Palladio's Theory of Proportions and the Second Book of the "Quattro Libri dell'Architettura"

The second of Andrea Palladio's Four Books on Architecture contains an insufficiently explicit theory of architectural proportions, hidden somewhere in the author's illustrations and text. Rudolf Wittkower (Architectural Principles in the Age of Humanism, London, 1949) suggested that harmonic proportions were the underlying principle of Palladio's designs, but he took into consideration only eight of Palladio's 44 examples. Deborah Howard and Malcolm Longair ("Harmonic Proportions and Palladio's Quattro Libri," JSAH, XLI, May 1982, 116-143) attempted a comprehensive statistical and quantitative analysis of all 44 buildings. The results were only partially satisfactory: in about two-thirds of all room plans, the ratios fitted Wittkower's theory, but the proportions of rooms in some of Palladio's best-known buildings, such as the Villa Rotonda, remained a mystery. Further, neither Wittkower nor Howard and Longair took into consideration the heights of the rooms; they were concerned only with their ground plan (length/width) ratio. This paper increases the number of explainable length/width ratios, analyzes data regarding the rooms' heights, and offers a theory concerning the influence of the method used to determine the height of one room on the proportions of another room on the same floor.