A multitude of definitions can be applied to the notion of musical complexity. Two categories can however be distinguished: the grammatological complexities, which mean the complexity of the thought of a writing (algorithmic complexity of a musical process for instance) and the apperceptive complexities, designating the psychological or cultural difficulties of perception. It is shown that the mechanisms of these two types of complexities are distinct : two procedures with identical grammatological complexity can result in dissimilar apperceptive complexities ; conversely, two analytically distant procedures can generate close perceptive results with the same apperceptive complexity.

However, the musical writing is not only a transcription, a graphemology. It carries a way of thinking the music. Western civilisation emphasizes for instance a musical notation with independent, discrete, and reduced parameters. Hence, studying the musical grammatological complexity requires a study of our analytical perception of the music. Conversely, the perception of the music is cognitive, which means that the listener seeks to understand and compress the musical information in unconscious schemes. In a way, the perception is a mental writing, and studying the apperceptive complexity requires a study of the analytical complexity of the algorithm reprocessed by the listener.

This work studies carefully these various complexities, their gap, and their similarity. This research uses concrete musical applications (the study of different processes and mechanisms of perception concerning rhythms, motivic transformations, consonance of an interval, etc.), but also the elaboration of theoretical concepts taken from the formalized social sciences (musical analysis, information and complexity theories, semiology, psychoacoustics), and the construction of musical models and paradoxes on writing and perception.