So would you say that time is the solution to the problem in our problem of equal temperament. Because the instrument cannot flux like a 3rd dimensional object that when folded makes a shape that cannot reconstruct the original object
Time is 3-dimensional, just like space. Or more accurately: There are three scalar dimensions that in our realm of coordinate space, gets projected into 3 spatial dimensions, which reduce the 3 dimensional aspects of time into a scalar motion in space. That dimensional reduction hides the fact that time is not just what we measure in space. Though in deep listening and inward focus we can sense the reciprocal aspects of time that are fully experienced by beings native to the coordinate time realm (where space is scalar), what is often considered non-material or inner planes.
What that means for music is that what we call frequency is an averaging out of a multidimensional motion in time and space into a standard measurement in space: namely the arbitrary measurement of meters per second. Because of the Fourier uncertainty principle we know that it takes a certain amount of time to measure certain changes in time, yet it has been proven that humans, especially good musicians can beat the uncertainty principle. The ear can do its own Fourier transform and hear the pattern before the time has passed in space where they could hear the spatial separation by which our scale measures the difference. A tempered scale short circuits the whole listening process and merely makes each interval conform to a commutative mathematics, where it is fastened to a spatial distance and scalar time and is disconnected from the relative phase relations that we can experience in the subjective experience of time.
This is only an inherent limitation of fretted instruments that have to fix each note. Without that limitation we are free to judge each interval in a moving relative way which according to esoteric thinkers is vital for the music to have the effect of resonating into the infinite instead of merely getting trapped within the closed loop of the octave and even-numbered powers, which geometrically is correlated with fields of containment (cub/octa symmetry) and misses the projective geometry of the pent symmetry (dodeca/icosa). At least that is my idea of it now. I am not sure if I understood your question and less sure if I answered it, but it was seeming to suggest some of these ideas in an interesting way and I wanted to take a stab at it…..