Rhythm
n. a succession of moments of varying lengths.
In music, there is a succession of notes, and rhythm is created when some of them are long and some are short. The rhythm can be predictable, falling into patterns, or quite random. Beat is foundational. Meter is structural. Rhythm is layered over and is relative to the beat and meter.
For example:
And I do love thee: therefore, go with me;
I’ll give thee fairies to attend on thee,
And they shall fetch thee jewels from the deep,
And sing while thou on pressed flowers dost sleep; (Shakespeare 1564-1616, A Midsummer Night’s Dream)
The hierarchy is as follows:
Beat is the base pulse. (the patter of the syllables.)
Meter reveals groupings of the beats. (the iambic pentameter)
Rhythms are the longs and shorts that provide novelty to the experience. (the specific choice of these words, some long some short, some heavy, some light)