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A native of Kraków, Trzaskowski learned to play the piano as a child and, in 1951, at the age of eighteen, helped to form Melomani, one of the first Polish swing and bop groups. Between 1952 and 1957 he studied musicology at the city's Jagiellonian University, took private lessons in composition and contemporary music theory and was active at the experimental studio of Polish radio.
In 1958 he played and recorded with the Jazz Believers, a quintet which included Wojciech Karolak and Jan Ptaszyn Wróblewski, and worked with another quintet, led by Jerzy Matuszkiewicz. The following year he formed his own hard bop group, the Wreckers, with which he toured the United States in 1962. As the leader of small groups, he performed and recorded with American musicians visiting Poland, such as Stan Getz in 1960 and Ted Curson in 1965-66. Many leading Polish musicians, including Zbigniew Namysłowski, Tomasz Stanko and Michał Urbaniak, played with his groups early in their careers.
Starting in 1964, Trzaskowski began to incorporate avant-garde techniques in his work. In the late 1960s he worked regularly in West Germany for the Hamburg-based public radio and television broadcaster Norddeutscher Rundfunk, writing more than 20 compositions and participating in workshops. From 1975 onward, he led an orchestra for Polish radio and television.
Although an acclaimed pianist, he decided, from the early 1970s, to concentrate more on composition. One of his early third-stream works, Nihil novi, was performed by Don Ellis at the 1962 International Jazz Jamboree in Warsaw. He subsequently wrote music for two jazz ballets and for numerous theater pieces and films, including Jerzy Kawalerowicz's Pociąg (The Train a/k/a Night Train) (1959), Mieczysław Waśkowski's Jeszcze słychać śpiew i rżenie koni... (Singing Still Heard, and the Neighing of Horses...) (1971), Andrzej Kotkowski's 1978 made-for-TV movie Gra o wszystko (A Gamble for Everything), Wojciech Marczewski's Dreszcze (Shivers) (1981), Janusz Kidawa's Bardzo spokojna wieś (A Very Peaceful Village) (1983) and Krzysztof Magowski's controversial 1990 TV miniseries Świnka (Piggy), which was not broadcast until 1994. He was also one of many musical celebrities making a cameo appearance in Andrzej Wajda's 1960 film Niewinni Czarodzieje (Innocent Sorcerers).
Andrzej Trzaskowski died in Warsaw at the age of 65, from undisclosed causes, and was buried in the city's Powązki Military Cemetery.
- The Wreckers (1960, Muza 0133)
- The Andrzej Trzaskowski Quintet (1965, Muza 0258)
- Andrzej Trzaskowski Sextet Featuring Ted Curson "Seant" (1966, Muza 0378)
- Poland (Polish Interpress Agency) (10): 42. 1968.
The composer's genuine jazz temperament is subjected to the rigors of strict intellectual discipline ... It might be added here that Trzaskowski is a musicologist as well and perhaps the best authority on problems of jazz composition.
- Liner notes (in English) for the recording of Andrzej Trzaskowski's Polish Jazz Quintet (includes a biographical sketch and an analysis of Trzaskowski's jazz compositions)