## 4 Method Evolution and Future Improvements
### Possible Pathways to Improvement  
Both chord grouping and transition support provide a framework that can integrate several further components. The first identified weakness of the current implementation concerns melody matching, which appears to be too \"stiff\" in some cases and too \"forgiving\" in others. This is possibly due to the rudimentary method for melody representation. To this end, melody representation, even in the current form of the 12-dimensional rPCP vector, needs to incorporate more musically meaningful aspects, e.g., duration, weak-versus-strong metrical position, etc. Additionally, a more refined method for chord tolerance to melodic mismatches can be introduced, possibly involving ad hoc rPCPs that can and cannot be acceptable for each chord type. E.g., all major group chords, regardless of their specific type and what they have harmonized in the dataset, could accept a melody note that corresponds to the 6 th of the chord, but could not accept a minor third note. In the current form, such simple musical considerations might be violated due to rare exceptions in data that do not apply to generic music knowledge. Additionally, characteristic melody matching information individually from Song A and/or Song B could be involved, instead of or in combination with melody matching information from the overall space of jazz standards, as in the current version. Such ideas, however, need to be tested in a study that provides results focusing on this specific aspect.  
Apart from melodic representation issues discussed above, chord representation may also be improved in more musically meaningful ways. For instance, chord grouping could be more refined, incorporating the functional and/or structural role of each chord, or the mode of the piece tonality (e.g., requiring transposition to the relative minor or major in Song B, to match the mode in the tonality of Song A. For instance, chord grouping could involve the function of each chord within the involved songs, or in the overall space, along with the metrical position of the chord, i.e., if it is placed on a weak or a strong beat. Such characteristics do not necessarily need to be integrated in the transition matrix as the current version of chord grouping, but can be added as a separate layer of probabilities during the computation of \(\Delta\) at each time step, i.e., instead of having two layers of probabilities at each time (transitions and melody matching), more probabilities per state/chord could be integrated directly as a product of probabilities, based, e.g., on the metrical position of the time step and the learned role of each chord in this metrical position.  
Another issue that relates to the overall statistical learning approach is the inherent attribute of such methods to focus on statistical \"normalities\", disregarding idiosyncratic aspects of data that are considered \"anomalies\", which, however, might be valuable for identifying useful characteristics in specific data points. For instance, in \"So What\", the most salient harmonic phenomenon is the semitone step in the entire tonality in Section B, which is, however, poorly reflected by the transition probabilities in the model of the piece that gives more weight to repeated transitions. Such idiosyncratic elements could be highlightedby introducing a \"salience\" component, e.g., as developed in [39], either in the formulation of the transition probabilities or as a separate layer in the formulation of \(\Delta\).