Pythagorean Music Theory and Its Application in Renaissance Architectural Design

Abstract

This article concerns Alberti's approach to architectural design integrates Pythagorean consonance ratios from music theory, not by direct application but as a conceptual guide for aesthetic ratios in buildings. He expands spatial dimensions using methods derived from past artisans, adhering to and building upon the foundational consonance ratios. While applying these two-number proportions to width and length poses no problem, calculating height in a three-dimensional space requires a three-number proportion. Alberti resolves this issue by adopting the mean value strategy from music theory, where the mean is typically the middle value in an octave ratio, to determine the height in the spatial configuration. Alberti advocates for architects to leverage the insights of skilled artisans. However, his own architectural work demonstrates deviations from his theoretical principles. This study highlights Alberti's application of musical intervals such as the major and minor thirds, sixths, and sevenths, which were not traditionally emphasized in the musical science of the quadrivium, focused primarily on octaves, fifths, and fourths. These choices reflect the broader evolution of music during the 15th century, marking a shift towards "practical music" and signaling music's departure from the liberal arts to become a significant element of the fine arts, showcasing the influence of Pythagorean consonance in European music and arts through the 16th century. Thus, this article reflects the interactions between music and architecture of knowledge received from ancient Greek civilization in the Renaissance. The art of music in this period is founded on the philosophy and knowledge of Pythagoras.