## 5 Results
### Macro-Parameters Learning  
Our formulation is the first to provide a continuous mapping between the audio \(\mathbf{z}\) and parameter \(\mathbf{v}\) spaces of a synthesizer. As latent VAE dimensions has been shown to disentangle major data variations, we hypothesized that we could directly use \(\mathbf{z}\) as _macro-parameters_ defining the principal dimensions of audio variations in a given synthesizer. Hence, we introduce the new task of _macro-parameters learning_ by mapping latent audio dimensions to parameters through \(p(\mathbf{v}|\mathbf{z})\), which provides simplified control of the major audio variations for a given synthesizer. This is depicted in Figure 5.  
We show the two most informative latent dimensions \(\mathbf{z}\) based on their variance. We study the traversal of these dimensions by keeping all other fixed at \(\mathbf{0}\) to assess how \(\mathbf{z}\) defines smooth macro-parameters through the mapping \(p(\mathbf{v}|\mathbf{z})\). We report the evolution of the 5 parameters with highest variance (top), the corresponding synthesis (middle) and audio descriptors (bottom).  
First, we can see that latent dimension corresponds to very smooth evolutions in terms of synthesized audio and descriptors. This is coherent with previous studies on the disentangling abilities of VAEs [6]. However, a very interesting property appear when we map to the parameter space. Although the parameters evolution is still smooth, it exhibits more non-linear relationships between different parameters. This correlates with the intuition that there are lots of complex interplays in parameters of a synthesizer. Our formulation allows to alleviate this complexity by automatically providing _macro-parameters_ that are the most relevant to the audio variations of a given synthesizer. Here, we can see that the \(\mathbf{z}_{3}\) latent dimension (left) seems to provide a _percussivity_ parameter, where low values produce a very slow attack, while moving along this dimension, the attack becomes sharper and the amount of noise increases. Similarily, \(\mathbf{z}_{7}\) seems to define an _harmonic densification_ parameter, starting from a single peak frequency and increasingly adding harmonics and noise. Although the unsupervised macro-parameters provide some clear effects on the synthesis, it appears that they do  
Figure 5: _Macro-parameters learning._ We show two of the learned latent dimensions \(\mathbf{z}\) and compute the mapping \(p(\mathbf{v}|\mathbf{z})\) when traversing these dimensions, while keeping all other fixed at \(\mathbf{0}\) to see how \(\mathbf{z}\) define smooth macro-parameters. We plot the evolution of the 5 parameters with highest variance (**top**), the corresponding synthesis (**middle**), and audio descriptors (**bottom**). (**Left**) \(\mathbf{z}_{3}\) seems to relate to a _percussivity_ parameter. (**Right**) \(\mathbf{z}_{7}\) defines a form of _harmonic densification_ parameter.  
not act on a single aspect of the timbre. This seems to indicate that the macro-parameters still relate to some entangled properties of the audio. Furthermore, as these dimensions are unsupervised, we still need to define their effects through direct exploration. Additional macro-parameters are discussed on the supporting webpage of this paper.