Two-Dimensional Visual Inspection of Pitch-Space, Many Time-Scales and Tonal Uncertainty over Time

Abstract

This work explores the representational limitations of toroidal pitch-spaces, when multiple temporal resolutions, tone center ambiguity, and the time dimension are considered for visualization of music pieces. The algorithm estimates key from chroma features, over time at many time-scales, using the key-profile correlation method. All these estimations are projected as tonal centroids within Krumhansl and Kessler’s toroidal space of inter-key distances. These centroids, belonging to a toroidal surface, are then mapped to colours by 3-dimensional geometric inscription of the whole pitch-space in the CIELAB colourspace. This mapping provides a visual correlate of pitch-space’s double circularity, approximates perceptual uniformity of colours throughout near regions, and allows for representing key ambiguity. We adapt Sapp’s keyscapes to summarize tonal centroids in pitch-space at many time-scales over time, in a two-dimensional coloured image. Keyscapes are linked with higher-dimensional tonal representations in a user interface, in order to combine their informative benefits for interactive analysis. By visualizing some specific music examples, we question the potential of continuous toroidal pitch-spaces in supporting long term analytical conclusions and tonal ambiguity description, when assisted by time vs. time-scale representations.