# Correlation between Acoustic Analysis and Psycho-Acoustic Evaluation of Violins
## 3 Results  
### Results of the Acoustic Analysis  
In the first stage of the signal analysis, the time and frequency analyses were obtained for each violin tested (Figure 5). In the time analysis graphs (those at the top of each figure), the signal for each recorded audio sequence (as shown in Figure 4) is distinctly observed. Although the acoustic fragment was performed by the same violinist, there were differences  
Figure 4: The acoustic signals in time domain, played on the violins. in the duration of the signals and their sound pressures from one violin to another. The graphs presenting the frequency analysis (at the bottom of each figure) show the frequency spectrums and their magnitudes expressed in arbitrary units (noted a.u.). Based on the FFT, the specific modes of each analyzed violin were extracted in the low frequency range (100-700 Hz), these being considered signature modes, providing the specificity of each violin and always being found in the spectral analysis of that violin, regardless of the musical sample performed [5,15,24]. Figure 5: _Cont._  
The values regarding the signature modes and the dominant frequencies were extracted and centralized in Table 1. It is observed that for violins AM2 and AP4 the dominant frequency with the highest amplitude in the frequency spectrum is identical with the frequency of the B1- mode. For the AM6 violin, the dominant frequency also corresponds to the CBR mode, and for the AP2 violin this corresponds to the B1+ mode frequency. For violin AP6, two dominant frequencies were identified, corresponding to the bending mode B1- and air cavity mode A2, respectively, while for violins A00 and AM4 the values are different. For all violins, the frequency of the B1- is in the immediate vicinity of the fundamental pitch (frequency = 440 Hz). From the statistical analysis of the signals processed with STFT, regarding the frequency of occurrence of certain frequencies, the values of the mode frequency were extracted with the highest frequency of occurrence (Table 1). The frequency mode for the free string and Pizzicato-style excitation corresponds to corpus mode C4, according to [13; 14; 15; 16; 17]. Figure 6 shows the spectrograms for the seven violins analyzed. Figure 5: The acoustic signals played on the violins: (**a**) AM6C1; (**b**) AM4C1; (**c**) AM2C1; (**d**) A00C1; (**e**) AP2C1; (**f**) AP4C1; (**g**) AP6C1. (Legend: a.u. represents the notation for arbitrary units. ). \begin{table}
\begin{tabular}{c c c c c c c c} \hline  & & & & \multicolumn{4}{c}{**Tested Violins**} \\
**Frequency (Hz)** & **AM6C1** & **AM4C1** & **AM2C1** & **A00C1** & **AP2C1** & **AP4C1** & **AP6C1** \\ \hline Mode A0 & 297.4 & 298 & 299.3 & 299.3 & 295.5 & 294.9 & 298.2 \\ Mode CBR (C2) & **395.5** & 393 & 399.0 & 398.1 & 392.8 & 394.7 & 396.7 \\ Mode B1- & 446.4 & 446.3 & **450.5** & 448.7 & 443.0 & **442.4** & **446.7** \\ Mode A2 & 596.1 & 596.1 & 597.9 & 599.5 & **591.0** & 592.0 & **596** \\ Dominant frequency & **395.5** & 499.4 & **450.5** & 499.4 & **591.0** & **442.4** & **446.7/596** \\ Mode frequency (free strings) & 668.34 & 669.30 & 674.19 & 674.5 & 665.7 & 664.63 & 671.31 \\ Mode frequency (Pizzicato) & 665.13 & 665.86 & 670.81 & 673.2 & 664.9 & 664.40 & 671.45 \\ Mode frequency (musical part) & 1846.20 & 2812.30 & 2360.10 & 2580.3 & 2804.2 & 1875.80 & 1874.30 \\ \hline \end{tabular}
\end{table} 
Table 1: The main frequencies extracted from frequency domain analysis. The bold values correspond to higher amplitudes from all frequency spectrums. Figure 6: _Cont._Figure 6: _Cont_. Figure 7 presents the comparison between the mode frequencies for the different acoustic sequences. In the case of free string and Pizzicato-style excitation, it is observed that the value of the mode frequency differs between the two styles of string excitation, regardless of the type of violin. On the other hand, there is a gradual increase in the values of the mode frequency from the violin with the thinnest plates (AM6C1) to the reference violin (A00C1).