Aristoxenus of Tarentum and the Birth of Musicology by Sophie Gibson

Author:Sophie Gibson [Gibson, Sophie]
Language: eng
Format: epub
ISBN: 9781135877460
Publisher: Taylor & Francis

2. THE DEVELOPMENT OF PYTHAGOREAN AND ARISTOXENIAN THEORY

In this section and the ones that follow, we shall trace briefly the major figures and works in the development of Aristoxenian and Pythagorean musical theory which followed the appearance of the Harmonics and the Sectio Canonis. It must be emphasised that the term Pythagorean is being used to reflect an approach to musical science and not a general philosophical stance. It means in this context, the adoption of the musical methodology started by Pythagoreans such as Philolaus and Archytas which highlighted the mathematical relationships between musical pitches. Later theorists who adopted the methods and expression of Archytas and Philolaus (such as Plato, Eratosthenes, and Ptolemy) are to be understood as Pythagorean only in a musical theoretical context. Even the elements of musical theory incorporating a cosmological emphasis such as in Plato, and later in Ptolemy and Aristides Quintilianus, can only be said to have their origins in Pythagorean thought.

In the subsequent centuries musicological methodology naturally continued to be reproduced, analysed and debated. Although no complete treatise survives from the period of Aristoxenus and Ps.-Euclid until the second century CE, there are some fragments which indicate how musical thought had developed in the meantime. They give us an idea of how an essentially Pythagorean understanding of musical structures recovered from the blow given to it by Aristoxenus’ treatise, principally by assimilating Aristoxenian empirical descriptions into its framework.

The dependence on arithmetic shown in the Ps.-Euclid is not the only area of concern in music for Pythagorean theorists and a significant difference in scope is an important distinction between the two methods. While Aristoxenus tried to limit his discussion to musical experience, the Pythagoreans, as Aristotle had noted in the Metaphysics,19 wished to grant to the numerical order of musical structures a cosmological significance. Side by side with this process, it should be noted that we have no evidence that Ps.-Euclid attempted to relate musicological description to a broader cosmological framework. Increased specialisation, probably necessitated by the delimitation of Aristoxenus’ work, was an important feature in the growth of Pythagorean musical theory.

However, Aristoxenus himself may not have been immune from considerations external to music. His ability to develop his conception of musical space may have been influenced by the developing science of geometry, in which irrational figures could now be expressed.20 Similarly, some of Aristoxenus’ tetrachordal divisions are so subtly distinguished (as Ptolemy later noted21) that there appears to be more of a concern to describe a balanced set of structures than to represent perceptibly different musical forms.22 Therefore, although Aristoxenus does not depend on the language or logic of another science, it can be argued that he is not entirely faithful to the task of maintaining an independent account of musical structures. It must also be acknowledged that an imperfect independence from external factors is frankly not as important as the fact that Aristoxenus’ work offers a significant opportunity for the development of musicological expression.

Incidentally, the Pythagorean and Aristoxenian methods were not the only approaches to describing musical phenomena in the fourth century.

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