Jakob Stainer was a violin maker from the 17th century, born in Absam in the Austrian Tirol. He was the most highly regarded violin maker for the next two centuries, until string instruments were transformed to achieve a louder sound.
Walter Senn and Karl Roy explain in their book Jakob Stainer (Ed. E. Bochinsky, 1986) that Bach and even Corelli had Stainer instruments at their disposal, and it seems that the Mozarts did as well.
The fact that Corelli had a Stainer and not an Italian instrument is very significant. It would have been easier for him to acquire an Amati than a Stainer, yet he chose Tirol over Cremona. It is not surprising, then, that Stainer instruments were, at that time, ten times more expensive than Italian instruments, as Senn and Roy explain.
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. Since the music of that era is full of chords (think, for example, of Bach's solo violin sonatas and partitas), one wonders whether musicians back then enjoyed having a difficult life. However, when mounted with a Stradivarian bridge, a modern instrument becomes more sensitive and gains sustain. Mechanical wave propagation shows that the very concept applied by Stainer to the entire instrument is the same one underlying Stradivarian bridges. This raises the question: how much more sensitive were Stainer's instruments, and how much more sustain did they 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 sound is—in this case, the ease of bowing—the lighter it becomes to finger the notes, a principle that also applies to wind instruments. Thus, it was not that musicians of that time loved difficulty. Instead, the language that musical instruments spoke before being transformed in the 19th century is the same language in which those musical texts are written.
Introduction to Stainer's Architecture
Thinking about Stainer's instruments from the point of view of mechanical wave propagation leads to a new explanation of how string instruments work. That physical principle also explains why instruments with lower arching produce a clearer and more direct sound than those with high arching.
Mechanical waves produced by the vibration of the strings enter the front of the instrument through the feet of the bridge. Once they have entered the front plate, a portion of the waves propagate toward the back of the instrument, first through the sound post and, a bit later, through the ribs.
Through that lens, one can envision what Jakob Stainer's instruments might have been like: the external shape still visible in some of his instruments, together with the thick middle part of the plates makes perfect sense. Leopold Mozart says in his violin method that at that time it was common knowledge that the plates of a violin had more wood in the middle than at the edges. This suggests that the difference in thickness was enough to be seen with the naked eye, unlike the difference in thickness of the plates of modern instruments. That thickness in the middle of the plates provides a wider path for mechanical waves to propagate, allowing them to even reach the ribs of the instrument directly and strongly.
About Sustain
Let's consider what exactly sustain is. I said before that a modern instrument mounted with a Stradivarian bridge gains sustain. That is because the sensitivity of these bridges makes the most of the waves created as long as the string still vibrates with enough intensity. Some high-tech modern strings are developed specifically to achieve exactly that: to keep the strings vibrating as long as possible, and they do indeed create a bit of sustain. So, that is one way: profiting as much as possible from the vibration of the strings. Another way to create sustain is to delay wood-to-air refractions.
Both ways of creating sustain are present in the old instruments with thicker plates, for those plates demand sensitive, open bridges, and Mr. Stainer would have brought the concept of delaying refractions to the extreme. As we will see, modern thin plates do not allow for this delay.
Let's proceed to the morphology of Stainer's instruments, and at the same time we'll see what this extreme delay of refractions is:
First of all, I want to focus on the place of the bridge. It was while considering this that I started thinking about the importance of the sound waves reaching the ribs of the instrument.
As one can see in old paintings, for example this one of the French Nicolas Tournier (1590-1639),
or this other of the Italian Orazio Gentileschi (1563-1639),
bridges were often placed in a lower position than they are today. Today bridges are placed between the notches of the middle of the f-holes.
Now observe these pictures of Stainer's instruments:
Always bearing in mind how mechanical waves propagate, I see a possible lower position of the bridge. This lower position suits the baroque instrument very well because baroque instruments had shorter necks, and a lower bridge position maintains the string length. When playing, I find that a shorter neck solves the problem of shifting down to the low positions, because then I can reach the first position with just one flick of the wrist. But this only regards the player.
Soundwise, placing the bridge in a lower position brings all four corner blocks of the instrument into the shadow of the f-holes. When I noticed this, I realized that there is indeed no point in letting part of the most intense waves reach those blocks of wood, given their damping effect. Avoiding them seems to me the logical course of action, putting those intense waves to better use. Another thing that became clear to me with the bridge no longer sitting within the C's is that their function just consists in letting the bow pass over the outer strings unobstructed by the sides of the instrument. With the bridge higher up, only the upper half of the C's serves that purpose.
The straight lines running from the feet of the bridge over the end of the f-holes and ending past the end of the corner blocks suggest the importance of mechanical waves reaching the ribs of the instrument: waves reach the back plate through the ribs as well.
So, how thick should that middle part of the plates be? And how should that thickness taper down to the edges? We can get an idea by looking at the next pictures of a Stainer violin located at the Musical Instruments Museum in Innsbruck, Austria. It is a detail of the upper part of the left f-hole. Please pay attention to the growth of the thickness from the internal notch of the f-hole along the curve reaching the dot at the end of the f-hole:
Must there indeed be mechanical waves directly reaching the ribs? I think so, though maybe not everywhere along the ribs, and maybe less in violins and more in violas. Maybe. And in what amount? Since mechanical waves lose intensity over distance and when encountering surfaces, the further away a point in the edges of the front plate is from the feet of the bridge, the more waves need to directly reach that point in order to arrive at the back plate with enough intensity.
The next drawing illustrates how waves directly reach the ribs from the feet of the bridge. I have not included the f-holes in it, because the first paths reaching the ribs go past them. However, the middle of the front plate may not have to be as thick all along as my drawings portray, because the longer a path from the feet of the bridge toward the edges is, the less thick the front plate needs to be to achieve the same direct paths all along the edges.
Once the waves have reached the edges of the instrument, we can pay attention to the shape of those edges.
Unfortunately for us, the edges of the front have been flattened almost entirely. I can only see a remnant of the original shape at the lower part of the C's.
On other instruments the sharp edges are completely gone, from both front and back plates. As I understand it, after those instruments were transformed, the sharp edges were of no use or not wanted help.
The next picture shows a violin made by Pieter Rombouts, known as the Dutch Stainer. He lived in Amsterdam in the second half of the 17th century until well into the 18th, and most probably had some knowledge of the morphology of Stainer's instruments. His instruments are only secondhand evidence of Stainer's edges, but they can give us a clearer picture of how sharp those edges were.
As I see it, the edges of the plates—rising from the fluting to a sharp point and curving back down to the ribs—are the W.A.S. of the plates, ensuring that the waves reaching them are redirected toward the ribs. On the back plate, the same edges let the waves coming from the ribs enter it most efficiently.
Now is the moment to look at how Stainer created the sustain in his instruments: the concept of delayed refractions.
The refractions that make for the sound of the instrument are the ones happening from the inner surfaces of both back and front plates into the air of the resonance box—refractions from the outer surfaces do not make for the sound because in the open air there is no superposition of those waves and no amplification occurs. There is sound from the very first refractions in the front plate, right under the feet of the bridge, until the very last refractions of the waves that travel through the ribs and across the back plate.
Once the waves coming through the ribs reach the back plate, we see that the first reflections and refractions happen right on and immediately next to the edges; from there on, most of the paths will find no boundaries until well past the middle of the back.
Thinking about that span, you can get an idea of the sustain that Stainer instruments would have had. This idea becomes even clearer when you compare these paths with the paths that thin plates allow.
When instruments were transformed to make them sound louder, the instruments of Jakob Stainer lost much more in that process than the Italian instruments. That would explain that the general taste turned to the sound of the instruments from Cremona, especially the ones made by A. Stradivari, which had lower archings than those of Stainer. When the plates were made thinner, the plates with high archings became hollow plates, and so disappeared the direct path that mechanical waves had from the feet of the bridge to the back plate through the ribs.
Not only did the direct path to the ribs disappear, but the thin plates now do not allow waves to propagate very far from the feet of the bridge before they encounter the inner and outer surfaces of the front plate. This causes many reflections and refractions in a very short time, while the waves are still very intense. So, while indeed creating a loud sound extremely rich in trebles, waves lose their intensity very fast, altogether resulting in the disappearance of the sustain. As mentioned earlier, quite a number of paths will lead to refractions back into the bridge.
The next picture is a drawing of a flat plate. Notice that in such plates, while only two are marked here, a lot of waves are reaching the ribs of the instrument in an undisturbed straight line from both feet of the bridge. That is why the flatter a plate is, the clearer is the sound it produces. This might explain why the front plates of Stainer's violas have a lower arching than his violins: to make his violins sound darker and his violas clearer. However, the broader the plates are, the less high the arching needs to be to create the same direct path. Testing is needed!
To summarize: the thick middle part of the plates creates a wide path from the feet of the bridge to allow waves to reach, undisturbed, points located farther away, including the ribs of the instrument. The sharp edge after the fluting of the plates facilitates the transit of the waves from the front to the back of the instrument through the ribs, which makes such an instrument much more sensitive and with more sustain than modern instruments.
The thinner plates of the modern instruments make waves get refracted into the air cavity of the resonance box with much more intensity because of the shorter way between the outer and inner surfaces of the plates and the many reflections and refractions that short way causes. These instruments need a modern bridge, because a baroque bridge is too direct. Therefore they also need a heavier bow. However, the thinner plates make it difficult for those waves to reach the ribs of the instrument.
On the other hand, the thicker plates of the old instruments need a baroque bridge, which is much more sensitive and lets the waves enter the front plate with much more intensity than a modern bridge. The sustain is the product of delayed wood-to-air refractions. The further away waves propagate without encountering wood-to-air boundaries, the later they reach the air. The later they reach the air, the later we perceive them. Waves reaching the back plate through the ribs will have been traveling in the wood of the instrument much longer before reaching our ears than waves being refracted into the air immediately after having entered the front plate. Waves reaching the back plate through the sound post will still reach the air cavity in the resonance box before waves reaching the back through the ribs.
Perhaps thicker plates will also call for lighter treble bars.
It is now time to look at the wind instruments through the lens of mechanical wave propagation:
