Schenker's Theory of Counterpoint
Like his theory of harmony, which adapts and draws together a number of older ideas, Schenker's Counterpoint (written in 1910), is a refinement rather than a replacement of previous work on the subject.
His main source was a method of teaching counterpoint that had been handed down generations of musicians known as species counterpoint. An understanding of this discipline is vital to a full understanding of what Schenkerian analysis is about.
Species counterpoint teaches the student how to write music in two, and eventually four, parts. The aim is to explain what musicians over the centuries had established as 'good' writing. The ideal exercise showed an elegant balance of ascending and descending motion, of steps and leaps, and of consonance and dissonance.
The reason Schenker considered species counterpoint so important was because he believed that these qualities could be shown to lie at the heart of even the most complex compositions. More specifically, his theory adopted many of the rules on how to use consonance and dissonance and the various patterns that arise out of these rules in two-part writing.