I sometimes hear a thrilling sound that oscillates in tone, but can't find the source (It's not nirn root, which has a constant tone). Just heard it at Dragontooth Crater after I killed the dragon.

If you mean a gong-like sound, it seems to be when you discover a place with a word of power in it. That is my assumption so far anyway, I have been wondering that myself and actually came online to confirm it.

Probably just one of the sounds of the environment. There's a wind sound that's really close to a dragon roar that always gets me looking..

Sometimes after I kill a mage character, the dead body makes chiming sound that does not go away. I think it's from a residue of alteration oakflesh or some other protection spell. Maybe.

Yes, I hear that sound all the time from some dead bodies. I haven't been able to isolate the cause. There's also a musical sound when you accomplish . . . something. I think it may be killing the last enemy in the area?

I think thats for killing the boss enemy of that area, i've had that sound a lot even when there are still lesser enemies alive nearby.

I found that having a healing spell readied produces a repetitive chiming sound.

That makes sense. You may be right. I'll try to verify it sometime. Thanks.

Too bad you can't link us to a sound bite, there are a couple of "thrilling" sounds I've come across....
If you're talking about that completion-type sound, I've heard that even when I kill the last frostbite spider at Shor's Stone.
And yes, I've heard it when there are lesser enemies nearby, as in Stony Creek Cave if I kill the guy in the alchemy room before moving on to the guy with the pickaxe. Kind of like a big exhale, like, "it's all downhill from here."

When you use a healing spell it does make a very pleasant sound...

That is correct! I verified it last night. Thanks for the tip.

There's a similar sound for finding a hidden area, and another for finding the last part of a dungeon.

Yeah I wondered that. I think it's when you clear an area.

One other sound I can't quite nail, a low frequency hum near the Thalmor Embassy. From a dungeon beneath ? Any ideas anyone ?