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 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:

root major minor
C I i
C# bII bii
D II ii
D# bIII biii
E III iii
F IV iv
F# bV bv
G V v
Ab bVI bvi
A VI vi
Bb bVII bvii
B VII vii

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 mixolydian. These have chords like "A G D". Instead of "A G D" being "I bVII IV", we can think of it using the corresponding major and use "V IV I":

While it's almost always I, IV, V, and vi, we have both II/ii and III/iii, differing on whether the third is major or minor. One way to handle this is just to drop the third from all the chords and play them open:

So: If we choose a few chords, what fraction of songs/tunes can we play?

Chords Thirds Open
I IV V 31% 31%
I iii IV V 32% 32%
I ii IV V 39% 50%
I IV V vi 41% 41%
I iii IV V vi 45% 49%
I ii IV V vi 56% 69%
I ii iii IV V vi 65% 96%
I ii iii III IV V vi 71% 96%
I ii II iii IV V vi 82% 96%
I ii II iii III IV V vi 91% 96%

We can actually do slightly better than this: while above I only adjusted for relative minor and mixolydian, we can be more aggressive and try interpreting the song against all 12 possible scale degrees. But it doesn't change things very much:

Chords Thirds Open
I IV V 32% 36%
I iii IV V 33% 37%
I ii IV V 43% 57%
I IV V vi 42% 45%
I iii IV V vi 47% 54%
I ii IV V vi 60% 78%
I ii iii IV V vi 68% 97%
I ii iii III IV V vi 75% 97%
I ii II iii IV V vi 83% 97%
I ii II iii III IV V vi 93% 97%

There are small differences between songs and contra dance tunes:

Dance Tunes Songs
Chords Thirds Open Thirds Open
I IV V 21% 25% 38% 42%
I iii IV V 21% 25% 38% 43%
I ii IV V 39% 56% 45% 58%
I IV V vi 35% 36% 46% 49%
I iii IV V vi 44% 50% 49% 55%
I ii IV V vi 65% 85% 58% 75%
I ii iii IV V vi 74% 99% 66% 96%
I ii iii III IV V vi 83% 99% 71% 96%
I ii II iii IV V vi 85% 99% 82% 96%
I ii II iii III IV V vi 98% 99% 90% 96%

What are those stubborn ones which we still can't play, even with this many chord options?

  • Most common are ones that use multiple keys/modes, especially a switch between major and minor. For example, "Kitchen Girl" needs "A G" for the first half of the tune (confusingly called the "A part") and "Am G E" for the second half.

  • Others, like "Be Prepared", use major versions of chords for effect: it uses "C E A D G C" ("I III VI II V I") for a turnaround, following the circle of fifths. You can play it with the minor versions, but it's not as punchy.

  • And a few, like "Gee, Officer Krupke", just use a ton of chords in a way I don't really understand.

As for how this applies to my own instrument-making, for now I've gone with "I ii iii IV V vi" and an option to use open chords.

All code and chords are on github.

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