On Dec 4, 2009, at 11:06 AM, Ron Nossaman wrote: >> >> Part of my assumption is based on the fact that bridges are >> curved to a scale, and it is not a logarithmic one that doubles >> lengths for every octave. A given string at the same tension should >> give an octave lower at double the length, two octaves lower at 4 >> times the length, etc. Scales foreshorten these distances. Hence, I >> reason that the given size wire would need to be at a lower tension >> if the octave lower length were shorter. Is this not true? > > It's certainly irrelevant to whether replacing a given string with a > different size changes break%, which has, I think, been the question. Let me make another stab at explaining this reasoning. We'll make a one octave piano (for simplicity) with one gauge. We'll make the bottom string length two times the top string length, and do a logarithmic scale between. All strings will be at precisely the same tension, and percent of breaking point, correct? Now we foreshorten the scale, still logarithmic, but the lowest string is less than twice the top string. Tension will reduce evenly as we go down the scale, correct? Hence we will be at a lower percent of breaking point as we go down the scale, correct? All pianos and harpsichords have foreshortened scales. It doesn't take a spreadsheet to see that if you strung a piano with 13 wire throughout, the tension would decrease as you went down the scale, and the percent of breaking point would also decrease. And that the same thing would be true if you started at the point where any other gauge began and strung the lower portion of the piano with that gauge. Or is there some fallacy I am missing in this reasoning? Regards, Fred Sturm University of New Mexico fssturm at unm.edu
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