It is not by one pulse of the air in a second of time from a vibrating string that we hear a sound. Our ear waits till the vibrations are somewhere about 32 in a second, and then there begins to be heard a very low and not very distinct sound of little service as yet in the musical range. It is when the vibrations become more numerous that the sounds ascend and take their place within the horizon of music. Vibrations are the protoplasm of music. As the nebulous mists which hang in the depths of space are, perhaps, the protoplasmof planets; and as the all-prevading ether is, perhaps, the protoplasm from which our so-called chemical elements are built up; and as the living cell is the organic protoplasm out of which all living tissues are differentiated for their proper functions and special ends, so these vibrations of the air are the protoplasm of music.
     When Nature, who weighs the mountains in scales and the hills in a balance, and number and names the stars, takes hold of this vibration-material, she subjects it to the most rigorous measurement in marshalling that series of notes which constitute The Musical System. She is in no hurry in giving us all her gifts in this matter. She first of all gives us the interval of an Octave at one stroke, and in generating the seven notes which compose the three chords of the Diatonic Scale she carries the process up through six octaves,¹ evolving the notes by multiplying the vibrations of the mother note so many

1 See the Genesis of the Scale, Plate II.