The mid RPM band of each gear? That makes me suspect either the engine or the input shaft of your transmission. What kind of transmission do you have?
If the vibration is due to the wheels, drive shaft, pinion angle, or output shaft of the transmission, then the vibration would be based upon the speed of the car and not the RPM of the engine. There will have a given speed where the vibration is most notable (usually); you're hitting the resonating frequency when this occurs.
Since the vibration seems to be dependent upon the speed of the engine, then I would suspect either the engine itself, or the input shaft of the transmission.
My advice is to do this. Drive the car up to whatever speed/RPM gives the most noticeable vibration, and then put the transmission in neutral and coast. If the vibration doesn't go away, then it is most likely a problem in your drive line (wheels, drive shaft, pinion angle, or output shaft of the transmission). If the vibration goes away, then I would suspect the engine or input of the transmission. If you have a manual, rev the engine with the clutch in and with the clutch out. See if one or the other produces the vibration.