I've been searching and thinking about this a lot since my mind got opened up to this possibility.
Is there any musical theory "formalism"/framework that deals with measuring the distance between two chords, note clusters or any 2 harmonies.
The premise is that such a notion of distance exists quasi universally in all domains, in different forms, but in harmony I haven't come across anything trying to define what the notion of distance would even mean, except maybe within the circle of fifths (distance between keys) or in modulations. Certain musician do talk about distance, but it's still blurry, and it is always based on some more fundamental assumptions.
I have come across nothing in particular that would describe such a notion at a "low-level", first principles derived, I've been toying with the idea of relative distance based on pitch alone and seeing everything from a chromatic scale POV, let's say we have a CMaj triad, Both Cmaj and Amin would represent "distance = 0", altering any tone within the triad up or down a semitone, for example augmenting the fifth would yield a distance of 1/3 (we altered 1 tone of the 3 possible) but then again how would such computation be if the distance is greater than a semitone? I have some ideas about how I would elaborate on this, but it still feels too arbitrary, and maybe not very informative in the long run concerning what could be done with the results... And how they're interpreted...
I hope anyone can help me with this query since I'm not the biggest theory oriented person, I'm pretty sure someone somewhere has already done some research on a similar topic but I couldn't find anything no matter how much I searched.
Ps: completety forgot about the closest thing (maybe) to what I'm looking for, which is Tonnetz grid, but it doesn't feel like the most encompassing general proposition which I'm lookign for..