it (Third Piano Sonata, 1957, deliberately left incomplete). The divergence produced the two main branches of postwar European composition. Third: when Takemitsu attended Darmstadt in 1968, he is said to have remarked that Japanese composers already had a route into Cage — via Toshi Ichiyanagi, who had studied directly with Cage in New York from 1954 to 1961 and premiered Cage's Piano Concerto in Tokyo under Ozawa in 1961. The Japanese line into postwar avant-garde thus ran through New York as much as through Darmstadt.