page_title: Gruppen
section_title: Material and form
hierarchical_section_title: Gruppen / Material and form
caption_attribution_description: English: Gruppen tone row (Stockhausen 1963b, 116; Harvey 1975, 58; Misch 1998, 161; Whittall 2008, 185).
context_page_description: Gruppen for three orchestras 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".
context_section_description: 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 (Kurtz 1992, 80), 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" (Stockhausen 1963a, 63). 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 (Stockhausen 1963c, 250–51). 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 (Smalley 1967, 795).
  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 (Misch 1998, 161). 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 (Harvey 1975, 56–57). 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 (Kohl 2004, 122–23).
  Many of the conceptual bases of the work are explained in Stockhausen's famous article, "... How Time Passes ..." (Stockhausen 1963b). 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 (Misch 1999, 53–54). 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 (Koenig 1968, 90–91).
  The twelve logarithmic metronomic tempos used in Gruppen, covering a tempo "octave" (doubling in speed) from  = 60 to 120 are (Stockhausen 2009, 172):
  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" (Stockhausen 2009, 169).
caption: Gruppen tone row (Harvey 1975, 58; Misch 1998, 161; Whittall 2008, 185; Stockhausen 1963b, 116, and Maconie 2005, 149 show this row transposed up a tritone).[why?] See tone row for Klavierstück IX.     Play
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