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https://www.youtube.com/watch?v=8LXZxcEdRCA
@8:03 - Boy Meets World (an original song)
https://www.youtube.com/watch?v=Xi31NAktYDw&playnext=1&list=PL9516BF3094B1946D&feature=results_video
- Bioshock
https://www.youtube.com/watch?v=VIwC9_VCZCY
- Bioshock again (an original song)
https://www.youtube.com/watch?v=eajTjs1n6T0
- Jeepers Creepers
I couldn't find one of "I Only Have Eyes For You" in context, even though it's one of the most popular to use. But I think the original songs are even better examples because they show that people associate the sound with a creepy atmosphere beyond just repurposing old music.
Ok... a couple of things going on. The Jeepers Creepers one is harmony, usually something like two or four part harmony. Annette Funicello on her beach songs would have her own voice overlaid twice, singing the same song two separate times that were then overlaid to give something of the same effect. A bunch of people singing at the same time.
The first Bioshock video is vibrato
, one voice with the sort of warble you described, one person singing and because of the muscles used, the pitch pulsates.
The second bioshock one I recognize but don't know the official name for; it's from back either before microphones, or sensitive microphones, and they'd sing through a small (unpowered) megaphone (Here's
Stone Temple Pilots doing it with a powered one in Crackerman) which gave that sort of hollow nasal sound. Obviously now its done for the effect of 'old timey' music, rather than because you'd otherwise have to shout your lungs inside out... The megaphone page
on The Other Wiki has "Applied to music, it gives the sound of an antique acoustic gramophone record player."
The boy meets world one is kind of a nasally singing, singing more through the nose than the throat, which gives it a different tone. Again, not sure of the specific name for it.
Hope that at least gives you a place to start looking. Or someone who knows more about the music will argue with me. :D
I think I have an idea of what you mean with 'Eyes', where it sounds like a wind up recorder or something that's running down, so it's pitch shifted lower, and warbles a bit like the first Bioshock video.
Edited by AzaramOh, sorry. :P Got distracted in the research and totally forgot the original question. Might be something findable in Music Tropes; the closest I found was Ominous Music Box Tune for the Eyes one, even though it's not literally a music box.
Edited by Azaram

There's a singing style in the 20s/30s that I can only describe as "warbling", even if I'm not sure that's correct. Anyway, it's frequently (and easily) used to add an eerie feel to a scene. Examples:
"I Only Have Eyes For You" in Jeepers Creepers and the Buffy episode of the same name.
"Welcome to John Adams High" in the episode of Boy Meets World that spoofs horror movies (the one with Jennifer Love Fefferman)
And I'm sure there are others I can't think of at the moment. Anyway, is there a trope for this?