To accompany the musically sophisticated answers already given, here is a mostly experiential attempt to muddy the distinction between two- and three-note harmonies. Do you sense faintly-dark blobs where they don’t exist in some corner gaps of this [Hermann illusion](https://en.wikipedia.org/wiki/Grid_illusion)?  A corner gap with an illusory blob is akin to a two-note harmony that ‘suggests’ an illusory third note. Actually playing that third note can, if so desired, solidify the sound that is all but there already. Not all grid patterns create illusory blobs, and not all two-note harmonies create illusory third notes, but many do.   C<sub>5</sub> and E<sub>5</sub> are a prime example, creating an illusory G<sub>4</sub> so comfortably familiar that it goes unnoticed. On a piano it can sound like a flute heard through a wall.           <img src="https://i.sstatic.net/CeWVt.png" height="150"> At its most dramatic (deep breath) this is a mathematically inevitable psychoacoustic phenomenon arising from how the 136 Hz frequency gap between C<sub>5</sub> and E<sub>5</sub> is similar to the 131 Hz frequency gap between C<sub>5</sub> and G<sub>4</sub>, and from how those gaps are nearly subharmonics of all three notes.   With voices and many instruments, the pitches of two sung/played notes can be fine tuned to produce mathematical relationships so exact that the illusory G<sub>4</sub> resounds outright. Most illusory notes do not work so neatly, however, and beg to be drowned out by an additional someone specifically singing/playing them in tune.   In the grid analogy above, illusory blobs might seem so fidgety that an actual drawn blob can be a welcome relief to our vision. Here is a sequence of intervals that might help to recognize illusory third notes, technically known as _combination tones_ and _difference tones_. Again, some are quite out of tune.           <img src="https://i.sstatic.net/dSELQ.png" height="100"> **Further Reading** <br> [Wikipedia: _Combination tone_](https://en.wikipedia.org/wiki/Combination_tone) <br> [Music SE: _Classical examples of a ‘fifth voice’ or ‘ghost soprano’_](https://music.stackexchange.com/questions/11848/classical-examples-of-a-fifth-voice-or-ghost-soprano) <br> [Music SE: _Is it possible to create the illusion of a sub-harmonic?_](https://music.stackexchange.com/questions/5824/is-it-possible-to-create-the-illusion-of-a-sub-harmonic)