A Rational Approach to Bowed String Instrument Design

For centuries musical instruments have been designed by an evolutionary process. Changes were made here and there and the most successful changes were incorporated into the design of various instruments. The marvelous instruments of today are not the result of careful analysis and invention, they are really the result of hundreds of years of tinkering. It is time that the old, incremental process that slowly improves our instruments or slowly leads them into blind alleys be abandoned, and by pure effort of mind, measurment and a scientific approach, we truly move ourselves into the twenty-first century.

Tho X. Bui built this experimental instrument using a speaker cone in the place of a soundboard. This is an excellent starting point. Soundboards are full of unwanted resonance peaks and no two are alike no matter if they come from the same tree and were shaped by the same maker. Speaker cones have an extremely flat response and are more alike than peas in a pod. Any differences between two of the same type of speakers are minor to the point of being almost impossible to detect accoustically. The hole on the right side improved the bass response and increased the volume of the instrument. The resonant frequency of the body is based on the volume and the area of the opening. How much the cone affects the resonance has to be established by making the same box with a rigid structure in the place of the cone, taking measurements then take the same measurments with the cone in place When I first saw a picture of this instrument I suggested that the bass response could be improved with a carefully weighted passive speaker cone acting as a resonator. The cone is tuned to a specific frequency by adding weight that is the same as the weight of the air in a tube the diameter of the cone, and the length of a tube that resonates on the desired freqeuncy. For the note C that would be the air in a tube of 2, 4, 8, 16, etc feet long, depending on the octave you want. This technique has been used to extend the bass on commercial high fidelity speaker systems in the past, and seems like fertile ground for experimentation in musical instruments. (I must add that as far as weighting of the cone, the article I read left out the "springiness" of the cone, which must have an effect also.) Below there are some more recent examples of speaker cone based instruments. Notice that the bridge assembly is evolving.

These comments by Tho X. Bui are from an e-mail, but I think are worth including here. What I've found from these instruments (just finished the 3rd one, a guitar), is that the bridge design can greatly influence the tone. I'm settling on a bridge system now that I'm reasonably happy with on the "guitar." By replacing various components of the bridge (substituting metal for wood), I can make the tone very similar to that of a Dobro, or alternately, to that of something like a guitar. I will try to make a picture of it available in a few days. The neat thing that I found is that by plucking it in different direction and different places, I can get a wide range of tonal quality as well as dynamics. Being a violin player, I hope to work out a bridge design that will be more conducive to bowing. What works for plucking so far has not been successully used with a bow.

A bit more thinking about it and I concluded that a passive cone was not the full answer. The "Q" of the system might be too high. Any resonant system with a high Q tends to want to ring on it's own frequency and no other. In a bowed string instrument this is the primary cause of wolf tones. My thought is to use an actual speaker. A speaker is a dynamic microphone. It generates current if driven by sound waves. My idea is to shunt a variable resistor across the speaker coil, adding a load to the coil and thereby having control of the amount of damping that can be applied to the (otherwise) passive radiator. The graph of the system without damping is narrow and very tall, with damping it becomes wider and less "peaky."

While the coupling of a speaker or even a (somewhat) passive speaker cone with the surrounding air is usually sufficient, the bell on the end of brass instruments is specifically designed to improve that coupling. The bell is an impedance matching device, and It would be interesting to funnel the passive cone's output into a short tube with a bell at the end. I suspect that a significant improvement in volume could result. The tube portion itself could be tuned also. Thinking more about it I realize that a single passive resonator will only give a little improvement, but that it is quite possible to use eleven passive resonators, one for each semitone, with the missing note of the chromatic scale supplied by the main cone that is driven by the bridge. With careful adjustment of the damping, and tuning of the horns to the intermediate quartertones it should be possible to get an extremly flat response across the entire accoustic spectrum.

An unsuspecting world awaits our advances in the art and science of music. I can hardly wait to get to work.

The rational cello as I envision it. The cellist's bow arm is placed between the two lower horns on the upper bout. It may be possible for the cellist to rest the entire cello on his or her knees using the upper horns on the lower bout, and do away with the end pin. Each horn acts as the output of one of the passive speaker cones. I have been considering using a co-pilot to adjust the damping pots on the fly for things like glissandi. I am hoping to find a high school that is dismantling it's marching band, as a source of parts for the project. Pete

Parts of this page may be tongue in cheek, but Tho built some real instruments and is experimenting with different bridge designs, and slowly improving his basic idea. Yes, Dobro and National have been there before, but Tho is learning things about instrument design, and the stuff I mention about passive cones in speakers was done years ago with some success by ElectroVoice. The idea of variable damping is practical too. The Stroh violin is another example of an instrument that uses a diaphragm and a horn to project sound, and it is still in use as a folk instrument in some parts of the world. In fact William Mutch e-mailed me to tell about a jazz cellist who made is own Stroh type cello that he plays in the area around Cornell. Click here to e-mail Tho if you have questions or are interested in some of his other projects.