Combination Tones in Music

Combination Tones are produced as the sum and difference of 2 pitches. For example: The ratio of an acoustically pure Major 3rd is 5/4. The first and second order difference tones would be 5-4=1 and 4-1=3. Those frequencies are not sounded but are "heard" by humans. It was initially thought that this occurred mechanically in the ear itself but studies where each of the original pitches were played separately into each ear still produced the combination tones.

TL;DR: Our brains appear to produce non-existent sounds based on mathematical relationships.