From renaissance musical proportions to polytonality in twentieth century architecture

Abstract

The predilection of Renaissance architects and theorists for proportional systems based on consonant musical intervals is well known to scholars of that period. For those who do not have the opportunity to peruse the relevant treatises and to measure exemplary buildings, the writings of Rudolf Wittkower, and especially his seminal Architectural Principles in the Age of Humanism (1971), published in the middle of the past century, provide a most helpful guide. In the chapter entitled The Problem of Harmonic Proportion in Architecture, Wittkower summarizes the principal reasons for this interest and focuses his attention on the writings and buildings of Leon Battista Alberti and Andrea Palladio, two of the most prominent and influential Renaissance architects, to provide tangible examples. He refers specifically to the Pythagorean monochord, by means of which the relationships between any two consonant sounds can be expressed as whole number ratios, and to the two Platonic sequences of numbers, traditionally shown in the configuration of a Lambda, which contains such “consonant” ratios. Wittkower argues that the Renaissance preoccupation with “harmonic” proportions, that is, specific relationships of whole number ratios, stemmed from an attempt to reflect in the built environment the cosmic order which, according to contemporary philosophy, was based on such proportions and revealed in music (1971: 101–154).