# Psychoacoustic Approaches for Harmonic Music Mixing +
## 4 Evaluation
### Results
#### 4.2.2 Effect of Parameterization  
Having looked into detail at the interactions between the difference conditions in terms of the ratings, we now revisit the properties of the roughness curve towards understanding the extent to which it provides a meaningful indicator of consonance for harmonic mixing. To this end, we now investigate the correlation between the ratings obtained from consonance and pleasantness compared to the corresponding points in the roughness curve for each associated pitch shift. While only three of the five conditions (**C**, **D** and **E**) were derived directly from each roughness curve, for completeness, we use the full set of 50 points (_i.e._, five conditions across 10 mixes). To gain a deeper insight into the design of our model, which is highly dependent on the extraction of partials using a sinusoidal model, we generate multiple roughness curves under different parameterizations and measure the correlation with the listener ratings for each. We focus on what we consider to be the two most important parameters: \(I\), the number of sinusoids, and \(\Gamma\), the number of temporal frames after averaging. In this way, we can examine the relationship from a harmonic and temporal perspective. To span the parameter space, we vary \(I\) from five up to 80 (default value = 20), and for the temporal averaging, we consider three cases: (i) beat level averaging (\(\Gamma\) = 16 across four-bar excerpts); (ii) 16 th note averaging (\(\Gamma\) = 64 and our default condition); and (iii) using all frames from the sinusoidal model without any averaging. The corresponding plots for both consonance and pleasantness ratings are shown in Figure 13.  
From inspection of the figure, we can immediately see that the number of sinusoids plays a more critical role than the extent/use of temporal averaging. Using more than 25 sinusoids (per frame of each track) has an increasingly negative impact on the Pearson correlation value. Likewise, using too few sinusoids also appears to have a negative impact. Considering the roughness model, having too few observations of the harmonic structure will very likely fail to capture all of the main roughness creating partials. While on the other hand, over-populating the roughness model with sinusoids (many of which may result from percussive or noise-like content) will also obscure the interaction of  
Figure 12: Comparison of extracted sinusoids after pitch shifting using Traktor (**a**) and min roughness (**b**) on Mix 8 from Table 2. Traktor applies a pitch shift of \(-\)2.0 semitones to Track 2 (solid blue lines), while the min roughness applies a pitch shift of +2.25 semitones to Track 2. In comparison to Track 1 (dotted black lines), we see that the min roughness approach (b) has primarily aligned the bass frequencies (under 100 Hz), whereas Traktor (a) has aligned higher partials around 270 Hz. the \"true\" harmonic partials in each track. Within the context of our (harmonically simple) dataset, a range of between 15 and 25 partials provides the strongest relationship between roughness values and consonance ratings. Looking next at the effect of the temporal averaging, we can see a much noisier relationship when using beat averaging compared to our chosen summarization at the 16 th note level. In contrast, the plot is smoothest without any temporal averaging, yet it is moderately less correlated with the data. As with the harmonic dimension, the 16 th note segmentation adequately captures the rate at which harmonic content changes in the signal, without losing too much fine detail through the temporal averaging process. Finally, comparing the plots side by side, we see a near identical pattern for consonance and pleasantness. This behavior is to be expected given the very high correlation between the consonance and pleasantness ratings themselves (\(r\) = 0.76, \(p\) < 1\(\times\)10\({}^{-6}\)).