''Mixtur'', for orchestra, 4

sine-wave A sine wave, sinusoidal wave, or just sinusoid is a mathematical curve defined in terms of the ''sine'' trigonometric function, of which it is the graph. It is a type of continuous wave and also a smooth periodic function. It occurs often in ma ...

generators, and 4 ring modulators, is an orchestral composition by the German composer

Karlheinz Stockhausen Karlheinz Stockhausen (; 22 August 1928 – 5 December 2007) was a German composer, widely acknowledged by critics as one of the most important but also controversial composers of the 20th and early 21st centuries. He is known for his groun ...

, 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. 16), and a re-notated version of the reduced scoring, made in 2003 and titled ''Mixtur 2003'', Nr. 16.

History

''Mixtur'' is one of the earliest compositions for orchestra with

live electronics Live electronic music (also known as live electronics) is a form of music that can include traditional electronic sound-generating devices, modified electric musical instruments, hacked sound generating technologies, and computers. Initially the pr ...

, 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 Norddeutscher Rundfunk (NDR; ''Northern German Broadcasting'') is a public broadcasting, public radio and television broadcaster, based in Hamburg. In addition to the city-state of Hamburg, NDR broadcasts for the German states of Lower Saxony, M ...

, Hamburg. The version for reduced orchestra was premiered in the large broadcasting hall of the

Hessischer Rundfunk Hessischer Rundfunk (HR; "Hesse Broadcasting") is the German state of Hesse's public broadcasting, public broadcasting corporation. Headquartered in Frankfurt, it is a member of the national consortium of German public broadcasting corporations, ...

, Frankfurt am Main, as part of the

Darmstädter Ferienkurse Darmstädter Ferienkurse ("Darmstadt Summer Course") is a regular summer event of contemporary classical music in Darmstadt, Hesse, Germany. It was founded in 1946, under the name "Ferienkurse für Internationale Neue Musik Darmstadt" (Vacation Cou ...

on 23 August 1967 by the Ensemble Hudba Dneska conducted by

Ladislav Kupkovič Ladislav Kupkovič (17 March 1936 – 15 June 2016) was a Slovak composer and conductor . Life Kupkovič was born in Bratislava, and studied violin and conducting there, first at the conservatory, then at the Academy of Performing Arts. He ...

, to whom this version is dedicated.

Pierre Boulez Pierre Louis Joseph Boulez (; 26 March 1925 – 5 January 2016) was a French composer, conductor and writer, and the founder of several musical institutions. He was one of the dominant figures of post-war Western classical music. Born in Mont ...

conducted a number of performances of ''Mixtur'' from the early seventies to as late as 10 June 1982 (at the

Théâtre du Châtelet The Théâtre du Châtelet () is a theatre and opera house, located in the place du Châtelet in the 1st arrondissement of Paris, France. One of two theatres (the other being the Théâtre de la Ville) built on the site of a ''châtelet'', a s ...

, Paris, with the

Ensemble InterContemporain The Ensemble intercontemporain (EIC) is a French music ensemble, based in Paris, that is dedicated to contemporary music. Pierre Boulez founded the EIC in 1976 for this purpose, the first permanent organization of its type in the world. Organi ...

), but was not happy with the score and problems with rehearsals and performances led to a falling out between the two composers. Beginning in the late 1990s, Stockhausen revised a number of his earlier

aleatoric Aleatoricism or aleatorism, the noun associated with the adjectival aleatory and aleatoric, is a term popularised by the musical composer Pierre Boulez, but also Witold Lutosławski and Franco Evangelisti, for compositions resulting from "action ...

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. 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. The world premiere of the new version took place at the

Salzburg Festival The Salzburg Festival (german: Salzburger Festspiele) is a prominent festival of music and drama established in 1920. It is held each summer (for five weeks starting in late July) in the Austrian town of Salzburg, the birthplace of Wolfgang Amad ...

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. The performers were the Deutsche Symphonie-Orchester Berlin, with electronics by the Experimentalstudio für akustische Kunst Freiburg, supervised by

André Richard André Richard (born 18 April 1944) is a Swiss composer and conductor. Life Born in Bern, Richard studied singing, music theory and music composition first at the Conservatoire de musique de Genève and later at the Hochschule für Musik Freibur ...

Material and form

''Mixtur'' is an example of

moment form In music, moment form is defined as "a mosaic of moments", and, in turn, a moment is defined as a "self-contained (quasi-)independent section, set off from other sections by discontinuities". History and definition The concept of moment form, and t ...

, made up of twenty formal units called "moments", each of which is "recognizable by a personal and unmistakable character". It possesses at the same time a "polyvalent form", in which the components may be performed in different sequences, and incorporates elements of

aleatory Aleatoricism or aleatorism, the noun associated with the adjectival aleatory and aleatoric, is a term popularised by the musical composer Pierre Boulez, but also Witold Lutosławski and Franco Evangelisti (composer), Franco Evangelisti, for compo ...

(called "variable form" by Stockhausen). The orchestra is divided into five groups, each of a particular

timbre In music, timbre ( ), also known as tone color or tone quality (from psychoacoustics), is the perceived sound quality of a musical note, sound or musical tone, tone. Timbre distinguishes different types of sound production, such as choir voice ...

: ''Holz'' (

woodwinds Woodwind instruments are a family of musical instruments within the greater category of wind instruments. Common examples include flute, clarinet, oboe, bassoon, and saxophone. There are two main types of woodwind instruments: flutes and reed ...

), ''Blech'' (

brass Brass is an alloy of copper (Cu) and zinc (Zn), in proportions which can be varied to achieve different mechanical, electrical, and chemical properties. It is a substitutional alloy: atoms of the two constituents may replace each other with ...

), ''Schlagzeug'' (

percussion A percussion instrument is a musical instrument that is sounded by being struck or scraped by a beater including attached or enclosed beaters or rattles struck, scraped or rubbed by hand or struck against another similar instrument. Exc ...

), ''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 A sine wave, sinusoidal wave, or just sinusoid is a mathematical curve defined in terms of the '' sine'' trigonometric function, of which it is the graph. It is a type of continuous wave and also a smooth periodic function. It occurs often in ...

, producing transformations of the natural timbres,

microtonal Microtonal music or microtonality is the use in music of microtones—intervals smaller than a semitone, also called "microintervals". It may also be extended to include any music using intervals not found in the customary Western tuning of tw ...

pitch inflections, and—when the sine tone frequencies fall below about 16 Hz—rhythmic transformations as well. 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. 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. 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 consecutive central tones), a tone to be omitted (sometimes two tones), an overall duration, a proportion of silence, a "density" (number of orchestra groups participating), and a timbral mixture: 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 In mathematics, the Fibonacci numbers, commonly denoted , form a sequence, the Fibonacci sequence, in which each number is the sum of the two preceding ones. The sequence commonly starts from 0 and 1, although some authors start the sequence from ...

: 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. 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 C or Do is the first note and semitone of the C major scale, the third note of the A minor scale (the relative minor of C major), and the fourth note (G, A, B, C) of the Guidonian hand, commonly pitched around 261.63 Hz. The actual frequen ...

, 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.

Discography

* Stockhausen, Karlheinz. ''Telemusik, Mixtur'' (version for small orchestra, Nr. 16, "erster Frankfurter Version 1967") Ensemble Hudba Dneska,

(cond.); Johannes G. Fritsch, Harald Bojé,

Rolf Gehlhaar Rolf Rainer Gehlhaar (30 December 1943 – 7 July 2019), was an American composer, Professor in Experimental Music at Coventry University and researcher in assistive technology for music. Life Born in Breslau, Gehlhaar was the son of a German roc ...

, David Johnson (sine-wave generators); Karlheinz Stockhausen (sound direction). Avant Garde. LP recording.

Deutsche Grammophon Deutsche Grammophon (; DGG) is a German classical music record label that was the precursor of the corporation PolyGram. Headquartered in Berlin Friedrichshain, it is now part of Universal Music Group (UMG) since its merger with the UMG family of ...

137 012. Hamburg: Deutsche Grammophon, 1969. * Stockhausen, Karlheinz. ''Mixtur: Kleine Besetzung (1967)—Rückwärts- und Vorwärts-Version''. Orchester Hudba Dneska, 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 (composer), James Dillon, Beat Furrer, Giacinto Scelsi, Chaya Czernowin, Kaija Saariaho,

Liza Lim Liza Lim (born 30 August 1966) is an Australian composer. Lim writes concert music (chamber and orchestral works) as well as music theatre and has collaborated with artists on a number of installation and video projects. Her work reflects her int ...

Rebecca Saunders Rebecca Saunders (born 19 December 1967) is a London-born composer who lives and works freelance in Berlin. In a 2017 ''Classic Voice'' poll of the greatest works of art music since 2000, Saunders' compositions received the third highest total ...

Adriana Hölszky Adriana Hölszky (born 30 June 1953) is a Romanian-born German music educator, composer and pianist who has been living in Germany since 1976. Biography Hölszky was born in Bucharest. In the years 1959-1969 she studied piano with Olga Rosca-Be ...

, and traditional music from Egypt and Iran. Fundación BBVA, Kooperation mit BR Klassik. 6-disc hybrid multichannel SACD set. NEOS 10926. unich NEOS Music GmbH, 2009. * Stockhausen, Karlheinz. ''Mixtur 2003 für Orchester''.

Deutsches Symphonie-Orchester Berlin The Deutsches Symphonie-Orchester Berlin (DSO) is a German broadcast orchestra based in Berlin. The orchestra performs its concerts principally in the Philharmonie Berlin. The orchestra is administratively based at the ''Rundfunk Berlin-Branden ...

, Wolfgang Lischke (conductor); Karlheinz Stockhausen (rehearsals); Joachim Haas, Thomas Hummel, Bryan Wolf, and Reinhold Braig (sound mixers); Sven Thomas Kiebler, Antonio Pérez Abellán, Sven Kestel, and Holger Busse (sine-wave generators); Experimentalstudio des SWR, André Richard (sound director). Recorded at the Lehrbauhof, Salzburg, 30 August 2006. CD recording, 1 disc: digital, 12cm, stereo. Stockhausen Complete Edition CD 106. Kürten: Stockhausen-Verlag, 2015.

References

Cited sources

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'' (9 January): 13. * Griffiths, Paul. 1988. "Stockhausen's Signals". ''The Times'', no. 63252 (30 November). * 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 ''The Observer'' is a British newspaper published on Sundays. It is a sister paper to ''The Guardian'' and ''The Guardian Weekly'', whose parent company Guardian Media Group Limited acquired it in 1993. First published in 1791, it is the w ...

'' (30 April): 19. * Hopkins, G. W. 1968. "Stockhausen, Form, and Sound". ''

The Musical Times ''The Musical Times'' is an academic journal of classical music edited and produced in the United Kingdom and currently the oldest such journal still being published in the country. It was originally created by Joseph Mainzer in 1842 as ''Mainze ...

'' 109, no. 1499 (January): 60–62. * Kelsall, John. 1975.
Compositional Techniques in the Music of Stockhausen (1951–1970)
. PhD diss. Glasgow: University of Glasgow. * Mooney, James. 2016. "Technology, Process and Musical Personality in the Music of Stockhausen, Hugh Davies and Gentle Fire". In ''The Musical Legacy of Karlheinz Stockhausen: Looking Back and Forward'', edited by M. J. Grant and Imke Misch, 102–115. Hofheim: Wolke Verlag. . * Peters, Günter. 2006. "Karlheinz Stockhausen, ''MIXTUR 2003 für Orchester''". Programme book for the world premiere. Salzburg: Salzburger Festspiele. * Schatt, Peter W. 1995. "Eine 'Kunst des Überganges': Funktionen der Ringmodulation in Karlheinz Stockhausens ''Mixtur''". ''

Archiv für Musikwissenschaft The ''Archiv für Musikwissenschaft'' is a quarterly German-English-speaking trade magazine devoted to music history and historical musicology, which publishes articles by well-known academics and young scholars. It was founded in 1918 as the su ...

'' 52, no. 2:121–44. * Souster, Tim. 1972. "On Stockhausen's ''Mixtur''". '' The Listener'' 87:59. * Stockhausen, Karlheinz. 1967. "Notes on ''Mixtur'' (1964)", translated by William Sylvester. ''Electronic Music Review'', no. 1:16–17. * Stockhausen, Karlheinz. 1968. "Cinq textes". ' 21, nos. 2–4 (April–November): 43–50. * Stockhausen, Karlheinz. 1978. "''Mixtur'' für kleine Besetzung (1967): Zur Aufführungspraxis" etter to Pierre Boulez, written 9 November 1971 In his ''Texte zur Musik'' 4, edited by

Christoph von Blumröder Christoph von Blumröder (born 18 July 1951) is a German musicologist. Career Born in Northeim, Blumröder studied musicology at the Albert-Ludwigs-Universität Freiburg in Breisgau with Hans Heinrich Eggebrecht, philosophy and history of the ...

, 73–76. DuMont Dokumente. Cologne: DuMont Buchverlag. . Untitled English translation by

. ''

Music and Musicians Hansom Books was a British publisher founded in 1950 by Philip Dosse to produce the magazine ''Dance and Dancers''. Magazines in a similar format were then founded to cover other arts, so forming the Seven Arts Group. The other titles were ''Art ...

'' 21, no. 2 (October 1972): 31–32. * Stockhausen, Karlheinz. 2014. "Elektronisch bin ich ja selbst—''Mixtur 2003''". In his ''Texte zur Musik'' 15, edited by Imke Misch, 377. Kürten: Stockhausen-Verlag. . * Stockhausen, Karlheinz. 2014. "Zu ''Mixtur 2003''". In his ''Texte zur Musik'' 15, edited by Imke Misch, 378–380. Kürten: Stockhausen-Verlag. . * . 2006. "Sinusgenerator als Festspielgast: Karl-Heinz-Stockhausen-Uraufführung im Lehrbauhof". ''

Der Standard ''Der Standard'' is an Austrian daily newspaper published in Vienna. History and profile ''Der Standard'' was founded by Oscar Bronner as a financial newspaper and published its first edition on 19 October 1988. German media company Axel Springe ...

'' (1 September).

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