Final answer:
Jazz is the musical style that combines African and European musical traditions with improvisation and syncopation, which became particularly prominent during the Harlem Renaissance and was popularized by artists like Duke Ellington.
Step-by-step explanation:
The musical style developed by African-Americans at the beginning of the 20th century that is an amalgamation of African and European music, featuring improvisation, syncopation, and a regular or forceful rhythm is 2) Jazz. This style emerged from the African American experience, particularly influenced by work songs, spirituals, and folk traditions. It incorporated elements like polyrhythms and syncopation, along with blue notes, central to the Blues, reflecting the different living conditions, cultures, and musical traditions. Historically, jazz became especially prominent during the Harlem Renaissance, as it mirrored and fueled the socio-cultural changes of the era. Musicians such as Duke Ellington and Cab Calloway helped to popularize jazz in notable establishments like the Cotton Club in Harlem, making this genre a quintessential part of American music history.