Rhythm, along with Melody and Harmony, is one of the three most fundamental components of a musical work. Rhythm refers to the organization of musical “events” – i.e., sounds, over time. Rhythm determines how sounds are deployed over time such that we perceive the sounds as music rather than as noise. Bird calls are musical in part because of their rhythmic element; a Cardinal’s pretty chirpings are more musical than a crow’s seemingly more random shrieks because the organization into relative durations, of the pitches and pauses that comprise them – i.e. their Rhythm – gives the Cardinal’s calls an element of order and predictability that pleases our ears.
Rhythm deals with the duration of musical sounds (and silences) relative to each other. Rhythm does not refer to the speed (Tempo) at which these organized sounds (and silences) are played and heard. This misapplication of the term “Rhythm” is fairly common and is occasionally found in music copyright decisions, like that of Dorchester v. NBC (1959) in which we find the following: “Concerning the structure of plaintiff's composition, this Court finds: Plaintiff's composition is a popular composition in the key of B flat written to be played … The tempo or rhythm of "Rendezvous" is moderately slow…”
“Tempo” has a simpler connotation than “Rhythm” and, for our purposes, simply refers to musical speed, and not structure. To illustrate this point, here are two clips of “Buffalo Gals” in which we hear the same music with exactly the same rhythms and pitches (indeed, from the same recording!) but played at different Tempos.
(You will recognize the tune of “Buffalo Gals” -- the heedless, rollicking music used so effectively in “High Noon” and “It’s a Wonderful Life” as a foil to the turmoil besetting the characters in the dramatically dark scenes it accompanies.)