Yeah That is Actually my exact plan in the future. I get into the statistics of this stuff too, I'd like to look over the math if possible.
Yeah That is Actually my exact plan in the future. I get into the statistics of this stuff too, I'd like to look over the math if possible.
Yeah so the equation for the fundamental frequency is f=1/2Lroot(T/µ), where F is the fundamental frequency, L is the length of the string, T is the tensional force, and µ is the mass per unit of distance, in the imperial system lb/ft or metric kg/m. This is derived from a couple things, but basically it says that if you increase the length of the string, pitch goes down, if you increase tension, pitch increases,and if you increase the mass per unit pitch will go up. Look up marssene's laws if I'm unclear.
String makers use these relations to get you the feel you want out of strings. A low guage string means low mass per unit (µ) which raises pitch, so to get the desired frequency they decrease the tension. Length (L) on a bass guitar is constant, that's your scale! Conversely a high guage string, or a string with a lot of mass like a flatwound string, will a higher tension. Tension (T) and mass per unit (µ) are inversely related.
The reason we perceive flats as thumpy and new rounds as bright is the difference in overtones. When a string vibrates it behaves like a weight suspended on 2 springs, it oscillates at a specific frequency when agitated (in our case by fingers, pick, slap, etc.) and the only way to affect that frequency is via the length of the springs, the mass of the weight, or the stiffness of the springs. Now a spring-weight system with just one weight would produce 1 pure tone with little to no overtones, and a system with 2 weights would 1 overtone, 3 weights 2 overtones, and so on and so forth, but an instrument spring behaves like an infinite number weights oscillating at the same time, producing mostly the fundamental but also every harmonic of that fundamental. The volume of those harmonics is our perceived scale of bright (more harmonics sounding with the fundamental) to mellow (less harmonics). A roundwound string produces more harmonic content because the winding adds a lot of masses to our system, and a flatwound string doesn't add all that many comparably. Thus the difference in sound.
Hope that helps, little more physics than statistics.
In other news I think
Sweetwater is having a sale on most of the light gauge roundwounds, might want to get some to try out!