Answer:
to better understand and appreciate their heritage
Explanation:
In the last line of the excerpt he wants these artists to "cause the smug Negro middle class to turn from their white, respectable, ordinary books and papers to catch a glimmer of their won beauty." In this line "their own beauty" is the heritage of African Americans. The "near intellectuals" aren't musicians and writers. They are African Americans who are paying attention more to white culture than their own history.
