Our mission here at Bits4Waves is to provide tools that facilitate the practical application of research advancements in the construction of fine string instruments. In our recent post Carving site recommendations for plate tuning, we provided a spreadsheet to help the process of plate tuning by recommending regions to carve in order to obtain the desired final frequencies. In this article we will talk a little bit about the scientific research behind the motivation to do the plate tuning in the first place.
A good summary of some of the main research results on plate tuning was provided in A Retrospective on the History of Stringed Instrument Acoustics and on Plate Tuning Techniques, from the research papers by the Catgut Acoustical Society.
In his article Tap Tones and Weights of Old Italian Violin Tops, Joseph Curtin asserts that
The tap tones of Old Italian violin tops and backs have long interested makers and researchers, both as clues to how the classical makers graduated their instruments, and as guides for graduating instruments today
He then provides the measured frequencies for modes #2 and #5 of nine Old Italian violins, as can be seen on the table below, extracted from the article.
He cites the paper Stradivarius Plate Tests, by Carleen Hutchins, that she motivates with
This study provides measurable documentation of the mechanisms involved in the tapping and flexing long used by master violin makers
She also points out there that these results are
based on a detailed analysis of […] over 200 plate pairs […] during the making of [instruments] with good tone and playing qualities
She adds that tests on “the best violins made thus far” suggest that the tap-tone resonance mode #5 should have
high amplitude, low damping […] the same frequency in both top and back […] between 360 and 370Hz […] mode #2 […] an octave below and at exactly the same frequency in the two plates
Sie Anton in Comment on the “Double Octaves” Tuned Violins, asserts that “ten finely crafted violins have been made consistently using ‘Double Octaves’ matching plates tuning”, sharing considerations that were “summarized from a considerable number of professional violinists, teachers and advance students, who more or less have carefully played and tried the instruments.”
He presented there a correlation between the players’ preferences and the frequencies of modes #2 and #5, in the form of a table, reproduced below¹.
A later article by Carleen Hutchins, Some Notes on Free Plate Tuning for Violins, Violas and Cellos, summarizes these results in the table reproduced below.
We would like to finish by citing excerpts from Carleen Hutchins’ article The Acoustics of Violin Plates², where she establishes parallels between the manual bending and tapping of the plates that has been done for centuries and recent research findings:
These plate resonances, or normal modes, are created by the physical properties of stiffness and mass
The modes that [are the] most important in tuning violin plates are 1, 2 and 5
When a violinmaker holds a plate at each end, twisting it between his hands to feel its resistance, he is actually sensing the main stiffness characteristics of mode 1
When a maker holds one end of a plate in both hands […] squeezing it and bending it slightly to assess the cross-grain stiffness of first one end and then the other, he is comparing the relative stiffness of mode 2
When a luthier holds a plate around the two ends in his fingertips and pushes down in the middle with his thumbs, he is actually checking the principal stiffness of mode 5
tapping with the soft part of a finger around the upper and lower edges will activate the sound of mode 1
Holding at one of the four points where the nodal lines of mode 2 intersect the edges and tapping on the antinodal area near the midline of either end of the plate activates primarily mode 2
Holding at a point along the nearly oval nodal line of mode 5 and tapping in the centre of the plate causes the sound of mode 5 to predominate
To conclude, we would like to repeat the following beautiful words of Carleen Hutchins:
It cannot be emphasized too strongly that before one can apply such methods one must learn the violinmaker’s craft, so that the basic instrument is built according to the principles of fine violinmaking. I learned violinmaking in the 1950’s under the tutelage first of Karl A. Berger and then of Simone F. Sacconi with Rembert Wurlitzer’s encouragement. It was eight years of slow, painstaking work.
Our mission as a software company is to do our best to help the community, by making it more practical and straightforward to apply the state-of-the-art research findings in the making of fine instruments.
1. The author calls the modes #2 and #5 “X” and “O”, respectively. This is related to the fact that some authors³
prefer to give them descriptive names like ‘T’, ‘X’, and ‘O’ […] because the [Chladni patterns of the] modes assume different shapes in other instruments or occur in a different order
2. Hutchins, Carleen Maley. “The acoustics of violin plates.” Scientific American 245.4 (1981): 170-187.
3. Carruth, Alan. “Free Plate Tuning, Part Two: Violins.” The Big Red Book of American Lutherie, vol. 3, 1991-1993