Adopting the measure of the Chinese foot to start with, I cut a slip to that length, and then cut one to half of that, and then cut one between these at the half of the half, and so on by progressive steps halving and half halving and doubling, and obtained a connected series of thirteen slips to represent the speaking pipes of my most mysterious little _Sheng_. I argued with myself that in some such simple way our worker would have evolved the instrument; that it was by no means the outcome of a system of music, but was built up on a visible relation of proportions; that the eye made it and that the ear accepted it. Steadied by faith, I drew my bow at a venture, and, lo and behold!—my arrow went home true, and I was astonished as one who sees his prophecy fulfilled and wonders how it came to pass. For when I came to compare and to measure the actual pipe lengths, they corresponded length for length with the series I had evolved by my archaic process. I confess that the situation was bewildering as I gazed upon the evidence before me, for it seemed too good to be true, and one had a fleeting suspicion of magic or hallucination of some kind. But no; reason and time only increased the strength of my conviction that in this process the _Sheng_ was constructively worked out; indeed, I do not see how by any other way the peculiar scale of the instrument could have originated. [Illustration: SEQUENCE OF EVOLUTION OF THE PIPES OF THE SHENG.] Remember that at the time of my investigation—now thirty years ago—I had no means of knowing what the scale should be, and I had to calculate from the relative lengths of the thirteen slips what the notes of the speaking pipes would be; and when in after years I came to possess other specimens of the instrument, I found that all my conclusions had been correct. A very impressive result is the discovery that the old Chinese musical basis was that of the Greeks,—the tetrachord; and the complete scale of this, one of the most ancient of Chinese instruments, consists of two conjunct tetrachords and one disjunct tetrachord; which scale, as I have said, being founded upon a natural law of progression from or through a connected series of proportional lengths, exhibits unchanged its record of evolution. For pipes of certain length give now the same tones and the same actual pitches as they gave thousands of years ago. They do not change, though modes and customs, peoples and empires change. How remarkably suggestive is this taken with the presence of the Pan’s pipes and the Phœnix, to which your attention was given in a previous chapter, as pointing to a common origin in some ancient era ere history began. Helmholtz notes that Olympos (_circa_ B.C. 660-620), who introduced Asiatic flute music into Greece and adapted it into Greek tastes, transformed the Greek Doric scale into one of five tones, the old enharmonic scale, _b_‿_c_— —_e_‿_f_— —_a_