So here's another method that doesn't rely on the song being detected or even a song at all:
The gyroscope on your phone is accurate enough to measure RPM to about the first decimal place at 33 1/3 - 45 rpm's just by placing your phone on the turntable flat and letting it spin.
The gyroscope on your phone is accurate enough to measure RPM to about the first decimal place at 33 1/3 - 45 rpm's just by placing your phone on the turntable flat and letting it spin.