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
10 - The instruments
Published online by Cambridge University Press: 22 September 2009
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
Summary
When we set out to use our ears to assess harmonic relations,
there is needed to help them, just as there is for the eyes, some rational criterion working through appropriate instruments, as the ruler is needed to deal with straightness, and the compasses for the circle and the measurement of its parts. For the ears, similarly, which with the eyes are most especially the servants of the theoretical and rational part of the soul, there is needed some method derived from reason, to deal with things which they are not naturally capable of judging accurately, a method against which they will not bear witness, but which they will agree is correct. The instrument of this kind of method is called the harmonic kanōn, a term adopted out of common usage, and from its straightening [kanonizein] those things in sense perception that are inadequate to reveal the truth.
(5.3–15)It is some measure of the importance Ptolemy attaches to the use of such instruments in harmonics that he devotes nearly six whole chapters, and substantial parts of two more, to descriptions of their design and discussions of their properties. Issues to do with the procedures by which propositions are to be submitted to perceptual tests by means of these instruments are examined, sometimes at length, in at least a dozen other passages.
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- Scientific Method in Ptolemy's Harmonics , pp. 192 - 229Publisher: Cambridge University PressPrint publication year: 2001
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