Pursuing the investigation, I cut slips on the system laid down, and found that the lengths and the pitches did not agree; and I also tried working out the _Sheng_ on a basis of fifths instead of fourths, of the relation 2/3 instead of 3/4, and found that the result did not correspond with the speaking lengths of the _Sheng_ pipes. The tale told of the twelve _lüs_ bears every evidence of being an invention; and I fancy that the fable originated in a scholastic endeavour to account for the existence of the perfected instrument the _Sheng_, so old that none knew how it came into being. The twelve _lüs_ comprised a scale of an octave and a fourth, and the scale of the _Sheng_ is also an octave and a fourth in compass; but neither constituted a semitonal scale, which was an idea of much later date. So also the making of a scale out of a succession of twelve fifths was a notion of the pedants, the men learned in book knowledge, and they fixed upon Ling Lun the credit of cutting each pipe by a succession of two-third lengths, on the principle of the fifth. The question has been raised whether the pipes were open or stopped, and the authorities say they were stopped, and they make their drawings of the pipes corroborate their view, but if so, what becomes of the affirmation that Ling Lun cut the bamboos _between_ the knots unless to secure an open tube? Although I may seem to have been wandering from the track, I have not lost sight of the central point to which my cogitations tend. I wished to impress the evidence of evolution in the appropriation of bamboo pipes for musical purposes, in the use of such bamboos in the earliest periods, all of similar diameters, and to show that variation in the diameters was an after development, even as was the use of metal pipes instead of the natural growth of bamboo or reed.