PSOLA
Pitch-Synchronous Overlap-Add: a time-domain method that changes the pitch or duration of speech by cutting out and re-spacing individual waveform periods.
A sung or spoken vowel is a train of nearly identical cycles. PSOLA marks where each period starts, cuts short windowed grains centred on those marks, and lays them back down closer together for a higher pitch or further apart for a lower one. To make the sound longer it simply repeats grains. Each grain keeps its own spectral envelope, so the formants stay put and the voice doesn't turn into a chipmunk.
Francis Charpentier and Eric Moulines developed it at the French research centre CNET in the late 1980s, mainly for concatenative speech synthesis. It assumes a single clear fundamental and reliable pitch detection. Feed it a chord and it has no idea which periods it is supposed to be looking for.