turntable motor speed

Increasing voltage will cause the DC motor run faster.
It's very important but nevertheless it's a large downside of DC motor that it depends on input voltage. The voltage stabilization circuits should be very precise.
There are motors that have quartz AC generators of a stable frequency.

All DC motors used for such a purpose have a tachometer and feedback regulation circuit that controls the motor voltage. It's most commonly built right into the motor itself (just like a cassette-deck capstan motor) but occasionally you'll find it as a circuit external to the motor.

Simply regulating the value of the input voltage will not keep a DC motor at an exact speed.

Ok, so what does the feedback regulation do to the motor to change its speed. Does it change the voltage, and if so, how? more for faster? I mean, its fine to say that a circuit regulates the motor, but my question is how does it do that. The motor only has two wires that feed it, so something in those wires is telling it to speed up or slow down. What is it? voltage?

Yes, the change in speed in a DC motor is directly proportional to its voltage input: more volts = more speed; less volts = less speed. A 24VDC motor typically exhibits its nominal operating characteristics (speed, torque) when operating at its rated voltage. Too much voltage and the motor will be destroyed; too little and the motor will stall.

The regulation can take on many different approaches: since most brushed DC motors have mediocre speed stability, constant compensation (closed-loop feedback) is a must. This compensation can take the form of a tachometer which measures some point of reference as it moves by (either on the motor itself, or the thing (like a platter or pulley) the motor is driving) and adjusts speed according to how far off the from the reference mark the resulting measurement is - more points of reference equates to higher levels of accuracy. Another form of feedback measures the average current draw of the motor, and compensates for any deviation from this ideal. There are several other types of feedback mechanisms as well.

Brushless DC motors behave much like multi-phase AC motors, and require substantially more complex drive and feedback circuitry to accurately 'time' each phase.

Given the complexities of DC motor control, one can understand why synchronous AC motors remain a mainstay of turntable manufacturers despite some of their drawbacks.