Pitch Perception and the Natural Scale: a Case-Study of the Logarithmic - Linear Dichotomy, in Acoustics and Music

摘要

The progression type to be found in building up the intervals of the natural system is governed by a variation law that is different from the one in charge of natural harmonics. This incongruity between the two types of progression is one source of mathematical-acoustic errors, whose consequences could be found all through the history of Western music. The natural system actually offers the clear-sighted image of this contradiction - partly surviving in the equal tempered system. On a closer scrutiny of this process, more adequate mathematical-acoustic solutions could be designed, in order to give a rigorous mathematical touch to the more flexible character of some sonorous structures built with more than 12 steps in an octave - more and more plausible today, consequent on the development of new ways to produce the sound.