Measurement and display of the arching of bowed stringed instruments. Example: Comparison of top plate archings by Carlo Bergonzi (Cremona), Domenico Montagnana (Venice 1729) and Antonio Stradivari (Cremona 1727).
There are many ways to record the arching of the two plates of a bowed stringed instrument. The three-dimensional shape is usually documented using casts. However, we have a much more practical approach to the analysis and documentation process: Using scanning sensors, we measure the arching profiles so as to allow
- Documentation as line graphs
- Printing as true-to-scale (1:1) template profiles
- Storage as a set of numerical data
- Arching measurement on a cello using the coordinate test setup and scanning sensors. Instrument by Domenico Montagnana (1740).
The test system consists of a coordinate test setup which records the three Cartesian coordinates (x = width; y = length; z = height) of a body using three displacement transducers and forwards the values to a computer. The special design of the height scanner makes it possible to measure the instrument in its playing state even under the fingerboard and tailpiece.
For each plate, six cross-sections are measured along with the longitudinal profile. The measurement accuracy is on the order of 0.1 mm. With the true-to-scale printout (1:1), the seven arching profiles produced for each plate are particularly handy for orientation purposes when building a new instrument modeled on an existing one.
Besides true-to-scale display, the documentation using line graphs is beneficial because it makes it very easy to compare data sets for different instruments. The following figure gives a comparative display of three classic reference instruments:
- Comparison of the top plate archings of three violins.
- Typical analysis result: The cross-sectional profiles of a violin back plate (true-to-scale).
Different scales are used for the x axis (longitudinal dimension) and y axis (height) in order to emphasize the differences in arching between the three violins. The accuracy of this arching measurement is about +/- 0.1 mm.
The following figure shows an example of a true-to-scale representation of an arching: