Why Jakob Stainer?
Walter Senn and Karl Roy explain in their book "Jakob Stainer" that Bach an 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.
We can remember as well what Leopold Mozart says in his famous violin method about italian instruments: compared to the "german type" of violins –Stainer's or those who followed him– were rough instruments.
Further there are musical and instrumental reasons to prefer Stainer: on one hand we have that the most difficult to play on a modern instrument are chords, and being the music of that time replete of chords (think only of Bach's solo violin sonatas and partitas) one wonders whether in that time were they masochists.
On the other hand, a modern instrument becomes more sensitive and gains in sustain only by mounting on it a Strad model of bridge, and mechanical wave propagation shows that the very concept lying on Stradivari bridges is applied by Stainer to his entire instruments. Then comes the question: how more sensitive were and how much more sustain did Stainer's instruments had before being transformed?
In any case, a sensitive instrument with sustain is exactly what is needed in order to perform music rich in chords. One must here 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 applies to wind instruments too.
The conclusion is not that musicians of that time loved having it very difficult. Instead, it is that the "language" that 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 we can already 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 is nothing but a wider way for mechanical waves to propagate and reach in a more direct and strong way the place they have to reach: the ribs of the instrument. From 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 soundpost, second through the ribs.
Observing some pictures of Stainer's instruments, and looking at them from the point of view of mechanical waves, we 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 fits very well with the baroque instrument for two reasons. First, regarding the shorter neck of the baroque instrument, because the lenght of the strings is in this way conserved. Shorter neck that solves the problem of going down to the low positions, for it allows to go down to the first one with just one stroke 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:
This concept 'feet of the bridge_end of the f holes_end of the corner blocks' is what makes clear the idea of mechanical waves reaching the ribs of the instrument and, through the ribs, 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.
Is at this moment that we can pay attention to the fluting of the blades on Stainer's instruments. The fluting of the front sends and the fluting of the back receives mechanical waves. The fluting of the front makes mechanical waves change their direction sending them to the ribs,
and the fluting of the back makes mechanical waves coming from the ribs rebound so that they enter the back blade:
The question is how thick that middle part of the blades must be and how they must dicrease... Must there be mechanical waves reaching directly the ribs or not at all? Probably yes, though probably not everywhere. 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.