I’m less interested in the lyrics of the Shakespeherian Rag as I am with how the song fits into the drama of The Waste Land. The quote pops up right in the middle of the dispute between the veteran and his wife. In fact it seems to cut right into the middle of the conversation, as if it was playing in the background during this scene and just happened to break through into the foreground. I believe Eliot was using this method to invoke a gramophone playing in the background. I think this can be supported by the extremely scene between the typist and the young man which explicitly includes a gramophone. Both couples are experiencing a similar breakdown of communication between the sexes which the inclusion of a gramophone comments on.
The idea of hollow voices, words without real soul or meaning behind them fits into the scene Eliot is building. The “canned voices” of a gramophone, especially when playing a fairly meaningless, or at least trivial, song like the Shakespeherian rag mirror the veterans words/thoughts well. The veterans thoughts and words are not in the present but rather a replaying of thoughts and words from the past. “I think we are in rats’ alley” is a thought which places the veteran back in the war. The veteran, like a gramophone, is playing words from the past that have no soul or reality in the present and this causes a breakdown of communication between him and his wife.