LISTEN TO THE INNER VOICE

Normally, acoustic measurements are taken from outside the instrument – but the internal vibrations can reveal even more. Colin Gough presents a method for listening inside the soundbox and demonstrates what it can tell us about the sound

Measurement set-up in the corner of the author’s research space

ALL PHOTOS AND IMAGES COLIN GOUGH

In this article we describe how the acoustic characteristics of any hollow-bodied stringed instrument can be investigated by simply tapping the bridge with a very light hammer, and measuring the sound radiated inside, rather than outside, its hollow body.

The inner cavities of the violin, viola, cello and double bass provide their own, reproducible, micro concert hall or recording studio, which travels around with the instrument itself. In addition, for any given class of instrument, the cavities are very similar in size and shape. The acoustic characteristics and differences between instruments can therefore be measured in a well-defined acoustic environment, avoiding the usual complications from the resonant acoustics of the surrounding space.

In addition to being a potentially valuable workshop facility, internal cavity sound measurements provide a way of measuring the intrinsic acoustic properties of an instrument. This includes the coupling of the vibrating plates to the internal cavity air modes, which is directly related to the excitation of radiated sound. We also describe a low-cost, high-performance facility for making such measurements. A computer and freely downloadable software can then be used to record, identify and display the acoustic characteristics of hollow-bodied instruments of any size – effectively determining the quality of the sound both outside and inside the cavity.

MEASUREMENT SET-UP

For our measurements we use a pair of sub-miniature, omnidirectional, electret microphones, with a useful frequency response extending to around 10kHz. We modify one microphone to record the frequency-dependent spectrum of the energy transferred to the instrument by the hammer tap, while the second measures the sound radiated inside the hollow cavity by the excited vibrations of the body shell.

The microphones are mass-produced in China, probably in their millions, for audio device applications, and cost less than a cup of coffee. They are simple two-terminal condenser microphones, using a permanently polarised dielectric to charge the internal diaphragm responding to the sound pressure. They also incorporate an internal amplifier, requiring a small external biasing current, which together provides the stereo hammer and microphone voltage line-inputs to an inexpensive, constantgain Behringer UCA202 stereo audio unit.

The audio unit is USB-connected to a laptop or computer with freely downloadable computer software used to record, process, store and display the intensity of the sound of an instrument at its acoustic centre, plotted as a function of excitation frequency derived from the hammer tap on the bridge.

MEASUREMENTS

Figure 1 shows the very simple compact experimental set-up, with the 5mm-diameter internal microphone removed from inside the cavity to illustrate its mounting. The microphone is attached to the end of a plastic cable tie, bent into a shape that can be passed through the f-holes without touching the inner edge of the central island area. This can then be supported externally, or temporarily fixed with a temporary adhesive like Blu-Tack to the outside edges of the instrument waist, with no damage to the instrument and scarcely any influence on the measured characteristics.

For quick and easy, routine, reproducible internal cavity measurements, we insert the microphone centrally through the f-holes, just a few millimetres in front of the bridge, opposite the f-hole notches, close to the acoustic centre of the cavity. For our purposes, the acoustic centre is defined as the node (zero acoustic pressure) of the A1 internal air mode, with air bouncing backwards and forwards along the length of the cavity. Moving the microphone a few millimetres to either side of the acoustic centre reveals a rather narrow resonance from this mode at around 480Hz, usually located between the strongly radiating B1- and B1+ modes. However, in contrast to the strong radiating A0 f-hole air resonance just below 300Hz, the A1 is acoustically unimportant; it cannot radiate strongly, as its amplitude is close to zero at the f-hole notches. The height between the top and back plates is not critical as, below around 3kHz for the violin, both the vibrational modes of the plates and the air inside the cavity are effectively two-dimensional.

FIGURE 1 Close-up of the measurement set-up, with the 5mm-diameter internal microphone removed from inside the cavity,

We then attach a second 10mm-diameter microphone to the end of a similar cable tie, to form a hand-held, pendulum supported, or flexural beam-mounted hammer, with the latter version illustrated above. This is used to tap the top bass-side corner of the bridge gently. This microphone is converted into an accelerometer instead of a microphone by forming a shallow hemispherical endcap, made from epoxy resin, over its front face. This stops sound from entering the device and forms the soft head of the hammer used to tap the bridge.

The acceleration of the hammer head as it bounces on and off the bridge now deflects the edge-supported recording internal diaphragm, in just the same way that sound pressure would otherwise have done. The acceleration of the hammer head measured over the very short time it takes to bounce on and off the bridge (only a few hundred microseconds), multiplied by its mass, then determines the total amount of energy transferred to the violin by the single tap as a function of frequency. A significant fraction of this energy excites the plate vibrations, which radiate sound equally outwards and inwards into the cavity, which is what we measure.

An easy-to-make ‘dongle’ between the outputs of the two electret devices and a Behringer UCA202 stereo amplifier unit provides the biasing current for the two devices, while two capacitors decouple the audio signals from the associated DC voltages across the devices. The Behringer amplifier is USBconnected to a laptop or dedicated older computer.

The software in the attached laptop or computer then does all the necessary analysis and processing of the stereo signals, from the short hammer tap and much longer ringing sound inside the cavity (a significant fraction of a second), to produce an acoustic spectrum for the instrument. This is what we will be plotting for all four instruments of the violin family in the following sections.

Details on how to set up your own measurement system are described in the Trade Secrets section of this issue. Additional information can also be downloaded at bit.ly/4b7WDii along with several related publications and notes for further guidance. The software used in the following examples was developed specifically for use by luthiers by George Stoppani, the Manchester-based luthier, gut string maker, historian of stringed instruments, acoustician and software expert. A slightly more user-friendly, freely downloadable version using standard commercial software, along with detailed guidance on its use, has recently been developed by Chris Rogers, professor of engineering at Tufts University in Boston, MA, US, who has a strong interest in violin acoustics.

We now illustrate typical internal cavity measurements for all four instruments of the violin family to demonstrate their value, validity and versatility.

THE VIOLIN Our first example (figure 2) shows a superposition of internal cavity sound measurements for a fine-sounding 2011 ‘tonally informed’ copy of the 1715 ‘Titian’ Stradivari by George Stoppani, first with damped (blue) and then undamped (red) strings. The measurements are plotted up to around 700Hz. Both plots show the familiar B0, A0, CBR, B1- and B1+ signature mode resonances, observed in radiation measurements on almost all high-quality violins. The characteristics are very similar to those published in many previous articles in The Strad. For well-understood acoustic reasons, the amplitude of the A0 mode resonance relative to those of the B1- and B1+ modes will always be around six decibels higher in internal cavity than in radiation measurements. This is a virtue, not a problem.

Leaving the open strings free to vibrate, as when normally played, introduces additional narrow resonances from all the sympathetically excited string partials (harmonics) indicated as g1, g2, g3, etc for the G string and likewise for the other strings.

Similar string resonances can be identified up to around 3.5kHz, above which they begin to disappear.

FIGURE 2 Internal cavity sound measurements for a copy of the 1715 ‘Titian’ Stradivari violin

FIGURE 3 Anti-resonances displayed in the bridge and ‘island’ areas of the violin

A LMOST ALL MODER N MEASUR EMENTS OF THE ACOUSTIC PROPERTIES OF AN INSTRUMENT ARE MADE WITH DA MPED STRINGS

This is illustrated in figure 2, plotted over an expanded frequency range in the so-called ‘island-bridge hill’ frequency range from around 2.6 to 3.3kHz. For clarity, the measurements with open strings have been shifted downwards by 20 decibels. The plots illustrate the continued existence of largely anti-resonance dips from the partials of all four strings over the plotted frequency range. This confirms the ability and validity of internal cavity sound measurements to examine important acoustical properties well into the kilohertz frequency range.

The anti-resonances of the strings can easily be understood. When a string partial is excited, less of the available energy from the original tap on the bridge can be used to excite the acoustically radiating vibrating plates. This accounts for the dips in the radiated energy inside the cavity and, by inference, outside as well. The same will be true whenever other body modes are excited, such as the rocking frequency of the bridge and vibrating modes of the island area between the f-holes.

Such resonances may well be responsible for the tentatively ascribed rather broad minima in the overall response, as illustrated in figure 3. The identification of which minima are associated with a particular vibrational mode of the bridge or island area clearly remains a challenge. The assumed rocking frequency resonance of the bridge was initially proposed as a candidate for the dip at around 3kHz, which is observed in almost all types of measurements on the violin. However, this has now been eliminated as, somewhat surprisingly, removing the rocking mode by wedging the side slots of the bridge makes no significant difference to the observed spectrum.

Almost all modern measurements of the acoustic properties of an instrument are made with damped strings, despite their potentially important contribution to the long ringing-time sound of an instrument. In addition, the excitation of such resonances, when using even the smallest amount of vibrato, strongly influences the perceived responsiveness and playability of an instrument. This is why violinists love to play the viola, because of its longer ringing sound from the vibrating strings, which is even more apparent when playing and listening to the cello.

Top soloists, commenting on the sound of great Cremonese instruments, invariably make comments similar to those made by Tasmin Little in an inspiring BBC broadcast. After demonstrating the sound of the 1722 ‘Joachim, Elman’ Stradivari in the old J&A Beare showroom, she remarks:

It has an incredible ring under my ear. If it wasn’t for the wonderful sound, it would be almost deafening. It is fantastically exciting and very vibrant. It’s alive; there’s a real spirit in there that’s absolutely desperate to get out.

If we are ever to be able to correlate comments like those above with measurable features of the acoustic spectrum, then I believe the last thing we should be doing is damping the strings and averaging measurements over many directions and frequencies. This removes all the complexities of the acoustic spectrum that give each instrument its individual characteristic sound. Internal cavity sound measurements with freely vibrating strings provide a very quick and easy way to avoid doing so, while maintaining the maximum useful information that any single measurement can provide about an instrument.

THE VIOLA

Figure 4 plots a superposition of internal cavity sound intensity measurements for 25 violas made for the ‘Obialto’ viola project at the time of the 2017 Oberlin Violin Makers Workshop. All the instruments were made using the same outline form, although makers were free to choose the materials used, the plate graduations, arching profiles, etc. The measurements were made in a single afternoon and early evening session, using a hand-held hammer (rather than a pendulum-supported one), illustrating how easily and quickly such measurements can be taken.

Not surprisingly, the measurements exhibit generic acoustic characteristics very similar to those of a violin, but with all the resonant modes scaled downwards in frequency, as expected from the violas’ increased size. The characteristics of individual instruments were compared with the average of all the instruments and potentially used to correlate differences in their acoustic spectrum with differences in the quality of their sounds.

FIGURE 4 Internal cavity sound intensity measurements for 25 violas

THE CELLO

The next example, illustrated in figure 5, demonstrates the use of internal cavity measurements to investigate, and hopefully understand, interesting acoustical features of much larger instruments such as the cello and double bass. Measurements can be made with the same experimental set-up, apart from using a longer strip to support the internal microphone. The plotted characteristics are for a cello held upright, lightly hand-held around the neck joint, with undamped strings. When resting on a wooden floor (upper green plot), it had a bad wolf note almost certainly associated with the strongly excited B1- mode resonance. Remarkably, when resting on an intermediate stone block (lower red plot, shifted down by 20 decibels for easy comparison), the wolf note was entirely eliminated.

FIGURE 5 Internal cavity sound intensity measurements for a cello held upright with undamped strings

ALL FIGURES COLIN GOUGH

REMOV ING THE ROCK ING MODE BY W EDGING THE SIDE SLOTS OF THE BR IDGE MAKES NO SIGNIFICA NT DIFFER ENCE TO THE OBSERV ED SPECTRUM

The measurements were made to investigate what changes in the acoustic characteristics were responsible for this effect. Again we note the large influence of the vibrating strings on the instrument’s characteristics, with the frequencies of the string partials indicated beneath the frequency scale. The ripples on either side of the string resonances are an artefact of the digital processing of the measurements and analysis. These arise for narrow, ringing string resonances, which require significantly higher rates and lengths of data acquisition than used in these measurements.

Supporting the instrument on a solid stone block rather than the wooden floor clearly introduces an additional vibrational mode as evident in the lower plot. This significantly reduces the amplitude and splits the B1- resonance responsible for the wolf note. Measurements on several other cellos, but not all, have shown similar effects in their low-frequency response. Further research is required to understand fully such features of great importance for players. Internal cavity measurements are ideal for this purpose, and for makers wishing to solve wolf note problems.

THE DOUBLE BASS

For the cello and double bass, it is extremely difficult to make conventional high-quality radiation measurements free from complications from the surrounding acoustic. In contrast, figure 6 shows some typical internal sound measurements for a double bass free of such complications.

The measurements were again made on an upright, handsupported instrument resting with its endpin on a solid surface. This time measurements were taken with damped strings, first with a rubber endcap between the spike and hard floor, then with the endpin resting directly on the hard floor with two different spike lengths. The emphasised horizontal lines represent equal sound intensities in all three plots.

We observe an A0 resonance at around 64Hz and a strong B1- mode around 110Hz, with a smaller amplitude mode at a little lower frequency when the bass is supported on the rubber end-stop. However, when the bass is resting directly on its endpin, the latter mode is significantly decreased in frequency and the initial B1- mode is significantly decreased in amplitude relative to the A0 mode. When the length of the endpin was increased, the characteristics over the whole range of frequencies remained largely unchanged. Although we have yet to understand such effects fully, the measurements strongly suggest they are unlikely to be associated with the length of the endpin or its material properties. Also, as for the cello, such features may well be related to a proposed bouncing mode of the body shell itself resting on its endpin.

FIGURE 6 Internal cavity sound intensity measurements for a an upright, hand-supported double bass with its endpin on a solid surface

FIGURE 6 COLIN GOUGH

Playing the copy of the ‘Titian’ Stradivari used in these experiments

WHEN THE LENGTH OF THE DOUBLE BASS ENDPIN WAS INCR EASED, THE CHA R ACTERISTICS OVER THE R ANGE OF FR EQUENCIES REMAINED L ARGELY UNCH A NGED

CONCLUSION We hope that makers will find the above examples are of sufficient interest to consider setting up an inexpensive measurement facility in a small corner of their workshop. This can be used at all critical stages in the making, final adjustments and restoration of any classical, historic or non-Western, hollow-bodied stringed instrument. As we have illustrated, such measurements can help identify the cause and potentially help solve problems like a wolf note, in addition to problems of tonal balance at both low and high frequencies. They can also be easily made when assessing the perceived tonal quality of different instruments. But, as argued above, we believe that attempts to correlate the sound of an instrument with its acoustical properties should always be made with the open strings left free to vibrate. For myself, as both a player and acoustician, internal cavity sound measurements have been invaluable in advancing my understanding of all instruments of the violin family, as I hope they will also be for others.