To begin, the terms rhyme and rhythm need to be defined.
Rhyme is the repetition of similar sounds. For example, sun, fun, done, run all rhyme.
Rhythm, on the other hand, is the "musical" quality of a line or complete poem which is constructed through the use of stressed and unstressed syllables. For example, I love to run and play each day. Here, the stressed syllables are bolded and the unstressed syllables are not. This, specifically, is an example of iambic tetrameter (four sets, iambs, of a pair of stressed and unstressed syllables).
In Edna St. Vincent Millay's "Afternoon on a Hill," both the rhyme and the rhythm is important.
I will be the gladdest thing
Under the sun!
I will touch a hundred flowers
And not pick one.
The first line contains seven syllables, the third line contains eight syllables, while the second and fourth both contain four. This repetition of the number of syllables in lines two and four create a sing-song effect (abcb-rhyme scheme). At the same time, the lines rhyme with each other.
In "Ashes of Life" the rhyme is far more prevalent than in the previous poem exampled.
Love has gone and left me and the days are all alike;
Eat I must, and sleep I will,—and would that night were here!
But ah!—to lie awake and hear the slow hours strike!
Would that it were day again!—with twilight near!
Here, the rhyme scheme is abab, giving the poem an very sing-song feel. The rhythm, on the other hand, is simple and contains very drastic stressed and unstressed syllables.
"Alms," like "Afternoon on a Hill," is a rather longer poem. That said, the lines all consist of eight syllables (four sets of stressed and unstressed- iambic tetrameter).
My heart is what it was before,
A house where people come and go;
But it is winter with your love,
The sashes are beset with snow.
Again, this poem mirrors the abcb rhyme scheme seen in the first poem. The regular number of syllables and the rhyme scheme add to the musical nature of the poem.