What a vision that of the flowing mass! It makes me think of a jazz piece, let's say avant-garde, in which the pinching function would be performed by a saxophone emerging in bursts from the moving sound mass, but what is interesting is that my young son found a rhythm in it, a pulsation, oscillating regularly and spontaneously.
I would like to say that, regarding rhythmic divisions and children, perhaps it should be considered that at a (very) tender age, one lacks exactly that mathematical background useful for rationally understanding the rhythmic issues of a piece, and therefore teaching methods should take this into account, finding other levers and points of view.
Regarding the general link between mathematics and music, it is certain that to govern a phenomenon we are tempted to do so, in large part, in a rational way just as one does with physics, especially in its reductionist approach, and physics uses mathematics heavily as a tool for calculation and investigation, in a sense as an engine. Therefore, it is quite natural and fascinating to frame the musical phenomenon within a mathematical context.
So there are two things I like to note. Often beauty derives precisely from deviating a little from the simplest mathematical patterns; see, for example, the non-linearity of the ear, the inharmonicity of strings, irrationality, perhaps in small doses, in compositions. But it is also true that these simple patterns were not invented by chance and probably lie at the base of nature, even if they do not exhaust it, so Pythagoras certainly had good reason, as do we moderns who see the harmonic oscillator everywhere...
regards and excuse the digressions
