I am completely unable to carry a tune in a bucket. I joke that my parents named me No-La for a reason. So you might expect me to be the last person to encourage singing to your child. Yet hear I am, four kids later, a musical advocate.
There are lots of studies linking music to brain development. These are not why I advocate singing to your baby. There are other studies that talk about bonding. Nope, not my reason either. The fact is, your baby doesn't know what an in-tune song sounds like. Your baby just loves it when you sing.
With my first child, I mostly stuck to the tried and true classical songs. Things that came with their own tune. We relied on "Twinkle Twinkle Little Star" and "Old MacDonald," along with songs from church like "I Am a Child of God" and "Jesus Wants Me for a Sunbeam" (special emphasis on the 'beam' there). These songs brought huge grins to all of my children's faces. Many times, when I sang, I would do so directly to them. I'd hold them in my lap and stare into their eyes. Other times, they'd sit on my lap with their backs to me and we'd sing. Still other times, we used music as a baby soother in the car. When your child is used to hearing your musical side, you'd be amazed at how much comfort you can give while driving down the road singing.
By the time my second child was born, my oldest was nearly 18 months. I had relaxed a bit as a mother. I was surprised at how much she really loved my made up "silly songs." I would take songs that we already knew and change the words. For instance, we'd sing "Old McDawn had a farm...." (Dawn being my child's name). As I grew more confident, we'd change the words altogether: "Silly Dawn liked to play..." (to the same tune). They loved when I used their names in the song; in fact, they still do. But they loved hearing their favorite tunes with different words, as well. And sometimes we got really nonsensical: "Twinkle twinkle up in space, How I wonder about your face." Yes, this makes absolutely no sense - but my kids die laughing. And when my kids got even older, we used songs to help them spell; the M-I-C-K-E-Y-M-O-U-S-E song has the same number of letters as my son's name, so we used that to help him remember how to spell it. We made up a song to help my daughter remember that "F-R-I-E-N-D" spells friend.
So sing to your baby, even if you don't think you are capable. They may grow up belting out songs that are completely out of tune, but they will enjoy it. You'll bond with your baby and make them smile. And who knows - you may even catch yourself having fun!