Maybe its somehow doing a harmonic?
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If its what I think it is its the string popping out of place and ending up at a lower pitch? Make sure its connected good at the bridge and pegs.
I think it might be the string slipping through the nut, causing a harmonic. My friends guitar used to do it, but I don't think it's anything to worry about.
Lubing the tuning head will stop the ping I think (could be wrong though).
It is probably the string getting caught in the nut and then releasing. To fix, get a sharp pencil (graphite) and rub it in the nut slots to provide lubrication for the strings. Simple as that.
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I remember the first time a string slipped when I was putting it on. It scared the crap out of me and when I saw that the string hadn't broken I was looking around wondering what the hell happened.

But yeah, sometimes when tuning up strings for the first time they slip or pop. It hasn't happened to me in forever so I don't know if maybe proper stringing technique and/or lube and setup reduce the likelihood of it.
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