Modelling Hierarchical Key Structure With Pitch Scapes

Musical form and syntax in Western classical music are hierarchically organised on different timescales. One of the most important features of this structure is the organisation of modulations between different keys throughout a piece. Music theoretical research has established taxonomies of prototypical modulation plans for different modes and musical forms. However, these prototypes still require empirical validation based on quantitative statistical methods and cannot be retrieved automatically so far.
In this paper, we present a novel method to infer prototypical modulation plans from musical corpora. A modulation plan is formalised as a transposition-invariant probabilistic model over the underlying pitch class distributions based on a hierarchical pitch scape representation. Prototypical modulation plans can be learned in an unsupervised manner by training a mixture model (similar to a Gaussian mixture model) on the data, so that different prototypes appear as distinct clusters.
We evaluate our approach by performing hierarchical clustering on a corpus of more than 150 Baroque pieces, with the extracted clusters showing excellent agreement with the most common prototypes postulated in music theory. Our method bears a great potential for modelling, analysis and discovery of hierarchical key structure and prototypes in corpora across a broad range of musical styles. An accompanying library is available at: github.com/robert-lieck/pitchscapes.