I have shown that Amiot misled us in assigning it to the _Sheng_, and I expect he has given currency to other errors. What I do note, and have assigned the cause for in the argument of the previous chapter, is the peculiar crowding of the scale with intervals less than a semitone between _f_ and _a_; and perhaps this crowding has helped towards inducing the belief, without question, that the semitonal scale was intended, but that the making of the instrument was not done with due exactness, or that the instrument was out of order if it did not bear out the theory of an equal tempered semitonal succession through an octave. The theoretical existence of such a scale is not here called in question: my contention is that the ancient instruments give no confirmation of having been planned in view of such a principle. Stranger still, the very scheme to which the learned writers refer as the basis of the principle, and carefully guarded by them as an authentic ancient treasure, gives a complete denial to the whole assumption. I take their own statements, the evidence of their own authorities, and wonder, when I examine the twelve _lüs_, why they never examined them, why from curiosity alone they sought no corroboration of their statements from the _lüs_ themselves. In Van Aalst’s book the scheme is fully set out in diagram, the twelve _lüs_ figured, and all the curious details inserted of the moons and the hours to which each pipe belongs by some mystical relation which the Chinese mind perceives; the pipes are arranged in the order in which they bear to the longest one, which is the prime genitor. Also there is another diagram, elaborately designed to display the affinities in a circle, having twelve compartments springing from a common centre; the _kung_ or fundamental sound being placed as the hub of a wheel with the other sounds rayed round, each sound being named. The diagram of pipes shows how the _lüs_ generate one another, whereas the circle or wheel diagram gives the notes as they follow in a series. I think that I remember seeing these diagrams in Amiot’s sixth volume. Very likely Van Aalst has taken them from the same source. Again, he says, “The _lüs_ are a series of bamboo tubes, the longest of which measures nine inches, and which are supposed to render the twelve chromatic semitones of the octave.” It appears to me that the great source of misunderstanding has been in the European persistence in regarding “the twelve _lüs_” as meaning “twelve semitones”: whereas the Chinese name _lüs_ means laws or principles. I have examined these pipes by measures and do not find them in any way corroborating the semitonal relation; and simply taking the names accorded to the _lüs_ and set forth in these diagrams, if we arrange the notes in successive order, neither do they bear out the scale claimed for them. Let us see: this is how they stand. Twelve semitones forsooth!