Plus-Minus (Stockhausen)

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.
History.
"Plus-Minus" is a "polyvalent process composition", designed as a project for the composition students attending the first Cologne Courses for New Music, held at the 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.
"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:
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. 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.
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. 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.
Analysis.
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. These oppositions include, for example, the confrontation of materials having definite pitch with others of indeterminate pitch. The score systematically catalogues its materials into:
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. The note material is all derived from the prime and inverted forms of the following twelve-tone row:
C D G A A G E B D F C F
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.
Reception.
The score of "Plus-Minus" is complicated, delivering the message that composing serial music is hard work. 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". 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".