Western art music as we now hear it — major and minor keys, modulation, the tension-and-resolution arc moving away from the tonic and back — was largely consolidated during the Baroque period. The system existed before and survived after, but the seventeenth and early eighteenth centuries are when tonal harmony settled into the unambiguous form most listeners now take as the default of 'classical' music. The period codified most of the canonical forms of Western art music: the concerto, the sonata, the suite, the fugue, the opera, and the oratorio. J.S. Bach, working at the end of the period and dead by 1750, brought all of them to a synthesis the field has never since matched.
The Baroque inherited a modal system from Renaissance polyphony and reduced it to two scales: major and minor. Functional harmony emerged here and became the grammar of Western music for the next three centuries: the felt difference between tonic, dominant, and subdominant; the way a dominant chord wants to resolve to the tonic; the convention of moving away from the home key and back. The period codified the forms most listeners associate with classical music. Vivaldi's Four Seasons (1725) is the concerto concentrated: a soloist trading material with a small orchestra in three movements, a recurring tutti ritornello anchoring each. Handel's Messiah (1741) is the oratorio — sacred music with chorus, soloists, orchestra, staged in concert. Monteverdi's L'Orfeo (1607), the first opera that stayed in the repertoire, set what opera would be: drama set throughout to music. The fugue reached its definitive form in Bach's Well-Tempered Clavier.
J.S. Bach (1685–1750) is the period's central figure for one reason: he wrote canonical examples of nearly every form. The Brandenburg Concertos are the textbook concerto; the cello suites and violin partitas the textbook unaccompanied solo dance suite; the St. Matthew Passion and Mass in B Minor the textbook large-scale sacred music; the Goldberg Variations the textbook variation set; the Art of Fugue, unfinished at his death, the textbook of contrapuntal technique. The breadth is unusual; the consistency of quality across the breadth is unprecedented and has not been repeated. The historically-informed-performance movement of the past sixty years has reconstructed Baroque playing technique to the point where recordings of Bach today sound substantially different from those of half a century ago.
Bach's reception is its own story. He was largely forgotten within decades of his death until Mendelssohn's 1829 performance of the Matthew Passion in Berlin began the nineteenth-century Bach revival. Pablo Casals found the cello suites in a Barcelona second-hand bookshop in 1890 and rescued them from obscurity. The Goldberg Variations in Glenn Gould's 1955 recording brought Bach to the broad postwar listening public. Today Bach is the most-recorded composer in history, and the structural arguments his fugues exemplify — subject, answer, episode, stretto, recapitulation — remain the standard introduction to how Western polyphony actually works.