One point that bears making. I believe that the tradition of fiddle tunes from the US Appalachian area would not have existed if not for Irish music. The Scots-Irish tradition of ornamental single melody style infused the dance music of the rural US. A lot has been attributed to the English due to Cecil Sharp's collecting but I think the Irish have had a more profound effect on Southern US dance music than any other culture. The main instrument is through the fiddle emulating pipes and flutes in a highly melodic ornamental style where the chords become secondary as oppposed to the standard European forms where harmony becomes more of an integral part of the music. Scots music is basically Irish derived. The English tunes are also. Irish music has played an important influential musical role. Galicia Spain may have also had some influence on the Irish music. The pipes have a role here as well.

Now it is possible that the Irish dance tune had some influence through the fiddle on the development of the minstrel show. Many of the minstrel performers such as Harry McCarthy drew much from their background. But Irish musical influence not through the banjo but more through the fiddle. But in some cases, maybe the musical hall songs.

The remains the question as to where tap-dancing came from. This may be of Celtic origin through step-dances and clogging and was picked up by African-American entertainers.

The tenor banjo, however, is of more recent derivation. The five-string is much older.
Actually, it was probably American jazz that brought the tenor banjo to Ireland. In New York, Irish musicians would have definitely picked it up as did Jewish musicians in early "klezmer" dance bands.

Also, the tenor and plectrum banjos serve a harmonic function more than a single-string melody in jazz bands. In Irish music, melody is first and harmony incidental. A case in point is the early fiddle recordings with Micheal Coleman, a master being literally abused by the misfiring of harmonies by a drunken piano accompanist.

Frank Hamilton