We have our first guitar chord, E major:

We can apply a simple transformation to it to generate all of the major chords (there are twelve of them). The transformation is called transposition, and it simply moves all the notes up the fretboard by the same distance. We can easily move the three fingers that form the shape of E, but there are also three open strings. They have to be shifted as well. This is where barring with your index finger comes handy. Your finger creates a new nut (that’s what the upper end of the fretboard is called).

Below is the A major chord created by shifting E five semitones, or five frets, down the fretboard. The intervals don’t change, but the root changes from E to A, and all the notes get renamed accordingly.

This is how you grip it.

Technically, barring a chord, is not easy for beginners. You have to develop enough strength and precision in your left hand. But conceptually, it’s very simple. Shifting the whole shape doesn’t change relative intervals, so a major chord remains a major chord. If you don’t have perfect pitch, and somebody shifted a chord, you might not be able to tell. It’s all relative.

That’s why it reminds me of special relativity. You are looking at the same chord from a different frame of reference. All laws of physics (relative intervals) are the same. There is even an analog of relativistic shortening of distances (Lorenz contraction): the distances between frets get shorter as you move down the fretboard. If the frets continued all the way to the bridge, the distances between them would shrink to zero, and there would be infinitely many of them. Reaching the bridge is like reaching the speed of light in special relativity.

It’s very useful to know the names of frets on the E string, because each of them can become the root of a shifted chord. They are, starting from the zeroth fret, or the nut:

E, F, F#, G, G#, A, A#, B, C, C#, D, D#, E.

The twelveth fret is E again, one octave higher, and then the pattern repeats itself. As you can see, there is some regularity in the naming of notes, but then there are the odd cases. Every note can be sharped (the # sign) but you don’t see E# there because it’s the same as F. Also, B# is identified with C.

G major is barred on the third fret (three semitones from E):

and so on.

Later we’ll see that almost all chords with un-sharped names have alternative grips that don’t require barring. The odd one is F, which is really hard to play for beginners:

There is an alternative fingering that requires pressing two thinnest strings with the index finger and either not playing the thickest E string (muting it), or pressing it with a thumb wrapped around the stock:

Just for fun, here’s the F# major chord in which all the notes are sharped.

Perhaps surprisingly, transposition on the piano is much harder, because of the white key / black key irregularities.

Next time we’ll talk about the transformation that generates the CAGED system.