Born in Cologne, he is the son of composer Karlheinz Stockhausen. At age four he appeared as "child at play" in his father's theatre piece Originals. He received his first piano lessons at age six, and at age twelve he began to play the trumpet. He attended the music secondary school in Cologne.
From 1974 he studied at the Cologne Musikhochschule, where he began on piano with Klaus Oldemeyer, then classical trumpet with R. Platt and jazz trumpet with Manfred Schoof, graduating in 1982. Further studies between 1978 and 1983 were with P. Thibaud, C. Caruso, T. Stevens, and C. Groth. His jazz and classical débuts were in 1974 with the group „Key“ at the Newcomer Jazz Festival in Frankfurt and in 1976 in his father's Sirius at the Washington Bicentennial. In 1981 he was the winner of the German Music Competition.
Already in 1974 Markus began to cooperate intensively with his father. The trumpet parts of the following works were written for and premièred by him: Sirius 1975-77 (with Aries 1980); Thursday from Light 1978–81 (especially the major parts in Examination, Michael's Journey around the Earth, Dragon-Fight, Vision, and the Thursday Farewell); Saturday from Light (Upper-Lip-Dance, 1984); Tuesday from Light (Invasion, Pietà, 1990–91); Europa-Gruss (1992); Michaels-Ruf, version for four trumpets (1978/1994); Trumpetent (1995); In Freundschaft (version for trumpet, 1998). In addition, his father composed cadenzas to the trumpet concertos by Haydn and Leopold Mozart for him.
In addition to his activities as a soloist, he has played in and led various jazz ensembles, the quintet "Key" (1974–79), Rainer Brüninghaus Group (1980–84), Kairos (1985–90), Aparis (1989–96), various formations with the Chilean bass player Enrique Diaz (1989-), Possible Worlds (1995-) and the performance lila with sculptor Norbert Müller-Everling at Leverkusener Jazztage. Partners today are Simon Stockhausen (keyboards, saxophone), Enrique Díaz, Arild Andersen (bass), Patrice Héral (percussion), the Hungarian guitar virtuoso Ferenc Snétberger, Antoine Hervé (piano), Angelo Comisso (piano) and Mark Nauseef (percussion), the pianist Fabrizio Ottaviucci and in the duo "Moving Sounds" he performs together with the Dutch clarinetist Tara Bouman, with whom he has lived and worked since the year 2002.
Concerts and Festival appearances, also for the Goethe Institute, have taken him around the world. His main interest as a trumpeter is improvised and contemporary music; therefore, in February 2003 he premiered Jetstream for trumpet and orchestra, which was written for him by Peter Eötvös, who also conducted the premiere in London with the BBC Symphony Orchestra, and in November 2008 he gave the first performance of Freedom Variations, a composition for trumpet and chamber ensemble written by Italian composer Lorenzo Ferrero. The classical repertoire he plays on request only. He increasingly performs his own music, also giving solo performances with intuitive music, often in churches.
As a composer he has, in close collaboration with his brother Simon, written several film and theatre scores and created two open-air spectacles for the 5th and 10th anniversaries of the Philharmonic Hall in Cologne, with 70,000 and 100,000 spectators respectively. Recently he composed Choral and Sehnsucht for jazz trio and orchestra. New works have been commissioned and performed by the London Sinfonietta and the Musikkollegium Winterthur.
An extensive discography documents his achievements (ECM, AKTIVRAUM, CMP, ACT, ENJA, Stockhausen Complete Edition). From 1992 until 1998 he was under contract to EMI Classics.
- Cosi lontano … quasi dentro, with Gary Peacock (double bass), Fabrizio Ottaviucci (piano), and Zoro Babel (drums). ECM 837 111-2. Munich: ECM Records, 1989.
- Aparis, with Simon Stockhausen (synthesizers and saxophone) and Jo Thönes (drums). ECM 1404. Munich: ECM Records, 1990.
- Karlheinz Stockhausen, Michaels Reise: Solisten-Version, with 9 other musicians. ECM New Series. ECM 1406. Munich: ECM Records, 1992.
- New Colours of Piccolo Trumpet (1993) (EMI, reissued Stockhausen Complete Edition)
- Clown (EMI)
- Sieben Psalmen, with Nóirín Ní Rían (singer), Pater Friedhelm Mennekes SJ (recitation), Simon Stockhausen (synthesizer and saxophone), Christoph Schumacher (percussion). EMI Classics 7243 5 55213 2 3. Cologne: EMI Electrola GmbH, 1994.
- Jubilee (1996)
- Markus Stockhausen plays Karlheinz Stockhausen", with Niek de Groot (double bass) and Annette Meriweather (soprano). EMI Classics 7243 5 56645 2 5. Cologne: EMI Electrola GmbH, 1998.
- Markus Stockhausen
- Solo I
- Close to you
- Thinking About
- Karta (ECM)
- Instantanés 1997 (ENJA) with the Antoine Hervé Quintet: Antoine Hervé, François Moutin, Louis Moutin, and Arnaud Franck
- Other Presences 2008 (SARGASSO)
With Rainer Brüninghaus
- Continuum (ECM, 1983)
With Ralph Towner
- City of Eyes (ECM, 1988)
- Anon. "Evento: Sonata Islands—Jazz & Notation: 25.11.2008", Teatro del Verme, Provincia de Milano website (Accessed 28 January 2011).
- Sanz, Pablo. 2006. "Markus Stockhausen, una mirada fuera de plano". Scherzo: Revista de música 21, no. 210 (July–August): 136–37.
- Tarr, Edward H. 2001. "Stockhausen, Markus". The New Grove Dictionary of Music and Musicians, ed. S. Sadie and J. Tyrrell. London: Macmillan.
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