♯ ♯ ♯ ♯♯ _a_—_d_—_e_—_f_‿_g_‿_g_‿_a_‿_a_‿_b_—_c_—_d_—_f_ Thus the development of the scale shows only a central crowding of semitones, and not even an octave relation, plainly indicating an ancient growth through the tetrachord. The diagram showing how the _lüs_ generate one another states that the longest pipe is nine inches; yet in the letterpress Van Aalst says that The first tube was one foot in length in reality, but that the foot was considered as being only nine inches, because nine is perfectly divisible by three, whereas ten is not. And further, that The twelve _lüs_ were used by the Chinese merely to regulate the instruments and give a uniform pitch to the music. The diameter of all the tubes must be the same. Mêne K’ang says that the circumference of all the tubes diminishes according to their length; but this is explicitly contradicted by Tas’i Tzü, who quotes Chêng K’ang-chêng and Ts’ai Yung (two great wine bibbers and famous writers on music), and he flatly declares that Mêne K’ang and his adherents know nothing about music. The tubes were all of the same thickness, circumference and diameter; only the length varied according to the sounds. And so on, which shows how almost European the Chinese are in their humanity. I have quoted largely from J. A. Van Aalst’s “Chinese Music” to which I am much indebted. The author is learned in the ways and in the literature of the Chinese, being himself in the Chinese Imperial Customs Service, and his work is published by order of the Inspector General of Customs, Shanghai. The first tube in the diagram bears this inscription:— _Huang-Chung_, or yellow bell, corresponds to the eleventh moon and the eleventh hour, emits the sound _kung_ (modernly called _yo_), is a _yang-lü_, was the first tube cut, and served as genitor to all the others. It measured one Chinese foot long, and contained exactly twelve hundred grains of millet. Two thirds of its length form the next tube. _Lin-Chung_, or forest bell, gives a note a fifth higher, etc. Description follows, in the same style of quaint symbolism, upon each of the twelve. At the third pipe, however, which it says ought to be two-thirds of the preceding length, a change comes, which it is important to notice,—viz., “that the sound would be too high compared with _kung_, and so the tube is to be doubled, and four thirds taken instead of two thirds.” This virtually introduces the three fourths relation, the fourth instead of the fifth; and in the remainder of the pipes some are calculated some way, and some the other. There is no twelve fifth scheme carried out as supposed.