Thickness Graduation

Measurement technique and representation of the thickness graduation (plate thicknesses) of bowed stringed instruments. Examples:

  • Thickness graduation of a cello with a top plate by A. Stradivari and back plate by G.F. Lott.
  • Comparison of the thickness graduation of two different violins (Stradivarius – Montagnana)
  • Comparison of the thickness graduation of six different violins by Guarneri del Gesu.

The MARTIN SCHLESKE MASTER STUDIO FOR VIOLINMAKING has developed its own sensor system for use in measuring the thickness graduation: The measurement sensor scans the surface of the plate whose thickness is to be measured. The signal is electronically displayed on a scale with millimeter precision. At the same time, a small loudspeaker emits a note with a pitch that is proportional to the measured plate thickness. An interval of a semitone corresponds to a change in the plate thickness of 1/10 mm. The flat design of the sensor system makes it possible to make measurements even under the tailpiece and fingerboard with no problems.

The Measuring Device

The following figure shows our prototype of a measuring device - here in use on a cello. The plate thickness (in mm) of the plate to be measured is scanned continuously on the closed instrument and displayed on an analog scale. The measured value is captured by a program running on the computer. The analog voltage of the sensor also controls the pitch of a function generator. This means the plate thickness is presented visually as well as acoustically: High pitches correspond to thin sections while low pitches correspond to thick sections (an interval of a semitone corresponds to a thickness difference of 0.1 mm). This means that when lines that are scanned on the instrument corpus produce the same pitch, they have the same thickness. 

Display of gray scale values

The thickness values and coordinates that the sensor sends to the computer are interpolated to produce a composite display of the overall thickness graduation: The result is a "thickness map". It can be displayed in color or using gray scale values. This figure shows a "thickness map" for a cello:

Fig.: Construction analysis of a cello (top plate by A. Stradivari; back plate by G.F. Lott). The thicknesses (in mm) were measured at 372 points using a specially developed electronic sensor and an XY coordinate table. This measurement is made on the closed instrument in its normal playing state. (The small size of the sensor makes it possible to measure even under the fingerboard and tailpiece.) Computation of the thickness contours (light gray = thin; dark gray = thick) involves subsequent interpolation of a total of 59,000 points.

This sort of analysis of the thickness graduation reveals many important construction perspectives for the instrument being studied.

Display of color values

Besides gray scale values, it is also possible of course to display the thickness graduation using colored contour regions. The following figure shows the colored contour map for the top plate thickness graduation of a violin by Antonio Stradivari (1712) with an optical resolution of 0.2 mm (the measurement accuracy is naturally greater than that of the resolution). The exact values as well as the variations in the plate thickness (in mm) can be read off at the transition between adjacent color regions. Analysis of multiple instruments by the same maker tends to reveal specific "graduation systems". The color maps also help to reveal typical features that one would probably be unable to discern from the plain numerical data. The Stradivarius top plate shown here clearly illustrates the notion of increasing the plate thickness in the region with steeply rising arching cycloids above the f-holes. It is also immediately apparent that the regions at the end of the bass bar have a thinner graduation than the other regions of the top plate. This produces additional decoupling of the large-scale antinodes in the region of the bass bar.

Analysis the thickness graduation of a violin top plate by Antonio Stradivari (1712).

Measurement of the plate thicknesses at 360 points on the closed instrument using a specially designed electronic sensor. A computer receives the data for processing.
Computation of more than 59,000 intermediate values through interpolation.
Display of the exact thickness curve using colored "contour maps". The thinner regions are red and the thicker regions are blue.

Comparison Display

Once the thickness values are compiled in numerical format, they can be displayed in other ways besides absolute values (as shown above). In many cases, it is useful to compare the thickness graduation of two instruments in order to reveal the characteristic differences. The difference between two sets of data is displayed graphically. The colored "thickness map" will then show the local differences in thickness between the two instruments.

Comparison of the thickness graduation of two different violins (Stradivarius – Montagnana)

In the white regions, both violins exhibit identical thickness graduation. The blue regions indicate where the plates of the Stradivari 1712 are thicker, while the yellow-red regions show where the Montagnana 1729 is thicker (scaling in millimeters). As we can see, the Stradivarius instrument from 1712 is significantly thicker than the Montagnana except in a few regions. By contrasting the relatively thicker edge of the back plate in the Stradivarius with the relatively thicker center of the top plate in the Montagnana, we can see that the two makers had different approaches to thickness graduation.

Displaying the thickness graduation using "thickness maps" (as opposed to pure numerical data) has a significant benefit in that the shape (the "graduation system") can be immediately discerned. For example, our presentation of the thickness distribution for six different violins by the renowned master Guarneri del Gesu shows us immediately that the top plate of one of these instruments (the "Kreisler" from the year 1730) is fundamentally different as it uses a completely different system than the other five instruments. However, this fact would not have been so obvious if all we had available was the numerical data.

This figure shows the thickness graduation (thickness distribution of the top and back plates) for six violins by Guarneri del Gesu. Dark-gray stands for thick areas and light-gray for thin areas. Top plate left, back plate right (for each instrument).

The graphical computations (interpolation) are performed by a program developed by the MARTIN SCHLESKE MASTER STUDIO FOR VIOLINMAKING.

The data which serve as the basis for this figure were taken from a fantastic work on Guarneri del Gesu by Biddulph, Peter et al.: "Giuseppe Guarneri del Gesu", London 1998. Our gray scale contour maps would make a very useful addition to the numerical data on the plate thicknesses contained in the book.