Engelmann first studied architecture and afterwards, in1946, he took private composition lessons with Hermann Heiss. Soon after the end of the Second World War, he got to know Wolfgang Steinecke and attended the first Summer Course for New Music (1946). In the participant lists of the IMD, Engelmann is enlisted as a student in piano courses with the participation number 1 (see picture). During the following years, he participated several times in the Summer Courses and was substantially influenced by the input of René Leibowitz (1948) and Ernst Krenek (1951). Some of his works were premiered or reproduced during the Summer Courses for the first time, for example the “Spielmusik für Streichtrio” (1945) and the “Divertimento” for string orchestra (1946), both even in his very first Summer Course year. The last premiere of one of his works was in 2006 during the 43rd International Summer Courses, when “Passatopresenza” for chamber ensemble under the direction of Daniel Carlberg had its premiere.
From 1947, Engelmann studied musicology (with Friedrich Gennrich and Helmut Osthoff) and philosophy (with Theodor W. Adorno, Max Horkheimer and Hans-Georg Gadamer) as well as literature and art history in Frankfurt / Main and took composition lessons with Wolfgang Fortner who had been lecturing – as well as Hermann Heiss – already since 1946 during the Summer Courses. In 1952, Engelmann did his doctorate on Béla Bartók‘s “Microcosm”.
After his marriage and a one-year stay in Iceland, Engelmann worked in several German theatres as a dramatic adviser, theatrical composer and directorial assistant, among others at the Staatstheater of Darmstadt. Between 1960 and 1968, he worked as a guest lecturer during the Darmstadt Summer Courses as well as during the Music Days in Bilthoven. From 1969 to 1986, Engelmann taught composition as professor at the Musikhochschule Frankfurt. He had been the teacher of for example Hans-Jürgen von Bose, Gerhard Müller-Hornbach and Wolfgang Kleber, last year’s Darmstadt Music Award winner. Engelmann was a guest professor in Gent, Offenbach, Tel Aviv and Jerusalem. Composition courses also led him to Moscow and Vilnius (1985) as well as to the Columbia University of New York (1995).
Engelmann´s honours include scholarships at the Harvard University (1949) and the Villa Massimo in Rome (1960, 1967, and 1983) and won numerous awards, such as the „Johann - Heinrich Merck Honour“ of Darmstadt (1971), the „Goethe Medaille des Landes Hessen“(1986) and the Hessian "Order pour le merite" (1997). Since 1995 he had been the chairman of the work committee of the GEMA. In 2006, Engelmann was bestowed the title of a Honorary Senator of the Frankfurter Hochschule für Musik und Darstellende Kunst being the fourth in row with Martin Gründler, Hans-Dieter Resch and August Leopolder.