Abstract
The fangufangu is made from a cylindrical section of bamboo closed by two adjacent nodes. Bore radii (a) range from 1.5 to 5 cm and lengths (L) from 20 to 60 cm. Typically, six identical holes are burned through the side walls: one at either end, two in the center, and two symmetrically placed near (L/4) from the ends. Hole radii (b) range from 0.5 to 0.9 cm. One end hole is blown through a slit between the bamboo wall and the player's nostril. The four traditional fingerings use the next hole and the farthest hole. All have two resonances within the lowest octave, but one mode does not sound and two are only about 50 cents apart. There are thus six playable notes in this range, but scale tunings vary widely among existing instruments. Multiple mode cooperations are rare. For a given value of (a), increasing (b/a) overall raises frequencies of most resonances in parallel, but one frequency rises faster than the trend and another falls. They cross when (b/a) = 0.2 (a = 1.6 cm, L = 48 cm). Individual hole sizes and positions can be perturbed for specific tuning effects, as shown by calculation and experiment.
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