[129] We might have hoped Zarlino's ranking of appropriate cadential degrees would complement the foregoing, but he was not very effective in this respect. His chapters on individual modes (Part IV, 18-29) subsume each under a rationalistic arithmetic system that unrealistically favors root, third, and fifth. This directly contradicts contemporary practice (as pointed out by Palisca, On the Modes, pp. xiii-xvi; Meier, The Modes of Classical Vocal Polyphony, pp. 105-7; and Carl Dahlhaus, Untersuchungen über die Entstehung der harmonischen Tonalität [Kassel, 1968], p. 198). Aaron gives a better idea of how modal counterpoint was actually being written (Trattato, Chaps. 9-12), even though his discussion is largely based on chant.