I have a 2.4 that was recently rebuilt. Has about six thousand miles on it. Recently I started hearing a strange noise around 2,500 rpm and 3,500 rpm. Its most noticeable in first and second gear, and is very faint in the rest. Its very picky on where the throttle is if it wants to make the noise also. Wide open it does not really occur but somewhere around 50% it usually comes in. I just changed the oil today and there was no metal in the oil or the filter. So Im possibly ruling out bearings. Any ideas?

Has this motor been a complete rebuild or just certain parts been replaced?.

It was a complete rebuild. Only reused parts were lifters and cams, springs. Anything head down is new.

Maybe you got wornout rocker arm or lifter, Could have a weak cyl hd spring,

Its DOHC it doesnt have rocker arms. I think its the timing chain tensioner,