Mosko died Tuesday of unknown causes, the Los Angeles Times reported Monday.
The Denver native told the Times in 1988 his family was "into nicknames and gambling" and started calling him "Lucky" at an early age.
Mosko taught at CalArts in Valencia for more than three decades and helped found a new music group, the California EAR Unit.
He was music director of the 1984 Los Angeles Olympic Arts Festival's Contemporary Music Festival and the 1987 Los Angeles Festival and for 10 years was music director of the San Francisco Contemporary Music Players and principal conductor of the Griffin Ensemble of Boston.
Mosko's compositions have been performed by the San Francisco and Sacramento symphonies, the Los Angeles Philharmonic, SONOR and the EAR Unit, among others.
He received two Fulbright/Hayes fellowships, which he used to become a leading expert of folk music of Ireland. He also received a National Endowment for the Arts Composers Fellowship, two Broadcast Music Inc. awards and a Fromm Foundation award.
He is survived by his wife, flutist Dorothy Stone, his father and a brother.