What I AM is a fully trained physical chemist, specializing in quantum mechanics and neutron crystallography. I have a tremendous amount of training in wave mechanics and the theoretical mathematics behind it.I am pretty sure that you're pretty intelligent and capable but this time-phase coherent thing is a lot more complicated than quantum physics and I am not kidding.
If we are concerned with the time/frequency domain, we must first agree on a mathematical definition of how to represent a sound wave propagating through atmospheric medium.The problem is not about the mathematics. As a matter of fact, the mathematics are rather simple.
Once we establish this, we can discuss things without any subjectivity.I agree in general but the problem is how to identify which part is objective and which part will always be subjective and you just have to deal with it. For example, it's difficult to say which is better sounding since it's also dependent personal tastes. No mathematical modeling can sort that out.
Of course, we will also need data to use with our expressions, and as we are dealing with wave functions, we will likely want a periodic eigenfunction of some sort, a la sine or cosine or perhaps e^(x), which gives a better representation, but is less well-defined when deriving or integrating with it.
Again, the problem is not the mathematics on the objectivity side of thing. In term of measurements, simulations and so on, all these are fairly well established. The problem is that our hearing is very complicated and no amount of mathematics can figure it out. I don't mean to obfuscate the issue. It's really true that nobody has been able to model our "hearing". Not even close.
It's actually not as daunting as it sounds, and we could easily develop a simple system from first principles.Already you have under-estimated the complexity of our hearing. "A simple system" will not do it!
let's quantify it!Amen .....
While I can't say which is better, whether time-phase coherent matters or not, I can give a clear definition of what is time-phase coherent is. Soon I hope!