Music was a significant part of George Bernard Shaw's life. His mother was a serious amateur musician, and music was very much part of his household when he was growing up in Dublin. Shaw actually worked as a music critic before he started writing plays. One book of particular relevance to this question is The Perfect Wagnerite, a work in which Shaw comments on Wagner's opera, The Ring of the Niblungs, arguing that it should be read as an endorsement of Fabian Socialism. More importantly for the purpose of interpreting the use of music in "Major Barbara," Shaw argues that musical themes in Wagner evoke not only the characters with whom they are associated but also specific emotions in the audience. This is important because as a playwright, Shaw is immensely skilled in writing dialogue, and does a very solid job of plot construction, but is often accused of being weaker at handling emotions. Thus the ability of music to evoke emotion serves to symbolize the emotional dimension of drama.
In "Major Barbara", musical themes are closely tied to religion. The first mention of music in Act I is Lady Britomart's statement that Cusins "pretends to be a Salvationist, and actually plays the big drum for her in public because he has fallen head over ears in love with her." We soon discover the Andrew Undershaft, Aldolphus Cusins, and Barbara herself share in common some form of active involvement with music, a connection foreshadowing the end of the play, when the audience comes to understand that Cusins and Barbara really are the true heirs of Undershaft in spirit. Even Lazarus, Undershaft's partner, as we discover towards the end of the play, enjoys string quartets.
In Act II, we encounter the role of music in the Salvation Army. It is portrayed as both a source and expression of emotional strength, and of emotions leading to positive actions rather than stifled in hypocrisy and convention. Cusins understands this as a new morality or religion connecting directly back to the ancient Greek Dionysian tradition:
The Salvation Army ... is the army of joy, of love, of courage: it has banished the fear and remorse and despair of the old hellridden evangelical sects: it marches to fight the devil with trumpet and drum, with music and dancing, with banner and palm,... it ... lets loose the rhapsodist ... reveals the true worship of Dionysos ...
Just as important as the existence of music is the type of music. When Barbara argues that Cusins should accept Undershaft's offer, she says:
If I were middle-class I should turn my back on my father's business; and we should both live in an artistic drawingroom, with you reading the reviews in one corner, and I in the other at the piano, playing Schumann: both very superior persons, and neither of us a bit of use.
Here, Barbara is asserting that the Dionysiac or Wagnerian strain in music, which is also that of the Salvation Army, carries with itself a sort of ideology not found in the restrained and symmetrical work of Schumann. The young couple's choice of cannons and gunpowder is a choice of primal Dionysian and musical energy against the strictures of convention.