The total length of the string is the length that determines the tension the string has to be brought to to attain a given pitch.
The bit behind the nut matters, as does the bit below the bridge if relevent on the guitar in quesion.
f=(1/2L).sqrt(T/d)
where f is frequency, L is the length of the string, T is its tension and d is the mass per unit length of the string, f is therefore inversely proportional to L (but we all knew that already, right?) and L has to be the total length. That means that if you increase the length behind the nut for the same pitch, tension as a funtion of length here is
T = 4df^2L^2
But we're keeping f constant d is also constant, and so was '4', last I checked, so may as well write
T~ L^2
= increase length, increase tension needed to attain the same pitch, so philly was right.
Sorry for the maths, but its a physics question, it gets a real physics answer :p.
I'm afraid that I can't sign up to this one mate.
What that formula doesn't take into account is the two MASSIVE dampers in the system (being the bridge and the nut). As the length between these two points remains the same, then I would say that for any gauge string, the tension between these two points remains the same (and therefore the tension of the whole string).
I would model the string behind the nut and bridge as a further damper to the system which has the affect Feline talks about.
I'm not a physicist, but that's my engineering opinion :lol:
There are myriad dampers in the system, but the string length in question is definitely the full length, not the scale length.
Anyone that has a floyd rose equipped guitar should know this all too well, and if you've got one you can prove the above with it.
Engineers and physicists both appreciate experiments :)
Tune up the guitar, lock down the nut clamps.
Take the string with the longest total travel and use the fine tuners to change the tuning by a tone/as much as you can
Unlock the clamp for that string.
If you tuned it up, the pitch will drop when the clamp is released because your increase in tension between the nut and bridge is now distributed over the whole string, so the tension per unit length is lower
If you tuned down the pitch will raise when the clamp is released, because your reduction in tension per unit length from the nut and bridge is now over the whole string, and averaged with the higher tension per unit length that the section above the nut was held at by the clamp.
The total load on the string doesnt change when you release the clamp, the distribution of load per unit length above and below the nut is is simply equalised. Ergo, the length of string in question as to what tension one must attain for a given pitch and gauge is the entire length of string, not just the length between the nut and bridge
