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Contents

Music from the Earliest Notations to the Sixteenth Century

MUSIC FROM MATHEMATICS

Chapter:
CHAPTER 8 Business Math, Politics, and Paradise: The Ars Nova
Source:
MUSIC FROM THE EARLIEST NOTATIONS TO THE SIXTEENTH CENTURY
Author(s):
Richard Taruskin

From a purely mathematical point of view, the Ars Nova innovations were a by-product of the theory of exponential powers and one of its subtopics, the theory of “harmonic numbers.” It was in the fourteenth century that mathematicians began investigating powers beyond those that could be demonstrated by the simple geometry of squares and cubes. The leader in this field, and one of the century’s leading mathematicians, was Nicole d’Oresme (d. 1382), the first French translator of Aristotle, whose writings (as we have already seen) encompassed music theory as well. His career as scholastic and churchman closely paralleled that of Philippe de Vitry: Philippe ended his ecclesiastical career as the Bishop of Meaux, northeast of Paris; Nicole ended his as Bishop of Lisieux, northwest of Paris. Nicole d’Oresme’s Algorismus proportionum was the great theoretical exposition of fourteenth-century work in “power development” (recursive multiplication) with integral and fractional exponents; but it was precisely in Jehan des Murs’s music treatise that the fourth power first found a practical application.

Citation (MLA):
Richard Taruskin. "Chapter 8 Business Math, Politics, and Paradise: The Ars Nova." The Oxford History of Western Music. Oxford University Press. New York, USA. n.d. Web. 23 Oct. 2014. <http://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-div1-008002.xml>.
Citation (APA):
Taruskin, R. (n.d.). Chapter 8 Business Math, Politics, and Paradise: The Ars Nova. In Oxford University Press, Music from the Earliest Notations to the Sixteenth Century. New York, USA. Retrieved 23 Oct. 2014, from http://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-div1-008002.xml
Citation (Chicago):
Richard Taruskin. "Chapter 8 Business Math, Politics, and Paradise: The Ars Nova." In Music from the Earliest Notations to the Sixteenth Century, Oxford University Press. (New York, USA, n.d.). Retrieved 23 Oct. 2014, from http://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-div1-008002.xml
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