## 3 Results and Discussion
The vibrato-like variation can decrease annoyance. Since lower \(\tau_{1}\) indicates higher pitch, a negative correlation between subjective preference and \(\tau_{1}\) values suggests that birdsongs and insect songs with a higher pitch are preferable. However, this finding is not consistent with previous findings regarding subjective annoyance caused by refrigerator noises [23]. These findings suggest that sounds with a higher and more salient pitch are preferred, whereas sounds with a higher but unnoticeable pitch cause annoyance. The negative correlations between subjective preference and loudness meant that quieter birdsong stimuli were preferable. Since SPL was fixed at 70 dBA in the current experiment, loudness may be a useful index for identifying birdsong stimuli that are pleasant when presented at high SPLs. Figure 6: Relationships between physical parameters and scale values of preference for birdsong stimuli. (**a**) \(\tau_{1}\), (**b**) \(\varphi_{1}\), (**c**) \(W_{\varphi(0)}\), (**d**) loudness, (**e**) entropy, and (**f**) spectral rolloff. The numbers represent correlation coefficient values. Asterisks represent the level of significance, i.e., **\(p<0.01\), * \(p<0.05\). Insect song stimuli with lower entropy were preferred, suggesting that abrupt changes in SPL were not preferred. Lower spectral entropy and rolloff were preferred, suggesting that insect song stimuli with broader bandwidth were preferred. Thus, spectral content appeared to play a more important role in determining preferences for insect song stimuli than for birdsong stimuli. A multiple linear regression analysis was performed with the SVs of preference for birdsong and insect song stimuli as the outcome variable. The final model showed that \(\varphi_{1}\), \(\tau_{1}\), loudness, and entropy were significant parameters for birdsong stimuli, while \(\varphi_{1}\), \(W_{\varphi(0)}\), \(\tau_{\rm e}\), loudness, and spectral rolloff were significant parameters for insect song stimuli:  
\[SV_{\rm birdsong}\approx\rm{b}_{0}+\rm{b}_{1}*\varphi_{1}+\rm{b}_{2}*\tau_{1}+ \rm{b}_{3}*\rm{loudness}+\rm{b}_{4}*\rm{entropy}, \tag{8}\]  
\[SV_{\rm insect\;song}\approx\rm{i}_{0}+\rm{i}_{1}*\varphi_{1}+\rm{i}_{2}*W_{ \varphi(0)}+\rm{i}_{3}*\tau_{\rm e}+\rm{i}_{4}*\rm{loudness}+\rm{i}_{5}*\rm{ spectral\;rolloff}. \tag{9}\]  
The ANOVA indicated the statistical significance of the model (\(F\) (4, 265) = 63.33, \(p\) \(<\) 0.001, for birdsong, \(F\) (5, 250) = 101.84, \(p\) \(<\) 0.001, for insect song). The adjusted coefficient of determination, R\({}^{2}\), was 0.54 for birdsong and 0.66 for insect song. The standardized partial regression coefficients in Equations (8) and (9) are summarized in Table 4.  
Figure 7: Relationships between physical parameters and scale values of preference for birdsong stimuli. (**a**) \(\tau_{1}\), (**b**) \(\varphi_{1}\), (**c**) \(W_{\varphi(0)}\), (**d**) loudness, (**e**) entropy, and (**f**) spectral rolloff. The numbers represent correlation coefficient values. Asterisks represent the level of significance, i.e., **\(p\) \(<\) 0.01, *\(p\) \(<\) 0.05. The maximum peak amplitude of the ACF, \(\varphi_{1}\), which signifies pitch salience and loudness were significant predictive variables for both birdsong and insect song stimuli. Although the partial regression coefficients of loudness for birdsong stimuli were negative, those for insect song stimuli were positive. The simple correlation between subjective preference and loudness was negative. Therefore, this difference suggests that the contributions from predictive variables other than loudness were much larger for insect song stimuli than for birdsong stimuli. Similar to the simple correlation analysis, spectral rolloff was also found to be a significant factor for the prediction of preferences for insect song stimuli. The width of the first decay of the ACF, \(\mathrm{W}_{\varphi(0)}\), which is equivalent to the spectral centroid, exhibited a larger and negative standardized partial regression coefficient for insect song stimuli.