Ptolemy wrote an earlier work entitled Harmonikon (Ancient Greek: Ἁρμονικόν), known as the Harmonics, on music theory and the mathematics behind musical scales in three books.[63] It begins with a definition of harmonic theory, with a long exposition on the relationship between reason and sense perception in corroborating theoretical assumptions. After criticizing the approaches of his predecessors, Ptolemy argues for basing musical intervals on mathematical ratios (in contrast to the followers of Aristoxenus), backed up by empirical observation (in contrast to the overly theoretical approach of the Pythagoreans).[64][65]
Ptolemy introduces the harmonic canon, an experimental apparatus that would be used for the demonstrations in the next chapters, then proceeds to discuss Pythagorean tuning. Pythagoreans believed that the mathematics of music should be based on the specific ratio of 3:2, whereas Ptolemy merely believed that it should just generally involve tetrachords and octaves.[66] He presented his own divisions of the tetrachord and the octave, which he derived with the help of a monochord. The book ends with a more speculative exposition of the relationships between harmony, the soul (psyche), and the planets (harmony of the spheres).[67]
Although Ptolemy's Harmonics never had the influence of his Almagest or Geography, it is nonetheless a well-structured treatise and contains more methodological reflections than any other of his writings.[68][69] It also exherted a strong influenced during the Renaissance and the seventeenth century; Kepler, for instance, read and was influenced by this work in his own musings on the harmony of the world (Harmonice Mundi, Appendix to Book V).[70]