We need to carefully distinguish between two terms: "Sound" and "Acoustics". Acoustics is a discipline within the field of physics. A physical language is used to characterize what happens in acoustics (e.g. using terms such as "mode shape", "frequency", "sound pressure level").

Sound is an aesthetic quantity instead of a physical one. Aesthetics is not a branch of physics. Instead, it belongs to the fields of art and philosophy. While sound has its origin in acoustic processes, it is not possible to describe the perception and quality of sound using the language of physics. The cause and effect must be different.

Otherwise stated: Acoustics involves intellectual insight while sound necessarily involves aesthetic or existential insight.
If sound is analogous to a painting, then acoustics can be likened to technical analysis of the colors of the painting. Of course, the painting is the result of a certain distribution of colors. But it would be absurd to believe that we could gain some insight into the aesthetic qualities or artistic content of the painting by analyzing the spectrum or frequency distribution of the colors.

Acoustics does not answer the question of whether the sound of a particular violin is more beautiful, more noble and so on when compared to another violin. We have to hear the sound and have some feeling for it if we want to say anything it. If this is true, however, what is the purpose of acoustic analysis? Acoustic analysis helps us to see the acoustic causes behind the sound we perceive. The production of very fine contemporary concert instruments can be qualified in a "revolutionary" manner if we are able to use acoustic analysis techniques to see the objective acoustic differences between, say, a "Stradivarius" violin and a basic student instrument.
These differences have their origin in the resonances of the instruments.

Sound radiation transfer function for four famous Cremonese violins. "Schreiber" Stradivarius (red); Stradivarius 1727 (blue); Carlo Bergonzi (violet); "Guarneri del Gesu" (black)  

A resonance profile represents the acoustic personality of a violin. An instrument's acoustic personality is determined by its acoustic "life", i.e. its resonances. Why do we refer to the instrument as having a "life" of its own in connection with the resonances? This is justifiable since unlike "forced" vibrations, resonances are independent of any external stimulus. They represent a fixed acoustic property of the structure (violin). They are known as the "eigenmodes of vibration". A musician cannot alter the eigenmodes of vibration. While playing, however, the musician does communicate directly with the resonances (meaning the acoustic properties) of his or her instrument. The resonances are the musician's counterpart.

A painter paints a painting. For a musician, the analogy is the interpretation of a composition. The painter's colors on a palette are like the resonances of the instrument for a musician. It is the resonances which the musician uses to "paint sound". Resonances (eigenmodes of vibration) are responsible for the tonal colors and the "luminosity" (projection) of the instrument..

The violin's eigenmodes of vibration are entirely independent of the musician. He or she has no way of influencing them. All the musician can influence is the vibrating string. The musician cannot influence how the vibrating string "communicates" with the eigenmodes of vibration of the corpus. However, the musician does perceive this highly complex communication process and is continuously involved in it by changing the vibrato, finger pressure, bow speed, bow pressure, contact point on the string and so on. This is how the musician "shapes" the sound. The musician can perceive whether he or she is "getting into the sound" and whether the sound can be shaped and modulated.

When a bow is drawn across a string, the violin "hears" the vibrations of the string. These vibrations cause the corpus to vibrate in its eigenmodes of vibration. The vibration movements of the top and back plates now undergo a periodic "pumping" action against the surrounding air molecules. In this process, they compress and decompress the surrounding air. The compression and decompression (over- and underpressure fluctuations in the air) propagate in the form of a pressure wave away from the instrument: Sound arises as a result. In other words, it is these vibration movements (mode shapes) of the top and back plates of the violin which actually produce the sound radiation of the instrument.

A given violin has a wide variety of eigenmodes of vibration. For example, at low frequencies (i.e. small number of vibrations per second) there exist eigenmodes of vibration for which the top and back plates of the violin are displaced in terms of very large-scale vibration regions. At high frequencies (large number of vibrations per second), the top and back plates are divided increasingly into small "vibration islands" which vibrate in opposition. The mode shapes can be measured and displayed using modal analysis. Every violin will have a different number of eigenmodes of vibration with their own unique shapes. This is something like a "fingerprint" for violins.

The actual eigenmodes of vibration that a given instrument has will depend on its construction (model, arching, thickness graduation, etc.) and material properties (elasticity and density of the wood, treatment with primer and varnish, etc.). For more information, please see Construction analysis and Wood and varnish analysis.

The harmonic levels of a played note represent the sound levels of the fundamental and related overtones. If we plot all of the fundamental levels for a chromatic scale alongside one another along with the related overtone levels above these fundamental levels, we will obtain a sort of "map" with mountains and valleys. If we now represent these mountains and valleys with colored contour lines, we will obtain a colored contour diagram. Due to its unique resonance profile, each and every instrument has its own unmistakable colored map.