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I've noticed a couple of pop songs that use one chord progression that alternates between swapping one chord (either fifth or fourth) with one that's three semitones below it (to third or second):

I was wondering if there was any musical significance behind this. My guess is that I feel the song could be played with one or the other - is the alternation just to add a bit of variety? And if so, is there a name for this technique, and is there any special relationship between the fifth and the third chord, and the fourth and the second chord that makes this possible?

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Let's say a song is in the key of C; three semitones below this is the key of Am, which is known as the relative minor key. In the same way, chords which are 'three semitones below' (e.g. F and Dm, G and Em) are the relative minor chords. These chords can often be substituted one for the other, as they have two common notes (F and Dm have in common F and A).

Sometimes a chordal instrument (guitar or piano) will continue to play a chord (e.g. F) whilst the bass descends from F to D. Is this chord now an F/D chord (aka F6) or Dm7? It depends on whether one can hear the bass. Structurally, it doesn't matter very much.

  • Thanks for the clear explanation, that makes a lot of sense! I'll be on the lookout for other songs that do a similar thing :) – xdl Dec 19 '17 at 18:05
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In addition to No'am's nice answer, there are two further points I'd like to make:

  1. In most (all?) of your instances, note that the chord in question changes from major to minor. This is thus an easy way to make a pretty big change in the harmonic environment.
  2. But perhaps more than that, let's think about how easy it is to do this change. Imagine we have a C-major chord of C E G. If we move to a chord rooted a minor third (three semitones) lower, we have A minor, or C E A. Note that only one pitch changed, and that one pitch changed by step (from G to A). Furthermore, if you go to an A-minor seventh chord, A C E G, the only thing that changes is the bass. As such, both of these are very easy changes to make.

When we put it together, we see that this change makes a big adjustment to the harmonic environment, and it's an easy change to make. It's a pretty good payoff for relatively little work!

  • Thanks for the elaboration on No'am's answer; the ease of doing the alternation is definitely a great observation! – xdl Dec 19 '17 at 18:13
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    For pieces in minor, similar motion is possible but it would be either up three or down four semitones. For example, Am (ACE) could go up 3 to become C major (CEG) or down 4 to become become F major (FAC). What's important is not that the distance is three semitones, but that it's the next convenient chord that shares two notes. – supercat Dec 20 '17 at 16:25
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There are great answers already written, and I'll just add a little more explanation for why this phenomenon exists. In the end, it's a result of the fact that we construct chords from stacked thirds.

How Chords Are Built

Consider a C major chord, which is C-E-G. The interval between the C and E is a third. The interval between the E and G is a third. Sometimes we add other notes beyond the fifth. For example, a CMaj9 chord is C-E-G-B-D. The interval between the G and B is a third, and so is the interval between the B and D.

Minor chords are the same way. Let's consider an A minor chord. You could continue stacking thirds until you've played almost every note in the scale: A3-C4-E4-G4-B4-D5. (McCoy Tyner uses this voicing on John Coltrane's recording of My Favorite Things.)

The takeaway here: chords are built from stacked thirds.

Choosing a Substitution

Let's consider a chord progression like vi-IV-I-V. We can add some variety by changing one of the chords every now and then. Let's choose the IV chord to modify. We achieve the smallest change by replacing the IV chord with a vi chord or a ii chord. In effect, this change entails moving the root note up a third or down a third (respectively). This creates the least amount of change because chords are built from stacked thirds, and hence we preserve much of the original chord. To see this, let's pretend our song is in the key of C major. The IV chord would be FMaj (F-A-C). The two possible substitutions are Dmin (D-F-A) and Amin (A-C-E). Each of these chords shares two common tones with the original FMaj chord:

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Given the similarities that Dmin and Amin share with Fmaj, these alternate chords are both capable of serving generally the same function as the Fmaj chord. They introduce some variety into the original chord progression without making any dramatic changes to the harmonic structure.

Relative Minor

I've described a broader way to approach the substitutions you've noticed. We could use the description I've given to create new examples beyond the ones you've found. That said, No'am Newton is correct to point to relative minor, because every example you've identified is a substitution between the major and relative minor chords.

In the example I created above, FMaj is arguably closer to Dmin than Amin. The reason is that Dmin7 (D-F-A-C) fully contains an FMaj chord, whereas Amin7 does not. Moreover, Dmin contains the root of FMaj, while Amin does not. So Dmin is closer to FMaj and thus makes for an even more seamless substitution.

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