Musical Information Dynamics as Models of Auditory Anticipation

Structure Of This Chapter

After a brief introduction to the theories of expectancy in music and some historical as well as modern musicological and computational background,the authors will address the question of modeling music as an information source and listener as information receiver. From this approachthey will develop a model of listening that is based on mutual information between the past and the present called Information Rate (IR) (Dubnov, 2006; Dubnov et al. 2006). This model will be extended to include Predictive Information (PI) (Bialek et al.) and Predictive Information Rate (PIR) (Abdallah and Plumbley, 2009).

The authors introduce a new notion of Information Gap as a measure of the salience of a present musical segment (instance in time) with respect to future and past of a musical signal. This measure combines notions of predictive information with a notion of momentary forgetfulness, determining saliency of the present instance in terms of how detrimental forgetfulness is on the ability to make predictions. They will show that the information gap unites the three notions of information dynamics through simple algebraic relations. Next theywill consider application of IR for simple Markov chains (Cover and Thomas, 2006), and consider actual musical data from MIDI representation and cepstral audio features from recordings. Dealing with multiple features requires orthogonalization, which establishes the basis for vector IR.