One of the best kept secrets of science is that physicists have lost their grip on reality . This quote, from the physicist Nick Herbert, could sum up the unconformist spirit of this work. They lost their grip on reality when they accepted matricial mechanics as opposed to wave mechanics, thinking that they were totally equivalent, and they lost grip when they renounced to unravel the wave-corpuscle duality, justifying even its impossibility in spite of the experimental evidence: Eppur si muove (and yet it moves) as Galileo would say. From that spirit, this work defines and sets the veiled organisation of elementary particles (fermions), how many generations there are and why, the exact value and raison d'etre of their masses, including those of the mass base of neutrinos, and more, and all from a sole expression (like a formula) deduced from wave theory, through which we come to understand what particles and the mass that forms them are, how they are created and take shape in primordial space, the basis of our spatial reality, and how its different generations are indeed generated from the preceding ones until they reach a common initial particle, and the intangible materiality.