A poem that
- Has rhyme
- Does not follow a rhythm
I know that if it has both, it's a lyric.
I know if it has neither it's a free verse.
And I know if it has no rhyme, but has rhythm it's a blank verse.
But what about rhyme, but no rhythm?
The form of the poem would be free verse.
Per the Poetry Foundation, free verse is a form of poetry with
Nonmetrical, nonrhyming lines that closely follow the natural rhythms of speech. A regular pattern of sound or rhythm may emerge in free-verse lines, but the poet does not adhere to a metrical plan in their composition. A regular pattern of sound or rhythm may emerge in free-verse lines, but the poet does not adhere to a metrical plan in their composition.
The primary premise of free verse is not the absolute exclusion of poetic devices, such as rhyme or rhythm. The emphasis of free verse is the freedom from poetic standardization, which creates the freedom for unique poetic expression. Poets may then, independently, include rhyme scheme or rhythm because of the nature of free verse writing. Thus, the poem described in the question lies neatly within the realm of free verse, despite its inclusion of rhyme.