ctanzio

Thanks for the info. I am always looking for products to quickly fill gouges and scratches on things other than violins. The challenge I found is when repairing something that may be subject to a range of temperature and humidity. Differences in expansion rates between the wood and the filler can cause the repair to fail in a variety of ways. Probably much less an issue for well cared for violins.

I had problems with Paypal and "free trials" and also cancellation of subscriptions. I am not sure the problem is solely with Paypal's or the vendor. But I got the distinct impression that Paypal pays nothing more than lip service to disputes, even after supplying documentation that cancellation had occurred before the charge and within the allotted time to cancel. I cancelled the payment with my credit card company and that certainly got Paypals attention. They sent it to collections. I sent the documentation to the collection agency. I then ignored all further notices. For one-time payments I found Paypal a good way to shield a credit card from the online purchases. But after cancelling the Paypal account years ago, I have yet to have a problem using a credit card directly on a reputable vendor's web site. Have you been able to contact Musescore directly? You might have more success there.

The question was not about the big drop off of elastic modulus with angle. Look at page 2 of the article you just posted. The equation predicting the variance of moduli with angle illustrates exactly what I mentioned. It is a rather complicated interaction of not only the elastic moduli, but also the shear and poison ratio properties. Hankinson's equation might be an adequate curve fit near the 0 and 90 areas for the elastic modulus because the curve fit is designed to do that. But it is obviously ignoring some major factors towards the middle.

Before using that equation to compute the elastic moduli for an angle other than 0 or 90 degrees, I would encourage people to thoroughly research the science behind orthotropic material constants and coordinate transformations. Maybe that experimental curve fit is "good enough", but I am skeptical. The equations used in material science investigations and finite element analysis of real structures are much more complicated. For example, the elastic modulus along the length of a beam that has been cut on a off-quarter contains sines and cosines to the fourth order and also include the shear moduli as well as the poison ratios.

Thank you for sharing. The attention to all the little details makes your instruments works of art of the highest order.

Thanks for the article. It is actually about maximum stress at failure rather than a measurement of the elastic moduli of the wood. It is worth noting how much weaker wood is when loaded cross-grain. If one is thinking of trying a sharply angled grain cut for the plates, one might be shocked to see a dramatic increase in fracture failures or creep deformation.

Back in the day I experimented with a bunch of natural dyestuffs. The stuff he used has the same spectacular brightness and intensity as turmeric based dyes. Sadly, turmeric color is highly fugitive. After a few months, the beautiful under glow of the top varnish fades and one is left with whatever the over varnish can provide. I would hope he is using a modern chemical dye that is color fast.

The formulas that relate stress and strain along the radial and tangential grain directions can be written in the form of a matrix equation. When you strain the wood along a direction that is not strictly in the radial or tangential directions, like cutting a beam from the wood along a quartering angle, you can rewrite the equations along the new direction. This coordinate transformation gives you a new set of elastic constants that are a mixture of the radial and tangential ones. Trignometric functions appear in the new equations and give the "shape" Don's plot contains.

When he pinched the plate at specific locations and listened for a tap tone, I could understand such a quick and simple way to make sure he got the plate weight and thickness in a zone that emphasizes some major resonances. But I always wonder if the time was spent carving many plates at different locations to understand exactly where to carve to get the frequency and response level that is "desirable". Then there is the age-old tap tone problem of knowing what frequencies and response levels yields a good sounding violin. Chladni patterns are a slightly more scientific method of detecting a wide variety of free plate resonances and resonance shapes but suffers from the same challenges as tap tones. Just with a lot more data points to juggle.

The plot you posted seems consistent with the typical range of radial and tangential MOE for spruce. A 0deg cut would correspond to the radial MOE being dominant for cross grain stiffness. 900MPa is about the average stiffness one would encounter in a typical sampling size of different trees. A 45deg cut would make the tangential MOE dominant. Your value might be a little on the low side of typical spruce wood. For finite element design, one would use something called an orthotropic plate. Technically, one would need a set of 9 elastic constants, but 3 of them could be estimated from the values of the other 6. Experimentally, one usually measures three elastic constants (radial, tangential and longitudinal to the grain), and the corresponding shear constants.

I thought the splitting of the back wedge with a hand saw at the start was odd given that later on he used a band saw to cut the outline. It would have been trivial to split the wedge using the bandsaw.

Two things here... First, I was not offering Chladni plates as a design approach. And I did not mention tap tones. It is a visually simple way (and cool looking) to illustrate the concept of vibrational "resonance". Second, the concept of a structure as a collection of resonances being excited by a dynamic load is widely practiced engineering and used in diverse areas like design of buildings and dams to resist seismic events, rotational fatigue of power turbines, vibrational loading of airplanes and construction of stable platforms for science experiments and military weapons. The application of the theory can be challenging, which is why I think it has not made much of an impact on violin design.

Maybe a video of a chladni plate being excited by a speaker at different frequencies. When different patterns form, it shows that plate vibrating in resonance with that "note". Now think of the strings on the violin as the speaker. The bow catches and releases the string, causing it to vibrate at a specific frequency. That frequency excites the various natural modes of the violin "plate". The closer each plate mode is to the string (speaker) note, the more the energy of the string is captured and amplified. The combination of all these plate modes vibrating together gives the "sound" of the violin and its loudness.

Dialectical doesn't mean what you think it means in that sentence. We CAN compare two opposing ideas (your feelings versus engineering principals successfully applied for decades) and realize there is a problem with your claims. Of course the natural harmonics of the bow are important as anyone can attest who ever attempted flying staccato or spiccato. It is also obvious that the bow hairs are not "relatively inert". They form an intricate part of the dynamic system with the stick. As Michael Darnton pointed out, change causes effect. People are simply pointing out that the effect is not worth worrying about.

There has actually been a lot of scientific research on material aging, including wood. There are even equations derived from theory, experiment and observation that do a decent job of predicting changes in a variety of material properties. If one is careful about selection of temperature and humidity, one can actually accelerate the natural aging of wood. What is missing is a solid relation between sets of material properties and tonal excellence (whatever tonal excellence means). Don Noon's observation about changes in damping due to aging is about the closest I've seen where one can make a reasoned statement about old wood being "better" than new wood. But lower damping doesn't always mean tonally better, because other factors like elasticity and density will also change and might offset the improvement in damping. As a general observation, the rate at which properties change with age start rather high and exponentially decrease over time. After about 50 years, further changes become functionally meaningless. So, if one is using accelerated aging techniques to age wood, shooting for a 50-year mark is a good reference point.