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A Free Energy Formulation of Music Generation and Perception: Helmholtz Revisited

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Sound - Perception - Performance

Part of the book series: Current Research in Systematic Musicology ((CRSM,volume 1))

Abstract

This chapter pursues the notion that, quintessentially, music enables the prediction of the unpredictable. Our focus is on the perception of music using ideas from theoretical biology and neuroscience to explain the nature of musical stimuli and their perceptual synthesis. In brief, we will consider music as a perceptual construct that supports (unconscious) inference on the causal structure of auditory input, in the sense of Helmholtz (1860). We examine the motivation for this particular perspective on music and consider the neuronal architectures that underlie its perception. The basic premises and supposed neuronal implementation—in terms of embodied inference—are then illustrated using simulations of (bird) song generation and perception; with a special focus on reproducing perceptual and neurophysiological responses that are seen in empirical neuroscience studies.

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References

  • Angelucci, A., Levitt, J. B., Walton, E. J., Hupe, J. M., Bullier, J., & Lund, J. S. (2002). Circuits for local and global signal integration in primary visual cortex. Journal of Neuroscience, 22, 8633–8646.

    Google Scholar 

  • Ballard, D. H., Hinton, G. E., & Sejnowski, T. J. (1983). Parallel visual computation. Nature, 306, 21–26.

    Article  Google Scholar 

  • Barlow, H. B. (1961). Possible principles underlying the transformation of sensory messages. In W. A. Rosenblith (Ed.), Sensory communication (pp. 217–234). Cambridge, MA: MIT Press.

    Google Scholar 

  • Besson, M., & Faita, F. (1995). Event-related potential (ERP) study of musical expectancy—comparison of musicians with nonmusicians. Journal of Experimental Psychology: Human Perception and Performance, 21, 1278–1296.

    Article  Google Scholar 

  • Botvinick, M. M. (2007). Multilevel structure in behaviour and in the brain: A model of Fuster’s hierarchy. Philosophical Transactions of the Royal Society of London B: Biological Sciences, 362(1485), 1615–1626.

    Article  Google Scholar 

  • Breakspear, M., & Stam, C. J. (2005). Dynamics of a neural system with a multiscale architecture. Philosophical Transactions of the Royal Society of London B: Biological Sciences, 360, 1051–1107.

    Article  Google Scholar 

  • Byrne, P., Becker, S., & Burgess, N. (2007). Remembering the past and imagining the future: A neural model of spatial memory and imagery. Psychology Review, 114(2), 340–375.

    Article  Google Scholar 

  • Canolty, R. T., Edwards, E., Dalal, S. S., Soltani, M., Nagarajan, S. S., Kirsch, H. E., et al. (2006). High gamma power is phase-locked to theta oscillations in human neocortex. Science, 313, 1626–1628.

    Article  Google Scholar 

  • Chait, M., Poeppel, D., de Cheveigné, A., & Simon, J. Z. (2007). Processing asymmetry of transitions between order and disorder in human auditory cortex. Journal of Neuroscience, 27(19), 5207–5514.

    Article  Google Scholar 

  • Dayan, P., Hinton, G. E., & Neal, R. M. (1995). The Helmholtz machine. Neural Computation, 7, 889–904.

    Article  Google Scholar 

  • Deco, G., & Rolls, E. T. (2003). Attention and working memory: A dynamical model of neuronal activity in the prefrontal cortex. European Journal of Neuroscience, 18(8), 2374–2390.

    Article  Google Scholar 

  • DeFelipe, J., Alonso-Nanclares, L., & Arellano, J. I. (2002). Microstructure of the neocortex: Comparative aspects. Journal of Neurocytology, 31, 299–316.

    Article  Google Scholar 

  • Efron, B., & Morris, C. (1973). Stein’s estimation rule and its competitors—an empirical Bayes approach. Journal of the American Statistical Association, 68, 117–130.

    MathSciNet  MATH  Google Scholar 

  • Felleman, D. J., & Van Essen, D. C. (1991). Distributed hierarchical processing in the primate cerebral cortex. Cerebral Cortex, 1, 1–47.

    Article  Google Scholar 

  • Feynman, R. P. (1972). Statistical mechanics. Reading, MA: Benjamin.

    Google Scholar 

  • Freeman, W. J. (1987). Simulation of chaotic EEG patterns with a dynamic model of the olfactory system. Biological Cybernetics, 56(2–3), 139–150.

    Article  Google Scholar 

  • Friston, K. J . (1997). Transients, metastability, and neuronal dynamics. NeuroImage, 5(2), 164–171.

    Article  Google Scholar 

  • Friston, K. J. (2005). A theory of cortical responses. Philosophical Transactions of the Royal Society of London B: Biological Sciences, 360, 815–836.

    Article  Google Scholar 

  • Friston, K., Kilner, J., & Harrison, L. (2006). A free energy principle for the brain. Journal of Physiology-Paris, 100(1–3), 70–87.

    Article  Google Scholar 

  • Friston, K. (2008). Hierarchical models in the brain. PLoS Computational Biology, 4(11), e1000211.

    Article  MathSciNet  Google Scholar 

  • Friston, K., & Kiebel, S. (2009). Cortical circuits for perceptual inference. Neural Networks, 22(8), 1093–1104.

    Article  MathSciNet  Google Scholar 

  • Haken, H., Kelso, J. A. S., Fuchs, A., & Pandya, A. S. (1990). Dynamic pattern-recognition of coordinated biological motion. Neural Networks, 3, 395–401.

    Article  Google Scholar 

  • Hasson, U., Yang, E., Vallines, I., Heeger, D. J., & Rubin, N. (2008). A hierarchy of temporal receptive windows in human cortex. Journal of Neuroscience, 28, 2539–2550.

    Article  Google Scholar 

  • Helmholtz, H. (1860/1962). Handbuch der physiologischen Optik. In J. P. C. Southall (Ed.) (Vol. 3). New York: Dover, (Translation).

    Google Scholar 

  • Helmholtz, H. (1866/1962). Concerning the perceptions in general. In J. Southall (Ed.) Treatise on physiological optics (3rd ed., Vol. III). New York: Dover, (Translation).

    Google Scholar 

  • Helmholtz, H. (1877). On the sensations of tone as a physiological basis for the theory of music. In A. J. Ellis (Ed.), Fourth German edition, translated, revised, corrected with notes and additional appendix. New York: Dover Publications Inc., 1954 (Reprint).

    Google Scholar 

  • Hinton, G. E., & von Camp, D. (1993). Keeping neural networks simple by minimising the description length of weights. In Proceedings of COLT-93, 5–13.

    Google Scholar 

  • Hupe, J. M., James, A. C., Payne, B. R., Lomber, S. G., Girard, P., & Bullier, J. (1998). Cortical feedback improves discrimination between figure and background by V1, V2 and V3 neurons. Nature, 394, 784–787.

    Article  Google Scholar 

  • Jirsa, V. K., Fuchs, A., & Kelso, J. A. (1998). Connecting cortical and behavioral dynamics: bimanual coordination. Neural Computation, 10, 2019–2045.

    Article  Google Scholar 

  • Kass, R. E., & Steffey, D. (1989). Approximate Bayesian inference in conditionally independent hierarchical models (parametric empirical Bayes models). Journal of the American Statistical Association, 407, 717–726.

    Article  MathSciNet  Google Scholar 

  • Kawato, M., Hayakawa, H., & Inui, T. (1993). A forward-inverse optics model of reciprocal connections between visual cortical areas. Network, 4, 415–422.

    Article  MATH  Google Scholar 

  • Kiebel, S. J., Daunizeau, J., & Friston, K. J. (2008). A hierarchy of time-scales and the brain. PLoS Computational Biology, 4(11), e1000209.

    Article  Google Scholar 

  • Koelsch, S., Gunter, T., Friederici, A. D., & Schröger, E. (2000). Brain indices of music processing: “nonmusicians” are musical. Journal of Cognitive Neuroscience, 12(3), 520–541.

    Article  Google Scholar 

  • Koelsch, S., Schroger, E., & Gunter, T. C. (2002). Music matters: Preattentive musicality of the human brain. Psychophysiology, 39(1), 38–48.

    Article  Google Scholar 

  • Koelsch, S., Fritz, T., Schulze, K., Alsop, D., & Schlaug, G. (2005). Adults and children processing music: An fMRI study. Neuroimage, 25(4), 1068–1076.

    Article  Google Scholar 

  • Koelsch, S., Kilches, S., Steinbeis, N., & Schelinski, S. (2008). Effects of unexpected chords and of performer’s expression on brain responses and electrodermal activity. PloS ONE, 3, e2631.

    Article  Google Scholar 

  • Kopell, N., Ermentrout, G. B., Whittington, M. A., & Traub, R. D. (2000). Gamma rhythms and beta rhythms have different synchronization properties. Proceedings of the National Academy of Sciences USA, 97, 1867–1872.

    Article  Google Scholar 

  • Laje, R., Gardner, T. J., & Mindlin, G. B. (2002). Neuromuscular control of vocalizations in birdsong: a model. Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, 65, 051921.1–8.

    Google Scholar 

  • Laje, R., & Mindlin, G. B. (2002). Diversity within a birdsong. Physical Review Letters, 89, 288102.

    Article  Google Scholar 

  • Levitin, D. J., & Menon, V. (2003). Musical structure is processed in “language” areas of the brain: a possible role for Brodmann Area 47 in temporal coherence. Neuroimage, 20(4), 2142–2152.

    Article  Google Scholar 

  • Loui, P., Grent-’t-Jong, T., Torpey, D., & Woldorff, M. (2005). Effects of attention on the neural processing of harmonic syntax in Western music. Brain Research. Cognitive Brain Research, 25(3), 678–687.

    Article  Google Scholar 

  • MacKay, D. J. C. (1995). Free-energy minimisation algorithm for decoding and cryptoanalysis. Electronics Letters, 31, 445–447.

    Article  Google Scholar 

  • Maunsell, J. H., & van Essen, D. C. (1983). The connections of the middle temporal visual area (MT) and their relationship to a cortical hierarchy in the macaque monkey. Journal of Neuroscience, 3, 2563–2586.

    Google Scholar 

  • McCrea, D. A., & Rybak, I. A. (2008). Organization of mammalian locomotor rhythm and pattern generation. Brain Research Reviews, 57(1), 134–146.

    Article  Google Scholar 

  • Mesulam, M. M. (1998). From sensation to cognition. Brain, 121, 1013–1052.

    Google Scholar 

  • Meyer, L. B. (1956). Emotion and meaning in music. Chicago: University of Chicago Press.

    Google Scholar 

  • Mumford, D. (1992). On the computational architecture of the neocortex. II. The role of cortico-cortical loops. Biological Cybernetics, 66, 241–251.

    Article  Google Scholar 

  • Murphy, P. C., & Sillito, A. M. (1987). Corticofugal feedback influences the generation of length tuning in the visual pathway. Nature, 329, 727–729.

    Article  Google Scholar 

  • Neal, R. M., & Hinton, G. E. (1998). A view of the EM algorithm that justifies incremental sparse and other variants. In M. I. Jordan (Ed.), Learning in graphical models, 355–368. Dordrecht: Dordrecht Kulver Academic Press.

    Google Scholar 

  • Neisser, U. (1967). Cognitive psychology. New York: Appleton-Century-Crofts.

    Google Scholar 

  • Nordby, H., Hammerborg, D., Roth, W. T., & Hugdahl, K. (1994). ERPs for infrequent omissions and inclusions of stimulus elements. Psychophysiology, 31(6), 544–552.

    Article  Google Scholar 

  • Pearce, M. T., Ruiz, M. H., Kapasi, S., Wiggins, G. A., & Bhattacharya, J. (2010). Unsupervised statistical learning underpins computational, behavioural, and neural manifestations of musical expectation. Neuroimage, 50(1), 302–313.

    Article  Google Scholar 

  • Rabinovich, M., Huerta, R., & Laurent, G. (2008). Neuroscience: Transient dynamics for neural processing. Science, 321(5885), 48–50.

    Article  Google Scholar 

  • Rao, R. P., & Ballard, D. H. (1998). Predictive coding in the visual cortex: A functional interpretation of some extra-classical receptive field effects. Nature Neuroscience, 2, 79–87.

    Article  Google Scholar 

  • Rockland, K. S., & Pandya, D. N. (1979). Laminar origins and terminations of cortical connections of the occipital lobe in the rhesus monkey. Brain Research, 179, 3–20.

    Article  Google Scholar 

  • Rohrmeier, M. A., & Koelsch, S. (2012). Predictive information processing in music cognition. A critical review. Int J Psychophysiol., 83(2), 164–175.

    Article  Google Scholar 

  • Rosier, A. M., Arckens, L., Orban, G. A., & Vandesande, F. (1993). Laminar distribution of NMDA receptors in cat and monkey visual cortex visualized by [3H]-MK-801 binding. Journal of Comparative Neurology, 335, 369–380.

    Article  Google Scholar 

  • Sherman, S. M., & Guillery, R. W. (1998). On the actions that one nerve cell can have on another: Distinguishing “drivers” from “modulators”. Proceedings of the National Academy of Sciences USA, 95, 7121–7126.

    Article  Google Scholar 

  • Sloboda, J. A. (1991). Music structure and emotional response: Some empirical fmdings. Psychology of Music, 19, 110–120.

    Article  Google Scholar 

  • Steinbeis, N., Koelsch, S., & Sloboda, J. A. (2006). The role of harmonic expectancy violations in musical emotions: evidence from subjective, physiological, and neural responses. Journal of Cognitive Neuroscience, 18(8), 1380–1393.

    Article  Google Scholar 

  • Tsodyks, M. (1999). Attractor neural network models of spatial maps in hippocampus. Hippocampus, 9(4), 481–489.

    Article  Google Scholar 

  • Verleger, R. (1990). P3-evoking wrong notes: unexpected, awaited, or arousing? International Journal of Neuroscience, 55, 171–179.

    Article  Google Scholar 

  • Yabe, H., Tervaniemi, M., Reinikainen, K., & Näätänen, R. (1997). Temporal window of integration revealed by MMN to sound omission. NeuroReport, 8(8), 1971–1974.

    Article  Google Scholar 

  • Zeki, S., & Shipp, S. (1988). The functional logic of cortical connections. Nature, 335, 311–331.

    Article  Google Scholar 

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Acknowledgments

The Wellcome Trust funded this work. We would also like to thank Larry Goodyer for invaluable discussions.

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Correspondence to Karl J. Friston .

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Friston, K.J., Friston, D.A. (2013). A Free Energy Formulation of Music Generation and Perception: Helmholtz Revisited. In: Bader, R. (eds) Sound - Perception - Performance. Current Research in Systematic Musicology, vol 1. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00107-4_2

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  • DOI: https://doi.org/10.1007/978-3-319-00107-4_2

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