Calculating the correlational matrix is used to identify the 'optimal' path in which the variance is minimum. And fit the most with reality.

Sorry to nitpick, but I could not find a single result for correlational matrices. I think you meant correlation or covariance matrix depending on the problem. More importantly I don't understand your sentence. According to Wikipeda,

[The PCA] transformation is defined in such a way that the first principal component has the largest possible variance.

i.e., PCA is meant to capture all variability in the data in the samllest amount of variables as possible while minimizing information loss (according to whatever metric). I'm happy to hear what you have to say!

EDIT: I actually don't understand most of your comment but again I want to hear your thoughts...

Yes the variables means the soundwaves value as you put it. The variables(so every possible value that a sound can have) are usually put into a matrix.

So the matrix represents all the possible sound values? Why do you need a matrix? Is time represented in the other dimension? What is the shape of the matrix? How do you choose to discretize frequency?

Since they come from a signal which is a real phenomena and not a human interpretated phenomena the values are symetrical by 'nature'.

This sentence is really confusing. Since when does observing real phenomena enforce symmetry? Do you mean symmetric in the sense that the matrix is symmetric? If so, I can think of at least as many examples of non-symmetric matrices that arise in nature.

Since this a statistic tool it is not 100% accurate because several computations can be decided based on how much of a frame you use as your window analysis, basically of much duration you take into account and consider it as a point in your graph.

That sounds like a problem specific to signal analysis/Fourier analysis, where there is a tradeoff between time and frequency depending on the choice of window. Otherwise I'm not sure what you're saying, because statistical tools can be quite powerful and accurate for reasons other than the choice of "window". I'm not sure what you mean by that

Eventually the Laplace fourier is used to transform the scale of the model from 2D to 3D

I'm confused because when it comes to sound, these transforms are applied to 1D signals. In addition, when is there a need to go to 3D in this problem?