ABSTRACT
Despite these problems we can assert that two basic trends of music theory existed in a fairly sophisticated form after the appearance of Aristoxenus' Harmonics. The first developed from the earlier Pythagorean experiments in acoustics and attempted to associate musical science with arithmetical laws. This association was often extended to the explanation of a cosmological order based on significant musical numbers and patterns. The other, that of Aristoxenus himself, attempted to establish music as an independent and empirical science and was concerned with a systematic description of musical phenomena, primarily melody but often also rhythm. Later Pythagorean theory was able to use the methods established in Aristoxenus' treatise to expand its own program for musical investigation, adopting in particular his description of basic musical elements and systematic description of forms.
