Beat tracking
Teaching a computer to tap its foot — estimating the tempo and placing every beat in a recording.
The starting point is an onset-strength curve. Autocorrelating it shows which periodicities dominate, which gives a tempo; then the beats have to be placed. In 2007 Dan Ellis proposed a tidy dynamic-programming solution that balances "this beat lands on a strong onset" against "the gap to the previous beat matches the tempo". Later systems, such as Sebastian Böck's recurrent networks in the madmom library, learn the whole pipeline from data.
The classic mistake is the octave error: the algorithm locks onto half or double the tempo and is, in a sense, not wrong. Four-on-the-floor dance music is close to solved; rubato-heavy jazz with syncopation is not. The technique sits behind the sync button in DJ software, automatic tempo maps in DAWs and every rhythm game that asks you to press in time.