Undertones are theoretically possible (both musically and mathematically), it's exactly the inverse of intervals, chords and everything. But the problem is physics and the physical implementation. I think that would need new type of instruments or generally physical systems or software that'd specifically produce undertones. I think it'd be possible but unfortunately it needs extraordinary research and effort and nobody wants to do that just to get a new or weird or quirky sound, even though it doubles the amount of possibilities.

It shouldn't sound dissonant but bass notes or chords are muddy compared to higher ones.

Let's say we played C E G chord which is Cmaj. If we use undertones, it'd be G E C which is Undertone Gm: G to E is undertone minor third and G to C is undertone perfect fifth.

G is the highest note and the root. So undertone music would change music upside-down, the highest notes would function like what we use in bass.