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.
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References
Krumhansl, C.L.: Cognitive Foundations of Musical Pitch. Oxford University Press, New York (1990)
Schoenberg, A.: Structural Functions of Harmony (rev. ed.), Norton, New York (1969) (Originally published, 1954)
Chew, E.: Towards a Mathematical Model of Tonality. Ph.D. dissertation, Massachussets Institute of Technology (2000)
Werts, D.: A Theory of Scale References. Ph. D. dissertation, Princeton University (1983)
Lerdahl, F.: Tonal Pitch Space. Oxford University Press, New York (2001)
Coombs, C.H.: A Theory of Data. Wiley and sons, New York (1964)
Krumhansl, C.L., Toiviainen, P.: Tonal Cognition. In: Peretz, I., Zatorre, R. (eds.) The Cognitive Neuroscience of Music, pp. 95–108. Oxford University Press, New York (2003)
Janata, P.: Navigating Tonal Space. In: Hewlett, W.B., Selfridge-Field, E., Correia Jr., E. (eds.) Tonal theory for the digital age. Computing in Musicology, vol. 15, pp. 39–50. CCARH, Stanford (2007)
Chew, E., François, A.R.J.: Interactive Multi-scale Visualizations of Tonal Evolution in MuSA.RT Opus 2. Computers in Entertainment 3(4), 1–16 (2005)
Sapp, C.S.: Visual Hierarchical Key Analysis. Computers in Entertainment 3(4), 1–19 (2005)
Eerola, T., Toiviainen, P.: MIDI Toolbox: MATLAB Tools for Music Research. University of Jyväskylä, Kopijyvä, Jyväskylä, Finland (2004), Electronic version http://www.jyu.fi/musica/miditoolbox/
CIE 015: 2004. Colorimetry, 3rd ed. Commission Internationale de L’Éclairage (2004)
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© 2011 Springer-Verlag Berlin Heidelberg
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Martorell, A., Gómez, E. (2011). Two-Dimensional Visual Inspection of Pitch-Space, Many Time-Scales and Tonal Uncertainty over Time. In: Agon, C., Andreatta, M., Assayag, G., Amiot, E., Bresson, J., Mandereau, J. (eds) Mathematics and Computation in Music. MCM 2011. Lecture Notes in Computer Science(), vol 6726. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21590-2_11
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DOI: https://doi.org/10.1007/978-3-642-21590-2_11
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