In the song As I Am by Dream Theater (Just one example of many), in the intro, there are some notes that are played, and then slowly get higher pitched to there at the pitch of a harmonic... Its kinda hard to describe. Its like you hit a note, and its not exactly tapping a harmonic, because theres a gradual pitch increase. It doesnt really sound like a whammy pedal either... does anyone have any clue how to preform this?
It's feedback, if you watch the ToT Dream Theater studio video I think it is, you'll see him playing it next to his speakers.
Quest for "the tone": pending.
It IS feedback. No other ideas are needed, sorry.

Daggorath pretty much covered that one.

I love that song. That guitar solo is what got me into guitar. Damn.
I always halfway pinch the string so it starts out somewhat higher then it fades into feedback and you raise it about half a step with the trem and vibrato it as your raising it.

I love this song a lot!
Major of 7 String Legion 7 > 6

Carvin DC747
Ibanez RG2228
Schecter Avenger Custom Shop
and my baby....
Gibson Explorer Studio
So how exactly would I go about preforming this... playing the note while standing right next to my speaker? I guess the volume would have to be cranked, right?
Yes, and gain up, bridge pickup; you can try hitting a false harmonic by tapping lightly 5/7/12 frets up from the note you picked, but that's not actually how he does it.
Quest for "the tone": pending.
Lots of distortion, lots of volume, stand really close.
Quote by corduroyEW
Cheap amps are "that bad". They suck up your tone like cocaine at Kate Moss' party.

I am Michael!