  The collaboration of mathematics in the two musical systems of Pythagorean
sounds and of equal sounds is evident and opportune for generating the elements
and managing their relationships. The only essential notion for a rational
intervention in the two sound worlds is that of distance between sounds. The
scale of natural sounds does not seem to dialogue directly with a purely
mathematical module that articulates its definition and is generally presented
as a manual adjustment of the ancient Pythagorean sounds. The model of
proportions that formed and inspired the architecture of the sixteenth century,
an era in which the natural scale emerges, provides a clear idea for
systematically adjusting natural sounds; on the other hand, the generation of
sounds based and started exclusively on the respect of the proportions proposes
interesting natural sound systems. The object is not so much to illustrate the
harmonic device of the already formed natural scale, as to implement the
formation of sound elements that respond to the unitary principle of proportion
and combine harmoniously.
