The Big Deal With Doubling the Third

It's one of these rules in music that one learns very early in music education (alongside the famous fifth parallel rule): In four part harmony don't double the third of the chord.

I'm not that great at just accepting rules that I have been told without knowing the reason behind them, so I remember asking my first music theory teacher at the age of maybe 10 why I should not double this third. The answer I got was "Because it doesn't sound nice." and "Because it sounds too thick then."

This was by far not satisfactory as an answer but it was the only one I got throughout the years. I could hear that it didn't sound that great when doubling the third but I still wanted to know why. So at one point I started to dig into this.

The reason for this phenomenon lies in physics, or more specifically in acoustics.

We all know about the phenomenon of the harmonic series. A tone we hear doesn't just include the frequency of the pitch we're hearing but a fixed series of higher (and softer) tones on top of it which is also part of what makes up the sound colour.

For instance the harmonic series on top of C looks (roughly) like this:

I'm saying roughly because most of these tones divert slightly from our tempered tuning but this is not super relevant for our current case. Depending on what your root tone is, this exact scale will be sounding on top of it, sometimes more prominently, sometimes really quitely.

To make things easier, let's reduce it to the first six notes as these are the most prominent notes anyway and the higher ones tend to get softer and softer.

So let's have a look at what happens when we incorporate that scale on top of all the chord tones when we build a triad.

For the sake of readability and to avoid too many ledger lines I'll keep it that low even if you would never want to write a chord that low as it will be super muddy.

So here's the shortened harmonic scale on C:

And here it is on G:

If we superimpose these on top of each other we get this: 

black = notes of harmonic scale of C

red = notes of harmonic scale of G

blue = notes shared by both harmonic scales

You see the resulting "chord" looks pretty stable and could be characterized as a Cmaj9 chord.

Now let's have a look at the harmonic scale that our third of the chord E would provide:

Adding this in the mix from above will result in this final "chord":

E harmonic scale = orange

I think the problem here is pretty obvious: The g and g# in the upper staff clash pretty heavily. There would be a compareable clash if we added the scale of a minor third on top.

Now in our perception of triads, we don't hear this as a clash, but rather as a "slight disturbance". A major chord remains a stable and consonant structure in our perception and a major third adds a lot of resonance and "definition" to a chord. However when overemphasizing the third of the chord this clash becomes a bit more prominent in our perception which we hear as "thickness" or "instability".

So the general idea behind the rule "don't double the third" is indeed pretty valid and should be taken into consideration. If we translate it to orchestral writing, it means that we should take care in our voicings and orchestration to not overemphasize the third. So when you double chord tones in different instruments, it is preferable to rather favour the root and fifth of the chord when doubling chord tones.