You famously only need four
chords to play everything, or maybe it’s only three. But how true is this really?

I decided to go look and see what was common. I looked at a large
number of transcribed songs, writing down which chords were used.
This isn’t perfect: some chords are more optional than others, but
it’s about right. I only wrote down the triad: C7 and Cmaj7 are just
C. I used three sources:

• Rise Up
  Singing: a songbook popular at singalongs. I flipped through and
  took the chords from the 277 songs that seemed most familiar to me.

• The Portland
  Collection: a tunebook popular among contra dance musicians. I
  did the same flipping through, with all three volumes, and took the
  chords from 89 tunes.

• Farm and
  Wilderness String Band Tunebook, Third Edition. All 42 tunes.

Out of these 408 songs, here’s how many include each chord:

This isn’t a great way to look at it, though, because it is absolute
and music is (mostly) relative. We perceive a song that goes “C F G”
very similarly to one that goes “A D E”. Musicians will often use
“Roman Numeral notation” to talk about chords in a purely relative
sense. If we look at “C F G” relative to “C”, or “A D E” relative to “A”,
we can call them “I IV V”: they are each three major chords using the first,
fourth, and fifth notes of the major scale. We indicate minor chords
by using a lowercase number: “iv” would be “Am” relative to “C”, or
“F#m” relative to “A”.

Here’s what this looks like in C, for example:

Here’s the same chart as above, but with relative chords:

This is mechanically converted, and assumes every song is using the
standard major scale, which of course they aren’t: see all those “i”
chords? Instead of thinking of a song with “Am C F G” as being “i
bIII bVI bVII”, we should think of it as “vi I IV V”, as if it is in C
(the relative major). This focuses our distribution:

Some songs are neither major nor minor, but in other modes, typically
mixolydi