Modelling the internal generation of rhythm as an extension of nonlinear psychophysics

Musicae Scientiae

Volumn 3, Issue 2, 1999, Pages 217-236

  Geake, John G ^a   Gregson, Robert A M ^b  

^a UNIVERSITY OF MELBOURNE   (Australia)

^b AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84990318067     PISSN: 10298649     EISSN: None     Source Type: Journal    
DOI: 10.1177/102986499900300204     Document Type: Article

References (42)

1. Abarbanel H. D. I. (1996). Analysis of Observed Chaotic Data. New York: Springer-Verlag.
2. Bain P. G. (1993). A combined clinical and neurophysiological approach to the study of patients with tremor. Journal of Neurological and Neurosurgical Psychiatry, 56, 839–44.
3. Bain P. G. (1998). Pathological Tremor. Oxford: McDonell-Pew Centre for Cognitive Neuroscience Autumn Workshop.
4. Besson M. Faïta F. Peretz I. Bonnel A.-M. Requin J. (1998). Singing in the Brain: Independence of Lyrics and Tunes. Psychological Science, 9, 494–99.
5. Boon J. P. Prigogine I. (1998). Le temps dans la forme musicale. In Darbellay E.,(ed. ), Le Temps et la Forme. Geneva: Editions de l’Université.
6. Carleson L. Gamelin T. W. (1993). Complex Dynamics. Berlin: Springer-Verlag.
7. Carroll M. Pecora L. M. (1993). Communicating with Chaos. Naval Research Review, 55, 4–11.
8. Chavoya-Aceves O. Angulo-Brown E Piña E. (1985). Symbolic Dynamics of the Cubic Map. Physica D, 14, 374–86.
9. Corless M. Glielmo L. (1998). New Converse Lyapunov Theorems and related Results on Exponential Stability. Mathematics of Control Signals and Systems, 11, 79–100.
10. Clynes M. (ed.) (1982). Music, Mind and Brain: The Neuropsychology of Music. New York: Plenum Press.
11. Dowling W. J. (1978). Scale and contour: Two components of a theory of memory for melodies. Psychological Review, 85, 341–54.
12. Dubischar D. Gundlach V. M. Steinkamp O. Khrcnnnikov A. (1999). A p- adic Model for the Process of Thinking Disturbed by Physiological and Information Noise. Journal of Theoretical Biology, 197, 451–67.
13. Essens P. (1995). Structuring temporal sequences: Comparision of models and factors of complexity. Perception and Psychophysics, 57, 519–32.
14. Geake J. G. (1996). Why Mozart? Information processing abilities of gifted young musicians. Research Studies in Music Education, 7, 28–45.
15. Geake J. G. (1997). Individual differences in the perception of musical coherence. Journal of New Music Research, 26, 201–26.
16. Geake J. G. (1999). An information processing account of audiational abilities. Research Studies in Music Education, 12, 10–23.
17. Gregson R. A. M. (1988). Nonlinear Psychophysical Dynamics. Hillsdale, NJ: Lawrence Erlbaum Associates.
18. Gregson R. A. M. (1992). n-Dimensional Nonlinear Psychophysics: Theory and Case Studies. Hillsdale, NJ: Lawrence Erlbaum Associates.
19. Gregson R. A. M. (1995). Cascades and Fields in Perceptual Psychophysics. Singapore: World Scientific.
20. Halgren E. Chauvel P. (1996). Contributions of the human hippocampal formation to the definition of mental contents. In Kato N.,(ed. ), The Hippocampus: Functions and Clinical Relevance (pp. 377–85). Amsterdam: Elsevier.
21. Jahanshahi M. Frith C. D. (1998). Willed action and its impairments. Cognitive Neuropsychology, 15, 483–533.
22. Jones M. R. Boltz M. (1989). Dynamic attending and responses to time. Psychological Review, 96, 459–91.
23. Jones M. R. Summerell L Marshburn E. (1987). Recognizing Melodies: A Dynamic Interpretation. Quarterly Journal of’Experimental Psycholog), 39A, 89–121.
24. Kantz H. Schreiber T. (1997). Nonlinear Time Series Analysis. Cambridge: Cambridge University Press.
25. Karma K. (1994). Auditory and visual temporal structuring: How important is sound to musical thinking? Psychology of Music, 22, 20–30.
26. Koffka K. (1909). Experimental-Untersuchungen zur Lehre vom Rhythmus. Zeitschrift für Psychologie, 52, 1–109.
27. Lerdahl F Jackenoff R. (1983). A Generative Theory of Tonal Music. Cambridge, MA.: MIT Press.
28. McMullen T. (1994). Frontiers in Complex Dynamics. Bulletin of the American Mathematical Society, 31, 155–72.
29. Milnor J. (1992). Remarks on Iterated Cubic Maps. Experimental Mathematics, 1, 5–24.
30. Nayfeh A. H. Balachandran B. (1995). Applied Nonlinear Dynamics. New York: John Wiley.
31. Nettheim N. (1992). On the Spectral Analysis of Melody. Interface, 21, 135–48.
32. Nicolis G. Prigogine J. (1989). Exploring Complexity. New York: Freeman.
33. Ott E.C. Grebogi C Yorke J. A. (1990). Controlling Chaos. Physical Review Letters, 64, 1196–99.
34. Palmer C Krumhansl C. L. (1990). Mental Representations for Musical Meter. Journal of Experimental Psychology: Human Perception and Performance, 16, 728–41.
35. Pecora L. M. Carroll T. L. (1991). Driving systems with chaotic signals. Physical Review A, 44, 2374–83.
36. Saffran J. R. Aslin R. N. Newport E. L. (1996). Statistical learning by 8-month-old infants. Science, 274, 1926–28.
37. Skjolding H. Braner-Jorgensen B. Christiansen P. L. Jensen H. E. (1983). Bifurcations in discrete dynamical systems with cubic maps. SIAM Journal of Applied Mathematics, 43, 520–34.
38. Stockis J.-P. Tong H. (1998). On the statistical inference of a machine-generated autoregressive AR(1) model. Journal of the Royal Statistical Society, Series B, 60, 781–96.
39. Tighe T. J. Dowling W. J. (1993). Psychology and Music: The understanding of melody and rhythm. Hillsdale, NJ.: Lawrence Erlbaum Associates.
40. Todd N. P. M. (1994). The Auditory “Primal Sketch”: A Multiscale Model of Rhythmic Grouping. Journal of New Music Research, 23, 25–70.
41. Wójcik K. (1998). Isolating segments and symbolic dynamics. Nonlinear Analysis, 33, 575–91.
42. Wolf A. Swift J. Swinney H. Vastrano H. (1985). Determining Lyapuniv Exponents from a Time Series. Physica D, 16, 285–317.