The Physics Behind the Erhu, a Chinese Stringed Instrument

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by Erika Rose McLaughlin

fall 1999

presented at the Whitman Undergraduate Conference, spring 2000

The purpose of this paper is to discuss the physical properties of the erhu. This will be done by first giving a bit of background to familiarize the reader with the instrument in general, then discussing the physical manner in which the instrument produces sound, followed by some specifics and peculiarities of the sound production of the erhu. A final section will address the physical aspects that contribute to the erhu's distinctive timbre.

Background

The exact origins of the erhu are not known, but its use in ensembles and particularly in Chinese opera have been recorded from the 18th century onward. It is thought to have been used to accompany folk music for a few centuries prior to its introduction into more formal music

The erhu is about 75 cm long with a bow of about equal length. It consists of a hexagonal or octagonal, or sometimes round, resonator box to which a long wooden neck is attached, drilled into one of the faces of the box. The box is covered in snakeskin on one end and usually has a carved sort of grate at the other end. The erhu has two strings that run from the base of the resonator box, over a bridge resting on the snakeskin side of the resonator, and parallel to the neck up to a set of large friction pegs. A nut is formed below the pegs by a strip of cord or fabric tied around the strings and around the neck. The top end of the neck is usually adorned with a carved head of some sort, or sometimes other ornamentation.

The bow of the erhu is curved toward the hair for most of the length of the stick, much like the bow used with western bowed instruments, but with a stick that simply curves toward the hair at the tip, rather than with a Tourte head as seen on a western bow.

The erhu is played with the hair of the bow between the two strings. The bow is held with the hand sideways much like a German double bass bow. The bow hold has also been likened to holding the Chinese writing brush. Because of the placement of the bow hair between the strings, the strings are bowed almost perpendicular to the plane on which the strings lie, rather than almost parallel to this plane as is the case with western bowed instruments.

The strings are tuned in fifths, though there are no definite pitches to which they are to be tuned, probably because of the instrument's origins as a folk instrument to accompany singing. In modern Chinese orchestras, A440 is a common tuning for the higher string.

The strings are stopped by lightly pressing down on the strings, just enough to produce a stopped tone rather than a natural harmonic. The fingers press only against the string, not against a fingerboard.

Physical properties

Like all bowed instruments, the initial energy source in the erhu's sound production comes from the bow setting the string into motion through a process based on friction.

The hairs of the bow are covered in rosin, which makes them grip the strings. It was originally thought that this string grippage was due to the barbs in the horsehair catching on the string, but tests using bows haired with fishing line (which is smooth) have disproven this, since the majority of players could not tell the difference between fishing line and horsehair.

The rosin causes friction between the bow and the string, which allows the bow to pull the string aside with its motion. When the string has been pulled aside far enough to build up potential energy outweighing the force of the bow, the string releases from the friction grip of the bow and moves in the opposite direction. This energy carries the string past its original straight position to where it is displaced in the opposite direction.

The string is now oscillating, and travels back and forth. When the string is back to where the bow originally displaced it, and it is moving in the same direction and about the same speed as the bow, the string sticks to the bow again.

This cycle of sticking to the bow and slipping away has the same period as the oscillation of the string.

The transfer of the energy in the oscillating string into the resonating parts of the instrument is less complex with an erhu than with western instruments, because of the angle of the bow. On a viola or similar instrument, the strings are bowed at an angle roughly parallel to the top of the bridge, and therefore they oscillate mostly from side to side, though the aim is to get the top plate of the instrument vibrating up and down. These instruments necessitate a complex structure of a carefully shaped bridge combined with a bass bar and soundpost to transfer the side-to-side oscillation into up-and-down oscillation.

With the erhu however, the strings are bowed in almost the same direction as that in which the top skin is to vibrate. For this reason, the bridge can be much more simple. The erhu bridge is basically a solid wedge that keeps the strings up off the skin. The bridge sometimes has a hole drilled through the middle of it, parallel to the strings, which causes the vibrations of each string to be transferred more directly down to the skin rather than causing additional sympathetic vibrations to travel across the bridge from string to string.

If the string is bowed parallel to the other string, as with a western instrument, the instrument will still sound, as the bow is also creating a traveling wave, and the string is not oscillating completely in a plane, but the sound is not nearly as loud or resonant as when the erhu is bowed normally.

Special considerations

Some peculiarities were noticed in the sounds produced by the erhu. That is, there appear to be some aspects that are quite different from the more familiar western bowed instruments. For instance, when the lower string, tuned to a D throughout this experiment, was bowed, the pitch was higher by about a quarter tone on the upbow stroke than on the downbow stroke, which matched the plucked pitch of the string. This occurred regardless of the contact point of the bow on the string. The reason for this was discovered when it was noticed that the higher string, tuned to A440, increased in pitch on the downbow. This made it apparent that somehow the strings were being lengthened by being pulled sideways toward each other.

This made it pretty apparent that the part of the instrument letting the strings slip back and forth was the nut at the top of the string, since it consists of a cord tied around the strings, which of course is not a terribly fixed setup. When the strings were held in place at the nut by a makeshift wooden nut - a piece of maple with grooves for the strings - the pitch no longer raised and lowered. The frequency spectrum graphs done on the computer also showed much cleaner more definite harmonics than when the instrument was played in its conventional form, indicating that the nut causes unstable oscillations, since that end of the string is not defined as clearly as on an instrument with a more fixed nut.

With the maple nut in place, the instrument sounded very much like a violin or a viola. The characteristic "Chinese" sound was no longer present, though the thinner "nasal" timbre was still prevalent.

The raising and lowering of pitch occurred similarly with stopped notes. Since the strings are not stopped against anything such as a fingerboard, stopping them with the finger also does not define a very fixed end of the string.