 Aristoxenus' theory had an empirical tendency; in music he held that the notes of the scale are to be judged, not as earlier Pythagoreans had believed, by mathematical ratio, but by the ear.Vitruvius in his "De architectura" paraphrases the writings of Aristoxenus on music.His ideas were responded to and developed by some later theorists such as Archestratus, and his place in the methodological debate between rationalists and empiricists was commented upon by such writers as Ptolemais of Cyrene.