Generalized Tonal Pitch Space with Empirical Training

A chord name can be interpreted in multiple ways, so a sequence of chord names has combinatorially many interpretations though most of which are inadequate. Tonal Pitch Space (TPS) is a music model which enables us to measure the distance between two chords, and thus we can rely on the theory to find most plausible interpretations, calculating the shortest path in the network of chord sequences. Although TPS is based on classical music theory, it is not based on data in a precise sense. As a result, the distance in the original TPS is somewhat rough to achieve high prediction accuracy.
In this study, we combine empirical observations with TPS, that is, to allow users to pick arbitrary combinations of features and calculate the distance of two chord interpretations. Then we propose a path probability formula to convert a path distance to a path probability, so that we can train the parameters from annotated datasets. We illustrate several experimental distance elements and show that some combinations of them can significantly improve the prediction accuracy, which resulted in over 86% in the test set.