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Re: multidimensional scaling of timbre
I see at least three possible factors that might contribute to a low
dimensionality of multidimensional scaling (MDS) spaces for musical timbres:
1. limited cognitive resources (e.g., attention);
2. noise in the neural representation of stimuli or in the
selection/emission of the response;
3. biases of model selection processes for MDS, which might favor
solutions with a low number of dimensions.
With the available empirical data, it is, in my opinion, not possible to
tell apart these factors.
I might also add that even if a researcher found, say, a six-dimensional
MDS space, he would think twice before asking reviewers to get confused
with such a "complicated" statistical model: they might just reject the
This said, I would like to comment on the two/three-dimensionality of
The general impression that the literature on the topic gives is,
indeed, that musical timbre is basically spectral centroid + attack time
plus some spurious dimension.
My personal opinion: this view is limited.
If this view was correct, we could make useless centuries of work on the
design of musical artifacts by creating an instrument that allows
control of large variations in:
4. spectral centroid
5. attack time
I have the impression that even if one such instrument could cover the
entire musical range for each of these five factors, it wouldn't be able
to reproduce the entire palette of musical sounds.
In a nutshell, a 2/3D view of timbre is in stark contrast with the
variety of subjective musical experiences I personally have.
Maybe I have this opinion because my playlists go also beyond classical
music, whereas the majority of timbre studies focus on classical
acoustical instruments ;-)
Bruno L. Giordano, Ph.D.
Music Perception and Cognition Laboratory
Schulich School of Music, McGill University
555 Sherbrooke Street West
Montréal, QC H3A 1E3
Christian Stilp wrote:
This is true across a wide array of studies, from those of John Grey and
David Wessel in the 1970s to more contemporary investigations of Stephen
McAdams, Carol Krumhansl, Suzanne Winsberg, and others in the 1990s and
2000s. Furthermore, two of the primary dimensions of musical
instruments in these tasks include the temporal envelope (rise time, or
attack) and spectral envelope (centroid, center of gravity, energy
distribution, "flow", etc.). Those two dimensions seem sufficient to
organize any set of instruments, no matter how diverse (e.g. different
spectral characteristics across all classes of instruments, or just
subdividing the woodwinds). While tertiary and beyond dimensions uncover
some interesting ideas (spectral flux, attentuation of even harmonics,
"richness", spectral irregularity, f0 intensity, inharmonic energy in
the attack, etc.), their sparseness in timbre MDS literature suggests
they are more artifacts of the particular instruments at test.
Christian Kaernbach wrote:
I seem to remember that one lesson from multidimensional scaling of
timbres was that the type of dimensions found depends strongly on the
selection of the stimuli. If my memory serves me right, the similarity
data would alway yield two- to three-dimensional spaces, regardless of
whether the stimuli were quite divers (all types of instruments of the
classical orchestra) or from a narrow subgroup (say, all woodwinds).
In other words, people seem to be able to manage two to three
dimensions in their cognitive space representing the entirety of the
stimuli of a certain experiment. Is that correct, and is there a
reference referring to this phenomenon?
Thanks in advance,