As you know, human brainwaves can be stimulated with binaural beats. While human perceptions of sound ranges from 20 Hz to 20,000 Hz, the frequencies of human brain waves are between 0 - 40 Hz.
Therefore to stimulate the brain is enough to produce different frequencies of sound in each ear to get the desired effect n the brain. For example, if a 315 Hz sine wave is played into the right ear and a 325 Hz one into the left ear, the brain is entrained towards the beat frequency -10 Hz- or the alpha range and in in the same way for the nexts braiwaves.
However, the pure tones can became boring. What happen if I mix binaural beats with music? The answer is that the mixing will work while you can hear the beats and the piece of music match with the intention of the therapy. For example you won't use heavy rock to mix with a stress relief session.
To illustrate the idea, in the following play you will listen the pure sounds of a stress therapy:
Now you will listen the pure piece of music:
Finally you will listen the mixing:
In conclusion, adding music to binaural beats sessions are effective to enrich the experience of brainwave entrainment if the binaural beats are listened enough and the music match the tempo of the therapy.