## 3 Results  
### The Just Noticeable Difference of Initial Reflection in a Sound Field  
In this study, there were two dry sources that simulated an instrumental solo: a trumpet piece (Prince of Denmark's March, by [PERSON]) and a cello piece ([PERSON], Toccata, by Arr. [PERSON]), whereas motifs were set at equal (1--IACC\({}_{\text{E3}}\)) and G values along the way. However, the frequency responses were higher than 300 Hz for the trumpet piece, and fluttered at 200 Hz, 400 Hz, \(\ldots\), and so on for the cello piece (Figure 5). In addition, the running autocorrelation function (ACF) of the two pieces proposed by [PERSON] (Chapter 3 in [17]) were calculated as shown in Figure 6. The average re values (ms) of two music pieces were 35.90 ms for trumpet and 46.92 ms for cello. However, the minimum re values of two pieces were 31.25 ms and 16.24 ms, which were calculated as a function of preferred initial delay time of the music signal in a sound field reported by [PERSON] [27]. According to the settings of amplitude of the first reflection (A1) and reverberation part (AR), total amplitude of reflections (A1 + AR) was equal to 1.5 (as the amplitude of direct sound A0 = 1), so the preferred IDTGs of the two instrumental pieces were estimated as 42.2 ms for cello and 32.3 ms for trumpet, respectively. Table 1 lists the total index of the autocorrelation function (ACF) calculated using both music signal sources. Figure 4: The continuous cues (91 samples) of the trumpet piece (as a trigger) and the alpha-wave signals recorded during the same period. According to Figure 7, the perceived ITDG changes of the 17 subjects were lower for the trumpet piece, as indicated by the lower number of _JNDc_ points compared with the cello piece. This shows that the \(\Delta\)Gap was often greater for the trumpet piece, and there was a greater difference between the subjects' responses, and it can be known that high-frequency sounds have larger _JNDc_ values. This can be explained by the fact that the stimulus was a musical piece; if white noise was used as a stimulus instead, the difference could be significantly reduced. As shown in Figure 7, the results revealed that the _JNDc_ values are higher than the _JNDc_ values. This is because the stimulus was a musical piece; if white noise was used as a stimulus instead, the difference could be significantly reduced. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Motifs/** & **Averaged \(\tau\)e** & **\(\tau\)e\_min** & **Tau\_1** & **Phi\_1** & **W\_IACC** & **JND** & **JND of ITDG** & **Preferred** \\
**Factors** & **(ms)** & **(ms)** & **(s)** & **(dB)** & **(ms)** & **(ms)** & **(ms)** & **ITDG (ms)** \\ \hline Cello & 46.92 & 16.24 & 0.41 & 0.26 & 0.08 & 0.059 & 7.40 \(\pm\) 2.75 & 42.2 \\ \hline Trumpet & 35.90 & 31.25 & 0.58 & 0.01 & 0.07 & 0.081 & 10.18 \(\pm\) 3.52 & 32.3 \\ \hline \hline \end{tabular}  
* Notes: Tau\_1, first peak delay gap in the curve of ACF of source signal; Phi\_1, first peak value in the curve of ACF of source signal; preferred ITDGs were calculated by short-term re\_min values of the ACF of music source signals (Figure 3) proposed by [PERSON] [32].  
\end{table} 
Table 1: The variable of autocorrelation function (ACF) derived from the music source of cello and trumpet. Figure 5: Frequency responses of the (**A**) cello and (**B**) trumpet pieces. of the cello piece and the trumpet piece were rated approximately 0.059 and 0.081 at a 50% \"different\" judgement range in most cases, respectively. Additionally, the JND of ITDG of the cello piece was measured as 7.4 \(\pm\) 2.75 ms, while that of the trumpet was 10.18 \(\pm\) 3.52 ms in the continuous variations of sound field structures. Furthermore, the subjects' perceptions of the spatial ITDG changes of both instrumental solos were significantly different.