Previously, we’ve seen how to transform the shapes of major chords by transposing them down the fretboard and across the fretboard. All these transformations can be composed. A mathematician would say that they form a group. Strictly speaking, one should introduce the identity transformation, which is just holding the same shape in place, and the inverse transformation. The latter is always possible, because the fretboard is cyclic: it repeats itself after the twelfth fret. So subtracting two frets is the same as adding ten frets.

Obviously, we can combine sideways shifts with vertical shifts and, for instance, produce the C chord by shifting down the A shape.

Even though all our shapes require only three fingers, the barred versions become progressively harder to grip as they require wider stretching of fingers. So the most common barred chords are either built from the E and A shapes, or use fewer than six strings (either by muting, or by finger picking).

And then there are some hybrid grips that merge multiple shapes. That’s because there is one more type of transformation, which I call “crawling,” where you move to a different triad note on the same string. We’ve already seen examples of creating variations of the G chord and the C chord by replacing the third by the fifth or vice versa. The third and the fifth are only separated by three frets, so they are often within easy reach. You have to be careful with replacing the third, though, if it wasn’t duplicated in the first place. For instance, here’s a version of the D chord that misses the third:

Such chords that only contain the root and the fifth are called power chords and are used a lot in heavy metal.

It’s also possible to replace the fifth by the root, as in this grip:

This is an interesting case of a hybrid grip. It started off as the A shape, but you may also see the beginnings of the G shape transposed down three frets, especially if you mute the two bass strings. The A shape has the ability to crawl down to a G shape.

Similarly, the D shape can crawl down to C shape (see the D triangle at the top?):

These two shapes (with the bass strings left out) can be easily transposed and are pretty useful in practice.

In fact, all chord shapes can be unified in one diagram, if you mark all triad tones across the fretboard. Here’s such a chart for the E chord. You can recognize, in order, the E shape, followed by the D shape, followed (and partially overlapped) by the C shape, which transitions into the A shape, which morphs into G, and finally goes back to E. You can use this diagram to play the same E chord in five different positions (after which it repeats itself).

You can, of course, produce such a chart starting from any of the five shapes, just by cycling it. Or you can cut this diagram out and glue it into a ring.

If you’re an astronomer, you might recognize some common constellations in this chart, like the Orion, or Draco, but that’s just pure coincidence.

Next time we’ll talk about minor chords.