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Example 12 from Stockhausen's article "... wie die Zeit vergeht ...", illustrating with a version of the series from Gruppen fur 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" (Stockhausen 1963b, 117). 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)" (Leeuw 2005, 174), or "a duration scale which changes its 'time register' ... corresponds to a twelve-tone scale that extends over more than one octave" (Misch 1998, 157-58).
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" (Smalley 1967, 794).
Paspels, the village where Stockhausen began work on Gruppen
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" (Stockhausen and Frisius 1989, 320). 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. (Cott 1973, 141)
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 (Kurtz 1992, 79-80).
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 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 (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).
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.
Cott, Jonathan. 1973. Stockhausen: Conversations with the Composer. New York: Simon and Schuster. ISBN0-671-21495-0.
Harvey, Jonathan. 1975. The Music of Stockhausen: An Introduction. Berkeley and Los Angeles: University of California Press. ISBN0-520-02311-0.
Koenig, Gottfried Michael. 1968. "Commentary". Die Reihe 8 ("Retrospective") [English edition], 80-98. (Originally published in German in 1962.)
Kohl, Jerome. 2004. "Der Aspekt der Harmonik in Licht." In Internationales Stockhausen-Symposion 2000: LICHT: Musikwissenschaftliches Institut der Universität zu Köln, 19. bis 22. Oktober 2000. Tagungsbericht. Signale aus Köln: Beiträge zur Musik der Zeit 10, edited by Imke Misch and Christoph von Blumröder, 116-32. Münster, Berlin, London: LIT-Verlag. ISBN3-8258-7944-5.
Leeuw, Ton de. 2005. Music of the Twentieth Century: A Study of Its Elements and Structure, translated from the Dutch by Stephen Taylor. Amsterdam: Amsterdam University Press. ISBN90-5356-765-8. Translation of Muziek van de twintigste eeuw: een onderzoek naar haar elementen en structuur. Utrecht: Oosthoek, 1964. Third impression, Utrecht: Bohn, Scheltema & Holkema, 1977. ISBN90-313-0244-9.
Misch, Imke. 1998. "On the Serial Shaping of Stockhausen's Gruppen für drei Orchester", translated by Dr. Frank Hentschel and Jerome Kohl. Perspectives of New Music 36, no. 1 (Winter): 143-87.
Misch, Imke. 1999. Zur Kompositionstechnik Karlheinz Stockhausens Gruppen für 3 Orchester (1955-57). Signale aus Köln: Beiträge zur Musik der Zeit 2, edited by Christoph von Blumröder. Saarbrücken: Pfau-Verlag. ISBN3-89727-048-X.
Stockhausen, Karlheinz. 1963a. "Gruppenkomposition: Klavierstück I (Anleitung zum Hören)". In his Texte zur Musik, vol. 1, 63-74. Cologne: Verlag M. DuMont Schauberg.
Stockhausen, Karlheinz. 1963b. "... wie die Zeit vergeht ...". In his Texte zur Musik, vol. 1, 99-139. Cologne: Verlag M. DuMont Schauberg. Revised and annotated version of the text first published in Die Reihe 3 (1957): 13-42. Translation by Cornelius Cardew, as "... How Time Passes ..." in the English edition of Die Reihe 3 (1959): 10-40.
Stockhausen, Karlheinz. 1963c. "Erfindung und Entdeckung". In his Texte zur Musik, vol. 1, 222-58. Cologne: Verlag M. DuMont Schauberg.
Stockhausen, Karlheinz. 1971. "Gruppen und Carré". In his Texte zur Musik, vol. 3, edited by Dieter Schnebel, 22-24. Cologne: Verlag M. DuMont Schauberg. ISBN3-7701-0493-5.
Stockhausen, Karlheinz, and Rudolf Frisius. 1989. "'Wille zur Form und Wille zum Abenteuer'". In Stockhausen, Texte zur Musik, vol. 6, 320-46. Cologne: DuMont Buchverlag. ISBN3-7701-2249-6.
Stockhausen, Karlheinz. 2009. Kompositorische Grundlagen Neuer Musik: Sechs Seminare für die Darmstädter Ferienkurse 1970, edited by Imke Misch. Kürten: Stockhausen-Stiftung für Musik. ISBN978-3-00-027313-1.
Whittall, Arnold. 2008. The Cambridge Introduction to Serialism. Cambridge Introductions to Music. New York: Cambridge University Press. ISBN978-0-521-68200-8 (pbk).
Abendroth, Walter. 1958. "Musikalische Atomzertrümmerung". Die Zeit no. 43 (24 October): 8.
Amaral, Pedro [pt]. 1998. "Espace-Temps dans Gruppen de Karlheinz Stockhausen". Master's degree dissertation at IRCAM, Formation doctorale en Musique et Musicologie du XXe siècle.
Assis, Gustavo Oliveira Alfaix. 2011. Em busca do som: A música de Karlheinz Stockhausen nos anos 1950. São Paulo: Editora UNESP. ISBN978-85-393-0207-9.
Beyer, Peter. 2000. "Regelwerk und Theorie serieller Musik in Karlheinz Stockhausens Gruppen für drei Orchester." In Musiktheorie: Festschrift für Heinrich Deppert zum 65. Geburtstag, edited by Wolfgang Budday, Heinrich Deppert, and Erhard Karkoschka, 209-60. Tutzing: Hans Schneider. ISBN3-7952-1005-4.
Carpentier, Alejo. 1958. "Grupos para tres orquestas". El Nacional [Caracas] (23 May). Reprinted in Carpentier, Ese músico que llevo dentro, edited by Zoila Gómez, 2:161-62. Havana: Editorial Letras Cubanas, 1980.
Decroupet, Pascal. 1997. "Gravitationsfeld Gruppen: Zur Verschränkung der Werke Gesang der Jünglinge, Gruppen und Zeitmaße und deren Auswirkung auf Stockhausens Musikdenken in der zweiten Hälfte der fünfziger Jahre". Musiktheorie 12, no. 1:37-51.
Decroupet, Pascal. 1999. "Cherché, mais aussi, ... trouvé. Gruppen de Stockhausen à travers ses esquisses". Musurgia 6, no. 1 (La génétique des oeuvres): 63-76.
Decroupet, Pascal. 2012. "Le rôle des clés et algorithmes dans le décryptage analytique: L'exemple des musiques sérielles de Pierre Boulez, Karlheinz Stockhausen et Bernd Alois Zimmermann". Revue de Musicologie 98, no. 1:221-46.
Del Mar, Norman. 1961. "On Co-Conducting Stockhausen's Gruppen". Tempo, new series, no. 59 (Autumn): 15-23.
Frisius, Rudolf. 2008. Karlheinz Stockhausen II: Die Werke 1950-1977; Gespräch mit Karlheinz Stockhausen, "Es geht aufwärts". Mainz, London, Berlin, Madrid, New York, Paris, Prague, Tokyo, Toronto: Schott Musik International. ISBN978-3-7957-0249-6.
Goldberg, Albert [and Peter Jona Korn]. 1958. "European Critics Protest New Electronic 'Music'". Los Angeles Times (23 November): E7.
Hedges, Anthony. 1961. "Music in the Provinces: Glasgow". Musical Times 102, no. 1421 (July): 431.
Mival, William. 2012. "Case Study: Karlheinz Stockhausen, Gruppen für drei Orchester". In The Cambridge History of Musical Performance, edited by Colin Lawson and Robin Stowell, 798-814. Cambridge and New York: Cambridge University Press. ISBN978-0-521-89611-5.