The two disciplines of theatre and music are inextricably linked to one another. Music simply cannot exist without some form of theatre; theatre, while it can exist without music, is enhanced ten fold in the presence of music. As a former music major, I chose to minor in theatre as a supplement to the training I would receive in the music department. I chose to stay in theatre for my new major, but that's a different post. In order for a musician to be the best musician they can possibly be, especially in the case of a singer, it is necessary that they have at least a fundamental understanding of what it is to be an actor. Musicians are actors; they bring a story to life in the form of a performance. As a singer, I felt that in order to be a singer worth my chops, I needed to be an actress as well. If a singer has the ability to extract a story from the music, create a character to tell that story, and be able to convey all of the emotions of that character in the singing and the movements and expression, the performance is made one hundred times more moving and more powerful than if they were to simply sing the notes and rhythms properly. Instrumentalists could also benefit, perhaps even more so, from theatrical training. Instrumentalists do not have the benefit of text to convey their story, so if they are able to create a story, a character and a unique voice for their instrument, it will facilitate the storytelling that is an essential element of live music performance.
On the other side, theatre depends very heavily on music to add to the depth of its meaning. Often, directors and sound designers will choose music to play during a scene in order to comment on the action or to add to the mood and tone of the scene. The proper music can take a scene from just a typical conversation to a whole new level of emotional power. Music can add suspense, tension, a sense of tranquility, or any number of other tones to a scene to which it is added. If you were to take the music away from any given moment it is written into, that particular moment would have a giant piece missing; music conveys feelings and senses that spoken word often lacks the ability to state.
Music and theatre are linked in the way that they are performed and how the performers connect with the audience. Most of the time, these arts are performed live in front of crowds, and there is little or no direct contact between the audience and performer(s). The exchange comes in the form of what is called temporal interplay. There is an exchange of energy that flows from performer to audience and back, and that energy can make or destroy the performance in both cases. Both of these arts are performance arts- they rely on an audience to make them come alive. They are also linked to each other in that, when combined, they make each other come alive.