2 Proportion Theory from the Renaissance to the Nineteenth Century

Pythagorean number aesthetics was again taken up in the Renaissance and further developed into a comprehensive theory of proportion in architecture. Leon Battista Alberti’s arrangement of the facade of the Florentine Palazzo Rucellai from 1455 is a striking example of the analogy between music and architecture passed down from antiquity. In his design of the exterior facade of the palace, Alberti, who, with reference to music, had already presented the ideal proportions for various room dimensions based on Pythagorean numerical ratios in his treatise De re aedificatoria (1485), realized a proportional arrangement that even went beyond Pythagorean consonances. In the facade’s organization, in addition to the eighth, the fifth, and the fourth, i.e., in addition to the ratios 1:2, 2:3, and 3:4 as well as their multiples, he also included proportions that are made up out of the number five and in terms of music correspond with pure thirds (major third 4:5, minor third 5:6) and sixths (major sixth 3:5, minor sixth 5:8). The inclusion of these proportions, which have major significance in the proportional organization (facade design, ground plan, and room arrangement) of Andrea Palladio’s buildings, incorporated an important music-theoretical innovation of the fifteenth and sixteenth centuries, according to which in addition to the eighth, fifth, and fourth, the thirds and sixths are now also acknowledged as consonant intervals. Thus, the musical way was clear for triad harmony, which replaced the medieval fifth and fourth organum and advanced to become a definitive musical feature that would remain valid until the late Romantic period.