I was told my music teacher that certain notes harmonize with other certain notes. So can anyone point me in the right direction as to what notes harmonize with what other notes?

My band is doing a demo soon and im trying to work on a harmonized guitar solo for one of the songs and its not coming together very well.

It depends on the key signature really, but usually an interval of a major 5th harmonizes quite well, but its all susceptible. or i could just be completely wrong i can't remember.
Well.. what kind of harmony do you want? There are pretty many ways to harmonize notes. But yeah..

I think some metalcore(?) bands are using this kind of harmonize, I'm not sure, I myself use it alot.

C-D-E (A string 3-5-7)
E-F#-G (A string 7-9-10)

You can continue this.
playing one string higher is also pretty brutal(?) harmony. You may chose yourself what you want.
Play the same thing in the same scale,except you move it a degree up. Like:

and over that you can play, for instance

Might soubd like dew, but its where it starts,
Quote by CoreysMonster
Why, my pasty danish cracker, I believe you've got it!
You can use 5ths and Octaves. That's about all I know.. My knowledge into music theory isn't too deep, I need to spend more time in the musican talk forum
any note will harmonize with any other note. it can sound happy or sad or dissonant or whatever depending on what notes youre using. i think what youre looking for is the intervals in music theory. you just assume any given note is the root and all the different notes you can play pertain to a certain interval relative to the root note. its the kind of thing you have to learn with your ears so i would advise finding some kind of interval printout and start connecting how it sounds with how many half steps the other note/notes are away from the root. its a lot simpler than it sounds after you just start learning with your ears.