Lutherie Myth/Science: Damping is Bad?

Damping and Resonances

Damping is the energy dissipation properties of a material or system under cyclic stress. In lutherie the most widely available example of this is damping of string vibration. When we pluck a string we impart a certain amount of energy into the instrument. If it wasn't for damping of the vibration of the string it would continue to vibrate forever.

Having taken part in many discussions among luthiers and also having read a number of discussions in various Internet-based groups on subjects as far ranging as wood and glue selection, I have observed that many opinions expressed on these topics rely on a tacit belief about damping. This generally held belief is that damping is detrimental in musical instruments and in the parts and materials of which they are made. Although excess damping could certainly adversely affect the tone of an instrument it is also true that not enough damping would be equally damaging to the tone. From a practical perspective, the idea that less damping is better is demonstrably false. In order to understand why this is so we need to understand something about the nature of resonating systems.

Most folks that have some exposure to the lutherie literature have seen a frequency response plot for a stringed instrument. These are obtained by exciting an instrument into vibrating by using an electromechanical device connected to a signal generator. The power from the signal generator is kept constant while the frequency of oscillation is swept from low to high. The power output from the instrument is measured by a microphone or other transducers. Note that there is a simpler and quicker way to take these measurements, by tapping the instrument with a hammer and performing a frequency analysis on the output. But the description above does give a better idea of just what the plot is showing. The resulting plot shows power output at different frequencies. The plot shows a number of peaks and valleys, which correspond to the various resonances of the instrument. The instrument produces more power when excited at or near one of the resonant peaks and less power when excited at or near one of the valleys.

At first blush it may seem that an instrument would sound a whole lot better if all of these peaks and valleys in its response could be flattened out. That way, it wouldn't be louder at some frequencies and softer at others. There are instruments in which the response is quite even across the frequency spectrum. These are called synthesizers, and the qualities of their tone that we find unappealing when compared to that of acoustic instruments is in part due to the fact that their frequency response is so flat. The peaks and valleys of the frequency response of a guitar or violin are part of what gives those instruments their characteristic natural tone. And we consider this tone to be "natural" because all physical entities that vibrate do so to some extent with a "peaky" response.

The peaks and valleys of the frequency response plot of a real stringed instrument are kind of jagged looking. This is because the response is the result of lots of different resonances which overlay each other. If we were to take a look at an individual resonance, its power over frequency plot would be sinusoidal. Each resonance can be fully described by three qualities: the frequency of the resonance, the amplitude (height) of its peak and the width of its peak. The frequency of the resonance is the frequency at the very center of the peak, that is, at its highest point.

In mechanical vibrating systems, the height of a resonant peak and the width of the peak are related to damping. The more damping present, the lower and wider the peak. The less damping, the higher and thinner the peak will be. To understand why damping is important to the tone of an instrument it is necessary to understand that a resonant peak can be driven by frequencies other than the center frequency of the peak. If you consider the plot of a low, wide resonant peak you can see that this resonance will be excited by frequencies both lower and higher than the center frequency of the peak. Amplitude drops off on either side of the center frequency of course. It drops off quickly for high narrow peaks and less quickly for low wide peaks. What this means in practical terms for a musical instrument is that wide resonant peaks in the instrument's response will radiate audible sound from a wide band of frequencies. Because the width of a resonant peak is related to the amount of damping at the frequency of the peak, damping is necessary for the resonance to be able to respond to a wide band of frequencies. This is an extremely important concept.

But too much damping can be a problem. Not only does damping increase the width of a resonant peak, it also decreases the height of the peak. The lower the height of the peak the less sound it radiates. At some level a peak would be so low that it would not contribute much to the sound at all.

On the other hand, too little damping can be a problem as well. We've already discussed that the peakiness of the response of a stringed instrument is generally a good thing, because it makes for a more natural-sounding tone from the instrument. But what if the response were to be made even more peaky, reducing the width and increasing the height of the peaks? This can be accomplished by reducing the amount of damping in the system. Doing so makes the peaks higher and thinner. But there are problems with high, thin resonant peaks. Since they cannot be driven by a wide range of frequencies, the sound emanating from such an instrument could have a number of audibly obvious "holes" in its response, with some notes sounding duller than others, other notes sounding shriller than others, some loud and some soft. So what we generally refer to as evenness of response could be adversely affected by too little damping. Another problem is that high thin resonant peaks tend to ring at the center frequency of the peak, and this could result in the kinds of howls and screeches normally associated with feedback from amplified instruments.

So, too much damping or too little damping can adversely affect the tone of an instrument. But this raises the questions of just how much is too much and just how much is too little. Unfortunately there are no simple answers to these questions. And the fact that there are no simple answers to these questions should inform consideration of any efforts to improve the sound of an instrument by either increasing or (more commonly) decreasing damping.

There are methods by which folks can experiment with extremes in damping. Most are costly and time-consuming and would yield results that are not conclusive, but there are tools available for engineering in the realm of digital signal processing that can be used to get some idea of the general effect of both high and low damping on musical instruments. Unfortunately such tools are not generally available, and they are not necessarily easy to use by non-technical folks either. But let me take a minute to explain what they are and how they would work in such experimentation, because this explanation is itself useful in gaining an understanding of how damping affects instrument tone.

A digital filter array is a series of digital filters, filters implemented as computer processors that work in the digital domain. They work a lot like audio parametric equalizers. The behavior of each filter can be specified by values for its center frequency, bandwidth and amplitude. Using such an array, the frequency response profile of a stringed instrument can easily be modelled and quickly modified. If you were to feed such an array an audio signal taken, say, from the bridge of a guitar, the resulting output would sound very much like that of a guitar. This is in fact just how audio processing devices like those made by Fishman work. Those devices have a switch that provides selection of the "sound" of a variety of different guitars. Each switch position selects a frequency response profile which is used to process the signal from the guitar's bridge transducer.

Although these consumer processors provide for selection of different types of guitars, the full blown engineering versions of these processors provide full control of each filter in the array. If you were to set these up to model the frequency profile of a guitar it would be a simple matter to adjust the bandwidth and amplitude of all the filters at the same time to hear what the general affect of increased damping would sound like. And these parameters could also be changed at the same time to give you an idea of the general tonal effect of decreased damping. Within a certain range the different tones would be pleasing, but too much damping would result in tone that was too even, too unnatural sounding and too quiet, and too little damping would result in tone that was uneven in timbre and volume from note to note and had a harsh ringing at certain notes.

Where Does Damping Come From?

Damping in Strings

Consider a plucked guitar string as we did before. Once the string is plucked it would vibrate forever unless its oscillation was somehow damped. There are various sources of damping, but only two general cases. String energy is either lost (to the end of keeping the string vibrating) to the production of sound or is lost to friction and converted to heat. The vibrating plucked string loses some of its energy directly to the air. As it vibrates back and forth it pushes the air surrounding it around. Given the small surface area of the string this is not the best way to make sound, and in fact the sound produced in this manner is quite small. Some energy is also lost through the anchor points of the string, the nut and the bridge. If these, and the rest of the instrument, were both very massive and very stiff, not much energy would be lost this way. But it is a good thing some energy is lost this way, because this is the mechanism by which the string drives the rest of the instrument to make sound. Of course not all the energy lost to the bridge ends up as sound energy. There are damping losses associated with the whole rest of the guitar as well as the air inside it.

A little side discussion. Just as it may at first blush seem that decreasing damping in an instrument would make it sound better, so it may also seem that increasing the amount of string energy "lost" to driving the bridge and the rest of the instrument would be beneficial. But this is another case where making such a change does not necessarily result in a better instrument, just a different instrument. Solid body electric guitars don't lose much string energy to the bridge. As a consequence they have a distinctive sound and are very long in sustain. banjos on the other hand dump energy from the strings very easily to the rest of the instrument, and their characteristic sound is in large part related to that.

Back to the ways in which a guitar string loses energy. We've already discussed energy lost by directly moving air around and energy lost by moving the bridge around. The vibrating string also loses energy to internal damping. The bending and stretching of the string convert some amount of energy into heat, resulting in a loss of vibrational energy. Now here it may seem that if it were possible to decrease this internal damping that it could only be a good thing. This may be true when it comes to the strings of plucked steel string instruments, although as a practical matter accomplishing this would be pretty tough to do. Consider also Nylon strung instruments, like classical guitars. The strings used in these instruments have a lot more internal damping than do the strings of steel strung instruments. Do these instruments sound worse than steel strung instruments as a consequence? Most folks would consider them to sound different, but not worse.

Let us also consider the strings of bowed instruments for a minute. Decreasing internal damping of bowed strings is not a good thing. In fact, all wound violin strings have damping added to the strings. Without it, the strings would not start readily when bowed. Double bass players know about this, because this instrument is played both arco and pizzicato. Bass strings are available for playing arco, and these are the strings most orchestral players use. Jazz and bluegrass players use strings with no internal damping because these sustain longer when played pizz. These strings cannot be bowed - it is too difficult to reliably get them to start vibrating when they are bowed. String manufacturers also generally make hybrid strings which can be bowed but also provide better pizz sustain than do orchestral strings.

Damping in Wood

What most luthiers would like to see is a collection of accurate damping values for various wood species and a simple relationship between damping value and some recognizable quality of instrument tone. Unfortunately such a thing is not available.

There is some good work which shows typical relative damping values for the wood species commonly used in lutherie. Haines¹ did some early work in this area, providing damping values using the logarithmic decrement method. As is usually the case with wood properties, there are a wide range of values for damping within a species and also a wide range between species. To make matters worse, measuring damping in wood is not a straight forward process. An excellent treatment of the subject of measuring damping in thin sheet materials was done by McIntyre and Woodhouse², and this work also points out one of the many difficulties in using wood damping values as a guide to wood selection for lutherie applications. That is that damping measurement must be performed using uniformly sized samples, and measurements must be relative to standard modes of vibration and at whatever frequency they naturally occur. Although there are many informal efforts at cataloging damping qualities on a per-species basis, all that I am aware of do not maintain the rigor in this area necessary to yield useful comparative information.

And such data, if it were to exist, would only indicate the damping properties of the material. There are damping properties that have to do with the geometry of the piece as well. Collecting this data in any meaningful way is further complicated by the fact that wood is anisotropic and will therefore yield different values depending on the direction of the deflection, even in the same piece.

Let me include here another bit of information from the violin world. There is a lot of research lately into using balsa and other very light weight wood in the construction of violin family instruments. Balsa has very high material damping and so would seem to be a poor choice of material for a musical instrument. But violins are bowed instruments and sustain of plucked notes is not an issue - bowing provides a constant source of energy into the system. Some of these experimental instruments sound very good, and they posses a very desirable quality in that they can be pushed very hard before they "bottom out." So as is the case with bowed instrument strings, radically increased damping in the materials of violin family instruments may actually be a good thing.

Considering plucked instruments, it may seem that choosing materials for construction that have low damping would help to increase sustain. There is no reliable data on this and no reliable data even on the desirability of this. Other material properties such as stiffness and mass affect the tone of an instrument, so experiments using materials with different damping values would have to hold these other properties constant in order to attribute any perceived difference to material damping alone. Such formal experiments have not been performed to the best of my knowledge.

Damping in Glue

Glue used in lutherie is chosen for a number of different properties such as drying speed, shelf life and open time. A number of luthiers also consider that damping may be important when choosing glue as well. I know of no formal studies that attempt to measure damping in glue and also know of no studies that attempt to quantify perceived goodness of tone based on the glue used in construction. Such tests would be time-consuming and costly to perform.

My suspicion is that performing these experiments would not be an efficient use of resources. Glue makes up an extremely small fraction of the mass of a finished instrument and, based simply on hardness data, all glue typically used in lutherie is very likely to posses substantially lower damping values than the wood which comprises the bulk of the instrument. Both of these factors would likely render any measured difference in damping among wood glues to be irrelevant to perceived tonal differences in a finished instrument.

Damping in Finish

As with other materials used in lutherie, finishing materials likely posses different damping values. The only formal experimentation I am aware of was performed by Howard Stephens³. Although this study involved only a few different materials, it concluded that there was no statistical difference in vibrational properties among the finishes tested. I know of no formal testing that shows any correlation with perceived tonal differences and the damping qualities of the finish. It is a widely held belief that violins sound better when finished than they do when strung up and played "in the white" (unfinished), due to increased damping of the elastic varnish used on those instruments. Again, no formal blind studies have been performed, but if the belief were to be substantiated it would be another indication that added damping is of value in bowed instruments.

Common belief for plucked instruments is that thin, hard finishes sound better than thick and soft finishes. Here again, no formal blind listening evaluations have substantiated this. And if such experimental work were performed it would have to hold stiffness and mass constant, as these material properties could also affect instrument tone.

Summary

There are many examples of increases in damping improving playability and tone in bowed instruments. For plucked instruments this is not the case, and so decreasing damping in the materials used in construction of these instruments may well improve those instruments, although it is likely that there is a limit above which decreased material damping would be detrimental. Formal research in this area is sparse. Damping plays an important role in the sound produced by all stringed instruments. Efforts to answer the question of how much is optimal have not yet been very illuminating.

1. Haines, D. W. "On musical instrument wood"
Catgut Acoust. Soc. Newsletter 31, 1979, pp. 23-32.

2. McIntyre, M.E., Woodhouse, J. "ON MEASURING THE ELASTIC AND DAMPING CONSTANTS OF ORTHOTROPIC SHEET MATERIALS"
Acra meroll. Vol. 36, No. 6, 1988, pp. 1397-1416,

3. Stephens, H.. "The Effect of Finishes on the Vibration Properties of Spruce Guitar Soundboard Wood"
Savart Journal, nov. 2015. Available at: http://www.savartjournal.org/index.php/sj/article/view/25/