While I was at work today the boss sung this song to our daughter. We decided to see if we had the chords in either of our two books of nursery rhymes as the baby seems to enjoy my guitar playing (at least for a while). The first one featured a tune which was not twinkle twinkle little star and the chords clearly did not work with the melody we know. So we tried the second book which came up trumps.
However it seemed to be in an unnecessarily fiendishy key (which on a guitar isn't so bad) and on top of that it featured some outlandishly complicated chords. I tried the usual trick of sending them back to their root but somehow it just didn't sound right.
So I started with Am7b5. This is more correctly written as "A minor seven flattened fifth" which isn't something to inspire confidence. Then on to the E° (or E diminished). Once I could play these chords fluently enough so the song could be sung and played simultaneously I was amazed at how beautiful, calm and generally tranquil they made the song. The baby seemed unimpressed but hopefully she will be one day.