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.