The ancient Chinese “calendrical” pitchpipes
Ernest G. McClain · The Journal of the Acoustical Society of America · 1986
The most important symbol of “order” or “natural law” in Han China (202 B.C. to 220 A.D.) was a set of 12 end-blown bamboo tubes known today as the “pitchpipes.” Each pipe sounded a single tone of the chromatic octave and served as “tonic” for a specific calendrical period. All weights and measures of the empire were derived from the dimensions and capacity of the fundamental pipe, from which the lengths of other pipes were proportioned according to string ratios. It is of interest to the history of acoustical physics and to the study of science and civilization in China to ask how much “order” such pipes display when blown. Within a narrow Han limitation to diameter/length ratios between 1/30 and 1/27, and to fundamental lengths somewhat shorter than the foot, the cyclic excess in “pure” wholetones of 9:8 offsets pipe “end correction” sufficiently to permit the wholetone scale on the tonic (i.e., the six yang, “male” tones, the only ones strictly designated lu, meaning “order”) to be sounded at or very near equal temperament values. Thus pitchpipes—within well-defined physical parameters—were arguably an appropriate cultural icon for cyclic orderliness. Sinologists overlook this lawfulness.