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On Instruments and Timbral Change


I imagine that there’s something analogous to this already, but I couldn’t find anything that does this. In what follows, I’ll take the piano as an example of a pitched instrument, but what I’m looking for applies to all pitched instruments in our european instrumentarium (and non-european ones as well, of course.)

I’m looking for a simple metric that, for any given pitch and its n first partials on a piano (as empirically measured), would translate it as a middle C and then compare it to the piano’s actual middle C and its n first partials (as empirically measured.) The idea would be to map it as a sort of distortion function intrinsic to the piano, going from its lowest pitch (A0) to its highest pitch (C8.) Here’s my question:

Does such a simple metric exist, or are there any (even likely much better and more precise) alternatives to map timbral change in a given instrument throughout the whole of its register (as some sort of distortion intrinsic to it)?

Any hints or insights on this issue would be much appreciated.

All the best,

Have you looked into audio descriptors? You could use it to measure specific aspects of any given sound and compare them. There are a lot of different spectral descriptors that you could use to measure timbral differences between different registers in the piano.

I don’t know if you looked into this already but there’s a paper published by Geoffroy Peeters at the IRCAM called “A Large Set of Audio Features for Sound Description” in which he explains how many of these descriptors work (if you google the name of the article, you’ll find a pdf of it).

You could implement this analysis in Max with MuBu externals library or maybe ircamdescriptors~ from the Max Sound Box external library.


Hi Raphael,

Yeah, I know Peeters’ paper (I studied it back in the day, first to learn how Orchids worked, and later on the Timbre Toolbox for MATLAB.) Actually, the metric I’m looking for is akin to inharmonicity, the major difference being that an actual (empirically measured) tone would take the place of the ideal case of the harmonic series (f0, 2f0, …, nf0.) Normally, it shouldn’t be too hard to compute it, but I’d really love to know if it already exists (and in that case, how it’s called.)

Thanks a lot for your input, it really helped me setting a path forward on this issue.

All the best,