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Re: multidimensional scaling of timbre



Dear list
The MDS techniques is made of several steps:
1. Collecting dissimilarity data (dissimilarity judgements, but not only)
2. Representing the data in a low-dimensional Euclidean or semi-euclidean space
3. Interpreting the dimensions of the space in terms of psychological dimensions (or auditory attributes). This is usually done by listening to the sounds along the dimensions to get an idea of the attribute to which the dimension might correspond
4. Correlating the dimensions with acoustical descriptors

As far as I understand this technique, it is based on a fundamental assumption: the dissimilarity can be represented in low-dimensional Euclidean space (i.e. the dimension are continuous). This assumption therefore requires that  the listeners focus on a few continuous auditory attributes. The most straightforward way to do that is to have a set of sounds that are rather similar. Bear in mind that the first studies used synthetic stimuli, build so as to vary along a few continuous parameters.
A consequence of this assumption is that the raw dissimilarity data must fulfil some mathematical constraints to be represented in a low-D Euclidean space. This can be checked prior to any MDS analysis: the data have to follow the triangular inequality, and not the ultrametric inequality (see Legendre and Legendre 1998). When the data follow also the ultrametric inequality, they would not fit a low-D space, and another technique (such as tree representation) is better suited.
The results of such studies have therefore not to be interpreted as "the timbre of all sounds is made out of 2 or 3 auditory attributes", but rather as "in set of sounds varying along a few acoustic parameters, the 2 or 3 most salient auditory attributes are ...". Winsberg et al. (1989, 1993) have developed extended Euclidean representations that include also specificities. Specificities are properties that are specific to one sound (i.e. not shared by all the sounds, as continuous dimensions). Such a representation has allowed to apply the MDS technique to sounds a bit more complex than synthesized sounds (McAdams et al., 1995, Susini et al., 1999, Susini et al., 2004, Lemaitre et al., 2007). However, as emphasized by Susini et al. (1999), this technique cannot be applied to sets of sounds that include sounds made by very different sources. For such sets of sounds, free sorting tasks and tree representation are, to my knowledge, the best suited techniques.

Again, I think that the results of these studies cannot be summarized as "the timbre is the combination of three attributes, related to the spectral distribution of energy, the attack time, and the spectral fluctuations". The fact that these studies have shown that these attributes are consistently related to the psychological dimensions highlighted by the restricted MDS studies tells us that these attributes play an important role in the perception, not that the perception is only based on these attributes.

Best regards
Guillaume Lemaitre
ps: in response to Paul Iverson, Marozeau et al. (2003) have shown that, when required to do so, listeners can ignore pitch when making timbre judgements.


P. Legendre and L. Legendre, Numerical ecology. Developments in Environmental Modelling, Elsevier,
second english ed., 1998.

Lemaitre, G., Susini, P., Winsberg, S., Letinturier, B., &  McAdams, S. (2007). The sound quality of car horns:  a psychoacoustical study of timbre.
Acta Acustica  united with Acustica, 93(3), 457-468. 89-114.

J. Marozeau, A. de Cheveigné, S. McAdams, and S. Winsberg, “The dependency of timbre on
fundamental frequency,” Journal of the Acoustical Society of America, vol. 114, no. 5, pp. 2946–
2957, 2003.

P. Susini, S. McAdams, and S. Winsberg, “A multidimensional technique for sound quality assessment,”
Acustica united with Acta Acustica, vol. 85, pp. 650–656, 1999.

P. Susini, S. McAdams, S. Winsberg, I. Perry, S. Vieillard, and X. Rodet, “Characterizing the sound
quality of air-conditioning noise,” Applied Acoustics, vol. 65, no. 8, pp. 763–790, 2004.

S. Winsberg and J. D. Carroll, “A quasi non-metric method for multidimensional scaling via an
extended Euclidian model,” Psychometrika, vol. 54, pp. 217–229, 1989.

S. Winsberg and G. D. Soete, “A latent class approach to fitting the weighted Euclidian model,
CLASCAL,” Psychometrika, vol. 58, no. 2, pp. 315–330, 1993.

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Guillaume Lemaitre


Equipe Perception et Design Sonores /

Sound Perception and Design Team


STMS-IRCAM-CNRS     UMR 9912

1, place Igor Stravinsky F-75004 Paris - FRANCE

tel  : (+33 1) 44.78.48.38

fax : (+33 1) 44.78.15.40

e-mail  : lemaitre@xxxxxxxx

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