We have already discussed several kinds of seventh chords. But if you can extend the chord by adding a third above it, why not top it with yet another third? This way we arrive at the ninth chord. But a ninth is one whole step above the octave. So far we’ve been identifying notes that cross the octave with their counterparts that are 12 semitones lower. A mathematician would say that we are doing arithmetic modulo 12. But this is just a useful fiction. A lot of things in music theory can be motivated using modular arithmetic, but ultimately, we have to admit that if something doesn’t sound right, it’s not right.

A ninth is 14 semitones above the root (if you don’t flat or sharp it), so it should be identified with the second, which is 2 semitones up from the root. That puts it smack in the middle between the root and the third: a pretty jarring dissonance. We’ve seen a second used in a chord before, but it was playing the role of a suspended third. In a ninth chord, you keep the third, and move the second to the next octave, where it becomes a ninth and cannot do as much damage. Instead it provides color and tension, making things more interesting.

To construct E9, we start with E7. It has the root duplicated on the thinnest string, so it’s easy to raise it by two semitones to produce the ninth.

There are many variations of the ninth chord. There is a minor version, with the third lowered; the seventh can be raised to a major seventh; and the ninth itself can be flatted or sharped. We won’t cover all these.

Following the same pattern, C9 can be constructed from C7 by raising the root by two semitones.

We get a highly movable shape, especially if we put the fifth on the thinnest string. In particular, it can be moved one fret towards the nut to produce B9–a slight modification of the B7 grip we’ve seen before.

If you look carefully at this shape, you might recognize parts of Gm in it (the three thinnest strings). This is no coincidence. The fifth, the seventh, and the ninth of any ninth chord form a minor triad.

Here is the E9 grip obtained by transposing C9 down the fretboard. It’s used a lot in funk:

The same chord with a sharped ninth is called the Hendrix chord, after Jimi Hendrix who popularized it:

The E9 shape is not only movable, but it’s also easy to mutate. This is the minor version:

and this is the major seventh version:

Such chords are quite common in Bossa Nova.

A9 is obtained by raising the root of A7 by two semitones:

Can you spot the Dm shape raised by two frets?

Similarly, G9 is constructed from G7, and it conceals a Dm as part of it.

Next: Extension chords.