Pal(l)adian Arithmetic as Revealed in the Palazzo Della Torre, Verona

Abstract

Room ratios in Palladio’s design for the Palazzo Della Torre mostly ignore his own canonical recommendations and none of the rooms exemplify his rules for room heights. Proportionately, however, the scheme, in plan and elevation, is a brilliant celebration of the cube root, just three years after Cardano published the solution to the cubic equation using methods passed to him by Tartaglia. Daniele Barbaro, Tartaglia and Cardano were all known to each other, and it seems most likely that Palladio would have taken a personal interest in the matter. The cube root that underpins the proportional scheme is Delian, that is, the cube root of 2 cited in Vitruvius. Palladio derives other roots of 2 in anticipation of the arithmetics which emerged in the early seventeenth century for the equal temperament musical scale. Of course, it must be understood that only rational convergents to the cube root of 2 are used. The relationship of room plan and elevation ratios in Palazzo Della Torre is illustrated by using the technique shown in Barbaro La Practica della Perspecttiva in which three-dimensional objects are unfolded to make two-dimensional “nets”, but figures are not used.