The simplest way to change pitch is to change playback speed, as with a record or tape: faster sounds higher, slower sounds lower, and the tempo moves too. Digital pitch-shifters separate the two. The Eventide H910 Harmonizer, unveiled in 1975, was an early studio unit able to shift up to an octave in either direction; today any DAW can transpose a sample by semitones while keeping its length, often with an option to preserve formants so that voices do not sound cartoonish.
Hip hop producers have long played with speed. Many sampled 33⅓ rpm records at 45 rpm and pitched them back down in the sampler, adding character along the way. In jazz lo-fi, samples are frequently pitched down to sound darker and slower, or detuned slightly to mimic a warped record.