## 3 Auditory Perception Study of Sound Field in Closed Spaces with Different Structural Parameters
### Experimental Process  
This experiment adopts a pairwise comparison method, and the stimulus is presented to the subject through the headphone. Participants are asked to choose the more preferable audio in each pair of stimuli presented. The receiving points in different closed space that have the same coordinate index are arranged as a group to compare with each other. At each index, each of the musical sounds has a total of 34 pairs of stimuli, as shown in Table 7. Therefore, the experiment includes 34 \(\times\) 4 (receiving point index) \(\times\) 3 (original signal) = 408 pairs of stimulation signals. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Space Model** & **b** & **g** & **h** \\ \hline
**Coordinates of sound source** & (3, 0, 2) & (3, 0, 1.6) & (0, 0, 1.6) \\ \hline \multirow{3}{*}{Coordinates of receiving points} & 1 & (1.5, 0, 1) & (1.5, 0, 0.8) & (1, 1, 0.8) \\  & 2 & (4.5, 0, 3) & (4.5, 0, 2.4) & (\(-\)1, \(-\)1, 2.4) \\ \multirow{3}{*}{} & 3 & (3, 1, 1) & (3, 1.5, 0.8) & (0, 0, 0.8) \\  & 4 & (3, -1, 3) & (3, \(-\)1.5, 2.4) & (0, 0, 2.4) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The positions of sound source and receiving points in closed-space models. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Structural Parameter** & \multicolumn{4}{c}{**Stimulus Pair**} & \multicolumn{4}{c}{**Number of Pairs**} \\ \hline \multirow{3}{*}{Volume} & (a,a) & (a,b) & (a,c) & \\  & (b,a) & (b,b) & (b,c) & \\  & (c,a) & (c,b) & (c,c) & \\ \hline \multirow{3}{*}{Absorption coefficient} & (c,c) & (c,d) & (c,e) & (c,f) & \\  & (d,c) & (d,d) & (d,e) & (d,f) & \\ \cline{1-1}  & (e,c) & (e,d) & (e,e) & (e,f) & \\ \cline{1-1}  & (f,c) & (f,d) & (f,e) & (f,f) & \\ \hline \multirow{3}{*}{Shape} & (b,b) & (b,g) & (b,h) & \\ \cline{1-1}  & (g,b) & (g,g) & (g,h) & \\ \cline{1-1}  & (h,b) & (h,g) & (h,h) & \\ \hline \hline Total & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Stimulus pairs of a musical sound at the same receiving point. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Space Model** & **Dimension Diameter/m** & **Volume Calculation** & **S/m\({}^{2}\)** & **V/m\({}^{3}\)** \\ \hline \multirow{4}{*}{b} & L—6 & \multirow{4}{*}{V = L \(\times\) W \(\times\) H} & \multirow{4}{*}{128} & \multirow{4}{*}{96} \\  & W—4 & & & \\ \cline{1-1}  & H—4 & & & \\ \cline{1-1}  & g & L—6, r—3.2 & V = 1/2 \(\times\) \(\pi\)\({}^{2}\)\(\times\) L & 98.72 & 96.51 \\ \cline{1-1}  & h & r—3.58 & V = 1/2 \(\times\) 4\(\pi\)\({}^{3}\)/3 & 62.76 & 96.10 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The dimensions of closed-space models with different volumes. In the experiment, the experimenter plays the stimulus pairs on the computer. One stimulus signal is played for three times in succession, and the other is played (three times in succession) after an interval of 2 s. After each pair of stimuli is played, the subject has 5 s to select the one they preferred and felt more comfortable with and marks it on the questionnaire. Then, the next pair of stimuli is played until all 34 pairs at the receiving point have been played. After 10 min of rest, the stimulus pairs of another type of musical sound is played at the receiving point until the stimulation of all the three musical sounds is played. After that, a rest for half an hour is scheduled to eliminate hearing fatigue of the subjects, which may lead to a deviation of experiment results. Then, in the same way, the stimulus pairs of all three musical sounds are played at the next receiving point. Until the stimulation of the four receiving points has been played, the auditory experiment is finished. In this experiment, the test sequences of the receiving points, of different musical sounds and of the stimulation pairs of the same receiving point and the same musical sound, are randomized by the Latin Square Scheme to eliminate the deviation of the experimental results that may be caused by the testing sequence.