Turntable Speed

If the speed is off then the pitch will be wrong. Especially noticeable on piano. Generally there are speed adjustments on motors, usually screws on the plinth under the platter. Sometimes you will see colored paint on the screws to mark their settings. They adjust the tilt of the motor and how the belt rides on the pulley which can adjust the speed. This along with a new oem belt and proper lubrication will usually correct speed problems. 

Those iPhone apps for platter speed are notoriously inaccurate at the level audiophiles want them to be accurate. What you get is the false satisfaction that you’ve seen a digital readout on the screen. I would recommend the KAB strobe system instead. Uses a large diameter strobe disc and a battery powered strobe light for constant frequency. But you don’t get a digital readout. Strobes built into turntables and any plug-in strobe light are subject to variations in AC line frequency.

@lewm, I have "RPM" on my phone and it seems pretty accurate. The Cosmos I have coming (hopefully soon) has a digital rev counter which I will compare to the phone. I made a hockey puck sized one inch thick platform with a center hole. It is placed over the spindle creating a dead center platform for the phone. It is made out of alder and is sized to match the weight of a 180 gm record. The phone is centered over the spindle. The phone also gives you wow and flutter. When it starts increasing it is time for a new belt.

The operative word is "pretty", as in "pretty accurate".  Most of us are looking for speed errors or more importantly speed variation of less than 0.1 RPM against a background of 33.XX RPM.  I am mostly basing my claim on reports of others who first monitored speed with a cell phone and then used other more accurate methods, e.g. the Sutherland Timeline or the Phoenix Engineering Roadrunner or even the KAB, and found that the cell phone app in question was off a bit.  I don't think absolute exact 33.333 rpm is a necessary goal. I do think that keeping speed constant within a very small bandwidth is much more important, as we are much more sensitive to warble than to absolute pitch.  For starters, the cell phone itself does not match the actual load of an LP being dragged by the stylus, neither in weight nor in distribution of mass.

Turntable speed for me needs to be accurate enough to tune and play a guitar to.  If the band is playing in "E", I want to be able to tune my guitar (using a tuning fork) and solo along to that (given a modern recording where the band had the right pitch in the first place.)   My KAB strobe gets me there, although I acknowledge it's not 100% accurate.