David, Forget it. There are formulae for calculating string length, and there are computer programs that will do it. But as one who is designing un-fretted instruments let me give you some input. It is too late at night for me to evaulate the formula below, it might be quite correct. But I've gone through twenty years of harp string calculations (no, I'm new, just two years, but I have the back articles).
I have found that there is a constant in the harp string formulae (remember that it is a direct pull off the soundboard in contrast to the lute), there is a constant of 32, which has been called acceleration, and matches the 32 ft/sec/sec acceleration of gravity. And is therefore patently ridiculous. Whatever, in the design I'm doing for a levered psaltery (like the harp, fixed and unstopped strings, but stopped by the levers at each string to give the chromatic scale key changes), I have found that the nylon, gut, and steel strings all have about the same characteristic as to the length to pitch. You got it close, but the harp people kept telling me that the guage of the string didn't matter as to the breaking tension. I didn't believe them, but I've built a test board that confirms it. (Guage of the monofiliment string, not the mass per unit length of a wound string, the harp goes to lower levels that would make the monofiliment impossibly long to reach the bass). If youl'd like (and even if you don't please) I'll send you the formula the harp makers use, but not tonight. And maybe not until I get back from my Tigertone reunion next week (a bunch of singers all over 65). I still can't get a reason why the acceleration factor of gravity should be a constant, but the other constants are the combination of tensile strength and mass per unit length, and the only material that is really out of line is bronze wire (something used very early, they had bronze before steel so it is possible that the lute, like the harp, started with drawn metal strings. Nylon, gut and steel wire each like about eight inches to be in the range of C2 (C6 in regular notation, where middle C is C4). Suffice to say two octaves above middle C. The bronze wires want about four inches for the same note, and that is my design problem. I don't know whether to make it a "bass psaltery", or to go with the high C. My string maker says bronze won't ring right if less than eight inches, but my test board (solid wood, no resonance) tells me different. Sorry to get off on a tangent, back to the beginning. The formula is a guide, not a rule. Until some of the information from you all on the list I'd assumed that the lute was a fixed fretted instrument, an ancestor of the guitar. But now I see there are other subtleties, the variable frets with the tied gut frets. But let none of that say that I don't know strings. Strings are crazy (not really), I slide my moveable bridges on my test board and they go lower as I shorten the vibrating length - oops, the level of the bridges and bridge pins I set were such that I increased tension as I shortened the string, the trade off. My mountain dulcimer was designed for .013 steel strings on the doubled treble, but I find .011 carries the sound and balances the tension with the other strings. The choice of guage is more a matter of balancing the tension of the feel than making the pitch, (again, neglecting those lower strings that need the windings to make the mass, and if one were to use monofiliment for those strings they would be so soft as to be out of balance). I'm new to the lute, but not new to strings. I do confess that my string experience is with both harp (direct pull) and psaltery (indirect pull across a bridge, like the lute). I resign for the evening, but welcome any comments on the nature of the strings. Best. Jon (I can give you the nominal mass per unit of the different string materials, excepting the wound strings (and I'll soon test them and make an empirical number). ----- Original Message ----- From: "LGS-Europe" <[EMAIL PROTECTED]> To: "Lute net" <[EMAIL PROTECTED]> Sent: Monday, September 22, 2003 1:58 AM Subject: formula > Perhaps one of the rocket scientists (Arto, Taco?) on the list can help me > with this. > Mersenne and Galileo already found out that: > - Frequency is inversely related to String Length. > - Frequency is related to the square root of String Tension. > - Fequency is inversely related to the square root of the String Mass per > unit length. > >From this I can deduce a formula for calculating string length / frequency / > material / diameter, much like Arto's Super String Calculator: > > T = constant * F^2 * L ^2 * Pi * (0.5 * d)^2 * D > > T = Tension > F = Frequency > L = String Length > d = String diameter > D = Density of String material > > The constant has to be 0,04 > My question is: why 0,04? Coincidence, some fixed constant in nature or just > a > stupid question because I am missing something obvious? > > David > > > > > > ***************************************** > David van Ooijen > Email: [EMAIL PROTECTED] > Http://home.planet.nl/~d.v.ooijen/ > ***************************************** > Read about my latest Japanese CD and hear a sample at > http://home.planet.nl/~d.v.ooijen/david/ensembles/chiyomi.html > > > >
