The Reciprocal Bow As A Workshop Tool
By Joseph Curtin, Journal of the Catgut Acoustical Society, May 1997
The obvious way to test a violin is to give it to a good violinist, then sit back and listen, just as, I suppose, the obvious way to test a race-car is to give it to a race-car driver and see how fast he can go. The trouble is that race-car drivers can drive fast in almost any car,and good violinists will make almost any violin sound good. It’s their job.
You could say that if you want to hear how a violin really sounds, a good violinist is the worst person to give it to. Good violinists impose their own sound on an instrument. They tone down harsh notes, smooth out unevenness, and like a chef using salad dressing, blend everything together with vibrato.
As often as not, good violinists are not really interested in testing a violin; they are interested in demonstrating how well they can play it. What you hear is not so much the sound of a particular instrument as the sound of violin-playing, which is a kind of magic trick they do, using the violin as a prop. Bad violinists are even less useful.
More seriously, when someone plays a violin, there is an unconscious tendency to adjust to the instrument. Slight changes in bow-speed, pressure, point-of-contact, etc., effectively normalize the violin toward the sound concept of the player. This makes it difficult to evaluate an instrument independently of a given player’s response to it.
Of course, there is a lot to be learned from talking to violinists. They tell you things you don’t hear while they are playing, such as how much or how little work it took to make an instrument sound good. And this is, after all, a major difference between good and bad instruments.
The trouble is, when players talk about sound, they often resort to highly personal, more or less improvised language. Such words as bright, dark, smooth, harsh, or muffled, seem fairly workable (though a client once told me, without apology, that he didn’t use the word dark the way other people do). But what about the player who says an instrument sounds a little too dry, or too moist, or too goosey? The fact is, when violinists talk about sound, it’s sometimes hard to know what they are talking about.
The problem has partly to do with how we hear. Each note on a violin is a complex mixture of fundamental and partials, but it is not these we hear. We hear notes, or more likely, we hear music. Is it possible to listen more analytically, more objectively? Musicians, after all, train their ears to hear not just the music, but the individual notes that make up the chords on which the music is built.
Though many research tools have been developed for analyzing violin sound, it is often difficult to connect the results of such analysis with the experience of listening to a violin. Response curves, input admittances, and radiativity charts mean something to physicists, but tend to induce in violinmakers a kind of `fight-or-flight’ response. What is needed, perhaps, are tools that bridge the gap between analysis and perception.
The Reciprocal Bow
The reciprocal bow evolved over the past few years in Gabriel Weinreich’s laboratory at the University of Michigan (Weinreich, 1996). It is a direct descendant of his well-known technique for measuring what he calls the “radiativity” of a violin – basically, the amount of sound radiated by the instrument in response to a given bridge motion (Weinreich, 1983). To measure radiativity, a swept sine wave is played over a loudspeaker situated somewhere near the violin – all this in an anechoic chamber. The sympathetic response of the violin to the test signal causes the violin’s bridge to vibrate. These vibrations are picked up by a phono cartridge resting on the bridge, and the resulting signal is sent to a computer for analysis.
It can be shown by the Reciprocity Principle (for a technical explanation, see ten Wolde, 1973) that the signal picked up at the bridge reflects the violin’s modification of the test signal as though it were applied directly to the bridge and listened to by a microphone positioned in place of the loudspeaker. Effectively, the violin is played backward. It absorbs sound, rather than radiating it, and the bridge, normally the input, becomes the output. If we think of the violin as a complex filter, removing or enhancing portions of the string signal until what comes out is violin sound, it happens that, under carefully specified conditions, the filter works equally well in both directions.
Imagine a beam of white light entering a prism, where it is refracted and emerges a rainbow. If this same rainbow were directed back into the prism, it would re-emerge on the first side as a beam of white light.
One of the elegant things about Weinreich’s method is a minimal disturbance to the violin, which can be tested while fully set-up, suffering only the very light contact of a phonograph needle.
Some years ago, the idea came up of using, instead of a sine wave, a signal emulating the string signal – namely, the force exerted on the bridge by the the bowed string. (I shall use the term string signal hereafter to refer to a signal proportional to this force.) Would one not then hear, listening through the bridge, the sound of the violin as though it were being normally played?
For example, imagine putting the test violin on-stage in a concert hall. A loudspeaker is placed at the back of the hall. A string signal derived from a violinist playing, let’s say, the opening bars of Bach’s Chaconne on a solid-body violin, is played over the loudspeaker. The signal from a phono cartridge resting on the violin’s bridge drives a pair of headphones. Would not a listener wearing the headphones hear just what they would hear if the headphones were connected to a microphone situated at the back of the hall and the violinist were playing Bach on-stage using the test violin?
Weinreich used a computer to synthesize the string signal for a slow three octave chromatic scale and a fast passage in thirds (Weinreich, 1996). The speaker (JBL Studio Monitor 4408) and a jig designed to hold the violin and a variable reluctance phono cartridge (Grado Elliptical ZCE + 1) were placed in an anechoic chamber. A monitor speaker was situated outside the chamber. The results were encouraging; different violins indeed produced characteristically different sounds. Even more exciting was that certain characteristics, more or less hidden when the instrument was played normally, became suddenly obvious.
Figure 1 shows a mock-up of one of several possible configurations for the reciprocal bow. A laptop computer with a sound-card generates the string signal. This signal can easily be stored on any digital medium – portable CD players and DAT machines seem like good candidates for a workshop system. The test-signal is run through an amplifier (not shown) and fed to the speaker (whose position in figure 1 is only for visual clarity – in use one would place it wherever one might naturally stand while listening to the violin being played in the normal manner.
Figures 2 and 3 show the jig a little more clearly. It is built to hold the violin securely, to allow for the violin’s easy placement and removal, and to stay out of the way acoustically. The clamp holding the neck does not touch the strings, so they remain undamped. The phono cartridge is balanced on a plane-blade resting in a V-groove cut in a relatively massive metal arm. The whole assembly can be moved back and forth so as to line up with variously positioned bridges.
The phono cartridge used here cost about $50. It is the bottom of the Grado line of pick-ups. I called Mr. Grado himself to learn more about them, and he assured me that, for my purposes, his cheapest cartridge would do as well as his most expensive.
The cartridge feeds a pre-amp. As the phono pre-amp on a normal stereo receiver introduces an equalization curve (compensating a complementary curve used in the recording process), a pre-amp with a flat frequency response was built by Colin Holmes in Weinreich’s lab. This pre-amp feeds a power amplifier, which drives either a monitor or a pair of headphones, and/or a tape recorder.
To get a good signal-to-noise ratio, one needs to play the string signal rather loudly over the speaker. For this reason, a monitor situated in another room is needed for simultaneous listening, though well-insulated headphones might do.
A few technical points: A stereo phono cartridge generates two distinct outputs, reflecting motion of the needle along two different axes. For our purposes, we have combined the two outputs into a single one, reflecting the horizontal, or side-to-side, motions of the bridge. This means that any vertical motion of the bridge is invisible to the system, and so any sound the violin radiates due to such motion will not be heard.
As each of the strings exerts force on the bridge in all three dimensions – longitudinally as well as horizontally and vertically – all three dimensions should be taken into account. It would be interesting to listen to a violin in each of these ways – making audible the contributions of each type of bridge movement. But arguably, the horizontal forces are most important, and these are what we have worked with so far.
I should point out a whole range of an instrument’s characteristics not accessible to the reciprocal bow, at least not in its present form. I refer to any effects the motion of the bridge has on the vibrating string itself. A wolf-note, for example, arises when the bridge, due to a strong body resonance, moves so vigorously that the normal Helmholtz motion of the string breaks down. Because the strings are never actually stopped when using the reciprocal bow, no wolf-note will heard – though the note at the corresponding pitch will presumably be colored by the prominent resonance which normally results in a wolf-note.
We have, to date, tested violins with the strings undamped. The presence of four continually-open strings presents some anomalies. The open strings resonate sympathetically, as they normally do, with the difference that the fingers of the violinist usually remove at least one open string from the mixture. With the reciprocal bow, the ring of the open A, for example, can be heard even during a passage apparently played on the A-string. A further complication arises when the strings of the violin being tested are not precisely in tune with the “virtual-strings” of the test-signal. Beats, corresponding to the mis-tuning, are heard whenever an open string is played. Of course the strings can easily be damped with a piece of cloth, but this creates an equally artificial lack of open-string resonance.
Figure 4 shows another configuration of the reciprocal bow. Here the string signal is produced by a violinist playing a solid-body violin fitted with a commercially-made electronic bridge (Zeta VR204). If the violinist wears headphones connected via the phono cartridge to the violin being tested, he is effectively playing that violin by remote control!
Alternatively, the violinist is allowed to hear only the neutral string signal from the solid-body violin. Thus no adjustments are made to compensate for the characteristics of any particular instrument. Test passages such as scales and short musical examples are recorded directly from the solid-body violin. This provides a library of test signals – more natural-sounding than those generated by computer, yet still repeatable with a consistency beyond the powers of even the best violinist.
Preliminary Results and Observations
Early on in our experiments with the reciprocal bow, I played (in the normal manner) a very poor violin and then a very good Stradivari. Weinreich noted that I seemed to produce about the same volume with each, though there was a vast difference in quality (favoring the Strad). Yet when played by the reciprocal bow, what was most evident was a difference in power more than quality. This suggested that poor violins may force the player to push the instrument into harsh tonal regions in order to produce an adequate amount of sound.
One of the first things noticed using computer generated string signals was the sometimes extreme difference in power and tone even very good violins exhibited from note to note. It must be remembered that when violinist plays scales, they instinctively play each note as loudly as the others, compensating for unevenness in the instrument with adjustments in bow-speed and pressure. The reciprocal bow makes no such allowances; one hears how the violin would sound if bowed in a truly even manner.
This said, some portion of the unevenness can be attributed to the violin’s directionality. Different frequencies are radiated in different directions, especially at frequencies above about 1000 hz (Weinreich, 1993). The acoustics of a normal room tend to sum up the total radiated sound for the listener. The anechoic chamber is less generous, offering only sound traveling directly from violin to listener, absorbing the rest. So the unevenness heard in an anechoic chamber demonstrates to some extent the directional properties of the violin.
For this reason, along with the fact that anechoic chambers are not readily available to violinmakers, it makes sense to use the reciprocal bow in a normal listening environment. For violinmakers, it would be most useful, I believe, in the space normally used for testing instruments. Of course, this re-introduces one of the problems of testing violins – they sound different in different rooms (while sounding the same, in principle, in any anechoic chamber).
One is struck, when using computer generated string signals, by the absolute, unnatural steadiness of the tone. Violinists, even when not using vibrato, introduce countless tiny fluctuations of pitch and intensity. While these fluctuations are essential to what we think of as violin sound, they make trying to hear the precise qualities of an individual note as difficult as trying to see the separate threads of a silk cloth that is fluttering in the wind.
But the dead even signal created by the computer makes it far easier, in my experience, to identify individual overtones. The reciprocal bow is therefore useful as a kind of ear-training tool. One develops an aural sense of how each note is a layering of overtones, and how these overtones recur from note to note, and perhaps how in the end what we hear is not so much the differences between notes as the overall spectrum from which each note is derived.
I think of the reciprocal bow as a tool less for analyzing violins than for listening to them in an analytical way. Because the violinist is replaced by a pre-recorded or computer-generated string signal, the subjective response of the violinist to the instrument is avoided. The reciprocal bow has the advantage over mechanical bowing systems of being relatively simple to build, easy to control, and flexible enough to be used for many different experiments. I believe it is useful to the violinmaker both in learning to hear in more objective way, and as a practical aid in comparing and adjusting violins.
ten Wolde, T. “On the validity and application of reciprocity in acoustical, mechano-acoustical and other systems,” Acustica, Vol 28 (1973): pp.23-32
Weinreich, G. 1996, Private Communication.
Weinreich, G. 1983, “Violin Radiativity: Concepts and measurements,” in SMAC 83: Proceedings, Stockholm Music Acoustics Conference, July 28 – August 1, Vol.II (Royal Swedish Academy of Music, Stockholm), pp.99-109.
Weinreich, G. 1993, “Radiativity Revisited: theory and experiment ten years later,” in SMAC 93, Stockholm Music Acoustics Conference, Taberg: Royal Swedish Academy of Music, No. 79 pp.432-437.
Copyright: Joseph Curtin, 1996