Swap adjacent out-of-order pairs, sweep after sweep. The sound is a slow ascending wash; the largest values bubble to the top one pass at a time, and you hear that ascent as a rising drone.
Slide each new element back into its place in the sorted prefix. Like sorting a hand of cards. The song is gentle and patient, with small ratchets backwards.
Scan, find the minimum, swap it to the front. The most architectural of the slow sorts — long quiet sweeps punctuated by single decisive thuds.
Bubble sort running both directions on alternate passes. The sound rocks back and forth, shrinking inward from both ends — a pendulum gradually settling to stillness.
Pick a pivot, partition around it, recurse. The most chaotic song: bursts of partitioning at different scales overlap into something like sparse jazz.
Divide, recursively sort, merge back. The merges are the music — long, even cascades. The most orchestral of the nine.
Sort by individual digits (LSD). Each pass is a sweeping wave, bucketing by the current digit. The sound is regular, cyclical, almost mechanical — sorting without comparison.
Reverse prefixes to flip the maximum into place, then flip it to its final position. Theatrical: you hear the whole stack fold and unfold with each theatrical reversal.
Dijkstra's comedically slow algorithm: sort the first two-thirds, then the last two-thirds, then the first two-thirds again. Recursive, lumbering, and oddly meditative.