Plus-Minus, 2 × 7 pages for realisation, is a composition for one or several performers by Karlheinz Stockhausen, first written in 1963 and redrafted in 1974. It is Nr. 14 in the composer's catalogue of works, and has a variable performing length that depends on the version worked out from the given materials. The score is dedicated to Mary Bauermeister.
Plus-Minus is a "polyvalent process composition" ( Kurtz 1992 , 133), designed as a project for the composition students attending the first Cologne Courses for New Music, held at the Rheinische Musikhochschule in October to December 1963. In it, various compositional premises of Stockhausen's are presented in such a way as to enable the most radically different concrete results ( Frisius 2008 , 149).
Plus-Minus was composed in September 1963 while Stockhausen was in Siculiana, preparing for what proved to be an aborted performance of Momente at the Palermo Festival (Bauermeister 2011 , 129–30; Kurtz 1992 , 128):
In 1963 I spent a couple of weeks in Sicily by the seashore, and as I couldn't take a lot of paper with me I tried to hide in the shadow of a rock and think clearly about a new piece, and Plus-Minus is what emerged. (I'd discussed all the possible transformations of the seven 'musical types' that occur in the score with Mary [Bauermeister], and we drew them in the sand together. ( Cott 1973 , 153)
The piece represents an extreme instance of the new, open type of composition Stockhausen was developing at the time, and evolved from a number of conversations with Mary Bauermeister in Siculiana and Palermo (Bauermeister 2011 , 130; Kurtz 1992 , 128). Stockhausen's intention was to enable a music that reproduces itself, within a strict framework. Twenty-five different versions were made by the students in 1963, for a wide variety of forces: one for four harps, one for three harps and two pianos, one for recorders and children's choir, one for large orchestra, one for percussion and piano, one for two percussionists, and another for choir and chamber orchestra (Cott 1973 , 153, 158; Stockhausen 1971 , 42).
The first public performance was given in Rome in June 1964 by Cornelius Cardew and Frederic Rzewski, each of whom realised one page of the score ( Fox 2000 , 19). When Stockhausen heard a tape of this performance, he was astonished that sounds he had usually avoided were being employed, exactly according to the score's specifications, to achieve a highly poetic quality ( Stockhausen 1971 , 42–43).
The course of the work is based on polarities of attraction and repulsion, of growth and decay. Material is systematically accumulated and eroded, in a process resembling a game of chess, where central and secondary notes either expand and proliferate, or are reduced until they disappear ( Maconie 2005 , 250–51). These oppositions include, for example, the confrontation of materials having definite pitch with others of indeterminate pitch. The score systematically catalogues its materials into ( Frisius 2008 , 149–50):
There are seven so-called "symbol pages", on which all musical events are represented by ideograms, and a second set of "note pages" on which the pitch material for the events is notated. One or several layers of events can be worked out from these fourteen pages, and be combined according to particular rules ( Stockhausen 1971 , 40). The note material is all derived from the prime and inverted forms of the following twelve-tone row ( Harvey 1975 , 93):
The types wax or wane according to the prescribed plus and minus processes, up to a maximum value of +13, which can result in very long sounds. If a process of diminution continues after reaching a value of 0, the events become represented by a "negative band of sound"—a "sound wall" of noise, such as breathing or radio noise, out of which silent events are cut until a value of –13 is reached, which is total silence. At that point, the event-type in question "dies" and may not be used again in the piece ( Cott 1973 , 152–13).
The score of Plus-Minus is complicated, delivering the message that composing serial music is hard work ( Maconie 2005 , 251). The openness of the score was itself seen at the end of the 20th century as a form of control, deterring all but the most committed musicians from undertaking performances. Nevertheless, anyone making a realisation does have considerable control over the nature of the piece, and "negative-minded realisers can kill the piece, the over-positive can encourage disproportionate growth" ( Fox 2000 , 18–19). At the first Cologne Courses, a student composer from Iceland, Atli Heimir Sveinsson, "assassinated" Plus-Minus by deliberately discovering the quickest way to end the piece. According to Stockhausen, "There were just a few blips and blobs and then lots of silences … that was it" ( Cott 1973 , 158).
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. A critic calls him "one of the great visionaries of 20th-century music". He is known for his groundbreaking work in electronic music, for introducing controlled chance into serial composition, and for musical spatialization.
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.
Zyklus für einen Schlagzeuger is a composition by Karlheinz Stockhausen, assigned Number 9 in the composer's catalog of works. It was composed in 1959 at the request of Wolfgang Steinecke as a test piece for a percussion competition at the Darmstadt Summer Courses, where it was premièred on 25 August 1959 by Christoph Caskel. It quickly became the most frequently played solo percussion work, and "inspired a wave of writing for percussion".
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.
Trans is a composition for orchestra and tape by the German composer Karlheinz Stockhausen, written in 1971. It is Number 35 in the composer's catalog of works.
Originale, musical theatre with Kontakte, is a music theatre work by the German composer Karlheinz Stockhausen, written in collaboration with the artist Mary Bauermeister. It was first performed in 1961 in Cologne, and is given the work number 12⅔ in Stockhausen's catalogue of works.
Carré (Square) for four orchestras and four choirs (1959–60) is a composition by the German composer Karlheinz Stockhausen, and is Work Number 10 in the composer's catalog of works.
Kurzwellen, for six players with shortwave radio receivers and live electronics, is a composition by Karlheinz Stockhausen, written in 1968. It is Number 25 in the catalog of the composer’s works.
Refrain for three players is a chamber music composition by Karlheinz Stockhausen, and is number 11 in his catalog of works.
Fresco is an orchestral composition written in 1969 by the German composer Karlheinz Stockhausen as foyer music for an evening-long retrospective programme of his music presented simultaneously in three auditoriums of the Beethovenhalle in Bonn. It is Nr. 29 in his catalogue of works, and a performance takes about five hours.
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.
Atmen gibt das Leben, is a choral opera with orchestra by Karlheinz Stockhausen, written in 1974 and expanded in 1976–77. It is Number 39 in the catalogue of the composer's works, and lasts about 50 minutes in performance.
The Konkrete Etüde is the earliest work of electroacoustic tape music by Karlheinz Stockhausen, composed in 1952 and lasting just three-and-a-quarter minutes. The composer retrospectively gave it the number "1⁄5" in his catalogue of works.
Formel (Formula) is a composition for chamber orchestra by Karlheinz Stockhausen, written while he was still a student in 1951. It is given the number 1⁄6 in his catalog of works, indicating that it is amongst the pieces preceding the composition he recognised as his first mature work, Nr. 1 Kontra-Punkte.
Stop is a composition for orchestra by Karlheinz Stockhausen, work-number 18 in the composer’s catalogue of works, where two performing realisations are also found as Nr. 18½ and Nr. 18⅔.
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.
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.
Drei Lieder, for alto voice and chamber orchestra, is a song cycle by Karlheinz Stockhausen, written while he was still a conservatory student in 1950. In the composer's catalogue of works, it bears the number 1/10.
Spiel is a two-movement orchestral composition by Karlheinz Stockhausen, written in 1952. Withdrawn by the composer after its first performance, it was later revised and restored to his catalogue of works, where it bears the work-number ¼. The score is dedicated to the composer's first wife, Doris.
Chöre für Doris, after poems by Paul Verlaine, is a three-movement a cappella choral composition by Karlheinz Stockhausen, written in 1950 and later given the number 1/11 in the composer's catalogue of works. The score is dedicated to the composer's first wife, Doris Stockhausen, née Andreae.