Rhythm, meter, cadence can all mean the more or less regular rise and fall in intensity of sounds that one associates chiefly with poetry and music.
Rhythm, which of these three terms is the most inclusive and the widest in its range of application, implies movement and flow as well as an agreeable succession of rising and falling sounds; it need not suggest regular alternation of these sounds, but it fundamentally implies the recurrence at fairly regular intervals of the accented or prolonged syllable in poetry or of the heavy beat or the accented note in music, so that no matter how many unaccented or unstressed syllables or notes lie between these, the continuing up and down movement is strongly apparent to the senses.
Consequently rhythm is used not only in reference to speech sounds and musical tones ordered with relation to stress and time, but also to dancing, games, and various natural phenomena where a comparable pulsing movement is apparent, and even to the arts of design, where fluctuations in line or pattern suggest a pulsing movement.
Meter implies the reduction of rhythm to system and measure. Poetry that has meter has a definite rhythmical pattern which determines the typical foot or sometimes the arrangement of feet in each line and either the number of feet in every line or, if a stanzaic pattern is implied, in each verse of a stanza.
In music meter implies the division of the rhythm into measures, all of which are uniform in number of beats or time units, and each of which begins with the accented tone.
Cadence is the least clearly fixed in meaning of these words. The term has often been used as though it were equal to rhythm, or sometimes to meter, especially when the reference is to poetry.
Cadence often stresses the rise and fall of sound or the rhythm as heard, whether in prose or in poetry, and as influenced by tone or modulation, choice of words, and association of sound and feeling.