Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Reason and perception
- 3 Pitch and quantity
- 4 The ratios of the concords: (1) the Pythagoreans
- 5 The ratios of the concords: (2) Ptolemy's hupotheseis
- 6 Critique of Aristoxenian principles and conclusions
- 7 Ptolemy on the harmonic divisions of his predecessors
- 8 Melodic intervals: hupotheseis, derivations and adjustments
- 9 Larger systems: modulations in music and in method
- 10 The instruments
- 11 The tests
- 12 Harmonics in a wider perspective
- Bibliography
- Index of names
- Index of topics
12 - Harmonics in a wider perspective
Published online by Cambridge University Press: 22 September 2009
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Reason and perception
- 3 Pitch and quantity
- 4 The ratios of the concords: (1) the Pythagoreans
- 5 The ratios of the concords: (2) Ptolemy's hupotheseis
- 6 Critique of Aristoxenian principles and conclusions
- 7 Ptolemy on the harmonic divisions of his predecessors
- 8 Melodic intervals: hupotheseis, derivations and adjustments
- 9 Larger systems: modulations in music and in method
- 10 The instruments
- 11 The tests
- 12 Harmonics in a wider perspective
- Bibliography
- Index of names
- Index of topics
Summary
Since the opening of 11.3 declares that the programme of harmonic science has now been completed, the rest of the work really falls outside the scope of this methodological study. I shall consider one part of it, the introductory section, in a little detail, and offer only a brief sketch of the contents of the rest. This will be enough, I think, to give us some purchase on Ptolemy's conception of the place of harmonics among the sciences, and its role in equipping us to interpret and engage with the universe we inhabit. We shall then be in a better position to understand why a scientist of Ptolemy's stature should have found this apparently small and insignificant corner of the Greek intellectual tradition worth the meticulous attention he has given it.
After drawing a line under the completed business of the science of harmonics, 111.3 proceeds as follows.
Since it is natural for a person who reflects on these matters to be immediately filled with wonder – if he wonders also at other things of beauty – at the extreme rationality of the harmonikē dunamis, and at the way it finds and creates with perfect accuracy the differences between the forms that belong to it, and since it is natural also for him to desire, through some divine passion, to behold, as it were, the class to which it belongs, and to know with what other things it is conjoined among those included in this world-order,we shall try, in a summary way, so far as it is possible, to investigate also this remaining part of the study we have undertaken, to display the greatness of this kind of power.
(92.1–8)- Type
- Chapter
- Information
- Scientific Method in Ptolemy's Harmonics , pp. 259 - 269Publisher: Cambridge University PressPrint publication year: 2001