Mystery solved.
It's Meet Me In The Middle by Zedd, Maren Morrice and Grey.
https://youtu.be/M3mJkSqZbX4
The wailing starts around 0:57
To be fair, the song does actually have words, and they're quite intelligible. I guess the song is so banal that I don't even hear the words, just the wailing parts. I hear her going INNA MEEEEEEEEEEDLE in the chorus and all I hear is "AIYE AIYYEEEE AIYYEE".
The rant below is not mine. But it sums up my feelings about the song more eloquently than I can ever express. (NSFW)
http://www.reddit.com/r/rant/comment..._in_the_middle