## 4 Results
### Correlation Between Perception and Simulation  
In the section above, we found a clear split between familiar and unfamiliar sounds, pointing to two different perception strategies. Therefore, in this section, correlating perception to simulation, the two subgroups, familiar guitar sound and unfamiliar sounds, are correlated separately with simulation. Figure 7 shows the Pearson's correlation between simulation and separateness as well as roughness perception for the guitar and non-guitar sounds using entropy S. The upper graphs are roughness, the lower two separateness correlations, the left plots are the guitar and the right plots the non-guitar sounds, respectively. Each plot varies the standard deviation \(\sigma\) of the ISI histogram blurring in the range \(0\leq\sigma\leq 2\) and a peak sharpness s in the range \(0\leq s\leq 0.002\) in 21 steps each (for details see above). Therefore, the left lower corner of each plot is the unprocessed ISI histogram, which might contain many peaks, most of them with low amplitude. With increasing \(\sigma\) a coincidence detection is performed, summing neighbouring peaks to a single peak. This reduces the number of peaks, but blurs them. When increasing s only sharp peaks are used. Of course, blurred peaks can only appear with higher values of \(\sigma\). Therefore, higher values of s prevent large values of \(\sigma\) peaks being detected when they are so broad that they cannot reasonably have been built in a coincidence detection process as they are too far apart. Examining the plots in Figure 7, concentrating on the left upper plot of roughness correlated with guitar tones, a ridge of positive correlation appears in the upper right corner. The rest of the plot is structured accordingly with a tendency of lower right to upper left ridges. Following the ridge with the highest correlation starting at \(\sigma\sim 1.5\) on maximum s and ending at s = 0.0011 with maximum \(\sigma\), the trade-off between \(\sigma\) and s leads to a reduction in the number of amplitudes down to only 3-5 amplitudes in the post-processed ISI histogram. This is a tremendous reduction taking into consideration that the number of amplitudes in the unprocessed lower left corner of the plots is between 700 and 800 amplitudes. On the right lower side of the ridge, with strong positive correlation, the peaks are not blurred to a maximum as the sharpness is very rigid, allowing only a few amplitudes. On the left upper side of the ridge the blurring is increased, still the sharpness criterion is eased, resulting in about the same number of amplitudes, 3-5. Indeed, in the upper right corner only one or even no amplitudes have survived. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sound** & **Roughness** & **Roughness Std** & **Sepateness** & **Sepateness** \\  & **Mean** & **Mean** & **Std** \\ \hline \hline \begin{tabular}{c} Unisono \\ \end{tabular} & 3.36 & 2.16 & 3.97 & 3.17 \\ \hline \hline \begin{tabular}{c} Minor second \\ \end{tabular} & 6.21 & 2.36 & 5.17 & 2.45 \\ \hline \begin{tabular}{c} Major second \\ \end{tabular} & 4.79 & 1.87 & 5.66 & 2.45 \\ \hline \begin{tabular}{c} Minor third \\ \end{tabular} & 3.89 & 2.06 & 5.79 & 2.57 \\ \hline \begin{tabular}{c} Major third \\ \end{tabular} & 4.18 & 1.84 & 6.24 & 2.10 \\ \hline \begin{tabular}{c} Fourth \\ \end{tabular} & 2.93 & 1.96 & 5.45 & 2.63 \\ \hline \begin{tabular}{c} Tritone \\ \end{tabular} & 4.93 & 2.37 & 5.34 & 2.41 \\ \hline \begin{tabular}{c} Fifth \\ \end{tabular} & 3.89 & 2.06 & 5.62 & 2.41 \\ \hline \begin{tabular}{c} Minor sixth \\ \end{tabular} & 4.25 & 2.17 & 6.10 & 2.16 \\ \hline \begin{tabular}{c} Major sixth \\ \end{tabular} & 4.71 & 1.90 & 5.83 & 2.32 \\ \hline \begin{tabular}{c} Minor seventh \\ \end{tabular} & 4.74 & 1.98 & 5.97 & 2.49 \\ \hline \
\begin{tabular}{c} Major seventh \\ \end{tabular} & 5.64 & 2.02 & 7.00 & 2.10 \\ \hline
\begin{tabular}{c} Octave \\ \end{tabular} & 3.93 & 2.18 & 5.03 & 2.91 \\ \hline \hline \end{tabular}
\end{table}