Personally I believe binaural music to be complete nonsense. I have tried it a few times just to test anything, but it doesn't do anything and certainly doesn't have a therapeutic effect as it advertised. If anything it just buzzes the brain, or could cause headaches because the sounds are disruptive rather than relaxing and calming.
This makes more sense when you realize that for Trance, what you need is quietness. Any sound or music is disruptive, even calming natural sounds like rain drops or a breeze of wind through the leaves of trees in your garden, at least for deep trance even these can be disruptive sounds. Light trance can be achieved by help of sounds, though not by binaural beats.
Sleeping with any kind of sound or music on is also a bad idea, as it only causes disruption of your regular sleep cycle, since the brain cannot relax properly and enter REM sleep when there is distractions of unnatural sounds around that keep the brain on edge and in an awake state. What you need to let the brain enter calm states and altered states is quietness allowing you delve deep inside your own mind by letting go of any external and even bodily distractions. Sleep is the same, except during sleep you are not conscious, Trance is the act of consciously entering altered states of brain activity.