What sorts of processes were going through the mind of J.S. Bach as he improvised a fugue in three, four, or even six parts? And what sort of training equipped an organist of the early eighteenth century to practice the art of accompaniment and improvisation successfully?

The practical method which linked keyboard technique, improvisation, performance, and composition in a continuum was the thoroughbass, the center of the Baroque musicians art. The Langloz Manuscript, originating in the era...