Non-Pythagorean proportions and the Diapasón in the design of iberian Harpsichord scales

Abstract

One of the tenets of modern organology is that the strings of keyboard instruments have generally been designed according to the theory that length is inversely proportional to pitch, resulting in a progression of string lengths known as a Pythagorean Scale. Recent research has begun to focus on surviving Iberian instruments, heretofore largely neglected. While few have survived, it would appear that a signifi cant number of their builders had a tendency to employ non-Pythagorean scales. One recent study suggests that these instruments represent a curious collective adherence to archaic methods used in the design of Medieval instruments. The present article offers an alternative viewpoint, showing how such scales could easily have been constructed using a traditional organ builder’s design tool, called a Diapasón. The geometric logic of the Diapasón is briefl y explained as well as the various progressions which can result from its use. The scales of several Iberian instruments are then examined in light of these alternative methods, arriving at the conclusion that their makers, rather than exhibiting an archaic conservatism, actually formed part of growing 18^th century movement towards the use of extended non-Pythagorean scales as are now ubiquitously found in the modern piano.