Along with an appreciation for the art of Western classical music, researchers are also passionate about the study of its expressive interpretation forms. They are interested in modeling the relationship between musical expression and its structural features.

In this paper, the authors introduce basis function modeling of the dynamics in both solo and ensemble musical performances, which capture various aspects of musical score, for example, note pitch, duration, legato articulation, and so on; in solo music, basis functions are defined as functions of notes; in ensemble, interest is given to the fusion of basis functions. Linear and nonlinear models are adopted for building the relationship between dynamics and basis functions. Recurrent nonlinear studies are proposed for investigating the temporal dependencies within model parameters.

Three datasets, two solo and one ensemble, are used for testing with a five-fold cross-validation method. Their results show that nonlinear models give higher accuracy of modeling musical dynamics. The authors also provide discussions on their qualitative analysis of the model, recurrent nonlinear models, limitations, and future works.

This work incorporates various aspects of music and types of music into their linear and nonlinear models with statistical analysis (for example, cross-validation to avoid overfitting) on the results. It will be of benefit to an audience interested in the modeling of musical expressiveness.