I am sorry, I don't really have any way to record it digitally. The sound is very faint and I only noticed it after reading about your problem. Even if I did have a way to record it, I think that the normal idle noise would overcome the "ringing" sound anyway. I had a 1992 Camaro that made a similar sound (though a lot louder) and it seemed to me that it was attributed to the idler pulley. I noticed that the idler pulley is underneath the alternator on this car and that's where it sounds like the noise is coming from. In a general sense, I would say that a ringing noise doesn't indicate something wrong with the engine as it can only be created by an open piece of metal, something that isn't attached to something else by very much. Most moving parts of the engine are pretty well attached or are muffled by fluids. I don't think it is anything to worry about, it's just very annoying cause it makes your car sound less quality.