Most musical instruments are designed to work with one or the other of two types of vibratory movement: transverse or longitudinal. Very Loosely speaking, transverse vibration typically involves cross-wise movements in the vibratory medium; it is what we normally see in strings, drum heads, kalimba tines and many other instrument types. Longitudinal vibration typically involves movements along the length of the medium; it is what we see in the air columns of tubular wind instruments. (For a fuller discussion of these two types of vibration, see this article.) But in the physical world around us, these two are not the only ways that vibration can arise. Other patterns of vibratory movement do appear; most notably, torsional vibration.
Torsional vibrations are those which involve twisting and un-twisting motions. To picture this, think of a flat bar of wood, such as might serve as one of the keys for a home-made xylophone. Imagine that you strike it with a beater, not in the normal fashion at the center of the bar, but at one corner. This is likely to cause the bar to twist slightly at the struck end. As the resulting movement plays out, it develops into a vibratory pattern in which the opposite ends of the bar repeatedly twist and untwist in opposite directions. If you were to suspend the bar vertically instead of horizontally, this movement would be remarkably akin to a dancer doing the twist (only much faster). I made a short video on the subject of torsional vibration, and for the video I had wanted to include the footage, still easily findable on youtube, of Chubby Checker on American Bandstand singing “Come on baby, let’s do the twist!” His dance movements in that video really do exemplify torsional vibration quite nicely. Due to concerns about intellectual property rights, and out of respect for the estate of Chubby Checker, I didn’t include that in my short video. Instead, I convinced a few friends and relatives — some of them excellent dancers and some maybe not so much — to allow me to shoot iPhone video of them doing the twist, and scattered these clips through my little video as illustrations of torsional vibration.
‘50s dance crazes aside, the study of torsional vibration does have practical applications; for instance, it’s a serious concern in the operation of drive shafts for motors in industrial applications.
Back to musical instruments: we’ve seen that xylophone bars can engage in torsional vibration. But they’re not meant to! Torsional movement is a form of xylophonic misbehavior. When operating as intended, xylophone bars and marimba bars, like so many other vibrating bodies in musical instruments, vibrate transversely. Marimba bar tuners seek to minimize torsional vibration, as do marimba players, because it tends to introduce extraneous unwanted frequencies into the sound.
OK then, but … are there any musical instruments in which torsional vibration is the primary intended mode? I have given this question some thought, and I haven’t been able to think of any. If you can come up with any, please let me know. Meanwhile, this leads to a follow-up question: Would it be possible to make one?
I took on this challenge, and came up with the instrument I’ve been calling Potwot (POssibly The World’s Only Torsional musical instrument). You can see it in the aforementioned short video, and I’ll describe it a bit more here. But before getting into the details, a short disclaimer:
It’s tempting to think “Gee, we’re gonna make a musical instrument which uses this exotic type of vibratory movement that no other instruments use. Maybe it will produce some uniquely exotic sound such as the world has never before heard!” This is an intriguing thought but, actually, I wouldn’t expect that to be the case. The reason is that, even though the underlying mechanics of the vibration may be unique among instruments, the resulting wave form would still be expected to be made up of an agglomeration of mostly sinusoidal patterns much like those of other, familiar instruments. Given that sort of not-radically-different wave form, we’d expect the resulting sound quality to likewise be not all that different from other familiar instruments. And, having now made and heard Potwot, I can confirm that this is the case: Potwot’s tone quality, while quite pleasant, is not notably unusual.
Potwot is a simple instrument, designed just to demonstrate an idea and not much more. It consists of four spring-steel bars, rigidly mounted at one end and free to vibrate at the other. Near the middle of each bar is a 90° bend. The bend makes it so that if you pluck the end in the right direction, the end portion of the bar will remain more or less rigid within itself as it moves, but the base section of the bar will to engage in a rapid twisting and untwisting motion — and that’s the torsional movement that we’re after. In addition, Potwot has a magnetic pickup, and the pickup is positioned in such a way as to be preferentially responsive to the torsional movement. You can also pluck the steel bars in a different direction which will preferentially excite transverse modes. Although the transverse modes don’t come through the pickup strongly, they can still be heard at least a bit. They add the option of one more flavor and a few additional available notes to the playing of the instrument. Being able to hear the transverse modes also helps to confirm the underlying idea of the instrument: we hear that the torsional modes and the transverse modes are producing different frequencies in the same bar, and this confirms that they really are two different modes of vibration in play.