Italian composer famous for his treatise, Del sonare sopra 'l basso con tutti li stromenti e dell'uso loro nel conserto (1607; “On Playing Upon the Thoroughbass with All the Instruments and Their Use in an Ensemble”), one of the earliest instruction books for performing from the thoroughbass (basso continuo).

Agazzari was chapelmaster of the German College in Rome in 1602–03 and the Roman Seminary in 1606. In that same year he became a member of the famous Accademia degli Intronati at Siena. He returned to his native Siena in 1607, where he was organist for a time at the Siena cathedral and served as chapelmaster there until his death. He composed in both the stile antico (“old style”) of the late Renaissance and the stile moderno of the early Baroque. His works include a pastoral opera, Eumelio(1606), five books of madrigals (madrigal), numerous motets (motet), and masses, psalms, and other sacred music.

In his thoroughbass treatise, he distinguishes between “foundation” instruments (organ, lute, harpsichord, theorbo, and harp) and “ornament,” or melody, instruments (lute, theorbo, harp, cittern, bass lira, violin, guitar, spinet, and pandora). The significance of that distinction lies in its recognition that, whereas in Renaissance music (music, Western) all voices of a composition had usually been of equal importance, in Baroque music (music, Western) a new and significant concept was emerging—that of the contrasted roles of the upper (melody) and lower (bass) parts. Agazzari gave practical instructions for the use of counterpoint in the improvising of melody parts upon the thoroughbass.