Formula composition

Formula composition is a serially derived technique encountered principally in the music of , involving the projection, expansion, and Ausmultiplikation of either a single melody-formula, or a two- or three-voice contrapuntal construction (sometimes stated at the outset).

In contrast to serial music, where the structuring features are more or less abstract and remain largely inaccessible to the listener's ear, in formula composition the musical specifications of pitch, dynamics, duration, timbre, and tempo are always directly evident in the sound, through the use of a concisely articulated melodic tone succession, the formula, which defines the large-scale form as well as all the internal musical details of the composition (Blumröder 1982, 184–85).

Though foreshadowed in Stockhausen's once-withdrawn ("Formula") of 1951, the technique made its first appearance in in 1970, and became the central focus of Stockhausen's music up to 2003. Stockhausen's mammoth opera cycle Licht is based on a three-strand "super-formula".

Hermann Conen (1991, 57) identifies two kinds of formula composition in Stockhausen’s works prior to Licht:

formula compositions in which the form results from projection of the formula, . . . [and] works in which melodies in themselves possess many internal characteristics of formulas, but where the formal idea itself does not originate from the formula(s) used in their realisation

Works of the first type include Mantra (1970), Inori (1973–74), Jubiläum (1977), and In Freundschaft (1977); works of the second type comprise Alphabet für Liège (1972), the “Laub und Regen” duet from Herbstmusik (1974), Musik im Bauch (1975), Harlekin (1975), Der kleine Harlekin (1975), and (1975–77). Other works from the 1970s, such as Sternklang (1971), (1971), (1972), the first three parts of Herbstmusik, Atmen gibt das Leben (1974/76–77), (1974–75), and (1976) do not employ formula technique, according to Conen, though the composer includes Atmen gibt das Leben amongst the works composed using "formula complexes" ().

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