• If a child can sing a melody after its first hearing, this child is “musical”;
• If a child can the same melody on the piano, this child is  “musical and smart”;
• If the child plays the melody with chords to make a suitable accompaniment, this child is a “little genius”;
•  those capable of substituting these chords to change the harmony as well as varying the melody are “prodigy”!
  

The “musical” child merely has good hearing (function of the right brain).

The “musical and smart” child not only has a good hearing (using right brain), but they also understand the structures of the high and low keys on the piano (function of the left brain), this child is therefore using both halves of the cerebrum.

The “little genius” child (whose abilities are very rare) understands (consciously or unconsciously) the structure of the melody! A melody is more than a mere sequence of tones, there is always an underlying harmonic structure. By varying the harmonic structure below the melody, the child exhibits his comprehension of the underlying harmonic structure.

The “child prodigy” is one who is able to vary both the melody and the harmony. If the child varies the melody in an arbitrary and random way, this is not talent - every one is capable of doing this, and sometimes, the origin of the "variation" is actually mere negligence and sloppiness. A true variation consists of consciously chosen changes in the rhythm and melody by using neighbour notes, trills, etc., or even accompanying an unchanged melody with a new chord sequence.