Figured Bass Notation: The Basics

In figured bass notation, an F written on the bass clef automatically "implies" the harmonies shown here on the treble clef. The normal harmony was a perfect diatonic triad built on the bass note, as shown here in the first measure. Numerical figures indicate alterations of the normal triad: a "6" meant that the fifth interval above the root would be replaced by the sixth. (See measure 2.) Adding a "4" to this figuration meant that the third interval (C) should be replaced by the fourth (D). (See measure 3.) Chromatic alterations could be indicated by adding marks such as a slash through the upper portion of a "6" to show that the sixth interval was to be raised by a half step. 

That's the system, in a nutshell, but what is amazing is the complexity of the instantaneous compositions that musicians could create over this simple framework. One can get a pretty clear idea of the art's complexities by viewing the next few multimedia pages. They show (and play aloud) famous examples of thorough-bass accompaniment drawn from Johann David Heinichen's Der General-Bass in der Composition [Thorough-Bass in Composition] (1728). Heinichen illustrates the development of a thorough-bass accompaniment from a bass line to final improvisation or to use the technical term, "realization" of a written thorough-bass. First, on the next page, see how the music looks to the improvising harpsichord accompanist: