Abstract
Seeking to identify the constituent parts of the multidimensional auditory attribute that musicians know as timbre, music psychologists have made extensive use of multidimensional scaling (mds), a statistical technique for visualising the geometric spaces implied by perceived dissimilarity. mds is also well known in the machine learning community, where it is used as a basic technique for dimensionality reduction. We adapt a nonlinear variant of mds that is popular in machine learning, Isomap, for use in analysing psychological data and re-analyse three earlier experiments on human perception of timbre. Isomap is designed to eliminate undesirable nonlinearities in the input data in order to reduce the overall dimensionality; our results show that it succeeds in these goals for timbre spaces, compressing the output onto well-known dimensions of timbre and highlighting the challenges inherent in quantifying differences in spectral shape.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aitkin, M., Anderson, D., Hinde, J.: Statistical modelling of data on teaching styles. Journal of the Royal Statistical Society, Series A (General) 144(4), 419–461 (1981)
Bismarck, G., von, G.: Sharpness as an attribute of the timbre of steady sounds. Acustica 30, 159–172 (1974)
Burgoyne, J.A., Saul, L.K.: Visualization of low-dimensional structure in tonal pitch space. In: Proceedings of the International Computer Music Conference, pp. 243–246 (2005)
Caclin, A., McAdams, S., Smith, B.K., Winsberg, S.: Acoustic correlates of timbre space dimensions: A confirmatory study using synthetic tones. Journal of the Acoustical Society of America 118(1), 471–482 (2005)
Carroll, J.D., Chang, J.-J.: Analysis of individual differences in multidimensional scaling via an n-way generalization of ‘Eckart-Young’ decomposition. Psychometrika 35(3), 283–319 (1970)
Gabriel, K.R., Sokal, R.R.: A new statistical appraoch to geographic variation analysis. Systematic Zoology 18, 259–270 (1969)
Grey, J.M.: Multidimensional perceptual scaling of musical timbre. Journal of the Acoustical Society of America 61, 1270–1277 (1977)
Grey, J.M., Gordon, J.W.: Perceptual effects of spectral modifications on musical timbres. Journal of the Acoustical Society of America 63(5), 1493–1500 (1978)
Hope, A.C.A.: A simplified Monte Carlo significance test procedure. Journal of the Royal Statistical Society, Series B (Methodological) 30(3), 582–598 (1968)
Jaromczyk, J.W., Toussaint, G.T.: Relative neighborhood graphs and their relatives. Proceedings of the IEEE 80(9), 1502–1517 (1992)
Krumhansl, C.L.: Why is musical timbre so hard to understand? In: Nielzen, S., Olsson, O. (eds.) Structure and Perception of Electroacoustic Sound and Music. Excerpta Medica, vol. 846, Elsevier, Amsterdam (1989)
McAdams, S., Winsberg, S., Donnadieu, S., Soete, G.D., Krimphoof, J.: Perceptual scaling of synthesized musical timbres: Common dimensions, specificities, and latent subject classes. Psychological Research 58, 177–192 (1995)
Peeters, G., McAdams, S., Herrera, P.: Instrument sound description in the context of MPEG-7. In: Proceedings of the International Computer Music Conference (2000)
Tennenbaum, J.B., de Silva, V., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290, 2319–2323 (2000)
Torgerson, W.S.: Theory and Methods of Scaling. Wiley, Chichester (1958)
Weinberger, K.Q.: Unsupervised learning of image manifolds by semidefinite programming. In: Proceeding of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (2004)
Weinberger, K.Q., Saul, L.K.: An introduction to nonlinear dimensionality reduction by maximum variance unfolding. In: Proceedings of the National Conference on Artificial Intelligence (AAAI) (2006)
Wessel, D.L., Bristow, D., Settel, Z.: Control of phrasing and articulation in synthesis. In: Proceedings of the International Computer Music Conference, pp. 108–116 (1987)
Winsberg, S., Carroll, J.D.: A quasi-nonmetric method for multidimensional scaling via an extended Euclidean model. Psychometrika 54(2), 217–229 (1989)
Winsberg, S., De Soete, G.: A latent class approach to fitting the weighted Euclidean model, CLASCAL. Psychometrika 58(2), 315–330 (1993)
Winsberg, S., De Soete, G.: Multidimensional scaling with constrained dimensions: CONSCAL. British Journal of Mathematical and Statistical Psychology 50, 55–72 (1997)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Burgoyne, J.A., McAdams, S. (2008). A Meta-analysis of Timbre Perception Using Nonlinear Extensions to CLASCAL. In: Kronland-Martinet, R., Ystad, S., Jensen, K. (eds) Computer Music Modeling and Retrieval. Sense of Sounds. CMMR 2007. Lecture Notes in Computer Science, vol 4969. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85035-9_12
Download citation
DOI: https://doi.org/10.1007/978-3-540-85035-9_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85034-2
Online ISBN: 978-3-540-85035-9
eBook Packages: Computer ScienceComputer Science (R0)