Define this music-related terms with electrical terms
There's a lot of questions in this post. In very brief attempt to summarize this topic, a pure note would be a sine wave in the time domain. In the frequency domain, this is represented by a single spike at a point on the x-axis (now the frequency axis starting at 0 and usually going up logorithmically).

"A harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency" http://en.wikipedia.org/wiki/Harmonic
So a harmonic is nothing more than frequency that's double or triple or quad etc. the original frequency. Most notes made by instruments aren't pure sine waves so you end up getting some kind of harmonics coming from it which can be seen somewhat here:
http://www.dspguide.com/ch11/5.htm

Bandwidth is simply a measure of a range of frequencies. A note isn't a bandwidth. A note and its harmonics could be filtered with a well chosen resistor and capacitor to filter a certain bandwidth that allows the note and it's harmonics to pass. Hope I made the frequency world a little less foggy...