> Certainly the real situation is a dynamic one and the static model is a > (gross) simplification. Gotta start somewhere though. > I'm skeptical. There is the static friction at the bridge pins that has to > be overcome. If my numbers were in the ballpark that amounts to about 10 > pounds or more at each pin. I don't think that the small changes in length > of the string segments due to the sort of temperature ranges that a piano > is normally exposed to would cause that much change in string tension. Possibly not. The point is it's movement, and the difference between the static friction supposedly holding a string above the bridge cap and the combination of downbearing, pin slant, and string offset angle trying to pull it down is much closer than 10 lbs. >So, > I think the string will stay put at the friction points and the string > segments will grow or shrink between them due to temperature changes. How > would humidity change affect the string? It wouldn't, directly, but the bridge would move relative to the pins. Again, I haven't measured it, but I don't see how the pins could avoid moving relative to one another (at least somewhat) as the bridge changes dimension more or less continuously. >As I see it the change would mean > soundboard movement up or down, which would change string tension and would > probably affect the speaking portion and backscale portion > differently. Perhaps enough to cause a 10 pound tension mismatch if the > movement was great enough. It isn't. There is much more tension change resulting from the bridge moving strings up and down diverging pins. Incidentally, while the soundboard is moving, the bridge top, and presumably the string, is also moving on the pin - breaking the friction enough for the string to render through from segment tension differences. That's going up. It remains to be seen if anyone can demonstrate that the string stays stuck to the pin enough to lose contact with the cap in the dry cycles. >However, if there is some other mechanism, such > as string vibration causing some minute movement of the string on the pin, > this may break the static friction and cause the strings to move past the > pins with much smaller tension mismatches. This is what I think happens. > I'm not sure I understand the mechanism that you're describing here. Are > you talking about the bridge cap trying to move up on a wet cycle, but the > pin holds the string in place, crushing it into the cap? Exactly. I've directly measured an 0.011" difference in pin height above the cap surface in a bridge model I cycled through a couple of cycles of from 4% - 12% MC. The force required to push the string up the divergently slanted pins is half again that required to render a string straight past a pin. That's a heck of a PSI load on a maybe 0.010" wide groove in a maple cap. Take a pin out of the speaking side of an old bridge. Hold a short length of straightened piano wire in the existing string groove with a screwdriver of knife blade at a right angle to the wire. hold down in the middle of the bridge first and note that the wire is pretty much parallel to the bridge top. Now hold it closer to the notch edge, and closer, and at the bridge pin hole and watch the tangent angle of that groove go to maybe 15° at the notch edge. Now imagine a wire under tension resting on the center of the bridge, and going down at a generous 1° angle to the agraffe. It will pass the pin hole some distance above the cap. The string has NOT climbed the pin. The notch edge simply doesn't reach the strings natural path any more because it has been crushed too low to make contact unless the bridge is in the expansion cycle. Forcing it down to contact by tapping the string or driving the pin has no chance of keeping it down there. It will once again seek it's straight line path and lose contact with the notch edge until the next expansion cycle. > Any ideas about why a flagpoling bridge pin causes false beats? > > Phil Ford Yes. The pin has nearly no stress on it below the surface of the bridge, so it hasn't greatly deformed the wood that surrounds it. At the cap surface, the side stress of the cap pushing the string up a slanted pin (combined with the normal side bearing) pushes the pin against the side of the hole. The deformation the pin makes in the hole is like the deformation the string makes in the bridge top. It curves, because the pin is slightly sprung by the forces involved just like the string is, only less because the pin is stiffer. So here's a pin, tight in the bottom of the hole, and looser at the top. At some point below the surface of the cap is the place where the back side (away from the string) of the pin parts company with the cap and is free to flagpole. It becomes a spring. The pin is still the string's vertical termination point, just like it always was if the bridge was notched deeply enough at manufacture. But the horizontal termination is a spring with a more solid termination somewhat beyond the spring on the bridge surface. The beat is the difference between the vertical excursion frequency and the horizontal excursion frequency of the string caused by the lossy horizontal termination. Tapping the string or driving the pin clamps the string down to the cap closer to the pin , courtesy of friction between string and pin and string and cap, and restricts horizontal movement of the springy pin. This makes the horizontal and vertical excursion frequencies close enough to the same to kill, or minimize the beat. If the friction between string and pin isn't sufficient to hold the string tightly against the notch edge, or if the pin or notch edge is too damaged to provide the necessary clamp, it doesn't "fix" the false beat. The unfocused sound that seating clears up is the string grazing, but not clearing the cap enough to produce a clear beat. Seating these, especially by driving the pins, should produce really nice false beats soon enough. In all these cases, the mechanism that produces the beat is the bridge pin that is not solid in the cap at the surface and can flagpole. It doesn't take much. I think we see this only in the top two sections because the differences in the two apparent speaking lengths the flagpoling pin provides quits producing clear beats as that difference becomes a small enough percentage of the speaking length and resulting frequency. The longer strings absorb the difference better, like they will in unison tuning. I need an animation. This would be so much simpler and more obvious to watch than to describe.
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