Discussion of the acoustic influence of varnish on the sound of a bowed stringed instrument. Methodology and terms for acoustic quality assessment of primers and varnishes.
Even more drastic than the quality variations in wood are the acoustic differences between different wood treatments (primers and varnishes). With the wrong primer or varnish, an instrument that is otherwise very well made can sound very poor. This is due primarily to the strong damping effect of many substances and formulations. On the other hand, good varnish can go a long way towards refining the sound of an instrument that is well made by affecting its modulability and response.
In view of the great potential that varnish has when it comes to influencing the sound of an instrument, the MARTIN SCHLESKE MASTER STUDIO FOR VIOLINMAKING has studied the acoustic effects of over 300 different varnish treatments in recent years in the aim of developing new formulations and refining existing ones.
By making measurements on primed and varnished test strips, it is possible to determine the extent to which individual treatments (formulations, individual substances, application techniques, absorption depth, etc.) influence the acoustically relevant parameters of wood. This approach allows us to draw conclusions about the benefit (or disadvantage) of a particular treatment in terms of the sound of the instrument. This has allowed us to optimize our own varnish and treatment process.
As a basic rule, any damping of the wood is to be avoided. In the time domain, damping is inversely proportional to the "reverberation time" of the vibrations. A heavily damped vibration will sound dull due to its shorter "reverberation time". In the frequency domain, the damping is proportional to the width of the resonance peak ("half-power bandwidth"). A resonance with little damping will have a steep, high resonance peak in the frequency domain while a heavily damped resonance will have a wide, flat resonance peak.
The following figures shows a sample result from an acoustic varnish analysis of a test strip. What we see is the transfer function a/F (f) , i.e. acceleration a vs. force F as a function of frequency f. The resonance peak of the first bending mode of vibration is clearly evident. A comparison of this resonance peak before vs. after the treatment reveals the effect (in this case unfavorable) of the varnish that was applied: Significant damping has occurred.
Investigation of the acoustic effect of a varnish through measurement of the transfer function of a test strip with free-free boundary conditions and evaluation of the resonance of the first bending mode of vibration. Measurement on the untreated strip: Black; Measurement on the varnished strip: Red.
Based on the change in the resonance peak, it is clear that the varnish under test here has an acoustically undesirable effect:
The damping of the resonance has increased considerably. This is evidenced by the fact that the resonance peak of the varnished strip has the same level dropoff but a significantly greater width ("half-power bandwidth").
The speed of sound decreased. This is evidenced by the fact that the resonant frequency of the varnished strip is lower.
There is no way that we would want to use this varnish on a violin.
If this varnish had been used on a white instrument and not just a test strip, it would have some undesirable consequences for the sound: Additional damping produces a reduction in the acoustic efficiency of the instrument's resonances. As a result, the dynamic range of the instrument as well as its projection and volume would be reduced.
Since an increase in the damping due to the primer and/or varnish also reduces the level differences between the resonance peaks and valleys and increases the bandwidth of the individual resonances, an increase in damping will cause the vibrato sensitivity as well as the modulability (variety of tonal colors) of the instrument to be reduced (for more theoretical details, see the article Schleske, M.: "Empirical Tools in Contemporary Violin Making: Part II: Psychoacoustic Analysis and Use of Acoustical Tools". CAS Journal Vol. 4, No.5 (Series II), Nov 2002. (See publications)
Numerous measurements made in the MARTIN SCHLESKE MASTER STUDIO FOR VIOLINMAKING have revealed large differences in the damping behavior of different wood treatments using primer and varnish. The spread is between 0.75 and 3.0 compared to untreated wood. In other words, some formulations produce an undamping (!) of the wood by up to 25%, whereas other substances triple the damping of the wood (!). Clearly, the choice of varnish can determine the success or failure of a new instrument.
Besides the change in damping due to the varnish, the change in the speed of sound is also significant. The speed of sound is determined by the ratio of Young's modulus to the density. In conjunction with the geometric dimensions of the structure, Young's modulus determines the stiffness. Wood treatments (primer, varnish, etc.) can affect the Young's modulus of the wood by either strengthening or weakening the grain structure.
In actual practice, it is common to ask whether the selected treatment tends to produce an (undesirable) increase in the vibrating mass since the substance is introduced into the vessels of the wood structure as a "load" material or whether the treatment actually results in a (desirable) increase in the Young's modulus by strengthening the grain structure. The varnish analyses performed by the MARTIN SCHLESKE MASTER STUDIO FOR VIOLINMAKING provide a quantitative answer to these questions.
An increase in the speed of sound indicates that the "strengthening" influence of the treatment has predominated over the "loading" influence. A wood treatment should never result in a decrease in the speed of sound since this would mean that the plate would need thicker graduation (to produce the same resonances) than would be the case without varnish. Certain (unfavorable) varnishes produce this effect in terms of the thickness graduation of the plates. On the other hand, we have investigated primers and varnishes which make it possible to use thinner graduations of the plates because the subsequent wood treatment will shift the resonances towards higher frequencies (due to the positive effect of the treatment on the speed of sound).
The MARTIN SCHLESKE MASTER STUDIO FOR VIOLINMAKING offers a service that violinmakers can use to determine the acoustic quality of individual primers and varnishes. Measurements are made on test strips and provide a "before vs. after" comparison. The results provide the violinmaker with quantitative data on how the chosen treatment (primer, varnish) affects the acoustic properties of the wood: The change in the resonance damping and the speed of sound are assessed in quantitative terms.
Our procedures are designed to guarantee complete confidentiality since the treatment (primer, varnish, etc.) used by the client will remain unknown (even to us): As the first step, the client receives untreated test strips which have already undergone acoustic measurement. The violinmaker then applies his or her treatment to these strips. There is no need to reveal any details about the formulation which is to undergo acoustic analysis. Following a set drying interval, the violinmaker returns the treated strips to our laboratory for acoustic measurement and evaluation.
Individual Tests
Individual tests provide information about the effect of individual substances or formulations on the acoustic properties of the wood and reveal in quantitative terms the acoustic benefit (or disadvantage) of the treatment.
The following diagram shows an example: We investigated many different resin solutions in terms of their influence on the speed of sound and damping of wood. Depending on the actual resin, we found considerable variations (internal research result).
Influence of different resin solutions on the speed of sound (x axis) and damping (y axis) of spruce wood strips (thickness: 3.0 mm; grain orientation transverse to the longitudinal direction of the strip) based on measurement of the first bending eigenfrequency with free-free boundary conditions. Comparison of the varnished wood strips (drying time: 9 years) with untreated wood..
Unless otherwise stated, the resins were dissolved with a mass ratio of 10:2 (= solvent:resin). The resins labeled in the caption with [T] were dissolved in turpentine oil. Those labeled with [S] were dissolved in spirit of wine. The changes in the speed of sound and damping were measured after a drying interval of nine years. Spruce wood strips were used as the support material with a grain orientation transverse to the longitudinal direction of the strip and a thickness of 3.0 mm. (With thinner strips, the acoustic influence of the resin solutions is even greater.)
The increase in the speed of sound is plotted on the horizontal axis labeled Δc/c*100% as a percentage compared to the untreated wood. These values increase the farther to the right the data points are located. The increase in the speed of sound varies between 0% and 20%. The resins and other substances listed in the caption are arranged according to the increase in the speed of sound which they produced. The leader is copaiba balsam (+18.8% compared to untreated wood).
The increase in the damping is plotted on the vertical axis labeled Δη/η*100% . Here, the range is between +40% (increase in damping compared to untreated wood) and –40% (decrease in damping compared to untreated wood). The further the data points are located below the zero line on the damping axis, the greater the "undamping" effect. The further they are located above the zero line, the greater the damping effect.
The blue group of data points is characterized by a significant increase in the speed of sound with a relatively small change in the damping. The green group of data points is characterized by a somewhat smaller increase in the speed of sound with a simultaneous but greater "undamping" effect. The red data group exhibits a considerable increase in the damping. The unfilled data points in the region of the zero lines exhibit a small change in the acoustic properties compared to untreated wood.
Even though the substances represented here do not include any composite materials (varnish formulations based on different substances), we already note some sizeable differences from resin to resin. Another interesting result is the fact that based on the effect of the individual substances, it is not possible to predict the effect of a varnish made of a combination of substances. Varnish formulations behave differently in acoustic terms compared to their individual components.
Test series
Test series (Measurement of multiple samples) are useful when the client would like to optimize the parameters that are most important to the acoustic success of a varnish type. These parameter studies are useful in answering the following types of questions:
- The most acoustically favorable combination ratio for a formulation
- The most acoustically favorable concentration
- The most acoustically favorable absorption depth for a substance
- The most acoustically favorable coating thickness
- The most acoustically favorable application technique
- The acoustic differences that result for different thicknesses of the plate graduation
- The most acoustically favorable structure (e.g. are any acoustically detrimental intermediate steps or coatings included?)
- Variations in the varnish over time (long-term acoustic influence)
- Research work at the MARTIN SCHLESKE MASTER STUDIO FOR VIOLINMAKING has provided some answers to this type of question, including the following:
- Certain varnishes might be acoustically superior to other varnishes on thin strips of wood (2.0 mm) but not on thicker strips (3.0 mm). This means that the acoustic benefit of a given varnish type can vary considerably with the thickness graduation of the instrument.
- With some varnish types, the first coats bring a clear acoustic benefit while subsequent coats of the same varnish work to cancel out the benefit. On the other hand, we have also seen varnish types where the first coats offer only a fairly small acoustic benefit while additional coats increase the acoustic benefit in a step-wise manner.
- Some primers have a clear acoustic benefit when applied on the surface but begin to ruin the wood in acoustic terms starting at a certain penetration depth. With this type of primer, an appropriate sealer is critical.
- Certain intermediate coatings within a varnish structure can be very detrimental. The primer itself might have a positive acoustic effect. However, a subsequent intermediate coating applied prior to the actual varnish layers negated this positive effect.
These are only a few of the results of our extensive studies in this area. These observations are examples reflecting some of our (internal) parameter studies which have shown the importance of understanding and properly manipulating the parameters of violin varnish that are relevant in terms of the acoustic behavior. The actual formula represents only a small part of a bigger picture. For violinmakers, optimization of these parameters is an important area to master if one hopes to build instruments that sound good. A lack of understanding can damage the sound of the instrument (or miss out on the potential of a good varnish).
MEASUREMENT TECHNIQUE
The measurement technique used in the MARTIN SCHLESKE MASTER STUDIO FOR VIOLINMAKING for varnish analysis is the resonance method which is an established technique in the field of structure-borne sound measurement. As shown in the next figure, the test strips are electromagnetically excited to produce vibrations. The vibration response is recorded with a microphone and evaluated.
Measurement technique for determining the acoustic influence of violin varnish.
The measurements described above provide a quantitative representation of the change in the following acoustically significant quantities as a result of the violinmaker's wood treatment:
- Speed of sound
- Resonance damping
- Vibrating mass
These quantities are the material properties which are most critical in determining the sound of the instrument. As we have seen, they can be modified (either positively or negatively) to a considerable extent in some cases depending on the type of primer and varnish.
For the theoretical background for this article, see:
Schleske, M.: "On the Acoustical Properties of Violin Varnish". CAS Journal Vol.3, No.6, (Series II), November 1998. (See publications)
Using a stereomicroscope on a cello by Stradivari. The stereomicroscope allows us to examine details of the wood anatomy and the varnish structure.