Just so you know, that song is called "Siege of Madrigal" and is actually from an earlier Bungie game called Myth (but it is in Halo). But that sounds good.

You can actually find this song, "Siege of Madrigal", in the Halo 1 level Assault on the Control Room. in the section where you walk out of a door and onto a rock path where two banshees are sitting, you must kill one of the elites and take the banshee. off to one side of the level, there are 3 objects that look like arches embedded into the wall and the apex is shooting out from the wall. take the banshee to the 2nd arch. the easiest trick to park it is to fly straight along the apex and grinding the center of the bottomw of the banshee. now, get out, turn to the right when facing the front of the u-shaped structure and walk along it. after walking around the curve, youll start to hear the middle of "Siege of Madrigal" being looped. hope this is informative.

check your pulse
you dead yet?

is the other instrument that comes in after the piano a flute? or is it something else?

He has the other instrument set as choir aahs. I probably should have done the same to my transcription earlier but sadly I did not know how at that time. I was considering posting it again but I don't think it's necessary. I did redo the file so if anyone actually wants it then let me know and I will put it up.