from Vince Mrykalo: >It seems to me that if you could have pressure points on the strings >(ie pressure bar), without friction, you could still fine tune.... I don't see friction in and >of itself as being of benefit to fine tuning. But of course pressure without friction is >impossible, so we take the good with the bad. Amazing Reply from Bob Davis: Okay, let's take for the sake of discussion a frictionless rotating bearing point made of a pair of opposing superconducting magnets revolving at zero degrees Celsius..... or.... something like that. I did some math on tuning pin rotation today, and here for your amusement (and my amazement) are the results: real 6'4" piano, note a4: frequency 440 Hz speaking length 15.3937 inches (391 mm), diameter .038 tension 154.26797 lbs. same note (a4) raised ONE CENT: frequency 440.25423 Hz tension 154.44629 (less than three ounces difference) Total string length, tuning pin to hitch pin, approx. 24 inches Elongation @440 Hz = 0.1120611 inches Elongation, 440.25423 Hz = 0.1121906 inches Extra elongation w/one cent rise = 0.0001295 inches Diameter of tuning pin = 0.281 inches Circumference of tuning pin = 0.8827875 inches Ratio of extra elongation to one full turn of tuning pin = 0.0001467 (one SEVEN-THOUSANDTH of a turn) Above ratio times 360 degrees (gives # of degrees rotation per 1 cent rise) = 0.0528234 (a twentieth of a degree) Circumference of rotation of 11" tuning lever = 69.115038" Distance end of lever moves for one degree rotation = 0.1919862" Distance end of lever moves for one cent rise in pitch = 0.0101414" (a hundredth of an inch) I realize I left out some subtleties like I probably should have added the thickness of the wire to the diameter of the tuning pin, BUT unless my figures are really wrong (math geeks please respond) I don't think we could achieve this kind of control of rotation without friction to help us (ahem) cheat. What we do is already nothing short of AMAZING!! Incidentally, in a frictionless screwstringer device with, say, 36 threads per inch, each full turn would elongate the string 1/36 inch, or 0.027777. For an elongation commensurate with a one-cent rise in pitch (0.0001295"), the screw would have to turn roughly 0.004662 of a full turn, or 1.678 degrees (easier than a tuning pin)? Yeah, you're right, I probably DO have better things to do...... Bob Davis, RPT
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