Most musical instruments have a primary vibrating body that serves as the main determinant of the frequencies we hear – think of the string itself in a string instrument, or the bar in a marimba. And then, most of those instruments have additional components which help to augment that original vibration. You can learn a lot about how musical instruments work by looking at the interactions and frequency relationships between the original vibrator and the secondary elements that may follow. Sometimes the relationships involve shared resonances, meaning that the initial vibrating body and the following components have some of their natural frequencies in common, creating extra layers of reinforcement between the two. In this article I’ll be talking about such shared-resonance interactions. Before it’s through, I’ll get into some unusual things you can do to manipulate and exploit them. With luck, cool sounds may ensue.
To help paint the picture, let’s use a marimba-style wooden bar as a starting example. You can set up a wooden bar so that it sounds pretty much on its own – that is, the sound you hear when you strike the bar is mostly just the soundwaves radiating directly from the bar itself. But you can greatly enrich the sound if you add some sort of resonant air chamber. One way to do this is with a trough-like chamber, typically underlying a row of many bars. In this case, the chamber’s resonance is general enough to reinforce a range of frequencies, so it can help with many differently tuned bars. The other approach for an instrument with many bars is to give each bar its own individual resonator with a more narrowly defined resonance peak, tuned to resonate specifically at the frequency of its associated bar. This is the case for the sort of marimba that has a resonator tube below each bar. For this article, we’re mostly interested in the second case: instruments in which a secondary body is tuned to match the frequency of the initial vibrator, so that the initial vibrator excites a corresponding vibration in the like-tuned secondary body.
This approach can be of interest in a couple of different ways. One, as we just saw, is that the shared resonance of the initial and secondary bodies can enrich and amplify the sound, as compared to the sound of the initial body alone. The other is that there may be ways to play with the interaction between the two in search of new and interesting sounds and effects.
An odd little bit of history: One of the important instrument designers of the early 20th century was J.C. Deagan, who was central in adapting bar percussion instruments for western music culture. He’s the one who developed the vibraphone and who did the most to standardize the orchestral marimba. He also developed a lot of other interesting and innovative instruments not as well known (although his place in musical history does have an asterisk*). Deagan advertised himself, in his company’s brochures, as “the world’s leading authority on acoustics” — quite a claim, given that his life overlapped that of Hermann von Helmholtz. One of his main acoustic tricks was to attach tuned air resonators, functionally equivalent to those in his marimbas, to just about everything, from sets of tuned bells to his big angklung-like Organ Chimes. Instruments whose sounds might have been a bit on the thin side became richer with added air resonance.
[*The unfortunate asterisk on Deagan’s legacy is that on at least two occasions he appropriated instrument designs from non-western music cultures and patented them as his own work.]
In this article I’ll talk a lot about string instruments, so let’s have a quick look at how these questions play out with strings. String instruments, if they do not have pickups, pretty much have to include some secondary component to help project the sound into the air, because a vibrating string by itself has so little surface area that it moves scarcely any air. Thus, most acoustic string instruments have soundboards and sound chambers. The air chambers in string instruments function similarly to the chambers in trough marimbas mentioned above: they enrich the overall sound, especially in the lower frequencies, but they are not made to be frequency-specific. Thus, in typical string instruments a single resonating air chamber serves to enhance all the notes across a large range. But is there a stringed equivalent to the marimba with its individual tuned resonators, a string instrument in which each note has its own individually tuned air resonator? I have often fantasized about this. I’ve even successfully tested the basic principle in the shop and done sketches for a more fully realized instrument. But I haven’t followed through to make such an instrument myself, and if someone else has made one, I’m not aware of it. The main reason I haven’t followed through on the idea is, I haven’t come up with a way to make such an instrument that isn’t impractically large. In short, it’s a cool idea for someone who has a lot of space in their garage. For anyone who is intrigued, I’ve included additional notes on what it might take to build such an instrument at the end of this article.
But there are other ways, aside from tuned air resonators, to add frequency-specific secondary resonating elements to string instruments. Unlike air resonators, some of these methods don’t do much to make the sound louder, so they would typically be used to add color to the tone quality on instruments that already have either pickups or sound boards and chambers. One way to do this is through additional strings which may be unplayed but which can be tuned to the same frequencies of the primary strings. When the primary strings are played, those secondary strings will naturally vibrate in sympathy, adding reverberation and chorusing effects to the sound. Sympathetic strings appear in established instruments like sitar, in historical instruments like viola d’amore, and in newly developed instruments like Mark Deutsch’s wonderful bazantar.
It’s worth noting too that in many cases sympathetic string vibration does a lot to enhance the sound even of stringed instruments that don’t have a separate bank of extra strings for that purpose. In piano, for instance, the plethora of shared harmonics among its 200+ strings greatly enrich the sound whenever the dampers are lifted. Later in this article I’ll discuss several instruments I’ve made which use sympathetic string vibration in more unusual ways.
Note that sympathetic strings, by their nature, are specific in the frequencies they’ll resonate. If you want to get a response out of a sympathetic string (one which is neither plucked nor bowed, but intended to spontaneously resonate along with sound from another source), it must be tuned to, or very close to, the frequency of that other source – or, more broadly, one or more of its overtones should be in agreement with one or more of the overtones of the source. However, there is an alternative approach which works better than you might expect. Rather than having a small-ish number of sympathetic strings on an instrument which must be kept in tune, you can have a large number of randomly tuned sympathetic strings, as with this instrument. Given the plurality of strings, each with its many harmonic overtones, you can do quite well in terms of broad-band reverberation across a wide range of notes, without requiring a terribly huge number of randomly tuned strings. And the quality of the resulting reverberation is very pleasant.
Another source of broad-band reverberation is whiskers. That’s the term Bernard and François Baschet used for their trick of adding several fairly long, semi-rigid spring-steel wires to their instruments (typically about 1/16” or .078” in diameter), attached to some solid part of the instrument at one end and free to flop about at the other. Because each of these wires had many modes and natural frequencies, a few of them on an instrument was enough to add a bit of extra richness and short reverb tail to the sounds across a range of frequencies – not as nice and clear as a bank of sympathetic strings, but a still pleasing touch.
Here’s another angle on frequency agreement between drivers and their resonating bodies, this time pertaining to sustaining instruments: wind instruments and bowed strings. When a violin bow scoots across a string, it engages in a stick-slip motion: it momentarily catches on the string, then makes a tiny jump, then catches again, and so forth, in the rapid series that gives rise to the vibration in the string. This is the sort of motion that occurs in any squeak or friction-type sound, except that in the violin the stick-slip frequency is dictated by the natural frequency of the string. The frequency of the driving mechanism (the stick-slip frequency) and the natural frequency of the main vibrating body (the string) come into agreement and you get a clear and steady sustained pitch. The situation is similar with most standard wind instruments. Taking reed instruments as our example (somewhat simplified here), the opening and closing of the reed over the opening in the mouthpiece creates periodic pulsations entering the main tube of the instrument, which activate the vibration in the air within the tube. If all goes as it should, the natural frequency of the tube (whatever it may be, given the configuration of open and closed tone holes at the moment) interacts with the reed, and the two come into agreement in frequency. In the coupled system, two reinforce one another to produce a clear and steady tone.
This kind of agreement doesn’t always happen. Consider the door squeaking on its hinges. Given what we’ve just seen with bowed strings and reeds, you could imagine a happy situation in which the natural resonance frequencies of the idiophonic body that is the door induce the stick-slip frequency of the squeaky hinge to come into agreement, resulting in a coupled system which produces a nice stable tone whenever the door swings. But no; in most door squeaks, as indeed in most squeaky situations in general, the stick-slip frequency has a mind of its own and doesn’t choose to cooperate with whatever resonance frequencies may be present in the adjoining elements (e.g., the door). Cooperation between the two elements is far from automatic. For things to work as we’d like, circumstances need to be just right. Having spent some time myself trying to induce uncooperative elements of various sorts to cooperate in frequency, I’ve learned to appreciate my instrument-making forebears for their work with both bowed strings and reeds. Over many years those makers did miraculously well in finding the right sorts of balances to induce the driver and resonator frequencies to cooperate as well as they do in the standard winds and bowed strings.
Some time ago I made an instrument called Spools & Wheels (see also this video and this essay). This instrument turned out well in the end, but at the time I was building it I had some ideas which did not pan out, but which happen to be relevant to this article. Each of the many “notes” of this instrument has four physical components in interaction, and each of these components potentially has a natural frequency of its own, namely: 1. The stick-slip of a string looped around the hub of a turning wheel; 2. the portion of the string itself that extends from there; 3. A diaphragm to which the other end of the string is attached; and 4) an air-resonating tube, covered at one end by the diaphragm. The question I asked myself was, would it be possible to get all these elements into agreement, frequency-wise? Doing so would presumably give rise to a strong and stable regime of vibration in the overall system and create a sure and clear tone. Even getting two or three of the four elements into agreement should have salubrious effects. Well, as the instrument took shape it turned out I couldn’t get anything to agree with anything else. Each of those four elements ended up with its own unrelated natural frequency. As it turns out, the frequency from one of the components (the air-resonating tube) comes through quite loud and clear, dominating the others in the sound, and giving the instrument recognizable pitch. The stick-slip system, like the door hinge, has a mind of its own and does not come into agreement with other components, but its frequencies turn out to be subsonic; they don’t compete with air resonance tube, but they do add a peculiar texture to the sound. It has turned out in the end to be an interesting and worthwhile instrument – but I still wonder what it might have been like had I been able to create a more coherent regime of frequencies in interaction.
This instrument, Spools & Wheels, highlights another relevant phenomenon. In a number of instruments (mostly homemade types rather than standard types), a broadband input serves to excite a resonator that has a single strong natural frequency. The resonator responds selectively to the broadband input, and the result is a clear tone at that frequency, but with an undercurrent of the original broadband sound. As an example, think of a gurgle flute constructed simply as follows: a blowtube is placed in a half-full bottle. When the player blows, the bubbling of the water excites the resonant frequency of the body of air enclosed in the bottle above the water, as you can hear in this gurgle organ. It’s quite a nice sound, and the pitch is clear. Given the broadband agitation of the gurgling, the resonator responds selectively at its own natural frequency, and that tone is most of what you hear (with a pleasant admixture of unpitched gurgling sound). In Spools and Wheels we have a similar situation, in which the impulsive, subsonic agitation from stick-slip activating the diaphragm is enough to excite the natural resonance of the tube, giving us a clear pitch to listen to (with the odd admixture of the diaphragm’s subsonic and irregular impulses). In case you’re still interested, here’s another instrument that works on this principle of broadband input into a specific-frequency resonator.
Let’s now talk about some instruments I’ve made which exploit shared resonances in interesting ways.
The initial sounding elements in Smoked Paprika (which you can also see in this video) are bent bars of steel, functioning a little like tuning forks. There are 23 of them covering a range of a little over two octaves. Each of these bent bars is suspended from a string tuned to the same note as the bent bar’s fundamental. When you strike one of the bent bars, in addition to producing its own sound, it excites a sympathetic vibration in its like-tuned string. The listener hears the sound of the bent bar directly, independent of amplification, while the string sounds are heard via magnetic pickups. The bent bars are full of inharmonic overtones, but a couple of these overtones have been retuned (by subtle reshaping of the bar) to achieve octave relationships with the fundamental. At the same time, most of the bent bar’s inharmonics remain, spicing up the tone. The strings, meanwhile, naturally have purely harmonic overtones. This means that there are shared resonances between the two elements at the fundamental and one or two tuned overtones, while their underlying tone qualities are quite different. The interaction of the two, both on a physical level and in the sound itself, is unusual and intriguing.
Miago Trod involves steel rods – threaded rods, actually – fixed at one end and free to vibrate at the other, played with percussion mallets. There’s an upper bank of 22 shorter, higher-pitched rods and a lower bank of 22 longer, lower-pitched rods. All are rigidly fixed to a heavy crossbar at middle height. But actually the upper and lower rods are one: Each upper bar extends through its mounting hole in the cross bar and extends down from there to form the longer rod below, sounding a couple of octaves lower. The cross bar is made heavy enough that the upper and lower bars can vibrate independently. Then again, the question of how heavy the cross bar is central to the way this instrument works. The bar is designed to be heavy enough to allow each part of the rod, above or below, to sustain its own vibration clearly enough, yet still light enough that when the upper part sounds, some of its vibration is transmitted across to the lower part with its octave-related tuning, and vise versa. Thus the upper and lower rods tend to share one another’s resonances, creating a richer and more complex tone. As with Smoked Paprika described above, the normally inharmonic rods both above and below each have one of the prominent, normally inharmonic overtones adjusted to harmonic alignment to help clarify the perceived pitch, while other overtones remain inharmonic to provide color to the tone. (In this case the overtone tuning is achieved by adding weights in the form of hex nuts to carefully adjusted locations along the rods.)
What I’ve just described was my theoretical ideal for how this instrument should work.
The description does apply, but it turns out that more than that goes on when the instrument is played. In practice I found that the whole instrument, with its single rigid cross bar supporting all of the rods, tends to behave monolithically, with the many resonances of each of the many bars being shared throughout. As a result, the tone of any one rod among the many on the instrument is much fuller and more complex than the same rod would produce alone.
Airy-Air and Bari Airy-Air
Earlier in this article I pointed to marimbas to introduce the idea of instruments with individually tuned resonators for each note. I further speculated about whether it would be possible to make a string instrument with marimba-like individual air resonators. Here now is an example of the same idea applied to a different instrument type. The instruments called Airy-Air and Bari Airy-Air are Lamellaphones (kalimba-like instruments). A typical lamellaphone has a soundboard, often coupled with an air chamber, designed to function like those on most string instruments. But Airy-Air is not a typical lamellaphone; it is designed to be marimba-like, with an individual tuned air resonator tube below each tine. To make this work, I made the tines on Airy-Air extra-wide, allowing each tine to push a lot of air as it vibrates over the open top of its resonator, thus doing a good job of activating the enclosed air. The air resonators add to the volume and the fullness of sound, especially in the lower frequencies, that the tines alone would otherwise lack.
I’ve made several string instruments with multiple bridges dividing each string into two or three segments. The bridges may be positioned to make the string segments on either side the same length, or else to make relative lengths of some other simple ratio like 2:1 or 3:1. This guarantees that these segments will include, between their fundamentals and harmonic overtones above, plenty of shared resonances. When any one string segment is plucked, it’s guaranteed to find a lot of sympathetic tones in the segment(s) on the other side of the bridge(s), and the tone is accordingly enriched. The instrument called 2+2+1 is the simplest embodiment of the idea, being a straightforward acoustic zither but with bridges placed so as to divide each string into three playable segments in 1:1 and 2:1 relationships. The sound is simply an unusually rich and warm string sound, to my ear quite lovely.
Handsome Dan and friends
Several other shared-resonance string instruments I’ve made make use of a clever idea developed independently by Glenn Branca and Hans Reichel in the 1980s. To understand the idea, let us picture it in its simplest form: imagine a string divided into two equal segments by a center bridge so that both share the same fundamental and harmonic frequencies. Imagine it has a magnetic pickup under the segment on one side but is plucked on the other side. The pickup is not in a position to respond to the plucked segment, but it will capture the sympathetic resonance on the unplayed side. The resulting tone is unusual, with a soft attack and an ethereal tone quality.
This idea, with additional variations, turns out to be rich in possibilities, and I’ve made several instruments employing it in various ways. Let’s look at the one called Handsome Dan. Handsome Dan has fourteen strings tuned diatonically across a range of just under two octaves. As in the above description, they’re divided by a center bridge into two equal segments, with a pickup on one side only. The strings on the no-pickup side can be played open, but they can also be played with a slide, and this is where the most striking effects come into play. If you place the slide at some random place along the segment and pluck, it’s likely that the resulting tone will not find much common ground with the segment on the opposite side, and the response on the pickup side will be minimal. But if you happen to place it at a location that coincides with one of the harmonics in the opposite segment, then the string there will come to life, and you’ll hear the result through the pickup. If you pluck and then move the slide, then you’ll hear the unique effect of the pitch-bending on the plucked side moving in and out of agreement with various harmonic frequencies on the unplucked side. This turns out to be a wonderful sonic playground to spend time in.
As mentioned, I’ve explored several variations on this idea. Here are a few: harmonochord, 2 + 1, Extremely Handsome Dan (no web page for the latter yet; hopefully coming soon). Plus this one, which is one of the more complex and interesting takes on the idea: Narrow Trillium. Most of the string instruments mentioned here can be seen in the Youtube video titled Shared Resonances.
The Other Side and Springtime
The instrument called The Other Side has some things in common with the shared-resonance strings described above, and also with Miago Trod described earlier. It’s a lamellaphone (a kalimba-like instrument) in which each tine extends through bridge and out on the far side. The extension on the far side is tuned to the same pitch as the segment on the front side. There are pickups, and they are placed under the unplayed segment on the far side. When you pluck on the front side, the unplayed segment on the back side joins in by sympathetic vibration, and that’s what the pickup monitors. To clarify the tone, small weights carefully located on the unplayed side bring the most prominent overtone on the unplayed side into octave alignment with the fundamental. The sound, as heard through the pickup, is once again of the sort that might inspire the word “ethereal.”
And here’s one more that works on related principles. The instrument called Springtime (AKA Stringtine) has zither-like bank of strings with each string attached at one end to a kalimba-like tine. The tine is tuned an octave above the string, aligning with the string’s octave harmonic. There are magnetic pickups positioned to monitor not the strings, but the tines. It’s played by plucking the strings, but the sound you hear is the string sound as filtered through the tine. The tone is unusual and distinctive; I won’t try to describe it, but I encourage you to check on the links above (including the Shared Resonance video) to hear it.