Pitch and quantity
Readers intent on the issues that are central to Ptolemy's methodology can be forgiven for ignoring some of the present chapter's more detailed ruminations in favour of their own, less pernickety reading of I.3. My remarks in this chapter amount to a partial commentary on that stretch of text, and on little else. As I remarked earlier, the phase of the investigation conducted here, which I labelled as Stage (i), is only a preliminary. It is designed to establish the proposition that pitch is a quantitative attribute of sound, and to identify the causal factors responsible for its variations. Ptolemy treats these questions as closely interconnected. The proposition about pitch cannot be established without a study of the causes; and in practice the two issues are pursued simultaneously. Both have important roles in the sequel. The first will legitimise Ptolemy's policy of expressing pitch relations as ratios of numbers, in accordance with their mathematical forms rather than with the corresponding pathē. The second will serve as a basis for correlating the one mode of description with the other; it will also provide an account of the principles underlying the construction of experimental instruments, and the groundwork for an understanding of their use. The main purposes of my project would be served well enough by a bare sketch of the arguments in this passage.
Nevertheless, the details are of some interest, and I shall spend a little time on them. I shall try to show, in particular, how Ptolemy's treatment of the subject, culled though most of its contents are from earlier writings in a well established tradition of acoustic theorising, is accommodated throughout to a particular conception of the relation between causes and effects. That conception, too, is borrowed by Ptolemy from elsewhere, and it is certainly open to criticism; but he adheres to its implications with remarkable, even obsessive, tenacity. We can recognise in this smallscale and relatively self-contained exercise the same generalised passion for methodological consistency as characterises the Harmonics as a whole. I shall also draw attention, on the other hand, to various difficulties of detail, anomalies and gaps in Ptolemy's account. Quite apart from issues about the reliability of its 'facts' and the truth of its
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Publication information: Book title: Scientific Method in Ptolemy's Harmonics. Contributors: Andrew Barker - Author. Publisher: Cambridge University Press. Place of publication: Cambridge, England. Publication year: 2000. Page number: 33.
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