David, And therein lies the rub (sorry Hamlet). The formulae for strings are predictive for known instruments and the physics of the strings. But you use the word "happy" in describing a string sound. (Although you say happy at E or F, or anything in between - what is between E and F that isn't in an Oriental scale <g>).
I'm getting a lot of good input from this list, and links to the math. But there seem to be some criteria for musical sound that aren't covered in the traditional formulae. Just for argument let us say that there is only one material for a string, we'll call it George so no one will think of gut or nylon or steel or whatever. George strings have a certain material strength (tensile strength) and a certain density (mass per unit). George strings are perfect in structure, there are no weak points from manufacture and the gauge is perfect to the angstrom unit, and there is no point where the density is greater due to an error in the mixture of ingredients used in making the "string soup" from which it is drawn. OK, we know that George strings have a breaking pitch at any given length, whatever the guage of the string. That is because the unitary tensile strength enables it to take more stress as the cross section increases. And the given pitch requires more tension at a given length when the unitary mass (guage) is greater. This is empirically true, although I'm not sure if it is actually so when one gets to extremes out of the range of musical strings (bridge cables or microfibers - so the math may not be perfect). We also know that there is a subjective factor as to "action", the harpist likes each string to feel similar from bass to treble, and the fnger stopped player (lute, guitar, violin) likes to feel the same pressure in stopping the string. And we know that the volume of the sound is a function of the amplitude of the vibration (along with amplifying factors such as the nature of the soundboard, and sympathetic strings - but let us forget then for now). What I am finding is that shorter string lengths (VL) seem to have a more musical sound when under less tension (which allows greater freedom for the string to sound on more nodal points, and therefore more overtones). The "full length" lute (my 63.5, but that is a bit long for a G lute - make it about 60cm) is quite comfortable with a chanterelle at near to the break pitch, but my 36cm charango is rather dull when the string is that close to full capacity. I go on too long, but I believe there is information here. My harp, and every harp I know, is "plinky" in the upper registers. I think that is because the strings are chosen to match the tension to keep the "action". On fingerboard instruments one must keep the amplitude of the vibrations down enough to not get a buzz on the frets, and yet try to balance the action of the several courses. As an old folk guitarist who doesn't strike the strings hard I just saved myself a lot of money by modifying the string height (filing the nut and the bridge) to "ease" the action on my old beastie. I tried a number of new guitars to get a faster action, and found that none of them matched my old beast in tone, so I figured I'd ease the action the other way - just lower the strings over the frets. And there is the trade off. Nothing is perfect. If the string is too low over the fret it will buzz, but that can be cured with a thicker guage so the amplitude is less. But then the greater tension for the pitch will change the overtones. That was simplistic, the other trade offs are a bit more complex. The musician wants a consistant action on all courses, but also the perfect tension on the particular length for the best sound. As the action/tension combination varies by the length of the string, and the freedom of vibration in the sense of overtones does also, this is an impossibility. The best one can do is strike a balance of the various factors. And I think that needs more work when one wants to cross from one instrument to another (or one size to another within a family). Best, Jon ----- Original Message ----- From: "David Cameron" <[EMAIL PROTECTED]> To: <lute@cs.dartmouth.edu> Sent: Thursday, December 23, 2004 4:34 PM Subject: Re: Tension and vibrating length > Jon Murphy wrote: > > "... I've noted before that my 63.5 lute is happy with about 35 N on the > chanterelle (disregarding the pitch, other factors there) - whereas the 36 > instrument I'm working with is recommended to be 27N..." > > Hi Jon, > > I find that very interesting. I just completed my first stringed instrument > last month, a 3/4 size guitar for my sister, who has very small hands. > > The scale length is 57.9cm, exactly equivalent to a 65cm classical guitar > stopped at the second fret. I strung it with the lightest guitar strings I > could find, and expected to tune the first string to F#. But there is no way > it wants to be up that high. It's perfectly happy at F or E, or anywhere > between. Even at E the action is very similiar to that of a full size > classical guitar, even though the actual string tension is considerably lower. > > David Cameron > > > > > To get on or off this list see list information at > http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html > > >
