Music theory is an amazing subject. You can actually make random notes sound reasonably musical by constraining them to just a few simple rules. Copy/pasting from Dmitri Tymoczko's Music 105 lecture notes:

1. Conjunct melodic motion. Melodies tend to move by short distances from note to note. Large leaps sound inherently unmelodic.

2. Harmonic consistency. The chords in a passage of music, whatever they may be, tend to be structurally similar to one another.

3. Acoustic consonance. Some chords sound intrinsically good or pleasing. These are said to be consonant.

4. Scales. Over small spans of musical time (say 30 seconds or so), most musical styles tend to use just a few types of notes, between 5 to 8.

5. Centricity. Over moderate spans of musical time, one tonic note is heard as being more prominent than the others, appearing more frequently and serving as a goal of musical motion.

(Not to say that everything that sounds musical follows these rules, just that if you follow these rules the output is likely to sound musical.)