Aristotle tells us rather little about empirical harmonics. His most significant reflections on the subject are concerned with the relation in which it stands to the mathematical form of the discipline, which he finds a good deal more rewarding, and we shall examine his views on this relation in Chapter 13. But before we move on to the next major phase in the history of the empirical approach, we need to review briefly some aspects of his Posterior Analytics. This pocket-sized treatise condenses into a mere seventy pages of text a meticulous study of the structure of scientific knowledge. We can only scratch the surface here, and in any case not all of it is relevant for present purposes; some other parts of it will be discussed when we come to consider Aristotle's comments on harmonics in their own right. But a sketch of some central theses is essential at this point, along with a rather closer account of certain details, because of the influence it exerted, a generation later, on Aristoxenus' conception of his project in the Elementa harmonica. I shall refer back to it repeatedly in Chapters 6–8. One of Aristoxenus' main aims was to improve radically on the manner in which his predecessors approached their research and set out its results, which he regarded as methodologically haphazard and inadequate, and to transform the discipline into a properly constituted science.