Jazz influenced reggae in Jamaica massively. Wealthy Americans were there at the beginning of first class carribean travel in the 50's.It may also be the other way round. My recollection is that back in the 50s/60s in Jamaica the radios could pick up predominantly New Orleans radio easily.
Jazz bands playing for posh holidaymakers. Plus radio Jamaica playing american jazz tunes.
A friend of mine has an original 7" record of Horace Silver Too much sake that his father bought in Jamaica.
