Minds and Machines

, Volume 20, Issue 4, pp 503–532 | Cite as

Unifying Conceptual Spaces: Concept Formation in Musical Creative Systems

  • Jamie Forth
  • Geraint A. Wiggins
  • Alex McLean


We examine Gärdenfors’ theory of conceptual spaces, a geometrical form of knowledge representation (Conceptual spaces: The geometry of thought, MIT Press, Cambridge, 2000), in the context of the general Creative Systems Framework introduced by Wiggins (J Knowl Based Syst 19(7):449–458, 2006a; New Generation Comput 24(3):209–222, 2006b). Gärdenfors’ theory offers a way of bridging the traditional divide between symbolic and sub-symbolic representations, as well as the gap between representational formalism and meaning as perceived by human minds. We discuss how both these qualities may be advantageous from the point of view of artificial creative systems. We take music as our example domain, and discuss how a range of musical qualities may be instantiated as conceptual spaces, and present a detailed conceptual space formalisation of musical metre.


Conceptual spaces Creativity Search Geometry Musical rhythm Similarity 



We are grateful to our colleagues in the Intelligent Sound and Music Systems group at Goldsmiths, and the computational creativity community at large, for many years of richly fruitful discussion. We also thank several anonymous reviewers for constructive comments on earlier drafts. The work reported here was supported by an Arts and Humanities Research Council Doctoral Studentship awarded to the first author and an Engineering and Physical Sciences Research Council DTA Doctoral Studentship awarded to the third author.


  1. Aisbett, J., & Gibbon, G. (2001). A general formulation of conceptual spaces as a meso level representation. Artificial Intelligence, 133(1–2), 189–232.MATHCrossRefMathSciNetGoogle Scholar
  2. Baars, B. J. (1988). A cognitive theory of consciousness. Cambridge: Cambridge University Press.Google Scholar
  3. Benjamin, W. E. (1984). A theory of musical meter. Music Perception, 1(4), 355–413.Google Scholar
  4. Boden, M. A. (1998). Creativity and artificial intelligence. Artificial Intelligence Journal, 103, 347–356.MATHCrossRefMathSciNetGoogle Scholar
  5. Boden, M. A. (2004). The creative mind: Myths and mechanisms, (2nd ed.). London, UK: Routledge.Google Scholar
  6. Bown, O., & Wiggins, G. A. (2009). From maladaptation to competition to cooperation in the evolution of musical behaviour. Musicæ Scientiæ (special issue on evolution of music).Google Scholar
  7. Brachman, R. J., & Levesque, H. J., (Eds.). (1985). Readings in knowledge representation. Los Altos: Morgan Kaufmann.MATHGoogle Scholar
  8. Caclin, A., Brattico, E., Tervaniemi, M., Näätänen, R., Morlet, D., Giard, M.-H., et al. (2006). Separate neural processing of timbre dimensions in auditory sensory memory. Journal Cognitive Neuroscience, 18(12), 1959–1972.CrossRefGoogle Scholar
  9. Carota, F., Posada, A., Harquel, S., Delpuech, C., Bertrand, O., & Sirigu, A. (2009). Neural dynamics of the intention to speak. Cerebral Cortex, 20(8), 1891–1897.CrossRefGoogle Scholar
  10. Chew, E. (2000). Towards a mathematical model of tonality. PhD thesis, Department of Operations Research. Massachusetts: MIT, Cambridge.Google Scholar
  11. Clarke, E. F. (1999). Rhythm and timing in music. In D. Deutsch (Eds.), Psychology of music (2nd ed. pp. 473–500). San Diego, CA: University of California.CrossRefGoogle Scholar
  12. Cooper, G. W., & Meyer, L. B. (1960). The rhythmic structure of music. Chicago, IL: University of Chicago Press.Google Scholar
  13. Dowling, W. J. (1978). Scale and contour: Two components of a theory of memory for melodies. Psychological Review, 85(4), 341–354.CrossRefGoogle Scholar
  14. Fraisse, P. (1978). Time and rhythm perception. In E. Carterette, & M. Friedmans (Eds.), Handbook of perception (Vol. 2, pp. 203–254). New York, NY: Academic PressGoogle Scholar
  15. Gabrielsson, A. (1993). The complexities of rhythm. In T. J. Tighe, & W. J. Dowling (Eds.), Psychology and music: The understanding of melody and rhythm (pp. 93–120). Hillside, NJ: Lawrence Erlbaum Associates, Inc.Google Scholar
  16. Gärdenfors, P. (2000). Conceptual spaces: The geometry of thought. Cambridge, MA: MIT Press.Google Scholar
  17. Gärdenfors, P. (2007). Representing actions and functional properties in conceptual spaces. In T. Ziemke, J. Zlatev, & R. M. Frank (Eds.), Body, language and mind (Vol. 1, pp. 167–195). Berlin, Germany: Mouton de Gruyter.Google Scholar
  18. Guilford, J. (1967). The nature of human intelligence. New York: McGraw-Hill.Google Scholar
  19. Haase, K. (1995). Too many ideas, just one word: a review of Margaret Boden’s The creative mind: Myths and mechanisms. Artificial Intelligence Journal, 79, 69–82.CrossRefGoogle Scholar
  20. Hasty, C. F. (1997). Metre as rhythm. Oxford: Oxford University Press.Google Scholar
  21. Jain, A., Nandakumar, K., & Ross, A. (2005). Score normalization in multimodal biometric systems. Pattern Recognition, 38(12), 2270–2285.CrossRefGoogle Scholar
  22. Koestler, A. (1964). The act of creation. London: Hutchinson & Co.Google Scholar
  23. Lemström, K., & Wiggins, G. A. (2009). Formalizing invariances for content-based music retrieval. In G. Tzanetakis & K. Hirata (Eds.), Proceedings of ISMIR 2009.Google Scholar
  24. Lerdahl, F., & Jackendoff, R. (1983). A generative theory of tonal music. Cambridge, MA: MIT Press.Google Scholar
  25. London, J. (2004). Hearing in time: Psychological aspects of music metre. Oxford, UK: Oxford University Press.Google Scholar
  26. Lustig, R. (1995). Margaret Boden, the creative mind: Myths and mechanisms. Artificial Intelligence Journal, 79, 83–96.CrossRefGoogle Scholar
  27. MacKay, D. J. C. (1998). Introduction to Monte Carlo methods. In M. I. Jordan (Ed.), Learning in graphical models, NATO science series (pp. 175–204). Dordrecht, The Netherlands: Kluwer.Google Scholar
  28. Müllensiefen, D. (2009). Fantastic: Feature analysis technology accessing statistics (in a corpus). Technical report, Goldsmiths, London, UK: University of London.Google Scholar
  29. Parncutt, R. (1994). A perceptual model of pulse salience and metrical accent in musical rhythms. Music Perception, 11, 409–464.Google Scholar
  30. Parsons, D. (1975). The directory of tunes and musical themes. Cambridge, UK: S. Brown.Google Scholar
  31. Patel, A. D. (2008). Music, language, and the brain. Oxford: Oxford University Press.Google Scholar
  32. Pearce, M. T., & Wiggins, G. A. (2006). Expectation in melody: The influence of context and learning. Music Perception, 23(5), 377–405.CrossRefGoogle Scholar
  33. Perkins, D. (1995). An unfair review of Margaret Boden’s The Creative Mind from the perspective of creative systems. Artificial Intelligence Journal, 79, 97–109.CrossRefGoogle Scholar
  34. Povel, D.-J. (1984). A theoretical framework for rhythm perception. Psychological Research, 45(4), 315–337.CrossRefGoogle Scholar
  35. R Development Core Team. (2010). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. ISBN 3-900051-07-0.Google Scholar
  36. Ram, A., Wills, L., Domeshek, E., Nersessian, N., & Kolodner, J. (1995). Understanding the creative mind: A review of Margaret Boden’s Creative Mind. Artificial Intelligence Journal, 79, 111–128.CrossRefGoogle Scholar
  37. Raubal, M. (2004). Formalizing conceptual spaces. In A. Varzi & L. Vieu (Eds.), Formal ontology in information systems, proceedings of the third international conference (FOIS 2004), Vol. 114 of frontiers in artificial intelligence and applications (pp. 153–164). Amsterdam, NL: IOS Press.Google Scholar
  38. Raubal, M. (2008a). Cognitive modeling with conceptual spaces. In M. Ragni, H. Schultheis, & T. Barkowsky (Eds.), Workshop on cognitive models of human spatial reasoning (pp. 7–11). Freiburg, Germany.Google Scholar
  39. Raubal, M. (2008b). Representing concepts in time. In C. Freksa, N. S. Newcombe, Peter Gärdenfors, & S. Wölfl (Eds.), Spatial cognition VI. Learning, reasoning, & talking about space. Lecture Notes in Computer Science (Vol. 5248, pp. 328–343). Berlin: Springer.Google Scholar
  40. Rickard, J. T. (2006). A concept geometry for conceptual spaces. Fuzzy Optimization and Decision Making, 5(4), 311–329.MATHCrossRefMathSciNetGoogle Scholar
  41. Rickard, J. T., Aisbett, J., & Gibbon, G. (2007a). Knowledge representation and reasoning in conceptual spaces. In Foundations of Computational Intelligence, 2007. FOCI 2007. IEEE Symposium on (pp. 583–590).Google Scholar
  42. Rickard, J. T., Aisbett, J., & Gibbon, G. (2007b). Reformulation of the theory of conceptual spaces. Information Sciences, 177(21), 4539–4565.MATHCrossRefMathSciNetGoogle Scholar
  43. Roberson, D., Davidoff, J., Davies, I. R. L., & Shapiro, L. R. (2006). Colour categories and category acquisition in Himba and English. In N. Pitchford & C. Bingham (Eds.), Progress in colour studies (pp. 159–172). Amsterdam: John Benjamins.Google Scholar
  44. Schank, R., & Foster, D. (1995). The engineering of creativity: A review of Boden’s The Creative Mind. Artificial Intelligence Journal, 79, 129–143.CrossRefGoogle Scholar
  45. Schwering, A., & Raubal, M. (2005a). Measuring semantic similarity between geospatial conceptual regions. In GeoSpatial semantics—First international conference, GeoS 2005, Vol. 3799 of LNCS (pp. 90–106). Berlin, Germany: Springer.Google Scholar
  46. Schwering, A., & Raubal, M. (2005b). Spatial relations for semantic similarity measurement. In Perspectives in conceptual modeling, Vol. 3770 of LNCS (pp. 259–269). Berlin, Germany: Springer.Google Scholar
  47. Shepard, R. N. (1982). Structural representations of musical pitch. In D. Deutsch (Ed.), Psychology of music (pp. 343–390). New York: Academic Press.Google Scholar
  48. Shepard, R. N. (1987). Toward a universal law of generalization for psychological science. Science, 237(4820), 1317–1323.CrossRefMathSciNetGoogle Scholar
  49. Steedman, M. J. (1977). The perception of musical rhythm and metre. Perception, 6(5), 555–569.CrossRefGoogle Scholar
  50. Thornton, C. (2007). How thinking inside the box can become thinking outside the box. In A. Cardoso & G. Wiggins (Eds.), Proceedings of the 4th international joint workshop on computational creativity.Google Scholar
  51. Thornton, C. (2009). Personal communication.Google Scholar
  52. Turner, S. R. (1995). Margaret Boden, The Creative Mind. Artificial Intelligence Journal, 79, 145–159.CrossRefGoogle Scholar
  53. Wallas, G. (1926). The art of thought. New York: Harcourt Brace.Google Scholar
  54. Wiggins, G. A. (2006a). A preliminary framework for description, analysis and comparison of creative systems. Journal of Knowledge Based Systems, 19(7), 449–458.CrossRefGoogle Scholar
  55. Wiggins, G. A. (2006b). Searching for computational creativity. New Generation Computing, 24(3), 209–222.MATHCrossRefGoogle Scholar
  56. Wiggins, G. A., Harris, M., & Smaill, A. (1989). Representing music for analysis and composition. In M. Balaban, K. Ebcioglu, O. Laske, C. Lischka, & L. Soriso (Eds.), Proceedings of the second workshop on AI and music (pp. 63–71). Menlo Park, CA: AAAI.Google Scholar
  57. Wiggins, G. A., Pearce, M. T., & Müllensiefenllensiefen, D. (2009). Computational modelling of music cognition and musical creativity. In R. Dean (Ed.), Oxford handbook of computer music and digital sound culture. Oxford: Oxford University Press.Google Scholar
  58. Zajonc, R. B. (1968). Attitudinal effects of mere exposure. Journal of Personality and Social Psychology, Monograph Supplement, 9, 1–27.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of Computing & Centre for Cognition, Computation and CultureGoldsmiths, University of LondonLondonUK

Personalised recommendations