Some time ago I posted on this site an essay under the title “Orientation of the Oscillation.”  In it I talked about the importance of the direction of the oscillation in an instrument’s main vibrating bodies (strings, bars, tines or whatever): how the orientation of the vibration affects the resulting sound and, where applicable, the efficiency of transmission to the soundboard. One of the instrument types discussed was chimes. A single chime can produce a dual fundamental if the chime is thicker, and thus more rigid, in one dimension than it is in the other – if, for example, it’s oval in cross section rather than circular, or rectangular rather than square. Which fundamental predominates in the sound depends on the direction it’s struck from.  Maybe you can picture why this would be so; if not, you might want to follow the above link and read the fuller discussion in there.

I have occasionally enjoyed goofing around with this dual-tone phenomenon. I have made chimes in which one dimension is just a little thicker and more rigid than the other, so that the two resulting fundamentals are quite close in pitch. This creates the wavering effect known as “beating” that arises when two very close but not identical frequencies sound simultaneously.  I’ve also made chimes in which the difference was greater, so that the two fundamentals produced a harmony between them, such as a third. If you’re interested in trying this, the easiest way to explore this idea is: start with a metal tube of suitable length and diameter so that it functions well as a chime. Aluminum tubing is ideal, but the steel conduit known as EMT, which is inexpensive and readily available at hardware stores, also works well. Place the tube at its midpoint in a vise, and tighten the vise enough to squash the middle of the tube a bit. This makes the tube a bit wider and more rigid in cross section across the middle when it oscillates one in one direction, and a bit thinner and less rigid for the other direction. You can choose which direction of oscillation predominates by the direction you strike from. The fact that the squash is at the middle of the tube is important because the middle region is the main flexing area for the vibration pattern of the fundamental mode in a tube like this. The result will be a slightly higher pitch when you strike from the direction that excites the vibration across the wider dimension; slightly lower when you strike the other way. For in-between strikes, you’ll get a little of both pitches. To make all this work, you’ll need mount the chime in a way that allows it to vibrate freely in the fundamental mode.  You can do this by suspending it by a cord looped through holes drilled through the chime at a point between a fourth and a fifth of the overall length from one end, or by resting it horizonal on a pair of narrow soft pads located between a fourth and a fifth each end.  Use a beater of suitable weight; one that is not so hard as to produce a terribly clangy sound and not so soft as to produce a hopelessly muffled sound. Try different degrees of squashing to see what sorts of beating, dissonance or harmony you can get.

I’ve often thought of doing something more serious with this idea.  How about creating a set of chimes tuned for particular relationships between the dual fundamentals, and possibly also duals at the most prominent of the overtones inherent in the chime tone, all deliberately set to frequencies that blend to form a distinctive and interesting overall timbre when the chime is struck?  Just recently, I finally got around to this project.  My name for the resulting instrument is North-South/East-West Chimes, reflecting the idea that you get different pitches depending on whether you strike them for a north-south direction or an east-west direction. The remainder of this article describes how the set took shape. You can see and hear the instrument here

I made the chimes from rectangular aluminum bar. You can get this material in various dimensions, so my approach was to look for the available length/width ratios that would come closes to producing the pitch relationships I wanted between the dual fundamentals. The arithmetic for this is simple in theory: the ratio of width to thickness should correspond to the ratio of the frequencies of the interval you want.*  Thus, for instance, if you want an octave relationship between the north-south fundamental and the east-west fundamental, you’d theoretically want a bar that is twice as wide as it is thick, since 2:1 is the frequency ratio that comprises the interval of the octave. For whatever reason, it turned out in practice that this wasn’t quite true – the ratios between the N-S frequency and the E-W frequency were close to the width/thickness ratios but not spot-on. It’s also true that I couldn’t always get the width/thickness ratio that I wanted: as you’d expect, those aluminum bars are available in some dimensions and not others.  So I set about getting bars that were as close as possible to what I wanted, knowing that further fine-tuning would be called for.

*[In a situation like this where rigidity plays a crucial role, you might expect a direct-proportion-squared relationship between thickness and resulting frequency. However, this is offset by the fact that an increase in thickness, while increasing rigidity, also has the contravening effect of increasing the mass of the bar, bringing us back to a simple direct proportion.]

For the fine tuning, I used a minimal-machining approach. To lower the bar’s fundamental mode for one direction, the method was to make shallow saw kerfs at the center of the bar on the front and back surfaces perpendicular to the direction of vibration, thus slightly un-rigidifying the bar for that direction. The deeper the kerf, the lower the resulting pitch for that mode. To tune for the next overtone as well, the method was to make pairs of kerfs on both sides at about a quarter of the bar length from each end. (Just as the middle of the bar is the main flex point for the fundamental mode, these two quarter-length locations are close to the main flex points for the next most prominent mode). Notice that if you’re tuning for both directions in each of two modes, that’s a total of four modes to be tuned in each bar. A lot of work! For many bars I did indeed tune to four chosen pitches, but for some of the higher ones, where the highest of the pitches were high enough to be less noticeable in the composite tone, I tuned only three.

I tried quite a few tunings to see which ones I might like. For example, it’s possible to tune the four most prominent tones within the bar to a major- or minor-seventh chord.  Imagine tuning an entire scale set this way: when you play up and down the scale, you get melodies running up and down in full chords. But not all four tones within the bar sound equally with each strike; different tones within the chord are more prominent depending on where you strike and with what sort of beater. As a result, the effect isn’t quite as dense as this description suggest, and there’s lots of room for variation in playing technique.

It’s also possible to tune all four tones to octaves and fifths. This has the opposite effect from the chord bars: the several tones within the bar tend to blend almost imperceptibly, creating an effect less like multiple pitches and more like a single tone that happens to be rich in overtones.

Oddly, my favorite turned out to be a tuning in fourths, as in {lower mode: G & C; upper mode C & F}.  In that example, the ear pretty consistently hears the C as the defining pitch. The overall flavor of this tuning is reminiscent of a naïve western attempt at orientalism – but strangely pretty.

In the end I made four sets: a couple of chordal sets in different inversions, a simple octaves-and-fifths set, and the fourths tuning just described. Each has a diatonic range of between one and two octaves. The tuning process, you may imagine, was laborious. It takes some practice to learn to hear and tune each separate mode within the bar’s tonal blend.  I won’t try to describe the process here, but if you’re interested you can learn more about it in my book Making Marimbas and other Bar Percussion Instruments, pages 40-42.

I was of two minds concerning how to mount the bars, so I made two mounting systems. One is a tall, free-standing upright structure allowing the bars to be hung like wind chimes (but playable with mallets). The other is more of a marimba-like arrangement, with the bar sets mounted in horizontal rows alongside one another or one above the other.  I much liked the idea of the wind-chime-like arrangement (which also had the great advantage of being weatherproof, thus reducing indoor storage issues), but in practice the bars have now spent most of their short lives in the horizontal arrangement, because they’re more playable that way.

I quite like the sounds, especially when played sparsely and with some restraint so that the individual bars don’t lose their identity in a wash of too many sustaining tones.  

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