The resonances (eigenmodes of vibration) of the instrument in its playable state represent the objective instrument properties which are decisive in determining the subjectively perceived sound. What is the musical function of the resonances? Does "plate tuning" make any sense?

Welchen Nutzen hat die Anwendung der Akustikanalyse für den Geigenbau? Der Klang einer Geige What is the benefit of using acoustic analysis in making violins? The sound of a violin arises through a highly complex communication process between the musician and instrument. The musician directly responds (both consciously and unconsciously) to the resonance of the instrument. When the "musical frequencies" of the bowed notes (each of which consists of a fundamental note and related overtones) "hit" the resonance of the instrument, they cause the instrument to produce strong eigenmodes of vibration. At such places, the "musical frequencies" of the bowed string "communicate" (in physical terms, we would say they are "coupled") with the resonant frequencies of the instrument.

What is the musical function of the instrument's resonances? The violin's resonances "respond" to the musician's playing in the following four ways:

  1. The resonances amplify the audible sound. Due to their mode shapes, they will cause more or less effective sound pressure fluctuations in the air surrounding the violin.
  2. The resonances color the sound with a certain tonal color (we could almost say a certain "vocal color"). Like a singer's resonance regions ("formants"), a violin has characteristic frequency ranges with more or less pronounced resonances. This is the main reason for the similarity to the human voice.
  3. The resonances determine the response of the violin. Based on their vibration strength and damping, the resonances will influence the vibration behavior of the bowed string.
  4. The resonances determine the modulability and variety of tonal colors of the sound. This is due to the fact that their spectral density (number of resonances per frequency range) determines how often and how strongly the "musical frequencies" of the bowed notes communicate with the resonances of the instrument. This is precisely how the resonances determine how clearly the listener can hear the musical nuances of thevibrato and bowing..

Investigations in the MARTIN SCHLESKE MASTER STUDIO FOR VIOLINMAKING have shown that in the frequency range up to 2500 Hz alone, a good violin will have about 60 to 70 different resonances (eigenmodes of vibration), each with its own frequency and damping as well as its own mode shape and sound radiation. The resonance profile of a violin allows us to characterize the sum, distribution, shape and damping of these resonances in terms of the diverse musical tasks that are described above. A Stradivarius will have a significantly different “resonance profile” than a "Guarneri del Gesu" or a basic student instrument (see the section on sound analysis for more details on this topic). Differences (and also defects) in the playability or tonal color of different violins can be demonstrated in an impressive fashion using the resonance profiles of the instruments.

The resonances of an instrument are a consequence of the stiffness-to-mass distribution of the plates, meaning the "craftsmanship" (thickness graduation, arching, wood properties and treatment of the top and back plates). In violinmaking, this is to some extent the origin of the practice of assessing the stiffness-to-mass distribution of the plates by tapping and listening to the "tap tones" produced while holding the free plates between the fingers at certain node points. As an alternative, this sort of "plate tuning" can be performed using sinusoidal excitation at the respective resonant frequencies to show "Chladni's sound figures" for the free plates. Typically, however, these methods of "plate tuning" do not sufficiently take into account the fact that it is the much more complex eigenmodes of vibration of the playable instrument (and not the eigenmodes of vibration of the free plates) which are responsible for the sound radiation (and thus the "sound" of the instrument).

In-depth studies at the MARTIN SCHLESKE MASTER STUDIO FOR VIOLINMAKING have made clear that the eigenmodes of vibration of the free plates respond completely differently to modifications of the thickness graduation of the plates (and thus the stiffness-to-mass distribution) than do the eigenmodes of vibration of the assembled instrument. This is why the results of "plate tuning" tend to be of little use (if not entirely misleading).

Here, we see the clear benefit of modal analysis: As an acoustic tool, modal analysis makes it possible to analyze the objective properties of the instrument which actually determine the subjectively perceived sound, meaning the eigenmodes of vibration of the playable instrument. It is these eigenmodes of vibration which shape the acoustic functioning of the instrument.

Modal analysis thus provides a very insightful answer to an important question: "How does this or that violin work?" Note, however, that it does not answer the question of how good the violin sounds. Any subjective question about the quality of the sound must be answered by the person (player, listener) who is doing the judging. With the aid of modal analysis, it is possible to obtain an objective (and visual) answer to questions about the acoustic sources of the sound. One of the basic principles of research at the MARTIN SCHLESKE MASTER STUDIO FOR VIOLINMAKING requires a clear distinction between the terms "acoustics" and "sound" (which are often mistaken for synonyms). (See also: Philosophy of violin acoustics)

"Martin Schleske: "Eigenmodes of vibration in the creation of a violin". Thesis, Munich Technical University, "Technical Physics" department, 1994. Publications by M. Schleske.