Assonance

Assonance is the repetition of vowel sounds to create internal rhyming within phrases or sentences, and together with alliteration and consonance serves as one of the building blocks of verse. Assonance does not have to be a rhyme; the identity of which depends merely on sequence of both vowel and consonant sounds.

Assonance occurs more often in verse than in prose. It is used in (mainly modern) English-language poetry, and is particularly important in Old French, Spanish and the Celtic languages.

English poetry is rich with examples of assonance:

That solitude which suits abstruser musings

on a proud round cloud in white high night

It also occurs in prose:

Soft language issued from their spitless lips as they swished in low circles round and round the field, winding hither and thither through the weeds.

English-language hip hop relies on assonance, which is sometimes hard to distinguish from slant rhyme:

Some vodka that'll jumpstart my heart quicker than a shock when I get shocked at the hospital by the doctor when I'm not cooperating...

Dead in the middle of little Italy little did we know that we riddled some middleman who didn't do diddly.

It is also heard in other forms of popular music:

...
Wikipedia