Marc said: > Although this article gives a good way to comprehend the working of the > chien I have some serious doubts about the 293 times... this is in no way > explained and up to me this frequentie depends from many factors ... > Weight of the chien, amount of rosin on the wheel and coton on the string, > lengt of the string diameter tension..... > Who has a good explanation for those???
Here's how it works. For a moment, we're going to ignore the movement of chien, and just look at the way the string and the wheel interact. The wheel imparts its motion to the string by what is called the "stick-slip" model. We tend to think of strings as just vibrating back and forth, with the center moving the most, and the ends staying fixed. While it's a reasonable model for visualizing what's happening with a plucked string, it doesn't really work for a bowed string. The wheel "sticks" to the string and moves it sideways. If we're looking at a chanter string, this deflection is away from the player, because that's the direction the wheel is pulling on the string. This local disturbance (we can think of it as a "kink") in the string moves up the string to the nut. The energy doesn't have anywhere to go, so it gets reflected back down the string, but now the deflection is toward the player. When this kink gets close enough to the wheel, the friction of the wheel on the string is no longer enough to keep the string stuck to the wheel, and the string "slips" back toward the player. The kink continues on and gets reflected by the bridge. Now it's deflected away from the player again, and the wheel and string are stuck together again. So - "stick, slip, stick, slip". If this isn't clear, check out this great website at the University of New South Wales: http://www.phys.unsw.edu.au/jw/Bows.html There's a really nice animation that shows what I'm describing. How often this cycle repeats depends on the string tension and length. If the string is tuned to g', which is 293 cycles per second, the cycle will repeat 293 times per second. If we shorten the string to an a', now the string will vibrate at 440 cycles per second. Now back to the chien. When the "kink" is moving along the string, it will move the bridge or nut if it can. Obviously the string can't compress the chien down into the soundboard, so it can't move down, but the bridge CAN move up, so the string lifts it up. When the string "slips" on the wheel, the chien moves back down, and taps on the soundboard. >From this we conclude that the chien will tap at the same frequency as the trompette string. For a trompette tuned in d', this will be 293 Hz (cycles per second). Alden
