# Modelling the Microphone-Related Timbral Brightness of Record Signals
## 5 Discussion  
Much of the literature regarding the perception of brightness suggested that the spectral centroid is a suitable metric which correlates with perceived brightness [3; 4; 5; 6]. Literature has also suggested that ratio models are suitable for modelling perceived brightness [7; 12]. However, the results from this paper show that a combination of the \(SC\) and Ratio\({}_{2}\) produces a better model. The reasons for this are unclear but the authors suggest that \(SC\) is perhaps too sensitive a measure of spectral balance (being affected by, for example, movement of a spectral peak from a bright-sounding 8 kHz to an equally bright-sounding 7 kHz) whereas Ratio\({}_{2}\) is perhaps too coarse (being entirely unaffected by spectral changes that are either wholly below or wholly above 500 Hz). (Adding energy above 20 kHz will lead our model (and any other based on the same \(SC\) and/or ratio metrics) to over-predict brightness. If significant energy variations above 20 kHz are considered likely, and a high enough sample rate is employed to represent them, then the problem can be fixed simply by setting the upper limits of the ratio and \(SC\) sums to 20 kHz.) The proposed model out-performed the existing metrics, as well as their logarithmic transformations, with all performance measures, shown in Table 3. Whilst the logarithmic transformation improved the correlation of the \(SC\) metric for both the training and validation dataset, a logarithmic transformation did not always improve the correlation of the ratio metrics. This is shown by the lower Pearson's r for the logarithmic models with the validation data. Interestingly, although the \(SC\) metric is far more commonly associated with brightness in the literature, the ratio metrics tended to produce higher correlation to the subjective brightness ratings. The best crossover frequency, \(f_{c}\), for the new model was identified as 500 Hz. This is within the range of crossover frequencies suggested by [PERSON] and [PERSON] [12]. Adding a A- or C-weighting filters, or using a perceptual frequency scale to calculate the \(SC\), did not improve the performance of the model. This was unexpected since these perceptual transformations were proposed to better relate metrics to subjective impressions. It may be that the logarithmic transformation applied to the selected metrics was sufficient to simulate the nonlinearities of the human hearing system. The most appropriate level of spectral smoothing was found to be \(\frac{1}{3}\)-octave, implying that the stimuli contained some degree of high-Q peaks/troughs in their frequency spectra that were adversely affecting the relationship between the metrics and perceived level of \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Model** & **Pearson’s r** & **Spearman’s rho** & **RMSE** \\ \hline \multicolumn{4}{c}{Tested against training data} \\ \hline New model & 0.922 & 0.902 & 8.52 \\ SC & 0.760 & 0.789 & 14.30 \\ log SC & 0.811 & 0.789 & 12.87 \\ Ratio\({}_{1}\) (1 kHz crossover) & 0.734 & 0.867 & 14.93 \\ log Ratio\({}_{1}\) (2 kHz crossover) & 0.907 & 0.887 & 9.28 \\ Ratio\({}_{2}\) (2 kHz crossover) & 0.888 & 0.887 & 10.11 \\ log Ratio\({}_{2}\) (3 kHz crossover) & 0.900 & 0.892 & 9.59 \\ \hline \multicolumn{4}{c}{Tested against validation data} \\ \hline New model & 0.955 & 0.954 & 14.46 \\ SC & 0.830 & 0.801 & 19.33 \\ log SC & 0.864 & 0.801 & 24.00 \\ Ratio\({}_{1}\) (1 kHz crossover) & 0.713 & 0.901 & 17.73 \\ log Ratio\({}_{1}\) (2 kHz crossover) & 0.862 & 0.822 & 23.62 \\ Ratio\({}_{2}\) (2 kHz crossover) & 0.851 & 0.838 & 24.05 \\ log Ratio\({}_{2}\) (3 kHz crossover) & 0.798 & 0.787 & 34.58 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparing the performance of all brightness models. brightness. Although the \(\frac{1}{3}\)-octave smoothing has likely removed these, applying a wider smoothing (half-octave or octave-band width) may have resulted in a loss of detail in the signal, and thus reduced the predictive ability of the metric.