# Signature Modes of Old and New Violins with Symmetric Anatomical Wood Structure
## 3 Results and Discussions
### Dynamic Analysis
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Violins** & \multicolumn{4}{c}{**The Frequency Spectrum (Hz) AVERAGE/STDV**} \\ \hline  & **f1 (A0)** & **f2 (CBR)** & **f3 (B1\(-\))** & **f4 (B1+)** & **f5** \\ \hline  & \multicolumn{4}{c}{Stainer 1716} & & \\ Frequency (Hz) & 283.55 (1.77) & 389.70 (0.28) & 449.50 (0.42) & 604.95 (2.33) & 857.00 (0.0) \\ Quality factor \(Q\) & 11.94 (2.03) & 14.32 (0.00) & 30.08 (2.03) & 22.28 (2.25) & 77.99 (0.90) \\  & \multicolumn{4}{c}{[PERSON] 1742} & & \\ Frequency (Hz) & 282.30 (0.00) & 415.80 (0.00) & 470.70 (0.00) & 561.50 (0.00) & 685.85 (1.06) \\ Quality factor \(Q\) & 17.35 (0.68) & 24.99 (0.23) & 20.69 (0.00) & 21.65 (0.45) & 24.83 (0.90) \\  & \multicolumn{4}{c}{[PERSON] 1747} & & \\ Frequency (Hz) & 290.65 (1.06) & 429.50 (0.00) & 481.05 (0.49) & 572.30 (0.14) & 681.70 (0.57) \\ Quality factor \(Q\) & 21.96 (2.25) & 51.09 (2.48) & 23.87 (0.45) & 44.40 (1.58) & 17.19 (1.80) \\  & \multicolumn{4}{c}{Babos 1920} & & \\ Frequency (Hz) & 288.00 (2.69) & - & 489.40 (0.57) & 535.20 (0.57) & 661.70 (0.42) \\ Quality factor \(Q\) & 14.32 (0.45) & - & 26.42 (1.35) & 42.34 (4.95) & 27.69 (4.05) \\  & \multicolumn{4}{c}{Copy Stainer} & \\ Frequency (Hz) & 294.20 (0.00) & 389.75 (0.07) & 458.65 (2.06) & 544.30 (3.82) & 823.35 (0.49) \\ Quality factor \(Q\) & 7.64 (0.00) & 43.77 (0.68) & 32.63 (0.68) & 33.42 (0.45) & 30.08 (0.23) \\  & \multicolumn{4}{c}{Unbranded} & \\ Frequency (Hz) & 275.75 (0.49) & 409.70 (0.00) & 479.85 (0.07) & 536.70 (0.57) & 838.20 (0.28) \\ Quality factor \(Q\) & 15.28 (1.80) & 49.66 (4.50) & 26.10 (6.30) & 22.44 (1.13) & 37.40 (6.53) \\  & \multicolumn{4}{c}{Gliga 1, 2020} & & \\ Frequency (Hz) & 273.10 (0.00) & 399.40 (0.57) & 473.80 (0.00) & - & 688.10 (0.00) \\ Quality factor \(Q\) & 25.46 (0.00) & 37.56 (3.60) & 20.37 (0.45) & - & 51.88 (0.00) \\  & \multicolumn{4}{c}{Gliga 2} & \\ Frequency (Hz) & 275.00 (0.00) & 407.00 (0.00) & 430.00 (0.00) & 523.50 (0.71) & 675.00 (33.94) \\ Quality factor \(Q\) & 21.33 (1.35) & 21.65 (0.90) & 33.58 (0.68) & 26.26 (0.23) & 28.01 (0.45) \\  & \multicolumn{4}{c}{Gliga 3} & \\ Frequency (Hz) & 274.50 (0.71) & 440.50 (0.71) & 476.50 (19.09) & 530.20 (6.79) & 664.50 (31.82) \\ Quality factor \(Q\) & 17.19 (0.00) & 35.65 (3.60) & 28.01 (0.90) & 24.19 (4.95) & 31.51 (0.45) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Eigenvalues for the first vibration modes of old versus new violins. Figure 8: The frequency spectrum plots for the dynamic analysis. In the case of the B1+ bending mode, the eigenvalues are between 523 Hz and 604 Hz, as can be seen in Figure 9d. The only violin that does not have this harmonica is the Gliga 1 2020 violin. The [PERSON], Klotz and Stainer violins show close values of B1+ mode, ranging from 550 to 600 Hz. According to [11; 24; 47], violins with a frequency of B1+ less than 510 Hz are characterized by a soft, dark sound, and those with a frequency greater than 550 Hz have a bright to harsh sound. Thus, the Babos 1920, Unbranded, Copy Stainer, Gliga 2 and Gliga 3 violins record a frequency of the B1+ mode in the range 510-550 Hz, while Stainer 1716, Leeb 1742, and Klotz 1747 have a frequency value over 550 Hz, according to [11; 24; 47; 48]. In the case of mode 5, there is a division into two groups of values: [PERSON] violins, all new violins, Klotz 1747 and Leeb 1742 record a frequency in the range 660-690 Hz, compared to Stainer 1716 violins, Stainer copy and Unbranded that form the second group of values in the range 820-860 Hz (Figure 9e). Figure 9: Comparisons between the values of the natural frequencies of the tested violins: (**a**) cavity mode; (**b**) CBR mode; (**c**) B1\(-\) mode; (**d**) B1\(+\) mode; (**e**) the 5 th resonance frequency. The Q quality factor defines the musical instrument's ability to dampen vibrations or how fast resonance will fade out after the system excitation has ceased.