Punkte (Points) is an orchestral composition by Karlheinz Stockhausen, given the work number ½ in his catalogue of works.
Punkte originated as a punctual orchestral work which was begun in September in Hamburg and had reached a first-draft stage by 30 September. The final draft was completed on 24 October 1952, but the work remained unperformed and unpublished .The work did not receive the title by which it is known today until much later, however. In a letter dated 4 November 1952 to Alfred Schlee (the editor from Universal Edition in Vienna who, at the premiere of Stockhausen's Spiel at the Donaueschingen Festival in October, had offered to publish his works), Stockhausen initially called his new score Zweites Orchesterspiel / Kontrapunkte / für Saiten- und Blasinstrumente, and in a letter to his friend Karel Goeyvaerts dated 14 January 1953, he calls the orchestral work Nr. 4 Kontrapunkte, adding, "It will be very difficult to perform this work". At this point in time, the chamber composition now known as Kontra-Punkte (with a hyphen) was instead called simply Nr 5…, für 10 Instrumente. After a heated discussion in March with Hermann Scherchen, who Stockhausen hoped would conduct the work at a festival in Cologne, he decided to withdraw the score, and substituted the chamber work for ten instruments, now redesignated "Nr 1", and eventually given the title Kontra-Punkte. The withdrawn orchestral score, which has never been performed, was renamed Punkte at some unknown point in time.
Stockhausen wholly recomposed this score in 1962, at which time it was given the retrospective work number ½ (the fraction indicating that it preceded his "work number 1"). Work was begun during a four-week stay in Finland in the summer, when Stockhausen was lecturing at the Jyväskylä summer university. It was intended for performance in Palermo later in the year, but the score was not finished in time and the event was cancelled. Having rescheduled the premiere for Donaueschingen the following year, Stockhausen resumed work in October 1962 while staying at the house of his Darmstadt pupil Jack Brimberg in Locust Valley on Long Island, New York. After some anxious correspondence with Heinrich Strobel, director of the Donaueschingen Festival, the score was completed and dispatched to Strobel on 28 February 1963.In its new form, the "points" of the original version scarcely ever appear as such. Instead, they have become centres for groups, crowds, swarms, and vibrating masses, become nuclei of micro-musical organisms. This "renewed" composition was premiered on 20 October 1963 at the Donaueschingen Music Festival, by the Orchestra of the SWF, conducted by Pierre Boulez, and was published by Universal Edition that year in facsimile.
Not yet satisfied with the result, Stockhausen made major changes to the new Punkte in 1964, and again in 1966.These versions were also published, and Stockhausen made further revisions in 1969, at which time Universal Edition began work on an engraved edition. Production stopped in 1973 only to restart in 1974 and, after Stockhausen made still more revisions in 1975, work resumed the next year. The engraved score was only finally finished (with further minor corrections made up to 1993) in 1996.
The original version was for a small orchestra of either 27or 30 players:
Punkte is divided into 144 overarching sections, characterised by sets of shapes and textures. Each isolated tone of the 1952 version was used as a "nucleus", and these nuclei were composed out into a variety of complex figures. There are six basic triangular shapes, with the nucleus at one apex:
The vertical width of each pitch band is controlled by a serial distribution of chromatic intervals, from a single tone, via the minor second, major second, minor third, and so on up to a major seventh.
Each of these six shapes may be composed in any of six textures:
Some of these textures can be combined. For example, the opening section of Punkte combines normal tones and trills.Similarly, there are places where the triangular sound shapes overlap so densely (due to the density of the points in the structure of the original 1952 version) that the entire space is filled with sound, leaving no silences. This situation suggested the idea of negative forms. The usual conception is that sounds are heard as being projected against a background of silence. In these negative structures, the situation is reversed. Sustained clusters are made to sound for a comparatively long time, from which some of the sounds are erased. The "holes" therefore are the music.
Both durations and pitches are distributed through the use of permutations, which serve as an aid to repetition, without repeating exactly the same thing. Diversity in unity is the principle of permutation, in dividing the larger elements into their smaller components.
Kontra-Punkte is a composition for ten instruments by Karlheinz Stockhausen which resolves contrasts among six instrumental timbres, as well as extremes of note values and dynamic levels, into a homogeneous ending texture. Stockhausen described it: "Counter-Points: a series of the most concealed and also the most conspicuous transformations and renewals—with no predictable end. The same thing is never heard twice. Yet there is a distinct feeling of never falling out of an unmistakable construction of the utmost homogeneity. An underlying force that holds things together—related proportions: a structure. Not the same Gestalten in a changing light. But rather this: various Gestalten in the same light, that permeates everything".
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.
Mantra is a composition by the German composer Karlheinz Stockhausen. It was composed in 1970 and premiered in autumn of the same year at the Donaueschingen Festival. The work is scored for two ring-modulated pianos; each player is also equipped with a chromatic set of crotales and a wood block, and one player is equipped with a short-wave radio producing morse code or a magnetic tape recording of morse code. In his catalogue of works, the composer designated it as work number 32.
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".
Klang —Die 24 Stunden des Tages is a cycle of compositions by Karlheinz Stockhausen, on which he worked from 2004 until his death in 2007. It was intended to consist of 24 chamber-music compositions, each representing one hour of the day, with a different colour systematically assigned to every hour. The cycle was unfinished when the composer died, so that the last three "hours" are lacking. The 21 completed pieces include solos, duos, trios, a septet, and Stockhausen's last entirely electronic composition, Cosmic Pulses. The fourth composition is a theatre piece for a solo percussionist, and there are also two auxiliary compositions which are not part of the main cycle. The completed works bear the work (opus) numbers 81–101.
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.
In Freundschaft is a composition by Karlheinz Stockhausen, number 46 in his catalogue of works, which is playable on a wide variety of solo instruments. It was first performed on a clarinet on 28 July 1977.
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.
Jubiläum (Jubilee) is an orchestral composition by Karlheinz Stockhausen, work-number 45 in the composer's catalogue of works.
Adieufür Wolfgang Sebastian Meyer is a composition for wind quintet by Karlheinz Stockhausen composed in 1966. It is Number 21 in the composer's catalog of works, and the second of Stockhausen's three wind quintets.
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.
Refrain for three players is a chamber music composition by Karlheinz Stockhausen, and is number 11 in his catalog of 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.
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.
Schlagtrio is a chamber-music work for piano and two timpanists composed by Karlheinz Stockhausen in 1952. It is Nr. ⅓ in his catalogue of works.
The Sonatine (Sonatina) for violin and piano is a chamber music composition by Karlheinz Stockhausen, written while he was still a student in 1951. It carries the work-number ⅛ in his catalogue of works.
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.