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The Scientific Revolution and the Rationalization of Music

  • The Journal of Aesthetics and Science of Art
  • Abbr : JASA
  • 2013, 37(), pp.125~157
  • Publisher : 한국미학예술학회
  • Research Area : Arts and Kinesiology > Other Arts and Kinesiology
  • Published : February 28, 2013

Jun-Sik Won 1

1대전대학교

Accredited

ABSTRACT

The Scientific Revolution has played an important role in the process of rationalization in music as well as in the inquiry into nature. The fact that music belonged to the research interests of many major scientists of the 17th century was not due to chance, because music until the 17th century was a branch of science and held a place among the quadrivium beside arithmetic, geometry and astronomy. Their scientific inquiry into music had the major influence on rationalization of music itself as well as developed the musical theses rationally. The connection between music and science forged by the Pythagorean school’s discovery of the relation between the length of a vibrating string and pitch – generally accepted as the first law of nature to be formulated mathematically. They discovered the perfect consonances of the octave, 5th and 4th, and their ratios (1:2, 2:3, 3:4), and the Pythagorean scale based on this system of consonances has been employed during Antiquity and the early Middle Ages. But with the development of polyphony in the later Middle Ages, it gave way to just intonation having consonant 3rds and 6ths, without which there can be no polyphony. Zarlino systemized the just intonation by substituting senario for Pythagorean tetractys, and thus the ratios of the consonances are contained within the numbers 1 to 6. Zarlino’s theory as well as Pythagoras’s can be characterized by number-mysticism, in the sense of taking the numbers to be the causes of consonances. Kepler, like Zarlino, advocated the polyphony and the just intonation, but insisted that the causes of consonances must be sought not in numbers but in geometrical figures. He looked for the criterion for distinguishing consonance and dissonance in the arcs of a circle cut off by the regular inscribed polygons; equilateral triangle, square and pentagon. In this sense, he also can be characterized by a kind of mysticism, a geometrical mysticism. The experimental approach to music began with Vincenzo Galilei, and his goal was to refute Zarlino’s theory. He discovered by means of experiment that the ratio of the string-lengths to produce octave is 2:1, but the ratio of the weights suspended from the strings is 4:1, not 2:1. Thus in order to get 5th, the weights have to be in the ratio 9:4. Consequently the ratios of the consonances are not necessarily contained in the first six integers. Galileo Galilei accepted the coincidence theory of consonance from Benedetti, according to which the degree of consonance of a two-note cord is determined by rarity of frequency with which the pulses of the sound-waves exactly coincide. If the pulses of the two notes coincide fairly often, then the interval is fairly consonant, and if less often, then less consonant. In spite of several weak spots, the coincidence theory became the starting point of all subsequent musico-scientific inquiry for at least half a century. The most important thing of the effects that the Scientific Revolution had on music was to expel mysticism from music theory. It is experiment that played an important role in the process of the expulsion. Experiment was the effective means to demonstrate the errors of number-mysticism and ultimately to overthrow it.

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