Cheapest way of rectifying 60hz -> 30hz 120V AC to halve speed of PSC induction motor
The system that you are describing is called a cycloconverter. An example is shown below. The example shows the frequency as 1/3 of the input power frequency. I believe that is about as high a frequency has cycloconverters can operate successfully with induction motors.



Excerpt from F. F. Mazda "Thyristor Control" John Wiley &amp; Sons 1973