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.
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.
If you have read the first part of this volume you will have understood that I take the view that the earliest musical notions of man in his primitive state were derived from the industry of his fingers, and the relations of a musical scale had the same basis, becoming afterwards hereditary. The Chinese foot is equal to a hand-span of a ruler or emperor, and has ten divisions equal each to a thumb’s breadth. The standard pipe is 9-7/8in. of our measure. Taking a pipe that length and halving it, or taking one half that length, the notes obtained are what we call tonic and its octave; but being of the same diameter the octave will be flat. This we find to be a peculiarity in Chinese music. Taking a pipe three quarters the length of the whole, a note is obtained from it which is a fourth; and this, the same diameter being kept, will be inevitably a flat fourth; hence the existence of a flat fourth in the ancient musical instruments of the Chinese and Japanese. And so everywhere, unless the diameters have varied as the lengths have varied, the intervals cannot then have been the exact intervals that we set down for our musical relations. Yet, strange it is: showing the persistence of heredity and tradition. The Chinese in later times perfectly well knew, as I shall show, the relations of the diameters of pipes according to geometrical laws.
Music with the Chinese, itself as an art so unprogressive, has from the first taken a unique position in the national life. Dr. Wagener tells us that the weights and measures that have been in use these 4600 years in the Chinese empire are based upon Lyng-lun’s work in determining the musical standards of the lüs. The first pipe which he cut as the foundation of his scale was the longest, and it was found to contain 1200 grains of millet seed. He chose a sort of millet, the sorghum rubrum, which is of a dark brown colour, as being harder and more uniform than the gray and other kinds. One hundred of these was made by him the unit of weight, and this was divided and subdivided on a decimal system until a single grain became the lowest weight of all. The length of this pipe was equal to 81 of these seeds placed lengthwise; but breadth-wise, it took 100 grains to make the same length: hence the double division 9 + 9 and 10 + 10 was naturally arrived at. This musical foot thus became the standard measure with decimal subdivisions. The breadth of a grain of seed was 1 fen (line), 10 fen = 1 tsun (inch), 10 tsun = 1 che (foot), 10 che = 1 chang, 10 chang = 1 ny. Lyng-lun also fixed the dimensions of the interior of the pipe at 9 grains breadth. The contents of the tube proved to be 1200 grains, and the weight of 100 grains was made by him the unit of weight. The pipe was thus made the basis of the musical system, and equally so the basis of the system for lineal measure, dry measure, and weight; ultimately for coinage.
Another interesting fact is that the Chinese had ascertained the geometrical relation of musical pipes. The problem had been thoroughly examined by a certain Prince Tsai-Yu (1596). In practical and scientific hydrodynamics, the relation of the diameters of pipes to the volume contained was well known; but it appears that, as applied to sounding pipes, the Prince Tsai-Yu was the first clearly to record its demonstration. Of two musical pipes of the same diameter, one two feet long and the other one foot long, the latter does not, as assumed, give a note the higher octave of the former, for the note will be flat. Neither if we halve the diameter, even as we halve the length, will the note prove true. The common practice with us in organ building is to give the half diameter to the seventeenth pipe; but this is merely an empirical decision. The prince, without explaining theoretically why, showed that the proper dimensions relatively of length and diameter were as follows. Assuming a pipe of 2ft. length to have an interior diameter of 5 lines, then correctly the pipe of 1ft. length should have a diameter of 3 lines 53 cent., and a pipe of 6in. length a diameter of 2 lines 50 cent.