It depends on individual baby whether music helps to improve their sleep. Since the above 2 answers propose the good effects of sleeping with music, I will share the adverse effects. You may weight the pros and cons and determine whether it's worth introducing music to soothe baby to sleep. The adverse effects: 1. Difficult to change when it becomes habitual. Parents may have a hard time making their baby sleeps at places with no access to their music. For example, if you forgot to bring their favorite music while traveling or at their grandma's place, you will have a problem making them sleep. 2. Prone to head banging Head banging is the act of children banging their heads against solid objects. Research has shown that headbanging occurance is higher with children who sleep while listening to music. 3. Music may cause disruption in children's sleep. While music helps to soothe children to sleep, it can also disrupt the sleep of certain group of children. Children who are sensitive to sound can be easily awaken by music. If your children share same room, you may have problem when one child is amenable to music at bedtime and another child is easily disturbed by music. Source: http://www.livestrong.com/article/549496-adverse-effects-of-children-falling-asleep-with-music/
Found an interesting article online with regards to lullabies, music and their effects on babies. Not about the music you described but i reckon it's relevant. This paragraph strikes me the most: "We know without having to be told that something very atavistic is going on here. A lullaby establishes a soothing correlation between an infant’s physiology, its state of mind, and the outside world. This is necessary because the infant’s first awareness of the world is of something bafflingly separate. It’s huge and threatening, a “great, blooming buzzing confusion”, as the philosopher William James described it." Whether or not baby knows what's happening, music does have an effect in terms of easing anxiety, pain and does a great deal in lulling babies to sleep. I suppose that's why in every culture, music and lullabies exist to soothe babies to sleep. As an adult, it still does, so why not a baby:) http://www.telegraph.co.uk/culture/music/classicalmusic/10412984/Why-lullabies-really-do-send-babies-to-sleep.html
It is proposed that music could tap into the emotional side of the brain and baby would respond to the singer’s voice and also to an instrument being played. (http://www.netmums.com/baby/sleep/relaxing-music-and-lullabies) Personally, I feel that there is no harm in playing the music for your child. Unless your baby respond negatively to it, then it is best not to play it since it is unnecessary stress on the baby. Otherwise, it may be beneficial and if it is effective in soothing your baby, you can benefit from the baby having a good rest as well! :)
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thanks