Among the other essays posted on this site is one called “Man, What a Weird World That would Be: Where Would We Be Without Hooke’s Law?”. It talks about the fact that most musical vibrations come about due to the natural resilience or springiness of whatever it is that’s vibrating, whether it be a string, a drum membrane, a kalimba tine, the column of air enclosed in the pipe of a wind instrument, or some other type of vibrating body. You can read that article for a fuller discussion of these mechanics. This article is about the opposite: sound sources which oscillate at the frequency they do not because of their inherent springiness, but because they are somehow forced to. As an example, consider … well, actually, there are almost no widely known musical instruments that obviously operate this way. But in this article I’ll discuss some not-widely-known examples and additional possibilities.
My number one example — chosen because it illustrates the idea very nicely — is an instrument I made many years ago called Savart’s Wheel. It is so called because it operates on a principle that first appeared in simpler form as an apparatus for acoustical investigation and demonstration devised by the 19th-century French physicist Felix Savart. (I learned of Savart’s device only after I had completed, but not yet named, my instrument.) The idea in its most basic form involves a scraper-like situation, in which a plectrum of some sort scrapes over a ridged surface, but with this crucial feature: the instrument is designed so that the number of ridge-bumps per second is stable, not varying as with other scrapers. That ridge-bumping frequency stands out as the audible pitch. My version brings together many such ridged scrapers to make available a scale’s worth of scraping frequencies.
The instrument consists of a series of disks of graduated size mounted alongside one another on a horizontal spindle. The disks range in diameter from about 2¼” to about 11”, covering a musical range of a little over two chromatic octaves. Each disk is about a half inch in thickness. The exposed 1/2” edge surface of each disk is covered with ridges, spaced about an eighth of an inch apart. The spindle is motor-driven so that the set of disks can rotate at a steady speed. The player plays by holding the plectrum against the exposed ridges as they rotate past. This agitates the plectrum at some number of ridge-hits per second, and that frequency corresponds to the pitch that you hear. With the smaller disks, the number of ridges rotating past per second is smaller, because with smaller circumference there are fewer ridges to go by for each 360 degrees of rotation of the spindle. The smaller disks thus have a lower ridge-hitting frequency and produce a lower note. The larger disks, with their larger circumferences, have more ridges whizzing by per rotation and produce correspondingly higher notes. There is a fairly simple arithmetic for determining the diameters of the disks relative to each other in order to get the ridge-number-ratios necessary for your desired scale. With the relative pitches thus established, you can control the actual resulting pitches — how high or low the notes of the scale are — by controlling the disk rotation speed.
Much of the sound comes off of the plectrums (the player uses two of them — one for each hand). I made some special plectrums, each consisting of a piece of plastic, shaped a bit like typical guitar pick at one end but larger, with a styrofoam cup attached at the other end. The cup provides a larger sound-radiating surface, analogous to a soundboard, projecting the vibration out into the air as the plectrum tip scrapes over the ridges. Styrofoam is good for this: lots of surface area, with a reasonable degree of rigidity, but with relatively little weight. By holding one of these styro-plectra in each hand and touching them against the rapidly passing ridges, moving them from disk to disk in sequence, you can play melodies. The tone is god-awful in a wonderful way: loud and harsh. But by varying the angle of the plectrum tip as it rides over the ridges you can vary the tone quality, and in this way you can also get some less aggressive and often very expressive sounds.
Notice that the frequency you hear is not caused by springiness in the materials. Instead it is forced by the arrival of one ridge after another striking the plectrum and pushing it out of the way. The frequency does not result from the way the materials naturally oscillate, as it would be for strings or a vibrating kalimba tine. Rather, it is imposed by the ridge mechanism. One result of this — something that comes up fairly often in forced vibrations — is a very angular wave form that gives rise to the harsh tone. This contrasts with most naturally vibrating bodies, which tend to favor sine waves (or accumulations thereof), typically giving give rise to smoother patterns of oscillatory movement and sweeter tones.
I regard this as an “events-per-second” machine. You can think of it as one possible answer to this question: “How can I make something audible happen at a controllably variable rate that falls within the hearing range?” The hearing range calls for an event rate typically in the tens or hundreds or thousands of events per second, which is fast enough to present a challenge if you are working at the crude mechanical level that I am. The question I was faced with when I first started thinking about the idea of an events-per-second machine was, what can I come up with that will have a mechanical repetition rate that is that fast, and controllable to boot? The rotating rasp idea of Savart’s Wheel, with ridges whizzing by and repeatedly striking a stationary plectrum, provided an answer that was, for my limited home-workshop chops, feasible.
That was many years ago. The Savart’s Wheel that I made then has lived a long and fruitful life, taking its place over the years as both one of my most popular and most despised instruments. More recently I have revisited the Savart’s idea, with the thought that changes in available technology have made feasible the notion of a more refined version of the instrument. I’m now working with Ian Saxton as a co-designer and fabricator to explore further possibilities using computer-aided fabrication methods. Our biggest initial problem was, most prosaically, to find a quiet-yet-strong-enough electric motor. We now seem at long last to have found something suitable and are on to next steps. Especially exciting are the further possibilities that appear when you have the option of finely controllable motor speed. Things are moving slowly (busy lives, you know) but I hope to report further on this project sometime before the end of the world.
What other forced vibration instruments are there in the acoustic realm? As mentioned above, not many. But how about the musical siren? This idea, which has been floating around in the acoustic literature at least since the mid 19th century, has some conceptual similarity to Savart’s Wheel. I’ve made a couple of them (here’s one) and several other makers have as well. It involves a disk, perforated with many concentric rings of holes, rotating in front of an air-blower nozzle. The nozzle should be set as close as possible to the disk. If it’s aimed near the outer edge of the disk so that it aligns with the outermost ring of holes, then as the disk rotates a puff of air will be allowed through each time one of the holes in that outermost ring passed in front of the nozzle. The number of puffs per second equals the disk’s rotations-per-second times the number of holes in that concentric ring, and the pitch you hear corresponds to that frequency. With many such concentric rings in the disk, each containing a different number of holes, you can play melodies by aiming the nozzle at different rings. There’s much more to be described here, but I’ll save that for another essay. Maybe too someday I’ll get Ian to help me in the fabrication of a more sophisticated musical siren.
If we’re willing to move beyond the realm of the purely acoustic/mechanical, we can find another sort of forced vibration in a certain well known electro-mechanical device, namely, the Hammond Organ. This wonderful instrument, a staple of mid-20th century popular music, was built around what were called “tone wheels”. These were steel disks, but with scalloped edges — think of many little round-ish protrusions around the circumference of the disk. Many such disks, mounted on motor-driven a spindle, rotated close to electromagnetic pickups positioned alongside. The wavy edge made it so that as the wheel rotated the disk-edge alternately was closer to or farther from the pickup, inducing a current in the pickup at a frequency corresponding to the number of close-edge-passes per second. The Hammond Organ had many such wavy disks on a spindle, with different numbers of scallops providing the range of pitches. The signal from the pickups were sent to an amplifier and loudspeaker. So there, if you’re willing to go electro-mechanical in this discussion,we have another musically useful audible vibration whose frequency is dictated by mechanics, rather than resulting from the natural springiness of the vibrating body.
Shall we talk about digital? In digital audio we have what could arguably be called the most perfectly manipulable forced vibration system imaginable (never mind that it’s mostly used to create or recreate wave forms very similar to sine-wave-based oscillations of sorts that commonly occur, unforced, in the natural world). Fantastic possibilities! But for a workshop tinkerer like me, it’s not as amiable as the hands-on material world of Savart and sirens.