What is the word for alliteration but with vowel sounds?

There isn't a specific word for alliteration with vowel sounds, but it's often referred to as assonance.

Assonance is the repetition of vowel sounds within a phrase or sentence, creating a sense of rhythm and musicality.

For example:

* The cat sat on the mat (repetition of the short "a" sound)

* The rain in Spain falls mainly on the plain (repetition of the long "a" sound)

While "assonance" is the most common term used, some might refer to it as vowel rhyme or vowel repetition.