Final answer:
The new style of music developed by African American musicians in Chicago after World War II was characterized by the dominance of jazz, which emerged from blues and ragtime influences.
Step-by-step explanation:
After World War II, the style of music developed by African American musicians migrating north to Chicago is best described by the emergence of jazz as a dominant genre. This innovative sound was born out of various musical traditions, including blues and ragtime, and became an essential part of the African American community's contribution to American culture. During the Jazz Age and into the 1920s, jazz expanded its reach from clubs in New Orleans and Chicago to New York and even international audiences. Despite other popular genres like rock 'n' roll emerging from the combination of electric instruments with gospel, blues, and jazz influences, it was jazz that characterized the musical innovations of African American musicians during this time period.