Sampling: playing a recording as an instrument
A sample is a frozen recipe. The deep question is what happens to time when you change its pitch.
A sample is just a recording — but treated as an instrument: pitched, shaped, and sequenced like any oscillator. Lesson 2 already gave you the right frame: a recording is a frozen recipe, harmonics and all. What synthesis builds from math, sampling borrows from the world. The interesting problems all come from one fact: unlike an oscillator, a recording has a length.
Repitch: pitch and time chained together
The oldest way to change a sample's pitch is to play it faster or slower — a tape sped up. An octave up plays twice as fast, so it lasts half as long; the whole recipe slides up together, chipmunk artifacts and all. Pitch and time are chained. That coupling has a sound of its own — jungle breaks, vaporwave slowdowns — and half of sampler history is people using the artifact on purpose.
Stretch: cutting the chain
Time-stretching breaks the chain: the machine slices the recording into tiny overlapping pieces and re-lays them at the original pace while playing each piece at the new pitch — so a loop can stay locked to your tempo while its pitch moves, or keep its pitch while your tempo moves. The cost is texture: at extreme settings the slicing becomes audible as a grainy shimmer. (Remember that grain — it is the whole next lesson.)
One melodic loop, one pitch slider, two machines. In repitch mode the playhead itself speeds up and the loop shortens — watch the duration readout. In stretch mode the playhead never changes speed: same slider, pitch moves, tempo holds. That one difference is an entire family tree of samplers.
Digitakt II ships this lesson as its machine lineup: ONESHOT plays the recording straight, REPITCH chains pitch to tempo (its BARS knob locks the loop's length to your pattern), STRETCH holds tempo while pitch moves, and WERP bends time in segments. Tonverk's SINGLE PLAYER is the same family with loop points: