Ancient Astrological and Musical Analogies in the Renaissance Palladio’s Villa Rotonda and Geometric Construction by Leonardo

The conclusions about the pure and exclusively musical nature of the proportions used by Palladio to illustrate the plates that accompany the Quattro Libri has traditionally, in modern criticism, been countered by the notable and unwieldy example of the relationships between the dimensions of the circular central hall and those of the rectangular rooms that surround it of Palladio’s most famous work of architecture, the Villa Almerico, known as the Villa Rotunda. Such an apparent exception to the harmonic ratios was underlined by Branko Mitrovic [1990]. Mitrovic, places the ratio 26:15 among the dimensions (in Venetian feet) of the larger rooms of the villa to the irrational ratio root of 3/1 and calls it “triangulature”, alluding to the fact that the ratio root of 3/1 is found in the right triangle with angles measuring 30° and 60° between the two catheti and the hypotenuse. In reality, the musical nature of the irrational proportions of the Rotunda, as with other analogous proportions as well, was destined to oblivion, which is perhaps in part due to the exclusive identification of the correspondences and musical analogies with rational ratios that exist between the first “small” integers (principally 1, 2, 3 and 4), linked to their Pythagorean origin of mathematical speculations on musical harmony. On the other hand, there is no doubt that at least part of the ratios of the Rotunda are irrational, derived, as was said, from the geometry of triangles. In this paper we shall indicate a key that is profoundly rooted in the culture of the Italian Renaissance, in order to shed light on the musical analogy to which the irrational proportions used by Palladio allude. In order to introduce the argument, it is useful and interesting to compare the dimensions of the plan of the Villa Rotunda with the concepts regarding the vesica piscis . This allows us to focus attention on the geometry, going beyond the horizon of simple arithmetic considerations. Further, before describing the analogies of the Villa Rotunda, in the context of concepts linked to the vesica will be compared to a sketch by Leonardo da Vinci which he draws, not very surprisingly, in the margins of a folio dedicated to studies of centrally-planned sacred architecture. Finally we will set forth an interpretation - in the spirit of the sensibilities and comprehension active in the Italian Renaissance which rediscovered and loved the ancient authors Vitruvius and Ptolemy - of the analogies and symbolism inherent in these same numerical and geometric ratios that are inseparably linked to musical harmonies.