Ausmultiplikation (literally, "multiplying-out") is a German term used by the composer Karlheinz Stockhausen to describe a technique in which a long note is replaced by shorter "melodic configurations, internally animated around central tones", resembling the ornamental technique of divisions (also called "diminutions") in Renaissance music. Stockhausen first described this technique in connection with his "opus 1", Kontra-Punkte , composed in 1952–53,but in his later formula composition there is a related method of substituting a complete or partial formula for a single very long tone in a much slower, "more background" projection of the formula. When this is done at more than one level, the result is reminiscent of a fractal.
Karlheinz Stockhausen was a German composer, widely acknowledged by critics as one of the most important but also controversial composers of the 20th and early 21st centuries. He is known for his groundbreaking work in electronic music, for introducing controlled chance into serial composition, and for musical spatialization.
Inori, for one or two soloists with orchestra, is a composition by Karlheinz Stockhausen, written in 1973–74.
Kreuzspiel is a composition by Karlheinz Stockhausen written for oboe, bass clarinet, piano and four percussionists in 1951. It is assigned the number 1/7 in the composer's catalogue of works.
Licht (Light), subtitled "Die sieben Tage der Woche", is a cycle of seven operas composed by Karlheinz Stockhausen between 1977 and 2003. The composer described the work as an "eternal spiral" because "there is neither end nor beginning to the week." Licht consists of 29 hours of music.
Formula composition is a serially derived technique encountered principally in the music of Karlheinz Stockhausen, involving the projection, expansion, and Ausmultiplikation of either a single melody-formula, or a two- or three-voice contrapuntal construction.
Momente (Moments) is a work by the German composer Karlheinz Stockhausen, written between 1962 and 1969, scored for solo soprano, four mixed choirs, and thirteen instrumentalists. A "cantata with radiophonic and theatrical overtones", it is described by the composer as "practically an opera of Mother Earth surrounded by her chicks". It was Stockhausen's first piece composed on principles of modular transposability, and his first musical form to be determined from categories of sensation or perception rather than by numerical units of musical terminology, which marks a significant change in the composer's musical approach from the abstract forms of the 1950s.
Gruppen for three orchestras (1955–57) is amongst the best-known compositions of German composer Karlheinz Stockhausen, and is Work Number 6 in the composer's catalog of works. Gruppen is "a landmark in 20th-century music. .. probably the first work of the post-war generation of composers in which technique and imagination combine on the highest level to produce an undisputable masterpiece".
Kontakte ("Contacts") is an electronic music work by Karlheinz Stockhausen, realized in 1958–60 at the Westdeutscher Rundfunk (WDR) electronic-music studio in Cologne with the assistance of Gottfried Michael Koenig. The score is Nr. 12 in the composer's catalogue of works, and is dedicated to Otto Tomek.
The Klavierstücke constitute a series of nineteen compositions by German composer Karlheinz Stockhausen.
Montag aus Licht is an opera by Karlheinz Stockhausen in a greeting, three acts, and a farewell, and was the third of seven to be composed for the opera cycle Licht: die sieben Tage der Woche. The libretto was written by the composer.
Samstag aus Licht is an opera by Karlheinz Stockhausen in a greeting and four scenes, and was the second of seven to be composed for the opera cycle Licht: die sieben Tage der Woche. It was written between 1981 and 1983, to a libretto written by the composer and incorporating a text by Saint Francis of Assisi, and was first staged in Milan in 1984.
Dienstag aus Licht is an opera by Karlheinz Stockhausen in a greeting and two acts, with a farewell, and was the fourth of seven to be completed for the opera cycle Licht: Die sieben Tage der Woche. It was begun in 1977 and completed from 1988 to 1991, to a libretto by the composer.
Zeitmaße is a chamber-music work for five woodwinds composed in 1955–1956 by German composer Karlheinz Stockhausen; it is Number 5 in the composer's catalog. It is the first of three wind quintets written by Stockhausen, followed by Adieu für Wolfgang Sebastian Meyer (1966) and the Rotary Wind Quintet (1997), but is scored with cor anglais instead of the usual French horn of the standard quintet. Its title refers to the different ways that musical time is treated in the composition.
Mixtur, for orchestra, 4 sine-wave generators, and 4 ring modulators, is an orchestral composition by the German composer Karlheinz Stockhausen, written in 1964, and is Nr. 16 in his catalogue of works. It exists in three versions: the original version for full orchestra, a reduced scoring made in 1967, and a re-notated version of the reduced scoring, made in 2003 and titled Mixtur 2003, Nr. 162⁄3.
Prozession (Procession), for tamtam, viola, electronium, piano, microphones, filters, and potentiometers, is a composition by Karlheinz Stockhausen, written in 1967. It is Number 23 in the catalogue of the composer’s works.
Pole (Poles), for two performers with shortwave radio receivers and a sound projectionist, is a composition by Karlheinz Stockhausen, written in 1970. It is Number 30 in the catalogue of the composer's works.
Unsichtbare Chöre is an eight-channel electronic-music composition by Karlheinz Stockhausen. A component part of the opera Donnerstag aus Licht, it may also be performed as an independent composition, in which form it is designated "ex 49" in the composer's catalog of works.
Expo, for three performers with shortwave radio receivers and a sound projectionist, is a composition by Karlheinz Stockhausen, written in 1969–70. It is Number 31 in the catalogue of the composer's works.
Ylem is a composition by Karlheinz Stockhausen for a variable ensemble of 19 or more players, and is given the work number 37 in his catalogue of compositions.
Sternklang, is "park music for five groups" composed in 1971 by Karlheinz Stockhausen, and bears the work number 34 in his catalogue of compositions. The score is dedicated to Mary Bauermeister, and a performance of the work lasts from two-and-a-half to three hours.