The CMW made its formal debut in the Mozart-Saal of the Vienna Konzerthaus in February 1962, and performed concerts regularly there until 1971.
Nikolaus Harnoncourt directed the ensemble from the cello until 1987, and subsequently led the CMW as its conductor and artistic director.
The CMW first toured North America in 1966, including its Boston debut for the Peabody Mason Concert series.
In succession to Nikolaus Harnoncourt, the CMW's current artistic leader is the harpsichordist Stefan Gottfried [de].
Among the CMW's recording projects with Telefunken and Teldec was their participation in the complete cycle of cantatas of Johann Sebastian Bach, over the period from 1971 to 1990.