## 6 Results and Discussion
### Effect of Latent Variable on Relative Pitch Distributions  
For the models trained on the PR dataset, an analysis of the latent space as in the previous section is not possible, because of the lack of ground-truth knowledge in terms of bass patterns. Needless to say in actual music such patterns probably exist, but they are much harder to define, and more mixed. This is confirmed by the fact that the data distribution of the latent space (not shown in this paper) is largely unimodal. However, the unimodality of the data distribution does not imply that there is no effect of the latent variable on the output. In this section, we explore how the distribution of \(f_{0}\) values in the predicted bass tracks changes as a function of the latent variable.  
Plotting the overall \(f_{0}\) distribution of the predicted bass tracks by itself is not very informative, since averaging distributions for songs with different tonalities would likely blur most of the structure in the distributions of individual songs or song sections. Therefore, we compute the distribution of the predicted bass \(f_{0}\) relative to the \(f_{0}\) of the mix. Such a distribution effectively tells us what pitches the bass plays with respect to predominant pitch of the instruments in the mix. That is, the histogram bin 0 would count the instances where the bass \(f_{0}\) is equal to the mix \(f_{0}\), whereas the bin \(-12\) (expressed in semitones) would count the instances where the bass \(f_{0}\) is an octave below the mix \(f_{0}\).  
Figure 8 shows the relative \(f_{0}\) distributions for different values of the latent variable \(z\) for the validation dataset. The plots have been generated from a model trained on the PR dataset using a window size of \(10/80\). To highlight the differences between the distributions, we have subtracted from each distribution the relative \(f_{0}\) distribution of the actual bass tracks in the validation dataset. Positive bin values thus indicate a higher occurrence of the relative \(f_{0}\)s than in the data, whereas negative values indicate a lower occurrence. Unsurprisingly, the variation in relative \(f_{0}\) distribution takes place mostly in the negative range (because the bass typically plays below the instruments in the mix). Furthermore, the peaks and valleys at \(-12\) and \(-24\) show that the latent space plays an important role in modulating the frequency of the octaves with respect to each other. Interestingly, the fourths (\(-19,\,-31\)) are also strongly modulated, occasionally with peaks that are as prominent as the octave peaks, for instance, at \(z=(0.4,0.0)\). This is surprising, since, based on music theory, we would have expected the fifth to play a more important role.  
Figure 7: Horizontal (**top row**) and vertical (**bottom row**) components of the two-dimensional (2D) latent space trajectories for an excerpt of the song _Date with the night_ by _Yaah Yaah Yaah_ (2003, Polybor). The columns show the trajectories of the models trained with cross-reconstruction loss (**left column**), and regular reconstruction loss (**right column**).  
Another notable trend is that the octaves and the fourth are strongly emphasized at the expense of the other diatonic and chromatic intervals in the lower plots, whereas, in the upper left corner, this pattern is reversed. Superficially =, this suggests that the latent space has learned to encode consonance vs dissonance. However, it is important to realize that the distributions are averaged over all songs, and they do not convey and information regarding melody and voice leading.