David Beard

To address the OP, the modern string quartet music form developed in the hands of Haydn, Mozart, Beethoven, et al. This was a little after the time that distinctions between sizes of violins and violas were a significant thing. The publication of Haydn's 1772 opus 20 quartets helped establish the form. By then, the time of making big tenor violas and small violins shorter than 350mm had faded about a century earlier. Not to say there weren't some later exceptions. I doubt Beethoven or even Haydn would expect physically different 1st and 2nd violins in a quartet, or 1st and 2nd violas in a quintet.

It's an original German commercial violin. Trump's not the first or only one in the world to habitually lie. And violin buyers aren't the world's only fools who stubbornly prefer an appealing lie to unappealing truth.

Benade. Fundamentals of Musical Acoustics and Pierce. Almost All About Waves are also very good books. Gough is good. Your point? Might point is that a violin is a driven system. A natural resonances only approach is incomplete and insufficient. A fuller picture includes standing waves and Q.

Not when a fixed frequency drives into the instrument! Violins are not marimbas. Other than for research, we don't normal strike a violin to simply excite the resonances, the situation you described. Instead, we normally send or drive a collection relatively fixed frequencies into the instrument for the duration of a note. If the instrument is to respond, it must set up into standing waves that match the driving signal. These standing waves will match the signal, which in general will not usually match the natural resonances exactly. This is where lower Q in the natural resonances is valuable. The higher the Q, the less the resonance will be able to bend and setup in a standing wave that is only near to the natural frequency but not an exact match. We don't normally talk of standing waves and Qs in the violin world, but it is in fact the relevant physics. Maybe we should expand our habits?

I don't believe 'light as possible' applies to violins the same as speakers. Speakers don't aim 'hold' the signal energy in standing waves. A speaker cone is slaved to it's driver, and aims ro radiate the energy directly and cleanly. For a violin, the energy sets up in standing waves, and then radiates. Mass is an essential component of these standing waves.

They move in all of the available modes, depending on the frequencies driving into the instrument. Gough's work is great to read. Also, look at motion studies and animations on the web. A violin sets up in 'standing waves' the express the driving signal. With lower frequencies, larger portions of the plates move in phase. For higher frequencies, the paterns break up into smaller patches of phase and anti-phase. The current design does a good job of responding to the whole range of musical input. As you explore, you don't want to focus on only one of the patterns of instrument movement, because that will reflect only a small range of actual response.

I don't. I look up on line to see what others have measured.

No. Depends on material and state of material, temp etc. In some materials like spruce it also depends on direction in relation to the wood structure.

Yes. Rubber bands are elastic for stretching. And, if you ball them up, for compression. Much more challenging to get elastic deflection from them. They simply don't return that shape or energy. Elasticity is the main reason spruce and maple are chosen. Other than that, relatively low material dampening is good. Maybe Don's bit about high radiation, I'm not sure. Definitely Diaboli's thing about wood that is 'lively'. Or 'talkative' when you tickle it. Attractive wood with basically normal properties is good while we're at it. After these basics for materials, I suspect shape is the real issue. Mainly, avoid going out of your way to make specific high Q resonances (that means tap tones that are too clear or pitch defined). Also, avoid putting resonances in simple interval relationships. Keep them 'off' from one another.

Elastic Energy Elasticity Plasticity Stiffness Ah! I was ready to accept all this on face. But you made me read more. It's a little bit complicated, but very relevant to understanding violin materials. Elasticity and elastic moduli are a little bit different things. And, stiffiness is a different thing again. Elasticity is the general property of restoring shape after a deformation. And, this is central to sound or most any vibrating system, because elastic deformation stores energy. Most of the vibrations we work with in violins involve the cycling of energy between storage in the kinetic energy of a moving mass and storage as elastic energy in a deformed or flexed mass. Elasticity does not for physics mean pliant or stetchy, nor does it mean stiff. It means the material restores it shape, and returns its elastic energy after deformation. The opposite of elastic is not stiff, but plastic. This physics word means a material absorbs and does return a deforming energy, it stays deformed. Good examples are tar and peanut butter. These are the opposites of elastic materials. To make matters more complicated, materials can have different elastic quailities for different kinds of deformation. Some materials are elastic under stretch or compression. Examples are air, rubber, spruce, maple, and even steel. The speed of sound in materials is based on this kind of elasticity. Notice that this elasticity is quite different than simple stiffness. Air is very elastic because it very efficiently stores and returns the elastic energy from its deformation. Steel is similar in elasticity, but vastly stiffer. Other materials can also be elastic in various forms of axial deformation. This includes spruce, maple, and steel, but not air, and not generally rubber. This sort of axial deformation is very important for violin wood. All the standing waves formed by the plates and body of a violin are cycling their energy between the moving mass of the wood, and flexing elastic deformation of the wood. Elastic moduli are methods of quantifying the different kinds of elastic deformations of a material. Elasticity itself is about a material's ability to restore shape and return deforming energy. 'Ideal Elasticity' means perfect return of shape and complete return of eneegy. But most materials will break or plastically deform at some point. In contrast, the elastic moduli essentially measure the stiffness encountered for the different deformations of an elastic material. They do this mostly as a ratio of force to strain. Higher moduli, stiffer elastic material. Simple stiffness is another matter again. Stiffness is the general resistance to deformation, not just to elastic deformation. So, cold peanut butter can be stiffer than warm peanut butter. Also, elasticity and the stiffness or moduli of elasticity are properties of the material itself. But stiffness is a property of a specific piece of material. So thickness and shape come into play. Similarly, resonances and therefore Q are not properties of materials but of specific pieces of material. Shape and thickness come into play. So, for example, the archings of a plate create areas of 'cupped' shapes. Cupped shapes have no impact on material properties like elastic moduli, but they do increase stiffness locally through geometry, and such things do impact resonances. Etc.

Thanks for the clarification!

You link is good, even if focused on a limited example. It contradicts none of the things I've asserted.

https://en.m.wikipedia.org/wiki/Q_factor Q is the quality factor of a resonance. We've been discussing things that contribute to Q.

I agree. Aging will change the material in ways that likely do matter. But, there are also shape aspects to Q, high or low. And these will change much less with time, and much more at the makers immediate control. Example, you make a marimba bar long and skinny to give it higher Q via shape. Shape can define or obscur a mode, and the associated size. The cleaner the definotion the higher the Q. The less direct and clear the size and path for the mode, the lower the Q. The lower shape Q, the less clear and efficient the natural resonance will be. But, the reaponse to driven input will be easier and broader. A long string under tension is very high Q. A soundboard with irregularly shaped edges is very low Q.

Absolutely. For physics, elastic means the material retruns energy. When you strike maple or spruce, they store your energy input as flex, then return that energy with good efficiency. That is elasticity. If you strike the wood with something too hard, or in the wrong way, the wood dents. That is 'plastic' deformation and wastes the energy. Not what we want. Rubber is different. If you stretch rubber, it behaves elasticsally and returns the energy by pulling to stretch back. But if you strike rubber to make sound, the material is quite dampening and wastes much of the energy. That is not eleastic behavior. So, for receiving and holding sound vibrations, maple and spruce wood are very elastic. Rubber is much less so.