Systematic Multi-scale Set-class Analysis

This work reviews and elaborates a methodology for hierarchical multi-scale set-class analysis of music pieces. The method extends the systematic segmentation and representation of Sapp’s ‘keyscapes’ to the description stage, by introducing a set-class level of description. This provides a systematic, mid-level, and standard analytical lexicon, which allows the description of any notated music based on fixed temperaments. The method benefits from the representation completeness, the compromise between generalisation and discrimination of the set-class spaces, and the access to hierarchical inclusion relations over time. The proposed class-matrices are multidimensional time series encoding the pitch content of every possible music segment over time, regardless the involved time-scales, in terms of a given set-class space. They provide the simplest information mining methods with the ability of capturing sophisticated tonal relations. The proposed class-vectors, quantifying the presence of every possible set-class in a piece, are discussed for advanced explorations of corpora. The compromise between dimensionality and informativeness provided by the class-matrices and class-vectors, is discussed in relation with standard content-based tonal descriptors, and music information retrieval applications.