He studied composition with Kees van Baaren (1952–1958) at the Utrecht Conservatoire and Royal Conservatory of The Hague.
Under van Baaren and Seiber, he combined traditional forms with dodecaphony in his 1954 Introductie en adagio in oude stijl and 1957 Septet.
[2] He was involved in the notorious 1969 "notenkrakersactie" (Nutcracker Action) in which a group of activists interrupted a concert by the Concertgebouw Orchestra, demanding an open discussion of music policy.
[3] That same year, Schat contributed, together with the composers Reinbert de Leeuw, Louis Andriessen, Jan van Vlijmen, and Misha Mengelberg, and the writers Harry Mulisch and Hugo Claus, in Reconstructie, a sort of opera, or "morality" theatre work, about the conflict between American imperialism and liberation.
It lends its name to a translation of his collected essays, The Tone Clock (Contemporary Music Studies) (1993, Taylor and Francis Verlag, ISBN 978-3-7186-5369-0).