I am new to setting up violins hence I have checked out this forum. I am a physicist so my view of the mechanics would be that the tension on the strings will compress the body slightly along the length of the belly and back. This must happen due to the longitudinal curvature of belly and back. I would think the flexibility of the glue and compressibility of the wood would be a factor in the bodies resistance to this longitudinal compression as the belly/back near the ribs will compress as the middle of the belly bows outwards. The exact thickness, design, wood type/ age of instrument, humidity, stiffness of the bass bar (and flexibility of glue?) must be critical in reducing any change of shape. All these factors would affect the increase in distance between belly and back when strings are tightened. However, the strings also push down on the bridge which would tend to counteract this expansion. This balance of forces is surely why violins last hundreds of years compared to say guitars where the string tension eventually destroys the top sound board. The construction variations and the wood / glue used would affect the balance of the two competing forces on the belly. Some belly’s may bow outwards under compression more than others and perhaps some not at all (unlikely I would think). This would depend on the uncompressed curvature of the belly which must vary slightly between violins. It does, I have two old violins in-front of me and they are different. The force down on the belly from the bridge would depend on string selection, bridge height and length from end pin to nut. In terms of the mechanics it’s the angle the strings deviate by as they pass over the bridge that affects the downward force. With all these variables it doesn’t surprise me at all that some sound posts fall when you tighten strings and some get tighter when you tighten strings. I guess the best method has to be checking the ‘tightness’ once tuned as this is where it’s obviously going to count. Other than this there seems to be little point in employing the same routine for all violins which will result in a massive variation in final sound post compressive force. The only other logical method is of course trial-and-error to see what sounds best. Which brings us back to the original question, how tight should a sound post be !
I have all the equipment so I am going to experiment. I have heard that I need a ‘swear box’ if a newbie to fitting sound posts’!
And by the way, I think the sound post may have multiple functions. It creates a node in just the right place to alter the harmonics you hear. It will change the resonant frequencies of the body. It may damp unwanted resonances. It may persuade belly and back to vibrate at the same frequency? It certainly must also transmit vibrations directly to the back of the violin. This vibration will have a phase difference depending on the density of the post (and compression). This phase difference will influence how the belly and back oscillate with respect to each other and the vibrating air within the violin. The phase difference is caused by the time it takes sound to travel through the post and arrive at the back. This phase difference is different for different frequencies and could cause reinforcement or cancellation of certain frequencies. This is why different tightness/ thickness/ material of sound post causes the changes in sound that many have described.
Its quite funny that I had an old broken violin many years ago and I thought the post was just a structural strut!