Engine Vibration

My car has 120K miles on it. I always perform a lot
of preventative maintenance just to be on the safe
side. Therefore, it still drives like a dream. However,
here lately, I've been experiencing very noticeable
engine vibration.

Vibration Characteristics:
-Between 2K & 3K rpms (any gear)
-Under *moderate* acceleration (typically when the
car is in 6th gear and the throttle is being applied
just enough for it NOT to downshift)

Now, the car does NOT vibrate when under normal
acceleration (when rpms don't go above 2.2K) or
when under max acceleration. I don't understand.

Any ideas? I feel like it's a motors mount on its last
leg... But I feel like if it's a motor mount, wouldn't I
experience vibration under all rpm ranges of
acceleration??