Karlheinz Stockhausen
Theories

In the 1950s and early 1960s, Stockhausen published a series of articles that established his importance in the area of music theory. Although these include analyses of music by Mozart, Debussy, Bartók, Stravinsky, Goeyvaerts, Boulez, Nono, Johannes Fritsch, Michael von Biel, and, especially, Webern, the items on compositional theory directly related to his own work are regarded as the most important generally. "Indeed, the Texte come closer than anything else currently available to providing a general compositional theory for the postwar period". His most celebrated article is "... wie die Zeit vergeht..." ("... How Time Passes..."), first published in the third volume of Die Reihe (1957). In it, he expounds a number of temporal conceptions underlying his instrumental compositions Zeitmaße, Gruppen, and Klavierstück XI. In particular, this article develops (1) a scale of twelve tempos analogous to the chromatic pitch scale, (2) a technique of building progressively smaller, integral subdivisions over a basic (fundamental) duration, analogous to the overtone series, (3) musical application of the concept of the partial field (time fields and field sizes) in both successive and simultaneous proportions, (4) methods of projecting large-scale form from a series of proportions, (5) the concept of "statistical" composition, (6) the concept of "action duration" and the associated "variable form", and (7) the notion of the "directionless temporal field" and with it, "polyvalent form".

Other important articles from this period include "Elektronische und Instrumentale Musik" ("Electronic and Instrumental Music", 1958), "Musik im Raum" ("Music in Space", 1958), "Musik und Graphik" ("Music and Graphics", 1959), " Momentform " (1960), "Die Einheit der musikalischen Zeit" ("The Unity of Musical Time", 1961), and "Erfindung und Entdeckung" ("Invention and Discovery", 1961), the last summing up the ideas developed up to 1961. Taken together, these temporal theories

suggested that the entire compositional structure could be conceived as " timbre ": since "the different experienced components such as colour, harmony and melody, meter and rhythm, dynamics, and form correspond to the different segmental ranges of this unified time", the total musical result at any given compositional level is simply the " spectrum " of a more basic duration—i.e., its "timbre", perceived as the overall effect of the overtone structure of that duration, now taken to include not only the "rhythmic" subdivisions of the duration but also their relative "dynamic" strength, "envelope", etc.

Compositionally considered, this produced a change of focus from the individual tone to a whole complex of tones related to one another by virtue of their relation to a " fundamental "—a change that was probably the most important compositional development of the latter part of the 1950s, not only for Stockhausen's music but for "advanced" music in general.

Some of these ideas, considered from a purely theoretical point of view (divorced from their context as explanations of particular compositions) drew significant critical fire. For this reason, Stockhausen ceased publishing such articles for a number of years, as he felt that "many useless polemics" about these texts had arisen, and he preferred to concentrate his attention on composing.

Through the 1960s, although he taught and lectured publicly, Stockhausen published little of an analytical or theoretical nature. Only in 1970 did he again begin publishing theoretical articles, with "Kriterien", the abstract for his six seminar lectures for the Darmstädter Ferienkurse. The seminars themselves, covering seven topics ("Micro- and Macro-Continuum", "Collage and Metacollage", "Expansion of the Scale of Tempos", "Feedback", "Spectral Harmony—Formant Modulation", "Expansion of Dynamics—A Principle of Mikrophonie I ", and "Space Music—Spatial Forming and Notation") were published only posthumously.

His collected writings were published in Texte zur Musik, including his compositional theories and analyses on music as a general phenomenon.
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