29 January 2009

Singing & Dry Mouth: Things You Might Not Have Tried


M    y mouth gets incredibly dry when I sing. Are there any new things to try out there? A gel I tried once felt greasy in my mouth, so that was the end of that. And sprays I’ve tried only last about 10 minutes.”
  —  Anonymous email to CMT.
T he short duration of action you experienced with the sprays isn’t unusual. You need to remember that any extraneous material in the mouth tends to induce reflexive/habitual motions (of tongue, etc.) to remove it and clear it out. Products that would have a longer duration of action for regular people just sitting around and not talking or singing may not last so long for you during a vocal performance. Years ago, I used to take care of cancer patients, both immediately after radiation treatment and later in palliative care, so I do know something about the strengths and limitations of the ‘artificial saliva’ products that are available.

S ubjective dry mouth sensation is known as xerostomia. But when sialometry (performed by a physician immunologist or laryngologist) objectively demonstrates a saliva flow rate of under 0.2 mL/min (resting salivation rate) and under 0.7 mL/min (stimulated salivation rate), the fancy medical terms ‘hyposialia’, ‘sialopenia’, or ‘salivary hyposecretion’ are used—basically, saliva production less than 500 mL of saliva a day, against ‘normal’ losses of saliva to (mouth-open breathing-related) evaporation and ordinary swallowing of saliva: a deficient production compared to normal losses.

L ow saliva not what the question above was about, though. The question has mostly to do with increased evaporative losses associated with large minute-wise airflow for singing, against ‘normal’ saliva flow rates that are unable to keep up with the rate of loss. In some cases, the dry mouth may be exacerbated by stage fright or allergies or medications you might be taking or a health condition that causes the mouth to be dry. But, for many singers, it’s just the mismatch between the (modest-but-normal) rate of saliva production and the (singing-accelerated) rate of saliva loss.

T he artificial saliva material may not only migrate down the throat into the esophagus, but also (in small amounts) into the larynx. So with regard to singing, please be sure to try out whatever solution you are planning to use in advance—in rehearsals long before any public performance. You don’t want to do anything radically new or un-tested on-stage.

D ry mouth is treated with liquid or gel artificial saliva solutions that are designed so that they will be retained on the mucosal surfaces for a period of some tens of minutes at least, to provide lubrication. These solutions contain bioadhesive polymers (chains that range from a few thousand Daltons molecular weight up to about 100 KDa MW), often sodium carboxymethyl cellulose (CMC). Some newer ones have an oxygenated glycerine tri-ester (TGO) active ingredient. Most of these have a rather slippery/sticky ‘mouth-feel’, but are well worth a try.

G ellan gum and alginate also both form mucoadherent gels, albeit by a different mechanism (ionic strength of moisture at physiologic mucosal surface) than the others. There are a few over-the-counter products that have these as their active ingredients.

G el-based artificial saliva products have traditionally been more effective and last longer than ‘spray’ type artificial salivas. This has been extensively studied in palliative-care patients, especially terminal cancer. But there are some mucin-mimicking artificial saliva products that have been introduced just in the last two years that have performed well in clinical trials.

P oloxamers in 2% w/v to 5% w/v solutions are liquids at room temperature but gel at body temperature, once they are applied inside the mouth.

T he polyvinylpyrrolidone polymer within an anionic polymer solution (Oasis®) enables higher concentrations of mucoadhesive polymer than older products achieve. These PVP copolymer films stay ‘stuck’ to the mouth tissues for longer, while at the same time giving improved mouth-feel due to reduced slippery/sticky mouth-feel, compared to carboxymethylcellulose (CMC)-based artificial saliva products. I have tried Oasis® and think it works very well.

 Polyoxamer F-127 N ote that the Oasis® spray does not have poloxamer in it. You can use as required, up to a maximum of 60 sprays per day. Each application of the Oasis® mouthwash lasts about 2 hours; each application of the Oasis® spray keeps your mouth feeling moist for, at most, 60 min or so. The Oasis® mouthwash would probably work better for a singer performing longer concerts. (Supposedly, Mariah Carey uses MouthKote® spray…)

T alk to your retail pharmacist. Those with training in clinical pharmacy are well prepared to advise you on the pros and cons of the various products. Some pharmacies don’t stock these products, or have a small selection since it’s a low-volume type of item, used by relatively few patients. So you may have to look for mail-order options. The hyperlinks embedded in this CMT post will give you a few options you can check out.

O r talk to your dentist. With the exception of palliative medicine physicians, oncologist physicians, ENT physicians, immunologist physicians and some gerontologists, most physicians have little experience with dry mouth and are not expert in managing it. Dentists are, in general, very knowledgeable about OTC and prescription approaches to treating dry mouth. In the U.S., artificial saliva products are regulated by FDA CDRH as Class II 510(k) dental medical devices, not as drugs.

S ome products (like Salivese®, Glandosane®, BioXtra®, and Salivix®) are only licensed for dry mouth due to radiotherapy or Sjogren’s Syndrome and require a prescription. You don’t have to have one of those ‘on-label’ conditions to get a prescription for these. A physician or dentist could legally write a prescription for you (‘off-label’). But you would have to explain to them what your performing activity entails, and why you need a powerful artificial saliva—get them to understand why other things have not been adequately effective for you and why you therefore would like to try a prescription for one of these ‘heavier-duty’ artificial saliva products.

27 January 2009

Bow Statics & Kinematics: Carbon-Fiber vs. Pernambuco

Wegst 2006 [small 'CFRP' ellipse in upper-right-hand corner is 'carbon-fiber reinforced polymer'][graph above is from Ulrike Wegst (Am J Botany 2006; 93:1439-48) who is now at Drexel Univ in Philly. In the blogpost below, roll-over 'alt-text' shows attributions of items reproduced from others' work, as well as results from my own measurements. DSM.]

I    wonder if you could shed some light on differences between pernambuco and carbon-fiber bows. Are there physics reasons why they should play or sound different?
  —  Anonymous email to CMT blog.
A ctually, yes. It’s been a subject of active interest and research for several academic acoustics teams for at least 20 years, probably longer. And there are several bowstick patents that have issued in recent years, which identify specific physical properties of the polymer carbon-fiber composite and the bowstick design as a basis for the bows’ proprietary advantages in terms of acoustics and playability.

PropertyCarbon FibrePernambuco
Density, ρ (gm/cm3)1.50 – 1.801.06 – 1.22
Speed of sound, c (km/sec)6.3 – 225.0 – 5.9
Young’s modulus, E (GPa)7.4 – 1505.0 – 22
Equation (my own regression) c = 0.02573 +  1.1435 (E/ρ)0.5  c = 0.08160 +  1.1896 (E/ρ)0.5
Acoustic impedance, Z (N•sec/m3 or MPa•sec/m)  3.3 – 402.3 – 7.2
Coefficient of sound radiation, R1.5 – 12.22.0 – 4.8

 3D plot of speed of sound, vs. Young’s modulus, vs. specific gravity (density in gm/cm3) in pernambuco, DSM, JAN-2009
I  myself found the different weight distribution of the bow along its length to be dramatically different between pernambuco and carbon-fiber, when I performed measurements on my own violin bows. The force applied by the weight of the right hand on the bow (and transmitted by the hand from the arm, etc.)—the forces are surprisingly different between the bows. The carbon-fiber generally has a higher elasticity and higher Young’s modulus (elastic modulus), compared to the pernambuco. Carbon-fiber-polymer composite’s stiffer and gives clearer tactile feedback, which enhances subtle, technical timing in bowing. You do not have to be an accomplished or professional string player to be able to perceive this when you play...

I t is, as you know, quite difficult to produce a constant volume of sound (with constant speed), for this result requires a non-constant amount of pressure so as to compensate for the changes in the weight of the bow. Even a beginner can feel this. So it takes some getting used to—switching to a bow of totally different material and design, with different weight and stiffness distributions along the bowstick’s length.

T he ‘ballistic’ effects of the bow’s motion have been extensively studied, but there is still a lot that is not adequately understood, and this CMT post will not go into dynamics/ballistics. It’s enough, though, just to look at the ‘statics’ and ‘kinematics’, as physicists and mechanical engineers refer to it—which is what this CMT post is about.

S o, in response to the reader’s email question above, I performed a series of measurements on my own two bowsticks—not a sample that is statistically generalizable, admittedly, but interesting/provocative as an illustration nonetheless.

M odern wood bowsticks are predominantly between 25 gm and 35 gm for the stick alone, without fittings or hair, etc. Then you add 6 gm of bowhair. The frog and screw and fittings bring the total weight up somewhere between 55 and 67 gm. Both of my bowsticks measure exactly 75 cm in length and both weigh exactly 61 gm total.

F or carbon-fiber bowsticks made according to the Glasser patent '353 , the bowstick shaft and head have a solid core of polyurethane foam and are wrapped with unidirectional carbon fibers running along the longitudinal axis of the shaft. Some companies inject a carbon mixture into the mold rather than wrapping. (The mixture is either completely dry, partially impregnated with resin, or totally impregnated with plastic resin.) These resins are epoxies or other ‘thermosetting’ plastics, meaning they cure to a hard solid when heated and can’t revert to their previous melt-y, liquid state when heated again. The assembly (called the ‘preform’ or ‘pre-preg’) is placed into a mold and the mold is closed about the perform. Glasser and other use a ‘resin transfer molding’ to infuse resin under pressure into the mold when the mold is closed. The mold is heated until the ingredients solidify or ‘set’. The whole thing is baked to cure the resin and make a nice, hard bowstick. Subsequently, the mold is opened, the stick is machined and finished and fitted out with hair and hardware.

I n any case, remember that the carbon-fiber bowstick is a ‘composite’ a molded ‘laminate’ comprised of various layers, usually around a cylindrical ‘core’, plus infused plastic. It is not a solid ‘lump’ of one thing called carbon-fiber. It is a complex, laminated ‘composite’. The longitudinal acoustic properties of the thing may be dominated by the outer plastic-carbon-fiber layers and the density and Young’s modulus of those layers. But the transverse and bending stiffness and other properties—overall, or at any point along the length of the bowstick—are not constant along the length and are strongly influenced by all of the materials that are present in the cross-section of the composite laminated structure at each point. The stresses are not constant either. They vary between and across the layers in cross-section...

 Kaw 2005, Fig 4.5
W hen I got my JonPaul Avanti™ bow, right away I noticed subtle differences in clarity, fullness of sound, surface noise, and so on.

 Bartholomew-Glasser patent
B oth of my bows are easy-playing, but the JonPaul one has a firmness throughout (at tip, middle, and frog) and seems much more ‘forgiving’. It is able to play more delicately and yet, paradoxically, it is also somewhat louder-playing than my pernambuco bow. The JonPaul has easy balance and emits a tone that forgives many of my misjudgments. The bowhair surface noise (frequencies from about 5KHz to 10KHz) is pleasant and has a somewhat ‘nicer’ personality than that of my other bow. The carbon-fiber bow feels, for some reason, “lighter” than the pernambuco one. If I want to apply more exuberant force I can do that. But the inherent pressure of the carbon-fiber bowstick and its bowhair on the string is less—several grams less for the carbon-fiber bow compared to the pernambuco bow—throughout the bowstroke.

T he firmness and flexibility were far different than my pernambuco bow, even though both of them weigh 61 gm and both of them are exactly 75 cm long. The balance and stability of the two bows are totally different. The center-of-gravity of the JonPaul is 24.5 cm from the screw-end of the bow, while the pernambuco one has its center-of-gravity a whole 3 cm closer to the midpoint of the bow.

I  made a simple spreadsheet to explore the ‘statics’—how the force and balance of the two bows compare, as a function what part of the bow I am using. You can click on the screen-shot below to download a copy of the Excel sheet and play with it yourself if you like. Slide the slider leftward and rightward to see how big the difference is in grams of force at various positions of the bow on the string...

 Spreadsheet to estimate balance and moment, DSM, 27-JAN-2009
I    t is generally agreed among musicians that the quality of a bow can be rated in two areas, dealing with; (1) the way the bow can be controlled in playing (‘playing properties’), and (2) the influence of the bow on the tone quality (‘tonal properties’). It seems reasonable to assume that both of these quality aspects are basically defined by the mass and stiffness distributions along the bowstick.
  —  Anders Askenfelt, KTH, Stockholm, 1995.
I    suggest trying something that costs, say, at least half as much again as the most that you think you might be prepared to pay, just to have an insight into what the difference would be for you to go to the ‘next level’. You will know a good bow when you know you are playing with something that really feels that it’s ‘lifting’ the style of your playing.
  —  Anonymous, teachers’ online forums, Associated Board of the Royal Schools of Music, 18-JUN-2007.
 VSA bow judging criteria
T he up-shot of my measurements and this simple statics/kinematics analysis is that (a) having the lighter, hollow tip on the JonPaul and (b) having the center-of-gravity 3 cm closer to the frog do make the ‘default’ inherent carbon-fiber bow’s pressure on the string several grams force less than the pernambuco of the same length and weight (see the plot in the screenshot, BROWN for carbon-fiber and BLUE for pernambuco) throughout the bowstroke. It ‘feels’ lighter than the pernambuco, even though the two weigh the same 61 gm and even though the carbon-fiber composite in the JonPaul is more dense than the pernambuco on a gm/cm3 basis. This seems counter-intuitive to me.

S o surprising, in fact, that I decided to do some deflection-vs-pressure measurements to shed further light on what’s going on. Here are two plots, which show that the carbon-fiber curves are left-shifted and have a smaller slope. The red-dot shows where the center-of-gravity is.

 Comparing stiffness and deflection of a pernambuco bow and a carbon-fiber bow, DSM, JAN-2009
I  am betting the paradoxical ‘louder-and-yet-more-delicate’ quality of the carbon-fiber bow is due to the higher sound radiation coefficient, R (also called ‘modulus of flexural rigidity’, equal to c/ρ), or, more accurately, R in combination with a slightly higher ‘loss-tangent’ for the carbon-fiber in the JonPaul bow compared to the pernambuco bow. The loss-tangent tan(δ) is a parameter that measures the degree to which a material internally damps or dissipates vibrational energy. Maximizing the ratio of the stiffness-per-unit-weight to the loss-tangent is what gets you peak sound intensity and responsiveness—it’s how they choose materials for piano soundboards, violin top plates, high-performance loudspeaker cones, stage and concert-hall floors and wall coverings, all sorts of things. Have a look at Bartlett’s 1997 paper if you’re interested in how R affects sound.

 Fostex speaker cone materials white-paper, pernambuco added for comparison
T he product ρ*c is called the acoustic impedance, Z. That, too, is far higher for the carbon-fiber compared to the pernambuco. See the nice 2006 paper by Ulrike Wegst (Max-Plank-Institut, Stuttgart; Lawrence Berkeley National Lab, Berkeley, CA) for more info on this. The efficient propagation (transmission and reflection) of acoustic energy from the slipping-sticking bowhair to and through the bowstick undoubtedly has a role. Evidently, the higher Z is, the better. I hope John McLennan’s group at Univ New South Wales or some other acoustical physics team studies this sometime...

I n polyethylene and other soft plastics (ones not suitable for bowsticks), sound velocity decreases significantly with increasing stick length. This is not as pronounced in hard thermosetting plastics like carbon fiber epoxy composites used for bowsticks. We do not expect noticeable differences in c caused by a length difference of a few centimeters between two bowsticks made of the same material...

 Wetzlinger-Müsing patent, bow tip (hollow), cross-sectional view perpendicular to bowshaft axis
I n polyethylene, there is a also nearly-linear relationship between sound velocity and density. But in pernambuco and carbon fiber composites and other ‘hard’ materials, c is approximately proportional to the square root of Young’s modulus divided by the density. I performed some statistical regressions of this from available published data, just to confirm the quantitative mathematical relationships between these quantities. (The regression coefficients I got are in the Table up at the top of this post.)

   E ~ K1*ρ*c2 or

   c ~ K2*(E/ρ)0.5

 Moon 1973, Fig. 16, Velocity vs. Frequency
E  and c are, of course, not strictly constant; they depend on frequency ω (wavelength), especially when the dimensions of the stick are comparable to the wavelengths of the [high-frequency] sounds.

   c(ω) ~ c0*(1 – K32) [left-hand portion of Figure above, anyway].

B ut the frequency effects are very small until you get up into the ultrasonic range of frequencies, so, for violin bows and music of normal tessitura, we can assume c is constant, to a good approximation.

 Wetzlinger-Müsing patent, carbon-fiber bow tip (hollow)
Y oung’s modulus, E, is measured in two ways: by mechanical bending and tension measurement, and by measuring the velocity of sound in the material. Interestingly, the two measurement methods don’t necessarily yield the same answer. The velocity measurement gives an E value that is up to about three times larger than values obtained from the bending and tensile tests in polyethylene. In wood and carbon-fiber composites, the difference is usually not so big—generally, the mechanical and acoustic values for E agree within about 50% (see Mann 1979). Why? For sonic stress-wave propagation, the displacements (strain) are microscopic—micrometers at most—whereas, for mechanical bending and tension, the displacements are at least three orders of magnitude bigger, millimeter-size in typical test-objects. The high sonic and ultrasonic frequencies used for acoustic determinations of E afford little time for ‘creep’ or other time-dependent effects to be manifested.

Y oung’s modulus obtained from sound velocity measurements can be plotted as a function of density and compared with Young’s modulus measured by bending and tensile tests. Some of the references below (links at bottom of this post) do this...

M aybe the most obvious discrepancy between mechanical and sonic measurements is seen as different dependencies on moisture content. The mechanical moduli decrease exponentially as moisture content of wood or plastic increases. Sonic data indicate that the acoustic Young’s modulus does not decrease nearly as fast as a function of percent moisture content. Maybe virtuosic performers can tell the difference between a humid bowstick and a very dry bowstick. But the opportunity to assess this almost never arises. The other variables (effect of humidity on bowhair, on instrument, etc.) would be far larger than the effect on just the bowstick. So assume c and E are constant in any particular bowstick...

M ost bow making and materials science literature neglects the fact that Young’s modulus is not a constant, fixed number. But Young’s modulus is the slope of the stress-strain curve. This curve is not necessarily a straight line; in fact, usually only portions of the curve are somewhat straight. It has bends and shoulders in it. The slope is not constant. And some materials are more non-linear than others. Polymers’ Young’s modulus values are especially curvy—they increase by up to 30% as strain increases, because of changes in molecular alignment of the polymer chains as the plastic is put under more stress and stretches. Would this influence the difference between the carbon-fiber bow and pernambuco bow sounds?

C arbon fiber can increase in modulus by 25% from zero strain to ultimate strain. Composite materials do change in modulus as fiber alignment changes due to strain. The fact that the speed of sound can increase with increasing stress is used in aerospace industry to accurately measure and QA the torque that’s applied to bolts and other fasteners in airplanes and spacecraft. An ultrasonic signal to measure the speed of sound in a torqued bolt is compared with a non-torqued control fastener. But the few Newtons of force generated by a violin bow screw tightening the bowhair are not enough to change E or c by even 1%. So assume these properties are constant, in any bow engineering or experiments we do...

C arbon fiber bows are, in general, more durable than pernambuco bows. They’re fairly impervious to humidity and temperature changes, so they resist warping. And they’re priced economically (especially when compared with wooden ones that deliver similar acoustics and mechanics).

F inally and not insignificantly, carbon-fiber bows are comparatively ‘green’ environmentally (see Baillie 2005), compared to pernambuco harvested in tropical rainforest South America.

B    y the end of the eighteenth century, the once common [pernambuco tree (Pau-brasil, Caesalpinia echinata) ] had become a rare species in the state of Pernambuco and, soon thereafter, the rest of its natural habitat. By the end of the twentieth century, it has been virtually extirpated from its range and is currently registered on the IUCN World List of Threatened Trees. It is not, however, list on Appendix I or II of the Convention on the International Trade of Endangered Species (CITES) and was not officially recognized as being in danger of extinction and protect under Brazilian law until 1990. Trade in pernambuco continues to contribute to deforestation of the Atlantic rain forest and its eventual disappearance as a commercial species.
  —  Yurij Bihun, Woodwork, 2000.
T hanks for the question! I had fun exploring some of the reasons why my own wood and carbon-fiber bows are so different. I feel that I now have a better understanding of what makes my own bows behave as they do. And I hope some of the things above and the links below are useful to you as well.

 Torque equations

22 January 2009

Frozen Inaugural Quartet & The Moral Standing of Instruments

 Yo-Yo Ma, freezing on Obama inauguration dais, Washington, D.C., 20-JAN-2009

D    ue to the mistake in administering the oath of office], if in fact Barack Obama is not the President, who is? Okay, the Constitution says that the President takes office at noon on Inauguration Day, oath or no. So I’m pretty sure that means the Presidency goes to whoever was on-camera at noon. The new President is Yo-Yo Ma! ... It’s still pretty darn historic to have the first Asian-American President and the first Vice President who is a cello.”
  —  Steven Colbert, Comedy Central , 21-JAN-2009.
S    upposedly, Oistrakh once recorded Paganini’s 17th Caprice in one take, in an unheated, freezing-cold studio in Russia in wintertime. Impressive.”
  —  Carl Fulbrook, Cambridge (Churchill College Music Society).
C ellist Yo-Yo Ma, violinist Itzhak Perlman, clarinetist Anthony McGill, pianist Gabriela Montero performed at the Obama Inauguration on Tuesday. The quartet played a piece by composer Williams called ‘Air and Simple Gifts’ immediately before Obama was sworn in. It was 31 °F (-1 °C). The wind was blowing at about 3 mph (5 km/h). Attendees seated nearby were bundled up in scarves and thick winter coats and knit hats pulled down over their ears. How is it possible to play in such conditions? Those of us who have performed outdoors in freezing weather—in a marching band or brass band, say—dread it. But violin? Cello? Piano? Inconceivable! At least Gabriela had some fingerless gloves on…

H ere is a YouTube of the performance:

T hink of the cello! Think of the violin! (And the clarinet and the piano, too, although those are not in such clear and present physical danger as the strings are.)

T hese are not mere inanimate objects. They merit care and ethical concern—in somewhat the way that animals do. If pets have rights, then instruments do as well. The violin and cello deserve a loving, respectful home. My moral character and virtue as a human being depend on how I treat them.

H ell, I take my violin into the supermarket rather than leave it in my car’s back seat, even if only for 30 min. Swaddling the instrument in a blanket for extra insulation is good. What musician knowingly mistreats her/his instrument? Well, don’t answer that...

 WeatherChannel, WDC temperatures hourly listing, 20-JAN-2009
S o never mind the human agony of playing in freezing conditions in Washington, D.C., this Tuesday. Never mind the aesthetic tuning and articulation issues that the humans are subjected to when performing in extreme temperatures. My hopes and prayers are for the instruments.

M y ethical feelings toward instruments do come with a distinction, not unlike that of 18th-Century Scottish philosopher, David Hume. Since the instruments are inanimate and cannot reciprocally behave virtuously toward me, they cannot have exactly the same moral standing as a person or an animal. My sense of an instrument’s ‘valor’ and ‘utility’ has to be combined with what philosophers would call ‘aprobation’—a moral calibration that takes into account its inanimateness: the fact that it is not a sentient creature. Just the same, I care about its wellbeing...

M y questions, though, are these: (a) is the physical risk of damage to the violin-family instrument mainly due to the temperature excursion or instead mainly due to the effects of sudden change in humidity? Is it (b) mostly a matter of stress between the top plate vs. saddle or instead a matter of temperature/humidity changing how the soundpost is fitting? And (c), what parts change dimension at the fastest rate? Will I (d) hear the fatal cracking of the top plate while the instrument is still cooling down, or will the distaster be more likely to happen when I bring it inside and warm it up? Finally, (e) after exposure to cold, what rate in degrees per hour would be best to allow the instrument to warm up, to prevent the instrument from cracking or the gluelines from separating upon thawing?

Violin saddle, photo © Stewart-Macdonald
T he thermal expansion coefficient of dry wood parallel to the grain (as for the ebony saddle) is essentially independent of wood species and density. For ebony, the thermal linear expansion coefficient αl is 3.1 x 10-6/°C. But the thermal expansion coefficient across the grain (radially, as for a sitka spruce top plate, or tangentially) are strongly dependent on wood species and density (gm/cm3).

   αr = (9.9 + 32.4ρ)  x 10-6/°C

S ince sitka spruce ρ = 0.42 gm/cm3, αr = 23.5 x 10-6/°C. In other words, the chilling top plate contracts about 7.6 times as much as the ebony saddle for a given temperature excursion.

 violin anatomy, including saddle
If we take the violin from at 68 °F (20 °C) room outdoors onto the inauguration platform at 31 °F (-1 °C) a contact area between the saddle and the top plate that is about 50 mm long will begin shrinking—the ebony will shrink -3.26 μm and the sitka spruce will try to shrink -23.5 μm, but will be prevented from doing so by the saddle. The woods and the glue between the spruce and the ebony will be under considerable shear and tensile stress while this is going on.

T he modulus of elasticity for the delicate sitka spruce is 9.86 GPa (1,430,000 psi), and the modulus of rupture is 65 MPa (9,430 psi). Since we don’t know—for any specific instrument, or for stringed instruments in general—the precise area A0 to use in the force equation (below), nor do we know how spatially uniform or variable the bond between the top plate and the ebony saddle is, it is not possible to calculate the stress-strain relationships with certainty. We would have to build a special violin to be able to measure it. But ‘ballpark’ calculations I have done indicate that the stresses can easily exceed the maximum tensile strength of 2.48 MPa (360 psi) for the sitka spruce in the top plate.

 equation for Force as a function of Elastic Modulus and area and length and strain (ΔL) W ood that is not totally dry reacts differently to varying temperature than does dry wood. When wood with non-zero moisture content is warmed, it initially expands because of normal thermal expansion but after a few hours begins to shrink because of loss in moisture content. Unless the wood is very dry initially (4% moisture content or less, which is unrealistic for an instrument), shrinkage caused by moisture loss on warming will be greater than any thermal expansion, so the net dimensional change on warming will be negative. Wood at intermediate moisture levels (say, about 8% as for a violin in its humidified case) will expand when first warmed, then gradually shrink if the warm, low-humidity condition persists. The net dimensional change will often be near zero if enough time is allowed to equilibrate at the new conditions. But at intermediate times the dimensions are expanded compared to the initial temp. For the wind conditions and high outdoor relative humidity at the Obama inauguration, I think we can safely bet that the humidity-generated effects were negligible compared to size of the thermally-generated dimensional changes and forces.

H ow rapidly do the strain and stress develop in the top plate, especially in the area that is constrained by the lower-expansion-coefficient saddle? Well, if the movement is sudden, from inside to outside, and if convection is efficient (e.g., wind at 3 mph or greater) then it will occur within 10 to 15 min.

T o fully model this process mathematically, we would have to solve the partial differential ‘Heat Equation’ for the conduction and convection of heat (cold) into the wood, from the cold-exposed surface inward. Readily doable using available software like MATLAB, but more than is reasonable to put in a CMT blog post.

A  simple Excel spreadsheet will give you some sense of the stress (force per unit area) that the top plate has to bear. Click on the screenshot below to open or download a copy to play with.

Spreadsheet estimating stress between violin saddle and top plate for temperature excursion of 21 °C
O bviously, stringed instruments do occasionally experience unintended temperature excursions that are this wide or wider—and yet a split top plate is amazingly rare. How can this be? Well, the rarity of it must be due to most such occurrences’ having a relatively slow rate of change of temperature—the interior of a closed violin case (with the instrument wrapped in cloth) in the rear seat of a car, for example, will take several hours to drop the first 10 °C when exposed to a new ambient temp that is 21 °C lower. And, in a slow cooling or slow warming excursion, the glue that bonds the various pieces of the instrument together has time enough to accomodate the shearing forces that develop. In a fast cooling or warming, the macromolecules in the glue don’t have time to relax and, as a consequence, the full stress developed (by the thermal expansion coefficients differential between the different woods and cross-grain orientation) is imposed on the joined parts immediately—with a much higher probability of catastrophic failure beyond the material’s maximum tensile strength.

W hich brings up a possibility. If you know in advance that you will be required to perform at a freezing inauguration, you might take your least-favorite instrument to a cold storage facility the day before, to incubate it at a temperature that is close to the outdoor temp that is predicted during the performance the following day. Retrieve it from the cooler, put the whole thing (the instrument in its case) in a big padded Igloo® portable insulated cooler, and schlep it to the performance venue, only pulling it out and tuning up when you are outdoors in the cold. Then when you are done, allow the instrument to warm up slowly in its still-cold case, over a day or so before opening it up at room temperature again.

A  simple example of physics / mechanical engineering in service of instrument health!

N ear the end of the film, ‘The Pianist’, the piece that Szpilman plays for the German officer is Chopin’s G minor Ballade. Yes, we suspend our disbelief when we think of the freezing room and prison-camp starvation and no opportunity for practice—yet, despite these things, the performance is excellent. But everybody thinks of the humans and their suffering and implausible virtuosity in the face of impossible odds; nobody thinks of the poor, suffering musical instruments and their impossible odds.

N ear the end of Tuesday’s inauguration, we had to suspend our disbelief at the remarkable style and grace that Ma, Perlman, McGill, and Morteno mustered. Would that their instruments had been weather-impervious fiberglass/plastic ones. I hope they are doing okay and none was injured...

T he ethics of how we treat instruments is, I want to tell you, just a ‘hop, skip, and a jump’ from the ethics of how we treat our environment and public goods. The world and its resources are ‘useful’ to us; they are ‘instrumental’ in serving the needs of humankind. But the ethics of environment is predicated on the notion that the world is a collection of ‘public goods’, not only for the human public but for animals and plants and other ‘publics’. In the case of privately-owned musical instruments, it could be argued that old, rare and historic instruments are indeed a sort of public good—with value to broader and future society beyond the scope of needs and utility of its present owner. But what about cheaper, commodity-grade instruments? Is it ever justifiable to recklessly abuse them or destroy them, or for politicians to command that they be abused/destroyed? (When a rock guitarist smashes a fine instrument on-stage, must one be a ‘virtue ethicist’ to say he is wrong to do so? S’pose so... )

 drawing of Sitka spruce, 1mm cube