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,