Let us picture him first as taking a bamboo reed, cutting it a foot long in Chinese length (9-7/8in.), and from this obtaining a note; then cutting other reeds promiscuously, until at last he is attracted by one exactly half its length, giving a baby note exactly the same in seeming as the other, and blending into it. This is what we call the octave,—a civilized perceptivity not yet dawning on his mind; to him it is the man’s voice and then the woman’s voice. The higher repetition of the same sound. He has halved the length and obtained unwittingly the octave; why not halve the other half between? This he does, and from the three quarter length of pipe obtains a new sound, which, sounded with his prime gives a pleasing concord; thus, he begins to recognise the new fact,—the family relationship. After this fashion of halving and quartering I imagined that the _Sheng_ grew and became an instrument; and, placing myself in this mood of representative thought, I also try and work the thing as he would have worked it out, and see if I can get coinciding results. The half and the half again seem to me so natural; the repetition is so akin to the Chinese tendency. A two thirds is a more artificial notion, and comes of later discernment. How natural too, it is on finding more that two pipes inconvenient within the mouth, to seek the first substitute similar to the mouth in size, such as a little bowl, a half gourd, or perhaps the same calabash that served him for a drinking cup. Except the four or five reeds that spoke in my specimen, I did not know what the notes should be as the scale of the instrument; I only knew that the scheme as told me by the writers with authority was wrong, and was also misleading; for the comparative speaking length of the pipes was at variance with the assumed musical system, and I could not make head or tail of the instrument until I resorted to the question of primitive design. Then everything fell into proper place with unlooked-for significance. So I took a number of slips of wood (easier to cut than bamboo), and proceeded to transmigrate myself into a dweller in “far Cathay.”