# Correlation between Acoustic Analysis and Psycho-Acoustic Evaluation of Violins
## 1 Introduction  
In the literature there are studies that address the link between the acoustic quality of a violin and artistic perception based either on surveys completed by performers or listeners, or by using machine learning tools [1; 2; 3; 4; 5]. The sounds produced by a violin are the result of the interaction between the bow and the strings. The strings begin to vibrate both transversely in the direction of the force applied by the bow and longitudinally along the string. The transverse vibrations are transmitted through the bridge to the top plate of the violin and further to the entire air volume inside the violin body, which behaves like a Helmholtz-type resonator and produces an intense sound [6; 7]. The fundamental frequencies of the generated sounds are determined by the geometric characteristics of the source from which the wave propagates, and the number of harmonics (violin timbre) is determined by the resonator that amplifies the initial sound, adding the series of its own frequencies [8; 9; 10]. Thus, it becomes obvious that the quality of the sounds generated by a violin greatly depends on very many factors. These are related to the quality of the wooden material used to manufacture the instrument and its accessories, the quality of the other materials used in the construction of a violin (e.g., strings), the type of varnish (lacquer) andthe varnishing technology used, the skills of the violin maker, the skills of the musician, etc. Any modification--e.g., using a different wood species than maple for the back plate [11; 12], or changing the position of the sound post, or increasing the number of varnish layers, or changing the drying time after applying each varnish layer, or changing the thickness of the plates--may affect the sound quality [13; 14; 15; 16]. Optimization is possible only by a combined assessment, which must take into account both an objective evaluation, based on the determination of some measurable parameters, and a psycho-acoustic evaluation, based on the perception by specialists in the field of music (soloists and listeners). Even if the latter is a subjective type of assessment, when correlated to the objective evaluation it might validate some results which are impossible to be proven otherwise. The modal analysis is one of the most commonly used methods of acoustic assessment of modern or heritage violins [6; 17; 18; 19; 20]. By this method, dynamic parameters such as the fundamental frequencies of the vibrating components (top plate, back plate, air) can be determined, which can then be related to certain parameters of the sounds generated by the violin [9; 10; 21; 22]. For instance, the first eigenfrequency, also called the fundamental frequency, is essential in tuning a musical instrument. In the case of the violin, the fundamental frequency is in the range of 270-280 Hz. The second eigenfrequency, corresponding to the 2# vibration mode, reflects the contribution of the top plate within the violin body. The eigenfrequency with the maximum amplitude indicates how intense the plate vibrates and how high its frequency values can reach [22; 23]. Another objective method is to evaluate the acoustic spectrum based on the processing of violin signals. By applying the time and frequency domain analyses, the frequency spectrum and the power spectrum are determined. It is also possible to calculate a statistical analysis of the mode frequency, which is defined as the frequency of the vibration frequency in the 1/1 dB band or the 1/3 dB band [4; 5; 24; 25]. The psycho-acoustic analysis is also a scientific method of evaluating sound quality, frequently applied in the evaluation of both old (heritage) and modern musical instruments. Such an assessment can be performed by experienced musicians, from the viewpoint of the soloist, and/or from that of the listener [1; 2; 3; 4; 5]. The main criteria on which such an assessment is usually based [4; 6; 8; 25; 26] refer to the sound amplitude, tone brightness, clarity, warmth, silkiness of the sounds, color, etc.