There are two basic approaches to counterpoint, one based on consonance, the other on independent melodic-rhythmic progressions. As a conservative, Hindemith employs counterpoint in the first sense only, yet uses dissonant counterpoint, the dissonance being the result of (1) non-traditional chords, (2) an extended application of non-harmonic notes, (3) certain melodic tehniques, and (4) polytonality.

These approaches were illustrated by examples from his Ludus tonalis. Under (1) the use of three-seven, four-seven, and five-seven chords was discussed. All of these and their inversions are employed not only as structural harmonies, but also often as the result of non-harmonic notes, and they lead to frequent parallel sevenths. As to (2), non-harmonic notes serve to bring about dissonance clashes between parts. They are freely used, but their function remains always clear; often their resolutions are delayed to provoke further clashes. They also serve to counteract the romantic effect of chromaticism.