By Flora R. Levin

During this ebook, vegetation Levin explores how and why song used to be so very important to the traditional Greeks. She examines the differences that they drew among the speculation of song as an paintings governed via quantity and the idea in which quantity is held to be governed via the paintings of track. those views generated extra expansive theories, quite the concept that the cosmos is a mirror-image of music's structural components and, conversely, that tune by means of advantage of its cosmic components - time, movement, and the continuum - is itself a mirror-image of the cosmos. those opposing views gave upward push to 2 opposing colleges of inspiration, the Pythagorean and the Aristoxenian. Levin argues that the conflict among those colleges may by no means be reconciled as the inherent clash arises from diverse worlds of arithmetic. Her e-book indicates how the Greeks' appreciation of the profundity of music's interconnections with philosophy, arithmetic, and common sense resulted in groundbreaking highbrow achievements that no civilization has ever matched.

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It is 2 and, as such, is not identical with a duo of musicians; rather, the duo of musicians is an instance of the number, 2; and the number, 2, is an instance of itself. 9 Given such an instance, the subject matter of music, like that of pure 7 The convention for indicating pitch adopted here is that of Carl E. Seashore, Psychology of Music, p. 73. This tautological type of formulation is seen by many as a logical trick that is a favorite device of mathematicians. For example, Susan Langer, Philosophy in a New Key, p.

L. Spitzer, Classical and Christian Ideas of World Harmony, pp. 10–17. 30 The diverse features of this conception that were henceforth to influence astro nomical thought for centuries converged with reality in the celestial physics of Johannes Kepler (1571–1630), who could not but stand in awe of his own discovery (Harmonikēs Mundi, proemium, Book 5, 179; Caspar, p. 289. ” 16 Greek Reflections on the Nature of Music in the models provided by geometry. For by assigning to each planet a path that conformed to its visible course in space, geometry assisted astronomy to determine whether its hypotheses were consistent with the observed phenomena.

The composer feels that he has a theme, a phrase which, when properly developed and embroidered, will produce beautiful music. Experience and a knowledge of music aid him in developing it. Similarly, the mathematician divines that he has a conclusion which will follow from the axioms. More recently, Edward Rothstein defined the link between music and mathematics as “something that mathematics and music share with our notions of the universe and our notion of the mind and soul – and 23 Thus, Edward Rothstein, Emblems of Mind, p.

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