Wow! I've been thinking about this too much over the past couple of days. I'm too lazy to look up the equations of vibrating strings and I'm not even sure they would help here.
I did come up with a rational thought experiment however.
Hypothesis: for a given length of string tunned to a given pitch, there will be a certain "window" of string diameters which produce a quality tone. Strings of too great a diameter will break before they reach pitch. Too narrow a diameter will allow the energy to be transmitted through the string material through other types of waves (eg torsional).
Convincing argument (?): Strings break from overtightening. I think we all see that so all I'll say is try to tighten your "G" string to the "E" a major sixth higher -- I bet it will break before that point.
For the other side of the argument: take your "B" string and lower it to the "G" a major third lower and compare how the two sound. If you can't hear the difference, keep lowering the "B" string to the "D" below that. There must come an area as the string slacks up where pitch becomes less distinct (probably sounds as if it is going from sharp to flat) and later that you become unclear as to whether you are hearing a pitch at all as it begins to flap.
I won't comment on the quality of the tone question, or the "crutch" question since those are both matters of taste. I'm just saying that there must be a difference, and it's possible that people will notice that difference.
|