Example 12 from Stockhausen's article "... wie die Zeit vergeht ...", illustrating with a version of the series from Gruppen für drei Orchester that, "if you start from the intervals of a proportion series, then with every step forward the register of each duration is also already chosen". There are "a number of basic durations, indicated in metronome marks and corresponding with the pitch proportions within the series, reaching far as the octave positions (basic duration units)", or "a duration scale which changes its 'time register' ... corresponds to a twelve-tone scale that extends over more than one octave".
Gruppen (German: Groups) 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".
Early in 1955 Stockhausen received a commission from WDR for a new orchestral composition, but his ongoing work on Gesang der Jünglinge prevented him from starting right away. In August and September, he took the opportunity to retreat to an inexpensive rented room in the attic of a parsonage in Paspels, Switzerland, recommended to him by a colleague, Paul Gredinger. Surrounded by the splendour of the Graubünden alps, he created the entire plan of Gruppen, "with a completely new conception of musical time". The surroundings provided more than just a conducive environment for work.
in Gruppen ... whole envelopes of rhythmic blocks are exact lines of mountains that I saw in Paspels in Switzerland right in front of my little window. Many of the time spectra, which are represented by superimpositions of different rhythmic layers—of different speeds in each layer—their envelope which describes the increase and decrease of the number of layers, their shape, so to speak, the shape of the time field, are the curves of the mountain's contour which I saw when I looked out the window.
Originally the work was to have been for multi-channel electronic music with large orchestra, with metrically indeterminate parts for the orchestra. Once having decided to divide the orchestra into three parts, each with its own conductor, Stockhausen gave up the electronic sounds and incorporated some of what had previously been thought of as electronic music into the orchestra. The indeterminate tempos also proved impractical, and were dropped after a few experimental pages of score had been written out.
A large orchestra of 109 players is divided into three orchestral units, each with its own conductor, which are deployed in a horseshoe shape to the left, front, and right of the audience. The spatial separation was principally motivated by the compositional requirement of keeping simultaneously played yet musically separate passages distinct from one another, but led to some orgiastic passages in which a single musical process passes from one orchestra to another.
The title refers to the work's construction in 174 units, mainly composed in what Stockhausen terms "groups"—cohesive groupings of notes unified through one or more common characteristics (dynamics, instrumental color, register, etc.): "a particular number of notes which are joined, by means of related proportions, into a superordinate experiential quality (namely, the group). The various groups in a composition have various proportional features—various structures—but they are interrelated in that the properties of one group may only be understood by comparing them in degree of relationship with the other groups". This category is contrasted with the "punctual" style of early Darmstadtserialism, which nevertheless also occurs in Gruppen, along with a third category of "collective" or "statistical" swarms or crowds, too dense for the listener to be able to accurately distinguish individual notes or their order of succession. Consequently, the importance of individual notes is relatively low, so that sonority, density, speed, dynamics, and direction of movement become the main features for the listener.
Nonetheless, a traditional twelve-tone row is used as its basis:
This is a symmetrical all-interval row, in which the first half consists of the intervals of a descending major third, rising perfect fourth, descending minor third, descending minor second, and ascending major second. The second half consists of the retrograde of the first half, transposed by a tritone. In other words, the row is "degenerate", in that the second hexachord is a retrograde of the first, transposed by six semitones. However, Stockhausen does not exploit the specific twelve-tone compositional applications of such a row, which suggests that either Stockhausen was not interested in or did not know about them. Because of the chord transformations that emerge between rehearsal numbers 118 and 120 it appears that Stockhausen was in fact aware of these properties, making it most likely that the relationship simply did not interest him compositionally.
Many of the conceptual bases of the work are explained in Stockhausen's famous article, "... How Time Passes ...". In this essay, Stockhausen developed a serial organizational principle at the center of which stood the concept of a twelve-step duration series possessing the same structural properties as the basic twelve-tone pitch series. This became the basis for the entire process of serial organization of Gruppen. This duration series, however, is expressed not as single units (which would correspond to single vibrations of a pitch) but rather as metronomic tempos in sufficiently long stretches of time to enable conductors and musicians to change tempo with precision. However, because the resulting "fundamental durations" are not small enough for use in the musical detail, subdivisions corresponding to the transposition of the overtones of a pitch's harmonic spectrum are used.
The twelve logarithmic metronomic tempos used in Gruppen, covering a tempo "octave" (doubling in speed) from = 60 to 120 are:
The composer recalled that, when Igor Stravinsky saw the score for the first time, he wrote that such fractional metronomic values as 63.5 and 113.5 were "a sign of German thoroughness".
reissued under the same LP disc number, in the first set of Deutsche Grammophon’s Avant Garde series. [Hamburg]: Deutsche Grammophon Gesellschaft, ca. 1972.
reissued on reel-to-reel 7-½ ips tape, as DGC 7002. Elk Grove Village, Illinois: Ampex/Deutsche Grammophon, ca. 1974.
reissued on Stockhausen Complete Edition CD 5. Kürten: Stockhausen-Verlag, 1992.
reissued (without Carré) on Die Neue Musik und ihre neuesten Entwicklungen, Opus Musicum OM 116 – OM 118 [6833 174–76] (3-LP set), (with works by Berio, Boulez, Earle Brown, Cage, Luc Ferrari, Henze, Kagel, Ligeti, Messiaen, Jens-Peter Ostendorf, Penderecki, Schnebel, Xenakis, Zimmermann). Cologne: Arno Volk Verlag; Hans Gerig KG, 1975.
1982. Deutscher Musikrat: Zeitgenössische Musik in der Bundesrepublik Deutschland 4: 1950–1960. WDR Symphony Orchestra, Cologne, cond. Karlheinz Stockhausen (orchestra 1), Bruno Maderna (orchestra 2), Pierre Boulez (orchestra 3). Recorded 24 March 1958 in four channels; stereo mix 1982. Deutsche Harmonia Mundi DMR 1010–12 (3-LP boxed set). Cologne: EMI Electrola GmbH.
2006b. Eötvös Conducts Stockhausen: Gruppen, Punkte. WDR Symphony Orchestra, Cologne, conducted by Arturo Tamayo (orchestra 1), Péter Eötvös (orchestra 2), Jacques Mercier (orchestra 3). Recorded by WDR at Messe Rheinlandsaal, Cologne 28 May/2 June 1997. (with Stockhausen: Punkte). BMC CD 117. [Budapest]: Budapest Music Center Records.
Gesang der Jünglinge is an electronic music work by Karlheinz Stockhausen. It was realized in 1955–56 at the Westdeutscher Rundfunk studio in Cologne and is Work Number 8 in the composer's catalog of works. The vocal parts were supplied by 12-year-old Josef Protschka. It is exactly 13 minutes, 14 seconds long.
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.
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.
Collegium Vocale Köln is a German vocal ensemble, founded in 1966 as a quintet when its members were still students at the Rheinische Musikschule in Cologne. It is directed by Wolfgang Fromme, who also sings tenor in the ensemble. They are best known as the group for which Karlheinz Stockhausen composed Stimmung in 1968, a work which they had performed more than three hundred of times throughout the world by 1986. The original impetus for the ensemble's founding, however, was an appearance by Alfred Deller at the Cologne Courses for Early Music, and the group has always performed both early and contemporary works.
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.
Mikrophonie is the title given by Karlheinz Stockhausen to two of his compositions, written in 1964 and 1965, in which "normally inaudible vibrations. .. are made audible by an active process of sound detection ; the microphone is used actively as a musical instrument, in contrast to its former passive function of reproducing sounds as faithfully as possible".
Hymnen is an electronic and concrete work, with optional live performers, by Karlheinz Stockhausen, composed in 1966–67, and elaborated in 1969. In the composer's catalog of works, it is "Nr. 22".
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.
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.
Studie I is an electronic music composition by Karlheinz Stockhausen from the year 1953. It lasts 9 minutes 42 seconds and, together with his Studie II, comprises his work number ("opus") 3.
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.
Punkte (Points) is an orchestral composition by Karlheinz Stockhausen, given the work number ½ in his catalogue of works.
Oktophonie (Octophony) is a 1991 octophonic electronic-music composition by Karlheinz Stockhausen. A component layer of act 2 of the opera Dienstag aus Licht, it may also be performed as an independent composition. It has a duration of 69 minutes.
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.
Ensemble is a group-composition project devised by Karlheinz Stockhausen for the 1967 Darmstädter Ferienkurse. Twelve composers and twelve instrumentalists participated, and the resulting performance lasted four hours. It is not assigned a work number in Stockhausen's catalogue of works.
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