Its common tuning is known as "My dog has fleas" (7)

I believe the answer is:

ukulele

(Other definitions for ukulele that I've seen before include "play this?" , "Instrument from Hawaii" , "Small guitar as played by George Formby" , "Eek - Lulu! (anag)" , "George Formby's little guitar" .)

I've seen this clue in the LA Times.

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