4-2 · Intervals, Revisited

Knowing where the notes are is half the job. The other half is knowing what they are: the interval each nearby note represents relative to the tonal center. Once you can read those intervals on the fly, every chord voicing tells you what it's made of, and every scale in the rest of the course ties back to elements you already know.

We covered the interval naming system back in 2-1, so here is just the quick version. An interval is a distance measured in semitones, one semitone per fret, and each of the twelve distances has a name taken from the major scale. In shorthand, it's the numbers 1 through 7, and every number has a flat neighbor one fret below it, except for the root and the 4.

The rectangle and stack make identifying intervals easy. We already know how to connect the shapes across the entire fretboard, so if we learn the interval names in and around the shapes themselves, we can find the interval of any location on the neck.

Start with what you already know from Module 3. The roots live in fixed positions in the minor and major shapes. There's a 5 inside every pentatonic shape, always one string below the root. The major shapes contain a 3, and the minor shapes a ♭3. From there, the two scales diverge: the major pentatonic adds the 2 and the 6, and the minor pentatonic adds the 4 and the ♭7.

Once you know the interval of every note inside the shapes, you can extend outward. All you need is the order of intervals in the chromatic scale. You know where the ♭3 lives in the minor rectangle; one fret higher is the 3, and one fret lower is the 2. You don't need a separate diagram for those, and you don't need to memorize them separately — you can infer them from the points you already know. Build outward from each known location, and you get a complete neighborhood containing all twelve intervals.

This is how you go from knowing five pentatonic intervals to being able to read any note on the fretboard in context. As an example, say I'm playing an A major barre chord at the 5th fret, and I want to know the interval of the note on the G string, treating A as the tonal center. I know there's an A at the 5th fret of the low E string, so I can place a major pentatonic stack there, build up through the rectangle above it into the next stack, and read the note directly: it's the 3.

I could just as well have used minor pentatonic shapes — the ♭3 is one semitone below the note in question, so counting up one gets me the same answer. Or I could have started from a different A entirely. No matter which path you take, you will always get the same answer.

One thing I really recommend is taking chord voicings you already know and working out what intervals they contain. For any major chord shape, you'll find only roots, 3s, and 5s; for any minor voicing, roots, ♭3s, and 5s. Seventh chords add one more note. Here's a movable seventh-chord voicing I like, with the root on the B string:

Exercise 4-4: Take a few chord voicings you already use, find the root inside each one, and work out the interval of every other note by building rectangles and stacks around the root. The chord names you've been using will start to make a lot more sense once you can see what's actually inside them.

You now have the third leg of the system. You know the rectangle and stack shapes, you know how to find roots by name, and you know how to identify any interval relative to those roots. Before Module 5 puts all three together on the major scale and its modes, 4-3 gives them a first job: reading chord tones straight out of the shapes.