Time quantization

Musical time can be considered as the product of two time scales: the discrete time intervals of a metrical structure, and the continuous time scales of tempo changes and expressive timing . In the notation of music both kinds are present, though the notation of continuous time is less developed than that of metric time (often just a word like rubato or accelerando is notated in the score). To make sense of musical performance timing it is necessary to separate the discrete and continuous components. We call this process quantization, although the term is generally used to reflect only the extraction of a metrical score from a performance.

• Cemgil A.T. & Kappen, B. (2003) Monte Carlo Methods for Tempo Tracking and Rhythm Quantization, Journal of Artificial Intelligence Research, 18, 45-81.
• Cemgil A.T. & Kappen, B. (2002) Tempo Tracking and Rhythm Quantization by Sequential Monte Carlo In: Advances in Neural Information Processing Systems 14, Tom Dietterich, Sue Becker and Zoubin Ghahramani (Eds.) (pp. 1361-1368), MIT Press.
• Cemgil A.T. & Kappen, B. (2002) Integrating Tempo Tracking and Quantization using Particle Filtering. Proceedings of 2002 International Computer Music Conference.147-150.
• Honing, H. (2002) Structure and interpretation of rhythm and timing Tijdschrift voor Muziektheorie. 7(3), 227-232.
• Desain, P. and Honing, H. (2001) Modeling the Effect of Meter in Rhythmic Categorization: Preliminary Results Journal of Music Perception and Cognition, 7 (2), ??-??.
• Cemgil, T., Kappen, B., Desain, P., & Honing, H. (submitted) Integrating Tempo Tracking and Quantization for Rhythm Transcription.
• Cemgil, T. and Kappen, B. (submitted) Bayesian Real-time Adaptation for Interactive Performance Systems.
• Desain, P., Jansen, C., and Honing, H. (2000) How identification of rhythmic categories depends on tempo and meter. In Proceedings of the Sixth International Conference on Music Perception and Cognition Keele, UK: Keele University, Department of Psychology.
• Desain, P. & Honing, H. (2003) The formation of rhythmic categories and metric priming. Perception. 32(3), 341-365.
• Cemgil, T., Kappen, B., Desain, P., and Honing, H. (2000) On tempo tracking: Tempogram Representation and Kalman filtering. In Proceedings of the International Computer Music Conference, 352-355. San Francisco: ICMA. [Received distinguished paper award]
• Cemgil, T., Kappen, B., Desain, P., and Honing, H. (2001) On tempo tracking: Tempogram Representation and Kalman filtering. Journal of New Music Research. 29 (4), 259-273.
• Trilsbeek, P. and Thienen, H van (1999) Quantization for Notation: methods used in commercial musical software. Nijmegen.
• Aarts, R. and Jansen, C. (1999) Categorical perception of short rhythms. In Proceedings of the 1999 SMPC, 57. Evanston.
• Jansen, C. & Desain, P. (in preparation) Quantization in context.
• Desain, P., & Honing, H. (1992). The quantization problem: traditional and connectionist approaches. In M. Balaban, K. Ebcioglu, & O. Laske (eds.), Understanding Music with AI: Perspectives on Music Cognition. 448-463. Cambridge: MIT Press.
• Desain, P., & Honing, H. (1991). Quantization of musical time: a connectionist approach. In P.M. Todd and D. G. Loy (eds.), Music and Connectionism. Cambridge: MIT Press.
• Desain, P., Aarts, R., Cemgil, T., Kappen, B., Thienen, H. van, and Trilsbeek, P. (1999) Robust Time-quantization for Music, from Performance to Score. In Proceedings of the 106th Audio Engineering Society Conference New York.
• Desain, P. (1993). A connectionist and a traditional AI quantizer, symbolic versus sub-symbolic models of rhythm perception. Contemporary Music Review, 9, 239-254.
• Cemgil, T., Desain, P., and Kappen, B. (2000) Rhythm Quantization for Transcription. Computer Music Journal, 24(2), 60-76.
• Cemgil, T., Desain, P., and Kappen, B. (1999) Rhythm Quantization for Transcription. In Proceedings of the AISB'99 Symposium on Musical Creativity, 140-146.