"But I was a bit puzzled by your statement: "A 24 pole motor turns at half the speed of 12 pole motor so the frequency of the cogs is identical in both (120Hz)." In a direct-drive turntable, doesn't the motor have to turn at 33.3333 rpm, regardless of the number of poles? And therefore might there not be a theoretical advantage to having double the number of poles?"
My statement was in response to the assertion that adding more poles reduces cogging (it doesn't). Doubling the number of poles does not change the vibration signature because it will also cause the motor to turn at half the speed (assuming the same 60Hz drive signal). Both a 12 pole and a 24 pole motor will produce vibration from cogging at 120Hz (10 revs/sec x 12 poles at 600 RPM and 5 revs/sec x 24 poles at 300 RPM). The amplitude of the vibrations is directly proportional to the power consumption of the motor, not the number of poles. If you go to the link I provided, you will see that the measurements bore this out.
The motor on a direct drive table does turn at 33.333 RPM so the number of poles will determine the drive frequency needed in that case (RPM=Freq x 60/pole pairs or Freq=RPM x pole pairs/60). If the motor uses steel pole pieces, it is subject to cogging and the frequency of vibration will be 0.555Hz x number of poles; in most cases, this would be below 20 Hz so it will show up as rumble. To run a DD motor from 60Hz would require 216 poles.
From what I've seen, most of the DD tables use a DC motor with servo control (feedback) to maintain proper speed. This of course, comes with its own set of problems.