strum on (something)
1. To play a stringed instrument by brushing or stroking the strings. A few of us were strumming on our guitars as we sat around the camp fire. It was such a classy wedding. They even hired someone to strum on a harp while the guests were being seated.
2. To play something, such as a chord or song, on a stringed instrument by brushing or stroking the strings. I never got past strumming a couple basic chords on the guitar. Anything more advanced than that was just too difficult for me. He loves strumming lighthearted melodies on his banjo.
strum something on something
to brush or play with the fingers some stringed instrument, such as a guitar. She strummed a nice little melody on her guitar. He strummed the accompaniment on the guitar.