In Honolulu town, A man known miles around Has turned things upside down, They call him Old Bill Bailey. Bill Bailey won his fame On his steel guitar. Ukulele was his fame In that land afar. The ships way out at sea All hear his melody.
Chorus:
When Old Bill Bailey Plays the ukulele Down in Honolulu They dance the hula-hulu Every evening, there they are, Swaying while he's playing his Hawaiian guitar. His ragtime motion Even has the ocean Bobbing up and down. Sometimes a whale gets to feeling flip, Wags his tail and sinks a battleship. When Old Bill Bailey Plays the ukulele Down in Honolulu town.
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This old pop song mixes the two instruments up freely, and I think it's a case of your Number two suggestion up there. I thin it's number two and three, intermixed, that results in this confusion of playing styles.