It's an interesting question. The preposition "out" is often used in phrases like "Let the bells ring out..." "Beat out that rhythm on a drum" (Song title and lyrics from "Carmen Jones") "She hammered out tunes on an upright piano..."' I think the word "out" is being used to suggest two ideas, both related to _transmission._ First, the sound is loud and can be heard a long distance away; and, second, that the sound _means_ something to those distant listeners. "He rang the church bells to see if they had been hung properly and were working correctly." "The church bells rang out to call the worshippers to services." "They didn't pay attention to the band, until the drummer began to beat out the rhythm. Then everyone stopped talking and began to dance." "You're singing to yourself. You're not reaching the audience. Now, take a deep breath, look out at the farthest row, open your mouth wide, and sing out!" "Drums out a tune" is puzzling. Obviously one person is tapping on the face of the bass fiddle, like beating a drum, while a second musician strums the strings. Usually one thinks of a "tune" as a melody. Obviously someone drumming on the face of the fiddle is not playing a melody in the usual sense. However, it is possible to imagine that the "tune" includes both the musical chords and melody and the drum-like rhythm. "Drumming out a tune" I think means that this musician is emphasizing the rhythm of the tune by making a rhythmic tap exactly once on every note. Quite often, it is possible to recognize a tune just from its rhythmic pattern.

Drums out means plays a song, So he is playing a song on a bass fiddle.