Structural characterization of musical harmonies

Understanding the structural characteristics of harmony is essential for an effective use of music as a communication medium. Of the three expressive axes of music (melody, rhythm, harmony), harmony is the foundation on which the emotional content is built, and its understanding is important in areas such as multimedia and affective computing. The common tool for studying this kind of structure in computing science is the formal grammar but, in the case of music, grammars run into problems due to the ambiguous nature of some of the concepts defined in music theory. In this paper, we consider one of such constructs: modulation, that is, the change of key in the middle of a musical piece, an important tool used by many authors to enhance the capacity of music to express emotions. We develop a hybrid method in which an evidence-gathering numerical method detects modulation and then, based on the detected tonalities, a non-ambiguous grammar can be used for analyzing the structure of each tonal component. Experiments with music from the XVII and XVIII centuries show that we can detect the precise point of modulation with an error of at most two chords in almost 97% of the cases. Finally, we show examples of complete modulation and structural analysis of musical harmonies.