# Trying to understanding resonance, harmonics wrt standing waves

I keep getting confused about this and I'm not sure if it's because I keep thinking of guitar harmonics, so I thought I'd just try to explain: please tell me if my understanding is correct or not. A string on a guitar has 2 nodes. One at nut and one at tuning peg. When string is plucked it will vibrate at its fundamental frequency, which means the middle of the standing wave has maximum displacement from its equilibrium position.

But I know that there's a harmonic on a guitar at 12th fret. But when I pluck a harmonic on 12th fret what exactly does this represent wrt the standing wave? By placing my finger at 12th fret, am I imposing a node at that location? If so, then what is difference if I actually press down fully at 12th fret.

Also, am I correct in saying that a string that has nodes at both ends is the same as a closed pipe. A string that is attached at one end but other end free (an antinode) is the same as an open pipe.

The fundamental frequency for string with nodes at either end is the same as the 1st harmonic. I don't understand why this wouldn't be the 0th harmonic. Its length will correspond to one-half of a wavelength because it must attach to nodes at either end... but if we add one node in middle of string, then the length of string will equate to one complete wavelength, which corresponds to 1st harmonic. How wrong or right is this?