A CT scan of the 1714 ‘Leonora Jackson’ Stradivari violin with a geometric overlay based on figure 4 (see page 57)
CT SCAN COURTESY STEVE SIRR
Antonio Bagatella’s treatise on violin making, Regole per la costruzione de’ violini, viole, violoncelli e violoni, was published in 1786. In it, the violin maker states he has rediscovered the design process behind the violins of the Brothers Amati. Both this book and the Librum Segreti de Buttegha were set to paper at approximately the same time and place, during the period when the Cremonese design process was lost – possibly indicating a common root. Among other things, both establish a 72-part scale for the body length of the instrument, and both contain numerical and geometrical rules for f-hole placement. Although it might seem odd to us to abandon standard measurements, a 72-part scale based on the length of the instrument form (see figure 2) is merely an elegant means of dealing with fractional mathematics: 72 can be divided by 2, 3, 4, 6, 8, 9, 12, 18, 24 and 36.
The jumping-off point for Stradivari’s calculations would have been the original string lengths. These, too, are difficult to ascertain, since almost all examples have had their necks changed in a process called grafting. By my calculations, and from measuring the original neck lengths of violins from other schools, I believe the relationship between the length of a violin’s internal form and its original string length was based on the ratio 18:17. The linear measurement between the locating pins of the back plate was eighteen 17ths of the intended string length (this ratio varied for the viola and cello), For Stradivari’s violins this indicates an actual violin neck measurement of around 12.7cm depending on the model. This is a little shorter than the modern neck and results in a shorter string length than the modern standard, but is commensurate with many historical examples of violins with their original necks.