## Music

# Mathematical Derivations in Rameau's Revolutionary Music Theory

#### Description

The Baroque Era encompassed some of the most important scientific advancements in the history of mankind while simultaneously containing some of the most significant progressions toward theoretical formality and tonality in music. Theorist Jean-Philippe Rameau organized his observations on overtones and principal tones, chords, and tonality in the TraitÃ© de l'Harmonie (1722) and later works. Many modern scholars, including Rameau-connoisseur Thomas Christensen, have arranged the theorist's delineations alongside mathematical theories, providing a chronological system of discoveries. Physicist Ian Johnson published extensive research on the science of intervals and vibrations, which provide the fundamental components of Rameau's music theory. I contend that these intellectual growths in scientific philosophy and music theory were not independent of each other, and that the two are clearly connected by a chain of scholarly discoveries in the 17th and 18th centuries.

I analyze the physics of overtones and vibrations, upon which Rameau's tonal theories are based. For example, overtones were discovered within Aristotle's lifetime, but they were not explored until integral calculus derived a formula for predicting the fundamental frequency of a string based on its known components, in the mid-17th century. This led to a mathematical calculation of frequencies above the fundamental tone, which formed a basis for Rameau's tonal theory. I examine Rameau's theoretical presentations in traditional musical techniques of the early and mid-18th century using historical and mathematical references. In short, I explore why tonal music became appealing to composers and musicians in the late Baroque Era, and I assert that the early discoveries of the Scientific Revolution led them there.

*This paper has been withdrawn.*

Mathematical Derivations in Rameau's Revolutionary Music Theory

Indianapolis, IN

The Baroque Era encompassed some of the most important scientific advancements in the history of mankind while simultaneously containing some of the most significant progressions toward theoretical formality and tonality in music. Theorist Jean-Philippe Rameau organized his observations on overtones and principal tones, chords, and tonality in the TraitÃ© de l'Harmonie (1722) and later works. Many modern scholars, including Rameau-connoisseur Thomas Christensen, have arranged the theorist's delineations alongside mathematical theories, providing a chronological system of discoveries. Physicist Ian Johnson published extensive research on the science of intervals and vibrations, which provide the fundamental components of Rameau's music theory. I contend that these intellectual growths in scientific philosophy and music theory were not independent of each other, and that the two are clearly connected by a chain of scholarly discoveries in the 17th and 18th centuries.

I analyze the physics of overtones and vibrations, upon which Rameau's tonal theories are based. For example, overtones were discovered within Aristotle's lifetime, but they were not explored until integral calculus derived a formula for predicting the fundamental frequency of a string based on its known components, in the mid-17th century. This led to a mathematical calculation of frequencies above the fundamental tone, which formed a basis for Rameau's tonal theory. I examine Rameau's theoretical presentations in traditional musical techniques of the early and mid-18th century using historical and mathematical references. In short, I explore why tonal music became appealing to composers and musicians in the late Baroque Era, and I assert that the early discoveries of the Scientific Revolution led them there.