Temporal multi-scale considerations in the modeling of tonal cognition from continuous rating experiments

Modeling tonal induction dynamics from naturalistic music stimuli usually involves slide-windowing the stimuli in analysis frames or leaky memory processing. In both cases, the appropriate selection of the time-scale or decay constant is critical, although rarely discussed in a systematic way. This study shows the qualitative and quantitative impact that time-scale has in the evaluation of a simple tonal induction model, when the concurrent probe-tone method is used to capture continuous ratings of perceived relative stability of pitch-classes. Music stimulus is slide-windowed using many timescales, ranging from fractions of second to the whole musical piece. Each frame is analysed to obtain a pitch-class profile and, for each temporal scale, the time series is compared with the empirical annotations. Two commonly used frame-to-frame metrics are tested: a) Correlation between the 12-D vectors from ratings and model. b) Correlation between the 24 key activation strengths, obtained by correlation of the 12-D vectors with the Krumhansl and Kessler's key profiles. We discuss the metric artifacts introduced by the second representation, and we show that the best performing timescale, minimizing the root mean-square of the frame-to-frame distances along time, is far longer than short-time memory conventions. We propose a temporal multi-scale analysis method as an interactive tool for exploring the effect of time-scale and different multidimensional representations in tonal cognition