It is thinking about Stainer's instruments from the point of view of mechanical waves propagation that I get a new explanation of how string instruments work. Using this physical principle I also understand why instruments with lower archings produce a clearer and more direct sound than instruments with high archings. 


Jakob Stainer was a violin maker from the XVII century born in Absam, in the Austrian Tirol. He was the most appreciate violin maker ever until somewhere in the XIX century. Walter Senn and Karl Roy explain in their book "Jakob Stainer" (Ed. E. Bochinsky, 1986) that Bach and even Corelli had Stainer instruments. The fact that Corelli had a Stainer and not an italian instrument is very significant: it was easier for him to get an Amati than a Stainer, and still he chose Tirol instead of Cremona. It is not surprising then that Stainer instruments, as Senn and Roy explain, were in that time ten times more expensive than italian instruments. 

Leopold Mozart wrote in his violin method that compared to the "German" violins (Stainer's), Italian instruments (Stradivari's, Guarneri's, Amati's) were rough, not very refined. He explains there too that it was common knowledge that the blades of a violin had more wood in the middle that in the edges, what suggests that the difference of thickness were big enough to be seen with the eye, not as the difference in the blades of modern instruments. 

             One of the lion heads made by Stainer for some of his violins.

I have found musical and instrumental reasons to prefer Stainer: being myself a viola player, I always found playing chords on a modern instrument most difficult. Being the music of that time full of chords (think only of Bach's solo violin sonatas and partitas) one wonders whether in that time they liked to have a difficult life. But when mounting a Stradivari bridge on a modern instrument, it becomes more sensitive and gains in sustain. Mechanical waves propagation shows that the very concept lying on Stradivari bridges is applied by Stainer to his entire instruments. Then the question raises: how more sensitive were and how much more sustain did Stainer's instruments have before being transformed? 

In any case, a sensitive instrument with sustain is exactly what you need to play music rich in chords. Remember that the easier the production of the sound is (in this case the ease to bow) the lighter it becomes for the fingers to put the notes, principle that also applies to wind instruments.
So it is not that musicians of that time loved having it very difficult. Instead, it is that the "language" that musical instruments spoke before being transformed in the XIX century is the same language in which those musical texts are written. 

Thinking of how mechanical waves travel through the matter I can figure out how Jakob Stainer's instruments could have been. Through this physical principle, the external shape that is still visible in some of his instruments, together with that thick middle part of the blades –as it is said they were– makes a lot of sense. That thickness of wood in the middle of the blades makes the way wider for mechanical waves to propagate and reach in a more direct and strong way a place they need to reach: the ribs of the instrument.
From the feet of the bridge, mechanical waves produced by the vibration of the strings enter the front of the instrument, and from the front they go to the back, first through the sound post, second through the ribs. 
Observing some pictures of Stainer's instruments, and always looking at them from the point of view of mechanical waves, I can find a lower position of the bridge (more or less clearly depending on the picture and the instrument). Next pictures are from a Stainer violin from 1679, which is in all its parts original. 
This lower position of the bridge suits very well the baroque instrument for two reasons. First, regarding the shorter neck of the baroque instrument, because the length of the strings is in this way conserved. A shorter neck solves the problem of going down to the low positions, because with such a neck you can go down to the first one with just one strike of the wrist.
Second, because that lower position of the bridge, regarding mechanical wave's propagation, unifies the concept on both halves of the instrument
The straight line "feet of the bridge – end of the f holes – end of the corner blocks" suggests the idea of how important mechanical waves reaching the ribs of the instrument are. Through the ribs they reach the back blade. The thick middle part of the blades appears now as a wide way for mechanical waves to go from the bridge to the ribs. The f holes prevent mechanical waves reaching directly the corner blocks. 

Now is the turn of the edges of the blades of Stainer's instruments. The edge of the front sends mechanical waves to the back and the edge of the back receives them. The edge of the front makes mechanical waves change their direction sending them to the ribs, and the edge of the back makes mechanical waves coming from the ribs rebound so that they enter the back blade. 
Unfortunately those edges have disappeared from some Stainer instruments that have reached our days. Some say that with the years they got worn out. I believe that those edges were consciously removed when the instruments were transformed.
This picture of a violin by P. Rombouts (Amsterdam 1667–1728), said to be "the Dutch Stainer", shows very sharp blade edges

The question is how thick that middle part of the blades must be and how must they decrease... Must there indeed be mechanical waves reaching directly the ribs or not at all? Probably yes, though probably not everywhere, and maybe not in violins and yes in violas. Maybe. And then, how much? Probably a little amount will do, being just enough to give the strongest signal to the ribs, doing the rest for the sound, for at each rebound inside-outside of the blades a little amount of mechanical waves will be refracted into the air, becoming sound. 

Some say that in the XIX century the general taste turned to the sound of Italian instruments, especially those made by Stradivari. Some others say that when in the XIX century instruments were transformed to make them sound louder, Stainer instruments lost much more in the process than the Italians. I can see that when Stainer's blades were made thinner, having those blades such a high arching, they resulted in hollow blades. So disappeared the much more direct way that mechanical waves had from the feet of the bridge to the back via the ribs.

In this picture I have drawn a flat front blade. Notice that in such blades, while I only have marked two, there would be a lot of waves reaching the ribs of the instrument in an undisturbed straight line from both feet of the bridge. That's why the flatter a blade is, the clearer is the sound it produces. So I think I understand why the front blades of Stainer's violas have a lower arching than his violins: to make his violins sound darker and his violas clearer.