In 1949, Wittkower proposed that musical harmonic ratios were a principle underlying Palladio's designs illustrated in the ground plans of Book II of the Quattro libri. This theory, expounded in Part IV of Wittkower's Architectural Principles in the Age of Humanism, has been widely accepted, despite the fact that his research was based on detailed analysis of only 8 of the 44 plans in Book II. In the present study, a systematic, quantitative analysis of all the plans in Book II of the Quattro libri is carried out to discover to what extent musical harmonic ratios were an important principle behind Palladio's ground plans. Our results show that Palladio did indeed have a definite preference for numbers which can be related in ratios corresponding to the standard musical intervals. However, he does not make any consistent attempt to render his designs completely harmonic. Only about two-thirds of all the dimensions in the Book II plans are numbers which can be incorporated into musical ratios. Palladio often made no attempt to make his published measurements accord with musical harmonies where this could have been done by minor alterations, such as insignificant changes in wall thicknesses. The actual buildings, too, show a preference for dimensions which can be related by harmonic ratios, although not quite to the extent of the plans published in the Quattro libri. A few, most notably the Villa Barbaro at Maser, are significantly more "harmonic" in the published versions than in reality. In view of Daniele Barbaro's well-known interest in harmonic proportion, it is significant that all the completely harmonic designs postdate Palladio's collaboration with Barbaro on the Vitruvius edition and the Villa at Maser. Most of the patrons of those designs closely based upon musical harmonies appear to have shared an interest in musical or architectural theory. While Palladio almost certainly used musical theory in some later designs, his dependence on musical harmonic proportion was by no means as great as Wittkower implied. Elsewhere, his preference for harmonic dimensions probably resulted either from his use of certain favorite room shapes, or from the practical advantages of using simple, easily divisible numbers.

This non-technical review of Maxwell's contributions to the quantitative theory of colour was presented at a symposium in Aberdeen to celebrate the 150th anniversary of his appointment as professor of natural philosophy at Marischal College. Maxwell maintained his interest in the science of light and colour from his childhood to the last decade of his life. He lavished the same care and imagination on these studies as he did on his epochal contributions to electromagnetism and statistical physics.

The period 1900 to 1930 saw fundamental changes in the basic laws of physics. The discoveries of the special and general theories of relativity and those of quanta and quantum mechanics transformed profoundly physicists’ understanding of the nature of space and time, as well as the fundamentals of physics at the atomic level, which have no counterpart in classical physics. Almost coincidentally, major changes took place in the processes of musical composition – that same period seeing the development of atonality, the liberation of rhythm, and twelve-tone music. This essay reviews in non-technical terms the profound changes in the thinking of physicists and compares the intellectual struggles involved with the extraordinary parallel changes in the approaches of composers to musical composition. No causal connection is suggested, but the common theme of the processes of innovation and creativity within very strict sets of rules in both physics and music is emphasised.

No abstract

No abstract