A simple explanation of the string-scaling design of the Urbino studiolo clavichord in the Palazzo Ducale, in Urbino.

 

           The second instrument described here is a highly-accurate intarsia ‘drawing’ of a clavichord in the studiolo (study room), 1473 – 1476) of the Palazzo Ducale in Urbino.  Although this clavichord is simply a drawing in wood, unlike most extant instruments of such a considerable age, this instrument has not suffered a single alteration to its case, string lengths nor fretting pattern, in the subsequent 550 years after its initial design and construction.  Therefore all of the features evident in this intarsia are represented without having to disentangle the later alterations from its original state.  What is truly remarkable and quite unexpected about this ‘drawing in wood’ is the amazing accuracy with which it was carried out.  This will be described later in this chapter. 

 

Section 1 – Federico da Montefeltro in the wider setting.[1] 

         Scholars at Federico’s Court could calculate the string scalings of the instruments that they were designing using ordinary long division or multiplication, without resorting to the use of logarithms which hadn’t yet been invented.  But Federico’s scholars did make use of Pythagorean scalings based on multiplying the string lengths successively by a number VERY close to the 12^th root of 2 =  = 1.0594631. .  .  But, surprisingly, multiplication factors based on the 11^th root of 2, =  = 1.06504, and on the 14^th root of 2, =  = 1.05076 were also incorporated into the design of their instruments.  These latter factors (very close but approximate) were used in their designs to take into account the variable strength of their wire which came about as a result of the work-hardening of the wire, which occurred during the actual wire-drawing process.  To my knowledge no historical maker has used anything but the 12^th root of 2 in the entire period after Federico’s Court in 1572, going right up to the beginning o the 19^th century – except for the Urbino harpsichord made c.1710, and now in the Ca’ Rezzonico in Venice - which is the subject of Chapter 6 below. 

          What has become clear as a result of the work done on RCM0001, and on the intarsia image of the clavichord in the studiolo of the Palazzo Ducale in Urbino, is that the designers of these instruments, who both attended at the Court of Federico, Duke of Montefeltro in Urbino, understood both the instruments and their musical use, and the properties of the wire they used in relation to the pitch of their instruments.  There is strong evidence that they did this at a level of total mastery and of the highest degree of sophistication.  The clavicytherium RCM0001 has been shown above to have been designed and made using the unit of measurement of Urbino itself.  This therefore points to the clavicytherium having its origins in Urbino, and having been made at the Court of Federico.  But, having ascertained this with a high degree of confidence, what has then come as a complete surprise is that, although the studiolo as a whole and the clavichord intarsia in particular, were clearly made for the Palazzo Ducale in Urbino where they are now located, the intarsia itself does not use the same unit of measurement as that used in Urbino itself, and therefore is also not the same unit as that used in the RCM0001 clavicytherium.  Hence, the intarsia of the clavichord was not made in Urbino!  This is discussed in detail below.  The measurements of Pierre Verbeek[2] of the case and of the string lengths of the clavichord all indicate, as will be shown below, that the intarsia was designed and made in the small towns of either Fossombrone or Castel Durante, both part of the Duchy of Urbino and located geographically just outside of Urbino.