Consonance is the repetition of consonant sounds in words. In "My Papa's Waltz," this quite simply occurs as part of the rhyme scheme, with many consonants rhyming every other line: breath/death, shelf/itself, knuckle/buckle, head/bed, dirt/shirt. To consider on a deeper level how the consonance contributes to meaning, consider that the end of lines actually suggest a pause to the reader. Thus, the reader allows that last word's meaning to linger unconsciously. Considering some of these words, their meanings are the most significant. Breath and death are opposites and certainly suggest the theme of life or death. Knuckle and buckle suggest violence, a sometimes misinterpreted conclusion to which students jump. Dirt and shirt also work together thematically, as they suggest the life of a working man who wants to just come home and relax, celebrating the end of another work day.

Assonance is the repetition of vowel sounds. It does not reveal itself as easily. For example, in lines 14–15, the sound of a short "a" vowel is repeated, giving stress to a specific set of words:

With a palm caked hard by dirt,
Then waltzed me off to bed.