A subject so vast and so incapable of classification cannot be discussed here, but its aesthetic principles may be illustrated by the extreme case of the trumpets and horns, which in classical times had no scale except that of the natural harmonic series.
We may regard quality, then, as determined by the members of the harmonic series present and their amplitudes and epochs.
But where it is appropriate, the disturbance sent out into the air contains the same harmonic series as the source.
The first overtone has frequency 6.25 that of the fundamental, and is not in the harmonic series.
Also W = (V +IA)w i; or w1=W/(V+/A), w p =W/(V+plA), and wn =W/(Vd-nIA), or the densities of the several liquids vary inversely as the respective volumes of the instrument immersed in them; and, since the divisions of the scale correspond to equal increments of volume immersed, it follows that the densities of the several liquids in which the instrument sinks to the successive divisions form a harmonic series.