Meandering Pitch, Where’s The Problem?

@goofyfoot , the sources of pitch variation are a bad motor control unit, warped records, slipping motor pulley and bad belts. First and relatively cheap is replace the belt, clean the rim of the drive platter with acetone or brake cleaning fluid and make sure the motor's pulley is tight. Also clean the motor pulley. Do not get finger oils on the belt. Use gloves when you handle it.

One other cause: if the suspension is being activated by footfalls or some other source of vibration, then the platter may move however minutely in the horizontal or vertical plane, while the motor is held stationary because it’s not suspended. This would cause intermittent stretching and compression of the belt, if the belt is compliant. Speed becomes unstable.

The first answer you got from Don is the best one and the first thing he told you bears repeating:  If the spindle hole is off, you will get wow.  That is pitch instability.  Piano is the most sensitive instrument to this problem of any.  Many piano music people tend to prefer CDs for this reason.  The only turntable that was ever developed that properly addressed this problem was the Nakamichi, which centered the record automatically.  Everything else can be perfect, but if the spindle hole is off center, even a small amount, wow is unavoidable.  It should be noted that not every person is equally sensitive to this problem.  Some people are quite tolerant, whereas others can't tolerate even small amounts.  Like so many things in our hobby it is important to know yourself first.  If you hear wow easily and cannot ignore it, and if you are a piano aficianado, then vinyl should probably be considered a secondary source, and digital should be primary for you.  Of course that needs to be tempered with source availability.   

Great advice from everyone. My thoughts regarding the spindle hole is that wow would be present in more than one or two spots if it were the cause, though I admit I don't know this for sure. Now regarding the pulley, there is an upgrade replacement that I should consider. Nevertheless, buying a new belt will be the first thing I do.

Hey everybody, let's get clear about off-centre spindle holes.  Do you have speed instability on EVERY record?  if so, it can't be off-centre records - they can't all be off-centre.  Anyway, you can see an off-centre record when it's in play - the arm swings a little left and right.

So if you have the problem on all or most records; some you will hear more than others - eg piano, as above - then it's your turntable.  Posts above rightly say change the belt, check the motor.  Also take off the platter, flush out the bearing pit , clean the spindle and add new correct oil per maker's instructions.

It's nothing to do with cartridge set-up - if that's wrong, you will hear other faults.