Mr. Mâche was born into a family of musicians and began composing at age eight. He studied harmony with Émile Passani at the Conservatoire de Clermont-Ferrand and graduated with prizes in piano in 1951 and harmony in 1952. He later studied with Olivier Messiaen at the Conservatoire National Supérieur de Musique de Paris, where he earned the Prix de Philosophie de la Musique in 1960. In addition to music, he had studies in classical literature at the École Normale Supérieure de la Rue d’Ulm from 1955–59 and there earned a diploma in Greek archaeology in 1957 and a teaching certificate (Agrégation de Lettres classiques) in 1958. He also took ancient art classes at the Université de Paris IV-Sorbonne in 1959 and later studied in Southeast Asia (Indonesia, Singapore and Thailand) in 1972.
His honors include the Prix de la Biennale de Paris (1963, for Safous Mélè, Op. 5), the Grand Prix du Disque (1971, for a recording of Danaé, Op. 21), the Prix Georges Enesco from SACEM (1973), and the Prix Italia (1977). More recently, he has received the Prix Chartier from the Académie des Beaux-Arts (1984), the Grand Prix National de la Musique (1988), the Prix Rossini from the Académie des Beaux-Arts (1998), and the Grand Prix de la Musique Symphonique from SACEM (2002) and has been a member of the Académie des Beaux-Arts since 2002, where he occupies the chair left by Iannis Xenakis. In addition, he received a composition grant from the Ministère de la Culture in 1978 and was named a Docteur d’État ès Lettres et Sciences Humaines in 1980 and a Commandeur de l’Ordre des Arts et des Lettres in 1990. More than 40 portrait concerts have been given in the Americas, Asia and Europe.