Final answer:
The Modern Jazz Quartet (MJQ) played a significant role in popularizing modern jazz and progressing the relationship between jazz and the concert hall by incorporating elements of classical music and presenting jazz in a sophisticated manner.
Step-by-step explanation:
The Modern Jazz Quartet (MJQ) played a significant role in popularizing the style of modern jazz. They helped progress the relationship between jazz and the concert hall by incorporating elements of classical music into their performances and by presenting jazz in a sophisticated and refined manner. The group, consisting of John Lewis, Milt Jackson, Percy Heath, and Connie Kay, achieved widespread recognition and success, performing in prestigious concert venues and collaborating with classical musicians. For example, they often incorporated classical compositions into their repertoire and even performed with symphony orchestras. Their fusion of jazz and classical music helped pave the way for other jazz artists to explore the concert hall as a performance space.