Question: [The Axis of Awesome](http://en.wikipedia.org/wiki/The_Axis_of_Awesome) has a song called "4 Chords", a medley of various songs all written, or so it's claimed, using the same four chords.

Now, from what I understand, a chord is just a bunch of tones played at the same time so they sound like one. For example, a 300 Hz note and a 500 Hz note played simultaneously will be a 100 Hz sound (because 100 is the greatest common factor of 300 and 500) with a lot of nuance in it, and that's called a chord. So the songs in the medley all have the same chords, that is, the same sounds with the same… what I called nuances.

They don't.

Never mind the lyrics: there are clearly more than four sounds in any of the songs when sung: just listen to 'em. But even watching the keyboardist's hands on the electronic keyboard (for [the one segment where you get to do so for any significant length of time](http://www.youtube.com/watch?v=oOlDewpCfZQ#t=310s) (warning, foul language in that clip)), you can see he hits more than four chords.

What gives? Am I hearing and seeing wrong, or is my definition of *chord* wrong, or is Axis of Awesome lying, or is there some explanation of how the songs in this medley are considered to have but four chords even though they have more?

Answer: 
**tl;dr - your definition of chord is wrong.**

Your initial assumption

> 
> a 300 Hz note and a 500 Hz note played simultaneously will be a 100
>  Hz sound
> 
> 
> 

is unfortunately incorrect.

When you play a 300Hz note and a 500Hz note what you will get is a 300Hz note, and a 500Hz note, **and** a 200Hz note (the difference between them) **and** an 800Hz note (the sum of the two frequencies) (Have a listen to the demos on **[this page](http://www.animations.physics.unsw.edu.au/jw/beats.htm)** for examples)

In addition to that, a chord can have any number of notes in it (typically on a piano it usually has 10 or less notes, and on a guitar you're usually expecting 6 or less)

And finally, a chord can be played in many different ways, so if I wanted to I could play a 4 chord song using 20 different variations of that chord.

**Update** After watching the actual video, the keyboard player is only playing 4 chords, and not really playing any variations of them. He is sometimes accenting certain notes more than the others, but the 4 chord shapes he is using are consistent throughout that segment. He is hitting and releasing **keys**, sure, but only as parts of the same chords.
Well, I don't know about all this hertz stuff, that's never interested me as a musician. A chord is a harmony that is created with a SET of usually three or four different notes (tones) that are not repeated. It does not matter which order you play them as long as they are played simulataneously. 

Now sometimes a band will have a song that is based on a three or four chords - these are the underlying changes - but often the musicians take liberty with this and insert additional chords, substitute chords, and so forth, so in fact they are not playing "just four chords." The guitarist or pianist might be playing more. It just depends.