Hi Snub
Your 1720 RPM is right for a 60Hz motor with 2 pairs of poles.
What you
may have is a motor designed to run via an external control circuit.
ie under a system known as Pole Amplitude Modulation (PAM)
.... and you don't have that!
Dunno how much you know about Induction motors but the general rule for rotational speed (sychronous) is :
Numbers of cycles per MINUTE / Number of pairs of poles
So, for 60 Hz you get 3600/1=3600 3600/2 = 1800 3600/3 = 1200 etc.
Less a bit for the slip you get 3450, 1725, 1150, etc. which is what you see on the Rating Plate
These are the more common numbers for 60 Hz motors.
By way of the switching some of the windings you get wider or narrower pole widths, effecively varying the number of poles.
The result of this is the motor speeds do not appear to correspond to the usual equation.
Instead of the sychronous speed following the equation each time, you get a set of speeds grouped together, as you seem to have
Tried to understand this stuff years ago, it's gruesome ..
You get this arrangment on desk fans, spin dryers etc.
I think you should get another motor

Try a search on the motor maker/type. See if any info.
Can't really help from here, but I can admire your problem

Dave BC