FOR GOOD MEASURE

In an age without a standardised measuring system, how is it that most Cremonese luthiers made instruments with such similar measurements and proportions? Simone Zopf argues that there was in fact a single unit of measurement from which most of the rest can be derived

FIGURE 1 This parchment, once part of Count Cozio di Salabue’s collection, shows the use of concentric circles in the patterns of Cremonese luthiers

COURTESY NATIONAL MUSIC MUSEUM, VERMILLION, SD, US

The measurements used by early Cremonese luthiers to create their instruments has always been a subject of debate. Without doubt, they used simple tools of the period, namely a ruler and compass, and applied the geometric principles of Pythagoras to achieve a perfectly balanced instrument. With this in mind, the idea of a standard unit of measurement is of particular importance. Previous research into the methods of the Cremonese masters has mostly dealt with their geometrical construction rather than measurement. Recent discoveries of tools and drawings, however, have allowed us to conclude that the makers of both the Brescian and Cremonese schools may have used a standard unit of length, and that this unit corresponds to the Roman oncia.

When we initially attempted to apply this unit to Cremonese violins, beginning with those made by Antonio Stradivari, the relationship did not emerge – until we utilised a completely new design system based around concentric circles. This system revealed the use of the oncia in all measurements needed to create the outline, and the radii of the necessary circles. This design system is also applicable to violas, cellos and even the smaller violins. We also successfully applied the principles to the violin scrolls and f-holes.

All students at the violin making school of Hallstatt, Austria, learn to measure and draw historical instruments, as well as understand the geometrical systems used by the makers of the Renaissance and Baroque eras. The proportions of instruments such as lutes, vihuelas and violas da gamba are well understood, but a clear and practical method for designing instruments of the violin family, accessible to luthiers with only a ruler and compass for guidance, was always missing. In 2014 the students undertook a research project to understand the design of Stradivari’s f-holes, based on his original sketches and Simone F. Sacconi’s 1979 book The ‘Secrets’ of Stradivari.

In 1980, researcher František Najmon published research on two brass rulers, part of the artefacts from the Stradivari workshop. From those, he identified a unit of 18.66mm, which he named the ‘Amati inch’. He also mentioned that the Roman oncia was very close to this value (between 18.58 and 18.75mm). In a subsequent study, Christian Pabst tried all relevant units linked to Cremona, including the unit Najmon had discovered, and looked for whole-number values in the measurements of violins; the measurement 18.66mm appeared to be relevant in 13 of the 22 instruments he examined. We therefore chose to focus on this unit for our own investigations.

Measuring systems in Renaissance Italy are a complex field, given the large number of local units for different materials, as well as their various subdivisions: palmo (hand), piede (foot) and braccio (arm) were common. For Rome, or more specifically, the Vatican city-state, there were three or four different measurement systems, although only one, the palmo romano architettonico, was used for all measurements of objects, buildings and woodwork. We also find references to the Roman oncia in the work of the 18th-century violinist and composer Francesco Galeazzi. In his writings on the best properties of a violin bow he states that the ideal bow length is 25 ‘pollici Parigini’ (‘Parisian thumbs’) or 37 once del palmo architecttonico (37 x 18.66 = 69cm). Roughly, the palmo architecttonico could be considered as the length from the tip of a human thumb to the tip of the little finger when both are outstretched; while the oncia approximates to the length of the thumb down to the first knuckle.

For this study, we examined high-quality photos of 38 violins, violas and cellos, scaled and calibrated to their exact measurements. The pictures were adjusted to take any camera distortion into account. This was necessary to discover possible similarities in their geometrical design. Most of the instruments chosen were made in Cremona, with a few from Brescia and some by Jacob Stainer, who was said to have been taught by Cremonese luthiers. All measurements were taken with callipers.

We also examined drawings, templates and sketches, including the templates from the Stradivari workshop as published by Stewart Pollens in 2010. These were also calibrated to their true size, and the Roman oncia measurement applied to them. A drawing on a piece of parchment once owned by Cozio di Salabue, probably part of the Stradivari legacy, was also investigated (figure 1). Now owned by the US National Museum of Music, the pattern shows concentric rings around an instrument. Finally, with the cooperation of the Musée de la Musique in Paris, we were able to examine and measure several original instruments from Cremona and Brescia.

For all the measurements taken relating to an instrument’s outline, we attempted to discover a relationship with the Roman oncia and simple fractions thereof. This idea stemmed from the fact that most of the other instruments (e.g. viols, lutes and guitars) seem to have been constructed in relation to this measurement. Furthermore, we used Sacconi’s drawings of Stradivari’s f-holes to measure their distance from the outline (not from the ribs), and find whether a relationship with the Roman oncia existed there as well (figure 2).

FIGURE 2 Construction of violin f-holes based on drawings of the ‘P’ mould from the Stradivari workshop. Red circles are of one oncia diameter, green = two oncias, yellow = 1.5 oncias. The blue circle (centre of lower eye to centre of upper eye) = 63mm. The lower eye is half an oncia in diameter, while the upper eye is one-third.

FIGURE 2 PHOTOS COURTESY MUSEO DEL VIOLINO, CREMONA

MEASURING SYSTEMS IN RENAISSANCE ITALY ARE A COMPLEX FIELD, GIVEN THE LARGE NUMBER OF LOCAL UNITS FOR DIFFERENT MATERIALS

FIGURE 4 Amethod for laying out an instrument pattern using concentric circles based on the measurement of the Roman oncia. For this process, an oncia is denoted by a ” mark. A video of this process can also be viewed at bit.ly/3WzwZLS

SIMONE ZOPF

• The main reference points of the violin shape could be constructed in the following manner. The maximum width of the upper bout is constructed by using the vertex of a 6-oncia circle; the lower bout by drawing a horizontal line to the vertex of a 5.5-oncia circle. The narrowest point of the violin is 1 oncia from the centre, and the radii forming the upper and lower bout are in most cases 3.5 oncias and 4 oncias (or a combination of both). The stop length can therefore be found very easily, in the first few steps of the process – unlike most other violin design methods. In 16 cases of the analysed instruments it was exactly one oncia from the centre, and 0.9 from the centre in four other cases.

• A step-by-step construction process for the violin was developed. It could be seen that the main values remain relatively similar, with only small variations in the construction of the corners from different types of violins.

• In 15 of the 32 cases the distance of the centre of the circles forming the upper and lower bouts are in a ratio of 2:3. In 10 cases it is exactly 2 oncias : 3 oncias. This value corresponds to the violin’s tuning (in 5ths), and may have been chosen deliberately.

• In our opinion, the difference between the value stated by Najmon (18.66mm) and the Roman oncia (18.617 mm) can be disregarded. In relation to the maximum width of a violin – 11 oncias – the difference amounts to 0.66mm and thus lies within the boundaries of shrinkage and craftsmanship.

• The construction of the f-holes can be explained by using quintisation, giving 42mm as the distance of the line from the centre to the lower f-hole, as seen on the Stradivari templates.

FIGURE 5 Violin scrolls of (left) the 1649 ‘Alard’ Amati and (right) the 1703 ‘Emiliani’ Stradivari. All measurements are shown in Roman oncia (”). ‘R’ denotes ‘radius’

FIGURE 5 PHOTOS SIMONE ZOPF. FIGURE

FIGURE 6 Two paper templates from the Stradivari workshop: Left Back part of a cello scroll, with distances of circles measured from centre to centre. Red lines = 1”, purple lines = 1.33” Right Side view of cello scroll and neck. The 4” line in the middle of the neck may indicate the maximum width of the scroll (4 x 18.66 = 74.6mm)

6 PHOTOS COURTESY MUSEO DEL VIOLINO, CREMONA

ON SEVER AL OTHER ITEMS, SUCH AS THE COZIO PARCHMENT AND STR ADIVARI TEMPLATES, CIRCLES USING WHOLE-NUMBER ROMAN ONCIA WERE FOUND

• The main sections of scrolls can also be identified by using the Roman oncia and its fractions (figure 5).

• The application of the Roman oncia was found directly on various Stradivari templates, showing multiples and simple fractions of the Roman oncia (figure 6).

• The parchment from Cozio’s collection shown in figure 1 shows three concentric rings at a distance of approximately 1 oncia (18.5, 19.0 and 18.6mm) from each other.

• The measurements of violins of Stradivari and other Cremonese makers from the Musée de la Musique in Paris confirmed the possible use of the Roman oncia.

In conclusion, the possible usage of the Roman oncia was identified in most instruments of the Cremonese luthiers, namely Andrea Amati, the Brothers Amati, Nicolò Amati, Antonio Stradivari, Andrea Guarneri, Guarneri ‘del Gesù’ and others such as Gasparo da Salò and G.P. Maggini. The preference of whole numbers for the total width and length of the violin is evident, since the mean value of 32 violins is 10.95 oncias for the width and 19 oncias for the length.

Also the main radii, used for the outline of the violin, can be expressed in whole-number or half-number values of the oncia. (4 and 3.5, 1 and 8 for the C-bouts). Furthermore, this unit was used in the design of violin scrolls and scroll templates. On several other items, such as the Cozio parchment and Stradivari templates, circles using whole-number Roman oncia were found.

This new approach to constructing a violin using the Roman oncia and concentric circles in whole-number distances from its geometric centre was applied to all investigated violins of the Cremonese luthiers. The construction itself is simple and straightforward, and requires only the use of a ruler and compass.

The author would like to thank all students from the department of violin making in Hallstatt, Austria for supporting this work with so much patience, diligence and passionate interest for this topic; and Jean-Philippe Echard at the Cité de la Musique, Paris, for the opportunity to work with these instruments.