A single spool gas turbine engine means that there’s only one common shaft on which are connected at one end a compressor and at the other end a turbine driving that same compressor. In this case, obviously, both will have the same rpm. The speed of two rotating elements where one drives the other can only be different if a reduction gearbox is fitted in between. This is never the case in a gas turbine engine, but only on turboprops and normal piston engines where the torque shaft turns way too fast (typically 10 000 – 15 000 RPM) for the propeller’s normal operation. Without the reduction gearbox, the propeller’s blades would most likely be entirely supersonic.