Jazz would have been merely syncopated brass band music without the infusion of blues, and there are other ramifications. American popular music genres that were offshoots of blues, such as R&B, rock and even country would probably not have been created.
Lindgren's article traces the influence via the Spanish, who were influenced by the Moors, to the New World. His assertion that Spanish-Arabic culture survived best in the New World rings true, and he also provides evidence of the disconnect between Africa and the development of blues (and jazz) as independent art forms in the US as a black American achievement.
Having lived in the Middle East I can attest to the similarities between Muslim song and prayer, and forms of US blues music. In fact, since I heard the athaan - call to prayer - five times a day, every day, while living in the Middle East I often wonder why that connection escaped me.
One final article by John Petters observed the influence of the Catholic Church on the development of jazz and blues in his convincing article, The History of Spirituals in Jazz. Here is an excerpt:
Although this music had its foundations in the Catholic Church, it was not long before other Christian denominations found this music influencing their services. Today when one thinks of Black Gospel music it is usually in the context of southern Baptists or other Protestant denominations.
The above are not the last (or even the definitive) words on the origin of blues and jazz. Those origins will be debated long after I have departed this Earth. However, they add unique perspectives and insights to the debate and body of knowledge.