Page  78 ï~~Foot-tapping: a brief introduction to beat induction As an example, have a look at the following pattern of lines and dots: I..11..... 1.1..11".....1.1..11 Do you see any emergent structure? Probably not. When you would listen to it, though, (e.g., the pattern being played from left to right, with every line being a 16th note and every dot a 16th rest) you would quickly hear a regular pattern -the beat-, and could probably easily tap your foot along with it. This relatively simple cognitive task is called beat induction or foot-tapping. Beat induction is a fast process. Only after a few notes (5-10) a strong sense of beat can be induced (a "bottom-up" process). Once a beat is induced by the incoming material it sets up a persistent mental framework that guides the perception of new incoming material (a "top-down" process). This process, for example, facilitates the percept of syncopation, i.e., to "hear" a beat that is not carried by an event. However, this top-down processing is not rigidly adhering to a once established beat-percept, because when in a change of meter the evidence for the old percept becomes to meager, a new beat interpretation is induced. This duality, where a model needs to be able to infer a beat from scratch, but also to let an already induced beat percept guide the organization of more incoming material, is hard to model. There are a number of aspects that make beat induction an interesting and important process to model, as will be shown in this chapter which results from the joint effort of some researchers of this field. The individual papers will elaborate on the different aspects. Their diversity reflects the large body of work on the subject and the different computational formalisms used (Rule-based systems: LonguetHiggins & Lee (1982); Lee (1985); Miller, Scarborough & Jones (1992), Lee (1991). Optimization methods: Povel & Essens (1985); Parncutt (1994). Search: Longuet-Higgins (1976), Allen & Dannenberg (1990). Control theory: Dannenberg & Mont-Reynaud (1987); Dannenberg (1993). Distributed systems: Desain (1992); Minskian models: Chung (1989); Pennycook, Stammen, & Reynolds (1993); Rowe (1993); Rosenthal (1992); Neural nets: Miller, Scarborough & Jones (1992); Statistical models: Palmer & Krumhansl (1991), Brown (1993)). Interactive computer music systems Interactive computer music systems make some interesting additional demands with respect to those mentioned above (see, e.g., Boulanger, 1990). First, they have to perform in real-time, which means that they have to be efficient enough and that they have to deal with the musical material incrementally (i.e., while the input is processed). They also have to deal with real performance data (containing expressive timing, performance errors, etc.), these systems have to be robust (i.e., they should recover gracefully from errors), they have to deal with instruments that exhibit some response delay (like mechanically driven piano's or shoes), and to do this, they need careful temporal planning (i.e., scheduling). Most of these systems, though, have only been informally tested. It is unclear how and how well they deal with the characteristics mentioned above. However, the interactive performance situations for which these systems were designed, forced the designers to think of solutions on problems that are rarely touched in cognitive models, problems that can not be ignored when aiming at a realistic cognitive model of beat induction. Figure 1. The mechanical shoe. Unfortunately, neither cognitive or technological approaches have been able to arrive at a general, robust beat extraction method. The big challenge seems to lie in a unification and generalization of the existing, partially successful theories, since they all, apparently model at least one valid aspect of beat induction. We hope that the special ICMC 1994 paper session on foot-tapping can make a contribution towards this goal. To enable the audience to compare their own foot-tapping with that of the presented models, some of the computational models will be demonstrated with on-line computer implementations connected to a mechanical foot-tapper (see Figure 1). Peter Desain & Henkjan Honing References (shared by papers in this chapter) Allen, P. & R. Dannenberg (1990) Tracking musical beats in real time. Proceedings of the 1990 ICMC, 140-143. Bamberger, J. (1980) Cognitive structuring in the apprehension of simple rhythms. Archives de Psychologie, 48:171-199. Boulanger, R. (1990) Conducting the MIDI Orchestra, Part 1: Interviews with Max Mathews, Barry Vercoe and Roger Dannenberg. Computer Music Journal, 14(2). Bregman, A. (1990) Auditory Scene Analysis. The MIT Press, Cambridge. Brown, J.C. (1993) Determination of meter of musical scores by autocorrelation. J. Acoust. Soc. Am., 94(4), 1953-1957. Chafe, C., B. Mont-Reynaud and L. Rush (1989) Toward an Intelligent Editor of Digital Audio: Recognition of Musical Constructs. In C. Roads (ed.), The Music Machine. MIT Press, Cambridge, MA. Chung, J. (1989) An Agency for the Perception of Musical Beats, M.S. Thesis, Massachusetts Institute of Technology. Clarke, E. (1985) Structure and expression in rhythmic performance. In P. Howell, I. Cross, and R. West (Eds.) Musical Structure and Cognition. London: Academic Press. Foot-tapping 78 ICMC Proceedings 1994

Page  79 ï~~Cooper, G. & Meyer, L. B. (1960) The rhythmic structure of music. Chicago: University of Chicago Press. Dannenberg, R. B. (1984) An on-line algorithm for real-time accompaniment. In Proceedings of the 1984 ICMC. Computer Music Association. Dannenberg, R.B. & B Mont-Reynaud (1987) Following an improvisation in real-time. In Proceedings of the 1987 International Computer Music Conference. 241 - 248. San Francisco: International Computer Music Association. Dannenberg, R.B. (1993) Music Understanding by Computer. In Proceedings of the IAKTA Workshop on Knowledge Technology in the Arts. 41-55. Osaka: IAKTA/LIST. Desain, P. & H. Honing (1989) Quantization of musical time: a connectionist approach. Computer Music Journal, 13:56 -66. Also Desain & Honing (1991) In Loy, G. & P. Todd (eds) Music and Connectionism. Cambridge, MA: MIT Press. Desain, P. (1992) A (de)composable theory of rhythm perception. Music Perception, 9(4), 439-454. Desain, P., & Honing, H. (1992). The quantization problem: traditional and connectionist approaches. In M. Balaban, K. Ebcioglu, & 0. Laske (eds.), Understanding Music with AL Perspectives on Music Cognition. 448-463. Cambridge: MIT Press. Desain, P., & Honing, H. (1994). From foot-tapper systems to beat induction models. Proceedings ICMPC. Liege: ESCOM. Driesse, A. (1991) Real-time tempo tracking using rules to analyze rhythmic qualities, Proceedings of the 1991 ICMC, pp. 578-581. Fraisse P. (1982). Rhythm and tempo. In D Deutsch (Ed.), The Psychology of Music (pp. 149-180). New York: Academic. Glass, L. & Mackey, M. C. (1988) From clocks to chaos: The rhythms of life. Princeton, NJ: Princeton University Press. Goto, M. & Y. Hashimoto (1993) A distributed cooperative system to play MIDI instruments - toward a remote session, IPSJ SIG Notes, Vol.93, No.109, 93-MUS4-1. (in Japanese). Goto, M. & Y. Muraoka (1994) A real-time beat tracking system for musical acoustic signals, IPSJ SIC Notes, 94 -MUS-7. (in Japanese, in press). Jackendoff, R. (1992) Musical processing and musical affect. In M. R. Jonesand S. Holleran (Eds.) Cognitive bases of musical communication. Washington: American Psychological Association. Jones, M. R. & Boltz, M. (1989) Dynamic Attending and Responses to Time. Psychological Review, 96, 459-491. Jones, M. R. (1976) Time, our lost dimension: Toward a new theory of perception, attention, and memory. Psychological Review, 83, 323-335. Jones, M. R., Boltz, M. & Kidd, G. (1982) Controlled attending as a function of melodic and temporal context Journal of Experimental Psychology: Human Perception & Performance, 7, 211-218. Katayose, H., H. Kato, M. Imai, and S. Inokuchi (1989) An approach to an artificial music expert, Proceedings of the 1989 ICMC, pp.139-146. Kelso, J. A. S. & deGuzman, G. C. (in press) Order in time: How the cooperation between the hands informs the design of the brain. In H. Haken (Ed.) Natural and Synergetic Computers. Berlin: Springer-Verlag. Large, E. W. & Kolen, J. F. (in press) Resonance and the perception of musical meter. Connection Science. Lee, C. S. (1985) The rhythmic interpretation of simple musical sequences: towards a perceptual model In R. West, P. Howell, & I. Cross (eds.) Musical Structure and Cognition. 53-69. London: Academic Press. Lee, C.S. (1991). The perception of metrical structure: Experimental evidence and a model. In P. Howell, R. West, & I. Cross (Eds.), Representing musical structure (pp. 59-127). London: Academic. Lerdahl, F., & Jackendoff, R. (1983). A generative theory of tonal music. Cambridge, MA: MIT Press. Longuet-Higgins, H.C. & C S. Lee (1982) Perception of musical rhythms. Perception. 11, 115-128. Longuet-Higgins, H.C. (1976) The Perception of Melodies Nature 263: 646-653. Also in Longuet-Higgins, 1987. Longuet-Higgins, H.C. (1994) Unpublished computer program in POP-Il, describing an algorithm named "shoe". Longuet-Higgins, H.C.(1987). Mental Processes. Cambridge, Mass.:MIT Press. McAuley, J. D. (1994) Finding metrical structure in time. In M. C. Mozer, P. Smolensky, D. S. Touretsky, J. L Elman & A. S. Weigend (Eds.) Proceedings of the 1993 Connectionist Models Summer School. Hillsdale, NJ: Erlbaum Associates. Miller, B. 0., D. L Scarborough, & J. A. Jones (1992) On the perception of meter. In M. Balaban, K. Ebcioglu, & O. Laske (eds.), Understanding Music with Al: Perspectives on Music Cognition. 428- 447. Cambridge: MIT Press. Page, M. P. A. (1994) Modelling aspects of music perception using self-organizing neural networks. Unpublished doctoral dissertation, University of Exeter. Palmer, C. and C.L. Krumhansl (1990) Mental representations of musical meter. Journal of Experimental Psychology: Human Perception and performance 16(4), 728-741. Pamcutt, R. (1987). The perception of pulse in musical rhythm. In A. Gabrielsson (Ed.), Action and Perception in Rhythm and Music (pp. 127-138). Stockholm: Royal Swedish Academy of Music. Parncutt, R. (1994). A perceptual model of pulse salience and metrical accent in musical rhythms. Music Perception, 11, 409-464. Pennycook, B., D.R. Stammen, & D. Reynolds (1993) Toward a computer model of a jazz improviser. In Proceedings of the 1993 International Computer Music Conference. 228 -231. San Francisco: International Computer Music Association. Povel, D.J. & P. Essens (1985). Perception of temporal Patterns. Music Perception. 2(4):411-440 Rosenthal, D. (1992) Intelligent rhtyhm tracking. In Proceedings of the 1992 International Computer Music Conference. 227-230. San Francisco: International Computer Music Association. Rosenthal, D. (1992) Machine Rhythm: Computer Emulation of Human Rhythm Perception, Ph.D. Thesis, Massachusetts Institute of Technology Rosenthal, D. (1992). Emulation of human rhythm perception. Computer Music Journal, 16 (1), 64-76. Rowe, R. (1993). Interactive Music Systems: Machine Listening and Composing. MIT press: Cambridge. Schloss, W. A. (1985 On The Automatic Transcription of Percussive Music - From Acoustic Signal to High-Level Analysis, Ph.D. Thesis, CCRMA, Stanford University. Schmidt, R. C., Beek, P. J., Treffner, P. J. & Turvey, M. T. (1991) Dynamical substructure of coordinated rhythmic movements. Journal of Experimental Psychology: Human Perception & Performance, 17, 635 -651. Schroeder, M. (1991) Fractals, Chaos, Power Laws. New York: W. H. Freeman and Company. Schulze, H. H. (1989) The perception of temporal deviations in lsochronic patterns. Perception & Psychophysics, 45, 291-296. Shaffer, L. H. (1981) Performances of Chopin, Bach, and Bartok: Studies in motor programming. Cognitive Psychology, 13, 326-376. Shaffer, L. H., Clarke, E. & Todd, N. P. M. (1985) Meter and rhythm in piano playing. Cognition, 20, 61-77. Shaw, M. and H. Coleman (1960) National Anthems of the World. London: Pitman. Sloboda, J. (1983) The communication of musical metre in piano performance. Quarterly Journal of Experimental Psychology 35. Todd, N. P. M. (1994) The auditory "primal sketch": A multi-scale model of rhythmic grouping. Journal of New Music Research, 23(1). Treffner, P. J. & Turvey, M. T. (1993) Resonance constraints on rhythmic movement. Journal of Experimental Psychology: Human Perception & Performance, 19, 1221-1237. Vercoe, B. (1985) The synthetic performer in the context of live music. In Proceedings of the 1985 International Computer Music Conference.199-200. San Francisco: Computer Music Association. Yeston, M. (1976) The stratification of musical rhythm. New Haven: Yale University Press. ICMC Proceedings 1994 79 Foot-tapping