Psychological Research

, Volume 58, Issue 3, pp 177–192 | Cite as

Perceptual scaling of synthesized musical timbres: Common dimensions, specificities, and latent subject classes

  • Stephen McAdams
  • Suzanne Winsberg
  • Sophie Donnadieu
  • Geert De Soete
  • Jochen Krimphoff
Original Article


To study the perceptual structure of musical timbre and the effects of musical training, timbral dissimilarities of synthesized instrument sounds were rated by professional musicians, amateur musicians, and nonmusicians. The data were analyzed with an extended version of the multidimensional scaling algorithm CLASCAL (Winsberg & De Soete, 1993), which estimates the number of latent classes of subjects, the coordinates of each timbre on common Euclidean dimensions, a specificity value of unique attributes for each timbre, and a separate weight for each latent class on each of the common dimensions and the set of specificities. Five latent classes were found for a three-dimensional spatial model with specificities. Common dimensions were quantified psychophysically in terms of log-rise time, spectral centroid, and degree of spectral variation. The results further suggest that musical timbres possess specific attributes not accounted for by these shared perceptual dimensions. Weight patterns indicate that perceptual salience of dimensions and specificities varied across classes. A comparison of class structure with biographical factors associated with degree of musical training and activity was not clearly related to the class structure, though musicians gave more precise and coherent judgments than did nonmusicians or amateurs. The model with latent classes and specificities gave a better fit to the data and made the acoustic correlates of the common dimensions more interpretable.


Latent Classis Common Dimension Class Structure Spectral Variation Latent Subject 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. American Standards Association (1960). Acoustical Terminology, S1.1-1960. New York: American Standards Association.Google Scholar
  2. Aitken, M., Andersen, D., & Hinde, J. (1981). Statistical model of data on teaching styles. Journal of the Royal Statistical Society Series A, 144, 419–461.Google Scholar
  3. Aikake, H. (1977). On entropy maximization. In P. R. Krishniah (Ed.), Applications of statistics (pp. 27–41). Amsterdam: North-Holland.Google Scholar
  4. Bentler, P. M., & Weeks, D. G. (1978). Restricted multidimensional scaling methods. Journal of Mathematical Psychology, 17, 138–151.Google Scholar
  5. Bockenholt, U., & Bockenholt, I. (1990). Modeling individual differences in unfolding preference data: A restricted latent class approach. Applied Psychological Measurement, 14, 257–269.Google Scholar
  6. Bogdozan, H. (1987). Model selection and Aikake's information criterion (AIC): The general theory and its analytic extensions. Psychometrika, 52, 345–370.Google Scholar
  7. Carroll, J. D., & Chang, J. J. (1970). Analysis of individual differences in multidimensional scaling via an n-way generalization of Eckart-Young decomposition. Psychometrika, 35, 283–319.Google Scholar
  8. Chowning, J. M. (1973). The synthesis of complex audio spectra by means of frequency modulation. Journal of the Audio Engineering Society, 21, 526–534.Google Scholar
  9. Dempster, A. P., Laird, N. M., & Rubin, D. R. (1977). Maximum likelihood estimation from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, Series B, 39, 1–38.Google Scholar
  10. De Leeuw, J., & Heiser, W. (1980). Multidimensional scaling with restrictions on the configuration. In P. R. Krishniah (Ed.), Multivariate analysis, vol. 5 (pp. 501–522). Amsterdam: North Holland.Google Scholar
  11. De Sarbo, W. J., Howard, D. J., & Jededi, K. (1991). MULTICLUS: A new method for simultaneously performing multidimensional scaling and cluster analysis. Psychometrika, 56, 121–136.Google Scholar
  12. De Soete, G. (1990). A latent class approach to modeling pairwise preferential choice data. In M. Schader & W. Gaul (Eds.), Knowledge, data, and computer-assisted decisions (pp. 103–113). Berlin: Springer-Verlag.Google Scholar
  13. De Soete, G., Carroll, J. D., & Chaturvedi, A. D. (1993). A modified CANDECOMP method for fitting the extended INDSCAL model. Journal of Classification, 10, 75–90.Google Scholar
  14. De Soete, G., & De Sarbo, W. (1991). A latent class probit model for analyzing pick any n data. Journal of Classification, 8, 45–63.Google Scholar
  15. De Soete, G., & Heiser, W. J. (1993). A latent class unfolding model for analyzing single stimulus preference ratings. Psychometrika, 58, 545–565.Google Scholar
  16. De Soete, G., & Winsberg, S. (1993). A Thurstonian pairwise choice model with univariate and multivariate spline transformations. Psychometrika, 58, 233–256.Google Scholar
  17. Donnadieu, S., McAdams, S., Winsberg, S. (1994). Caracterisation du timbre des sons complexes. I: Analyse multidimensionnalle. Journal de Physique 4(C5), 593–596.Google Scholar
  18. Ehresman, D., & Wessel, D. L. (1978). Perception of timbral analogies. Rapports IRCAM, 13, Paris: IRCAM.Google Scholar
  19. Formann, A. K. (1989). Constrained latent class models: Some further applications. British Journal of Mathematical Psychology, 42, 37–54.Google Scholar
  20. Gower, J. C. (1966). Some distance properties of latent root and vector methods using multivariate analysis. Biometrika, 53, 325–338.Google Scholar
  21. Grey, J. M. (1975). An exploration of musical timbre. Unpublished Ph.D. dissertation, Stanford University, Stanford, CA. Stanford University, Dept. of Music Report STAN-M-2.Google Scholar
  22. Grey, J. M. (1977). Multidimensional perceptual scaling of musical timbres. Journal of the Acoustical Society of America, 61, 1270–1277.Google Scholar
  23. Grey, J. M., & Gordon, J. W. (1978). Perceptual effects of spectral modifications on musical timbres. Journal of the Acoustical Society of America, 63, 1493–1500.Google Scholar
  24. Hope, A. C. (1968). A simplified Monte Carlo significance test procedure. Journal of the Royal Statistical Society, Series B, 30, 582–598.Google Scholar
  25. Iverson, P., & Krumhansl, C. L. (1993). Isolating the dynamic attributes of musical timbre. Journal of the Acoustical Society of America, 94, 2595–2603.Google Scholar
  26. Kendall, R. A., & Carterette, E. C. (1991). Perceptual scaling of simultaneous wind instrument timbres. Music Perception, 8, 369–404.Google Scholar
  27. Krimphoff, J. (1993). Analyse acoustique et perception du timbre. Unpublished DEA thesis. Université du Maine, Le Mans, France.Google Scholar
  28. Krimphoff, J., McAdams, S., & Winsberg, S. (1994). Caractérisation du timbre des sons complexes. II: Analyses acoustiques et quantification psychophysique. Journal de Physique, 4(C5), 625–628.Google Scholar
  29. Krumhansl, C. L. (1989). Why is musical timbre so hard to understand? In S. Nielzén & O. Olsson (Eds.), Structure and perception of electroacoustic sound and music (pp. 43–53). Amsterdam: Elsevier (Excerpta Medica 846).Google Scholar
  30. Kruskal, J. B. (1964a). Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 29, 1–27.Google Scholar
  31. Kruskal, J. B. (1964b). Non-metric multidimensional scaling: a numerical method. Psychometrika, 29, 115–129.Google Scholar
  32. McAdams, S. (1993). Recognition of auditory sources and events. In S. McAdams & E. Bigand (Eds.), Thinking in sound: The cognitive psychology of human audition (pp. 146–198). Oxford: Oxford University Press.Google Scholar
  33. McAdams, S., & Cunibile, J-C. (1992). Perception of timbral analogies. Philosophical Transactions of the Royal Society, London, Series B, 336, 383–389.Google Scholar
  34. McLaughlin, G. J., & Basford, K. E. (1988). Mixture models. New York: Marcel Dekker.Google Scholar
  35. Miller, J. R., & Carterette, E. C. (1975). Perceptual space for musical structures. Journal of the Acoustical Society of America, 58, 711–720.Google Scholar
  36. Plomp, R. (1970). Timbre as a multidimensional attribute of complex tones. In R. Plomp & G. F. Smoorenburg (Eds.), Frequency analysis and periodicity detection in hearing (pp. 397–414). Leiden: Sijthoff.Google Scholar
  37. Plomp, R. (1976). Aspects of tone sensation. A psychophysical study. London: Academic Press.Google Scholar
  38. Plomp, R., Pols, L. C. W., & van de Geer, J. P. (1967). Dimensional analysis of vowel spectra. Journal of the Acoustical Society of America, 41, 707–712.Google Scholar
  39. Plomp, R., & Steenecken, H. J. M. (1969). Effect of phase on the timbre of complex tones. Journal of the Acoustical Society of America, 46, 409–421.Google Scholar
  40. Pols, L. C. W., van der Kamp, L. J. T., & Plomp, R. (1969). Perceptual and physical space of vowel sounds. Journal of the Acoustical Society of America, 46, 458–467.Google Scholar
  41. Ramsay, J. O. (1977). Maximum likelihood estimation in multidimensional scaling. Psychometrika, 42, 241–266.Google Scholar
  42. Sattath, S., & Tversky, A. (1977). Additive similarity trees. Psychometrika, 42, 319–345.Google Scholar
  43. Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 6, 461–464.Google Scholar
  44. Serafini, S. (1993). Timbre perception of cultural insiders: A case study with Javanese gamelan instruments. Unpublished Master's thesis, University of British Columbia, Vancouver, BC.Google Scholar
  45. Shepard, R. N. (1962a). The analysis of proximities: Multidimensional scaling with an unknown distance function. Part I. Psychometrika, 27, 125–140.Google Scholar
  46. Shepard, R. N. (1962b). The analysis of proximities: Multidimensional scaling with an unknown distance function. Part II. Psychometrika, 27, 219–246.Google Scholar
  47. Shepard, R. N. (1982). Structural representations of musical pitch. In D. Deutsch (Ed.), The psychology of music (pp. 344–390). New York: Academic Press.Google Scholar
  48. Takane, Y., & Sergent, J. (1983). Multidimensional scaling models for reaction times and some different judgments. Psychometrika, 48, 329–424.Google Scholar
  49. Torgerson, W. S. (1958). Theory and methods of scaling. New York: Wiley.Google Scholar
  50. Tukey, J. W. (1977). Exploratory data analysis. Reading, MA: Addison-Wesley.Google Scholar
  51. Wedin, L., & Goude, G. (1972). Dimension analysis of the perception of instrumental timbre. Scandinavian Journal of Psychology, 13, 228–240.Google Scholar
  52. Wessel, D. L. (1979). Timbre space as a musical control structure. Computer Music Journal, 3(2), 45–52.Google Scholar
  53. Wessel, D. L., Bristow, D., & Settel, Z. (1987). Control of phrasing and articulation in synthesis. Proceedings of the 1987 International Computer Music Conference (pp. 108–116). Computer Music Association, San Francisco.Google Scholar
  54. Winsberg, S., & Carroll, J. D. (1989a). A quasi-nonmetric method for multidimensional scaling via an extended Euclidean model. Psychometrika, 54, 217–229.Google Scholar
  55. Winsberg, S., & Carroll, J. D. (1989b). A quasi-nonmetric method for multidimensional scaling of multiway data via a restricted case of an extended INDSCAL model. In R. Coppi & S. Bolasco (Eds.), Multiway data analysis (pp. 405–414). Amsterdam: North-Holland.Google Scholar
  56. Winsberg, S., & De Soete, G. (1993). A latent class approach to fitting the weighted Euclidean model, CLASCAL. Psychometrika, 58, 315–330.Google Scholar
  57. Zwicker, E., & Scharf, B. (1965). A model of loudness summation. Psychological Review, 72, 3–26.Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Stephen McAdams
    • 1
    • 2
  • Suzanne Winsberg
    • 3
  • Sophie Donnadieu
    • 4
  • Geert De Soete
    • 5
  • Jochen Krimphoff
    • 6
  1. 1.Laboratoire de Psychologie Expérimentale (CNRS)Université René Descartes, EPHEParisFrance
  2. 2.Institut de Recherche et de Coordination Acoustique/Musique (IRCAM)ParisFrance
  3. 3.IRCAMParisFrance
  4. 4.Laboratoire de Psychologie Experimentale (CNRS) and IRCAMParisFrance
  5. 5.Department of Data AnalysisUniversity of GhentGhentBelgium
  6. 6.IRCAMParisFrance

Personalised recommendations