Dave - with an Induction motor, the motor speed follows the frequency of the supply. This is the type motor used in simpler machines like a grinder, belt sander, band saw, etc. 60 Hz is the same as 3600 Cycles per minute. We typically see induction motors rated 1725 RPM. These are 4-pole motors meaning they turn one revolution for every two power system cycles. Induction motors also have what's called a Slip Frequency. If you put 60 Hz voltage to a 1/2 HP 1725 RPM motor but put no load on the motor, it will spin at close to 1800 RPM. As you add load, it slows a little as torque is added to the shaft, until at rated load (1/2 HP in this case) it has slowed to 1725 RPM. There's nothing wrong with this - it's just how it works. The difference between no-load and load speed (1800-1725) is the slip frequency. Put the same motor on a 50 Hz source at it will turn at 1500 RPM no load. But you cannot run a 120V motor at 240V, so the transformer is needed.
BUT I don't think (I don't have a schematic so I can't prove it right now) you are running an induction motor. The scroll saw uses a variable speed DC motor. Whatever frequency you give it is converted to DC by the saw's electronics then chopped to the motor to control motor speed. If you can get an electrical schematic, or anyone has one, we could check and be sure. Or check with DeWalt or maybe even Seyco (I think Seyco would know and actually give an answer). A DW788 manual might even specify that 50 or 60 Hz can be used as long as it's 120V.
BTW - it is correct that in most cases a transformer cannot change frequency (there's an exception used in the power system). If you put 240V 50Hz in, you'll get 120V 50 Hz out.
