Contextual Set-Class Analysis

In this chapter, we review and elaborate a methodology for contextual multi-scale set-class analysis of pieces of music. The proposed method provides a systematic approach to segmentation, description and representation in the analysis of the musical surface. The introduction of a set-class description domain provides a systematic, mid-level, and standard analytical lexicon, which allows for the description of any notated music based on a fixed temperament. The method benefits from representation completeness, a balance between generalization and discrimination of the set-class spaces, and access to hierarchical inclusion relations over time. Three new data structures are derived from the method: class-scapes, class-matrices and class-vectors. A class-scape represents, in a visual way, the set-class content of each possible segment in a piece of music. The class-matrix represents the presence of each possible set class over time, and is invariant to time scale and to several transformations of analytical interest. The class-vector summarizes a piece by quantifying the temporal presence of each possible set class. The balance between dimensionality and informativeness provided by these descriptors is discussed in relation to standard content-based tonal descriptors and music information retrieval applications. The interfacing possibilities of the method are also discussed.