Gruppen
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". History. 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. Upon returning to Cologne, Stockhausen resumed work on "Gesang der Jünglinge" and then composed the wind quintet "Zeitmaße" and "Klavierstück XI", before turning to working-out the details of "Gruppen", which occupied him for all of 1957. The premiere of the work took place in the Rheinsaal of the Kölner Messe in Cologne-Deutz, as part of the WDR's concert series Musik der Zeit, on 24 March 1958 with the Cologne Radio Symphony Orchestra, conducted  by Stockhausen (orchestra I), Bruno Maderna (orchestra II), and Pierre Boulez (orchestra III). The score is dedicated to Herbert Eimert, director at that time of the WDR electronic music studio. "Gruppen" was performed twice on the programme, with the world premiere of Pierre Boulez's Third Piano Sonata, performed by the composer, in between. Material and form. 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 Darmstadt serialism, 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". Instrumentation. Orchestra I. Woodwinds Brass Percussion (4 percussionists) Keyboards Strings Orchestra II. Woodwinds Brass Percussion (4 percussionists) Keyboards Strings Orchestra III. Woodwinds Brass Percussion (4 percussionists) Keyboards Strings Discography. In chronological order of first issue.