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Re: MDS-distances

Oooh.. thank you Dave.  This only confirms my suspicion.. the best way to get the right answer on the Internet is to post the *wrong* answer. :-)  !!!

On Jun 23, 2006, at 12:16 PM, David Wessel wrote:

Failed at what?   Malcolm, I think you have missed the point. 

Fair enough.. We have different goals.  I want a model of timbre perception (for speech and music sounds) that rivals the three-color model of color vision science.  Spectral brightness and attack time are not enough of an answer for me.

I don't think the timbre interpolation work I've seen (the vibrabone?) shows that we understand timbre space yet.  As I remember the data, the synthesized instrument was not on a perceptual line directly between the source sounds.

Recently, I've taken a new look at the timbre space representations obtained by myself, Grey, McAdams, Wedin and Goude and am struck by how well Les Atlas's Modulation Spectrum describes what is a common feature of many of the 2-D spaces wherein one of the dimensions is related to the spectral envelope and the other the temporal envelope.   

Actually, they are all related.  We're only looking at static timbre for now.. and our models are consistent with static modulation spectrum...  One outcome of Terasawa's work.. modulation spectrum based on ERB scale (ala MFCC) works better than modulation spectrum based on linear-frequency scale.  (We're not saying that MFCC is best.. just the best model we've tested so far!)

However, such tests should be carried out in a direct manner as suggested by Krantz and Tversky in their work on the foundations of the geometric representation of perceptual data (see  Suppes, Krantz, Luce, & Tversky's  Foundations of Measurement Vol 2).   I doubt that MFCC's will pass the straightforward qualitative test of  "interdimensional additivity" essential to a geometric representation.      

I need to read that book.  Thank you for the reference.

But I think based on the description you gave ... interdimensional additivity is inherent in our Euclidean test.  If the model axis are not orthogonal and do not add then our Euclidean test on the perceptual data will fail.

Thanks Dave.

-- Malcolm