How can the tempo/BPM of a song be determined programmatically? What algorithms are commonly used, and what considerations must be made?
This is challenging to explain in a single StackOverflow post. In general, the simplest beat-detection algorithms work by locating peaks in sound energy, which is easy to detect. More sophisticated methods use comb filters and other statistical/waveform methods. For a detailed explication including code samples, check this GameDev article out.