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 (Nr. 16½), and a re-notated version of the reduced scoring, made in 2003 and titled Mixtur 2003, Nr. 16⅔.
Mixtur is one of the earliest compositions for orchestra with live electronics, and is amongst the first compositions using live-electronic techniques generally.
The original version for large orchestra was premiered on 9 November 1965 at the Norddeutscher Rundfunk, Hamburg (Stockhausen 1971, 51). The version for reduced orchestra was premiered in the large broadcasting hall of the Hessischer Rundfunk, Frankfurt am Main, as part of the Darmstädter Ferienkurse on 23 August 1967 by the Ensemble Hudba Dneska conducted by Ladislav Kupkovič, to whom this version is dedicated (Stockhausen 1971, 53).
Pierre Boulez conducted a number of performances of Mixtur from the early seventies to as late as 10 June 1982 (at the Théâtre du Châtelet, Paris, with the Ensemble InterContemporain) (Vermeil 1996, 225), but was not happy with the score and problems with rehearsals and performances led to a falling out between the two composers (Maconie 2005, 259–60).
Beginning in the late 1990s, Stockhausen revised a number of his earlier aleatoric scores, making versions in which the details were worked out and fixed in conventional notation. The last of these was Mixtur, reworked in 2003. In several moments of the original version, the players choose what they play from a selection of written material. Mixtur 2003 eliminates such indeterminacy by completely writing out all the parts (Worby 2006). The overall form is also fixed in the new version, which eliminates the movability of some moments permitted in the two previous versions. Many earlier performances had presented two different versions, usually the backwards version first, followed by the forwards version. The score of Mixtur 2003 is written out twice, first in the forwards and then in the backwards version. In a programme note Stockhausen characterised this back-and-forth motion as a metaphor for the interplay between life and death (Frisius 2008, 164–65). The world premiere of the new version took place at the Salzburg Festival on 30 August 2006. Stockhausen was to have conducted (and had led the rehearsals in Berlin the previous June), but was forced to cancel because of an attack of sciatica, and his place was taken by Wolfgang Lischke (Worby 2006). The performers were the Deutsche Symphonie-Orchester Berlin, with electronics by the Experimentalstudio für akustische Kunst Freiburg, supervised by André Richard (Spinola 2006).
Material and form
Mixtur is an example of moment form, made up of formal units that are "recognizable by a personal and unmistakable character" (Stockhausen 1963, 200). It possesses at the same time a "polyvalent form", in which the components may be performed in different sequences, and incorporates elements of aleatory (called "variable form" by Stockhausen).
The orchestra is divided into five groups, each of a particular timbre: Holz (woodwinds), Blech (brass), Schlagzeug (percussion), Pizzicato (plucked strings), and Streicher (bowed strings) The sounds from each group except the percussion are picked up by microphones and ring modulated with sine tones, producing transformations of the natural timbres, microtonal pitch inflections, and—when the sine tone frequencies fall below about 16 Hz—rhythmic transformations as well (Stockhausen 1971, 52). In some moments, such as "Ruhe" and "Blech", the ring modulation serves mainly a coloristic purpose, while a moment like "Translation" plays on foreseen effects in such a way that the electronics become an essential structural component (Maconie 2005, 259). In other moments, the sine-tone frequencies are directly connected to the larger-scale structure. In "Spiegel", for example, the sine tones focus on the upper octave of the central tone, F♯. In "Tutti" and "Stufen", on the other hand, the sine tones change with each prominent note in the orchestra in such a way that the output difference or summation tones remain constant on the central tone of that moment (Kohl 1981, 79, 123–24, 129–30).
The division of the orchestra into five groups is decisive for the overall form of the composition. Each moment is given a name describing its overall character, a "central tone" (in a few cases, two central tones), a tone to be omitted, an overall duration, a proportion of silence, a "density" (number of orchestra groups participating), and a timbral mixture (Kohl 1981, 52–62):
Moments in Mixtur name central tone(s) omitted tone(s) duration rest (proportion) density timbres 1 Mixtur C7 F♯ 12 0 4 H/B/P/S 2 Schlagzeug — — 30 ⅕ 1 Sch 3 Blöcke B5 F 78 ½ 3 H/P/S 4 Richtung C♯6 G 48 ⅓ 2 Sch/P 5 Wechsel A♯6 E 18 ⅛ 4 H/B/P/S 6 Ruhe D5 G♯ 78 0 2 B/S 7 Vertikal A4 D♯ 12 ⅛ 3 Sch/P/S 8 Streicher D♯4 A 18 ⅕ 1 S 9 Punkte G♯5, E3 D, A♯ 30 ⅓ 3 H/B/S 10 Holz G3, F2 C♯, B 48 ½ 1 H 11 Spiegel F♯4 C 48 0 4 H/B/P/S 12 Translation G3, F2 F♯, F 30 ½ 2 H/P 13 Tutti G♯5, E3 G, E 78 ⅛ 5 Sch/ H/B/P/S 14 Blech D♯4 G♯ 12 ⅕ 1 B 15 Kammerton A4 D♯ 18 ⅓ 3 H/P/S 16 Stufen A♯6 D 30 0 4 H/B/P/S 17 Dialog D5 A 18 ½ 2 Sch/B 18 Schichten C♯6 A♯ 48 ⅛ 3 B/P/S 19 Pizzicato B5 C♯ 78 ⅕ 1 P 20 Hohes C C7 B 12 ⅓ 2 H/S
The duration unit is to be determined by the conductor, from between 40 and 60 beats per minute according to the score instructions for the kleine Beasetzung (the original, large-orchestra score specifies 50 to 60 beats per minute, but by 1971 Stockhausen favoured the slower tempo of 40). The numbers of units per moment are taken from five steps of a scale proportioned according to the Fibonacci series: 2, 3, 5, 8, and 13, with each value multiplied by 6: 12, 18, 30, 48, and 78. The usefulness of this series lies in the roughly constant proportion between successive members—the deviations of which diminish as the series is extended (Kohl 1981, 56–57).
The twenty moments can be played in numerical order, ascending or descending. The former is referred to as the "forwards version", the latter as the "backwards version". The sequence of events within each moment, however, is the same in either version. Certain moments may also be exchanged: no. 1 with 5, 11 with 16, and 15 with either 3 or 20. Moments 14 and 15 may be played simultaneously in place of no. 5, in which case the brass parts from no. 5 replace 14 and the remainder takes 15's place. When the order is reversed or exchanges made, some details in neighbouring moments are altered. For example, the central tone of moment 11 ("Spiegel"), the F♯ above middle C, is to be continued through whichever moment follows it, and this may be nos. 12, 10, 17, 15, 5, 3, or 20, depending on the chosen permutation of moments and the direction of the version (Kohl 1981, 64).
- Stockhausen, Karlheinz. Telemusik, Mixtur (version for small orchestra, Nr. 16½, "erster Frankfurter Version 1967") Ensemble Hudba Dneska, Ladislav Kupkovič (cond.); Johannes G. Fritsch, Harald Bojé, Rolf Gehlhaar, David Johnson (sine-wave generators); Karlheinz Stockhausen (sound direction). Avant Garde. LP recording. Deutsche Grammophon 137 012. Hamburg: Deutsche Grammophon, 1969.
- Stockhausen, Karlheinz. Mixtur: Kleine Besetzung (1967)—Rückwärts- und Vorwärts-Version. Orchester Hudba Dneska, [Ladislav Kupkovič (cond.); Johannes Fritsch, Rolf Gehlhaar, David Johnson, Harald Bojé (sine-wave generators); Karlheinz Stockhausen (sound projection). Recorded by WDR, 23 August 1967, in Frankfurt. CD recording. Stockhausen Complete Edition CD 8. Kürten: Stockhausen-Verlag, 1993.
- Musica Viva Festival 2008. Stockhausen, Mixtur 2003, Symphonieorchester des Bayerischen Rundfunks, Lukas Vis (cond.); Experimentalstudio des SWR, André Richard (sound director). With works by Karl Amadeus Hartmann, Aribert Reimann, Jörg Widmann, Matthias Pintscher, Iannis Xenakis, James Dillon, Beat Furrer, Giacinto Scelsi, Chaya Czernowin, Kaija Saariaho, Liza Lim, Rebecca Saunders, Adriana Hölszky, and traditional music from Egypt and Iran. Fundación BBVA, Kooperation mit BR Klassik. 6-disc hybrid multichannel SACD set. NEOS 10926. [Munich}: NEOS Music GmbH, 2009.
- Frisius, Rudolf. 1996. Karlheinz Stockhausen I: Einführung in das Gesamtwerk; Gespräche mit Karlheinz Stockhausen. Mainz: Schott Musik International. ISBN 3795702488
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- Geysen, Frans. 1968. "Prognose voor een eucharistieviering". Adem: Tweemaandelijks tijdschrift voor liturgische muziek 2:50–53.
- Kohl, Jerome. 1981. "Serial and Non-Serial Techniques in the Music of Karlheinz Stockhausen from 1962–1968." Ph. D. diss. Seattle: University of Washington.
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- Souster, Tim. 1972. "On Stockhausen’s Mixtur". The Listener 87:59.
- Spinola, Julia. 2006. "Eine Todesfahrt rückwärts in die Erinnerung: Verwunschene Schönheitsempfindungen: Karlheinz Stockhausens Mixtur von 1963 in einer Neufassung in Salzburg". Frankfurter Allgemeine Zeitung no. 203:39.
- Stockhausen, Karlheinz. 1963. "Momentform: Neue Beziehungen zwischen Aufführungsdauer, Werkdauer und Moment". In his Texte zur Musik 1, edited by Dieter Schnebel, 189-210. DuMont Dokumente. Cologne: DuMont Schauberg.
- Stockhausen, Karlheinz. 1967. "Notes on Mixtur (1964)", translated by William Sylvester. Electronic Music Review, no. 1:16–17.
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- Stockhausen, Karlheinz. 1971. "Mixtur (1964) für 5 Orchestergruppen, Sinusgeneratoren u. Ringmodulatoren". In his Texte zur Musik 3, edited by Dieter Schnebel, 51–56. DuMont Dokumente. Cologne: Verlag M. DuMont Schauberg. ISBN 3-7701-0493-5.
- Stockhausen, Karlheinz. 1978. "Mixtur für kleine Besetzung (1967): Zur Aufführungspraxis" [Letter to Pierre Boulez, written 9 November 1971]. In his Texte zur Musik 4, edited by Christoph von Blumröder, 73–76. DuMont Dokumente. Cologne: DuMont Buchverlag. ISBN 3-7701-1078-1. Untitled English translation by Richard Toop. Music and Musicians 21, no. 2 (October 1972): 31–32.
- Vermeil, Jean. 1996. Conversations with Boulez: Thoughts on Conducting, translated from the French by Camille Naish. Portland, OR: Amadeus Press, ISBN 1574670077.
- Worby, Robert. 2006. "Karlheinz Stockhausen—Mixtur (2003) Salzburg Festival. 30 August 2006". Diffusion, magazine of the Sonic Arts Network (September). Reprinted, Stockhausen website (Accessed 27 June 2011).
- Anon. 2006a. "Uraufführung des neuen Stücks von Stockhausen: Wolfgang Lischke leitet die MIXTUR 2003". Nordbayerischer Kurier (29 August).
- Anon. 2006b. "Kritik Salzburg: Rückwärts in die verträumte Erinnerung: Festspiel-Finale II: Ein neuer alter Stockhausen ohne Stockhausen im alten Lehrbauhof". Die Presse (1 September).
- Anon. 2006c. "Wenn nur der Automotor wärmt". Wiener Zeitung (1 September).
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- Clements, Andrew. 2005. "Review: Classical: London Sinfonietta/Valade, Queen Elizabeth Hall, London: 4/5". The Guardian (27 April): 38.
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- Holden, Anthony. 2006. "It's Those Swinging Sixties: London Sinfonietta/Valade Queen Elizabeth Hall, London SE1 BBC Symphony/Vanska Barbican, London EC2 Philharmonia/Lazarev Queen Elizabeth Hall, London SE1". The Observer (30 April): 19.
- Hopkins, G. W. 1968. "Stockhausen, Form, and Sound". Musical Times 109, no. 1499 (January): 60–62.
- Peters, Günter. 2006. "Karlheinz Stockhausen, MIXTUR 2003 für Orchester". Programme book for the world premiere. Salzburg: Salzburger Festspiel.
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- Karlheinz Stockhausen - Mixtur 2003 Sound example, beginning of the forwards version. Experimentalstudio des SWR; Symphonieorchester des Bayerischen Rundfunks, Lucas Vis (cond.). BR Klassik website, archive from 01.06.2010 (Accessed 27 June 2011).
- Karlheinz Stockhausen - Mixtur 2003. Interview with conductor Lukas Vis (German), and excerpts from the forwards version (15 mins.). Experimentalstudio des SWR; Symphonieorchester des Bayerischen Rundfunks, Lucas Vis (cond.). BR Klassik website, archive from 26.06.2011 (Accessed 06 July 2011).
- Ball, Timothy. 2006."Stockhausen Mixtur: London Sinfonietta, Pierre-André Valade, Sound Intermedia (sound design), Thierry Coduys—La Kitchen (computer development) Queen Elizabeth Hall, London, Monday, April 24, 2006". Classical Source website (Accessed 27 June 2011).
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