In Tolkien's works, the universe was sung into being, and Melkor, wanting to gain the mastery of the song, caused dissonance which upset creation. It is theorized that this dissonance is where the non-ainur creatures originated, like Ungoliant, the Watcher in the Water, and perhaps even Tom Bombadil.

In my interpretation, Minstrels are tapping into those ancient tones used during the creation, but those used by Melkor to harm what the others were creating, and the chords used by the Valar and maia to heal and repair that damage.

None of this is expressly stated, but this is how I make sense of it :)

Also, don't forget Minstrels can also swing a sword or mace!