Originally Posted by: ELKAT100[p]
If the string length between the bridge & the nut is the same and you would barre at the first fret or at the nut why do you get different notes if the length is the same.
I wanted to focus on the bold stuff.
The actual note is not ringing off your finger pressure. The actual pitch of the note is ringing off the fret. Meaning, your finger pressure is to push the string down hard enough on the fret so that the string can ring off the pitch (note) that fret represents. Think of it literally this way; when you hear descriptions of '6th string/3rd Fret' (G), it literally means that the G is the third fret, not the fretboard space between the 2nd and 3rd fret. The distance (per Chris' explanation below) is always the distance between that fret (eg - 3rd/G) and the bridge.
So, when you barre on the first fret (F - if doing a full 6 string barre chord), no matter how close or far from the nut you place your finger within that space between the nut and the 1st fret, the string is ringing off that first fret and is why it is an F note and not a variation of the open E.
Also to add to Chris' explanation on length; tuning and detuning don't materially change the length of the string per se (this is a fixed point based on the tuning peg, nut and bridge) but it does change the tension. From a physics standpoint, that tension change alters that wavelength that string is projecting. Tighter? Faster wavelength and higher pitch. Looser? Slower wavelength and lower pitch.