Harmonized Scales

Just a little more theory and we’ll be ready to put triads to practical use.

As we discussed in the section on diatonic theory, a diatonic scale contains just seven scale degrees.

The C Major scale (Ionian mode) comprises the following notes:

We can form a chord (triad) at each scale degree by stacking thirds. Basically skip the next note in the scale, use the next one, skip another, and use the next:

Notes and triads in «C Major»

As we discussed previously, we can create different modes by starting on different scale degrees. The most common mode after Ionian by far is Aeolian which is built off the sixth scale degree.

In other words, «A Aeolian» (AKA «A minor») uses exactly the same notes as «C Major»

Notes and triads in «A Aeolian»

Harmonizing a scale

We can use this information to play “harmonized” scales using triads along any string set.

For example, harmonizing «C Major» along the top three strings would look like the following:

First you play the CMaj triad at the nut, then Dm two frets higher, then Em, then FMaj, and so on.

I demonstrate the technique here:

I recommend practicing the harmonized major scales on the top four scales.

Becker triads

In addition to simply playing the harmonized scale in order (which doesn’t sound particularly musical) you can, of course, play the diatonic triads in any given order. One particularly useful ordering is progressing through the scale in sixths. Here’s an awesome YouTube video of David Becker explaining the idea (the exercise itself starts at 3’22” but I highly recommend watching the whole thing).

Sixths are interesting because each pair of triads differs by only one note. You either raise the 5th of the triad up to the next scale degree, or lower the root.

C major is the notes CEG. Raising the G to an A gives you CEA (Am, 2nd inversion). Lowering the root gives you BEG (Em, 1st inversion). The process works with every diatonic triad: raising the fifth or lowering the root gives you another diatonic triad a sixth away.

I’m still unpacking all the ideas in that video myself. There’s an awful lot of somewhat advanced thinking there for a single ten minute video.

The basic exercise was a bit of a mental struggle the first few times, but the more I work on it, the more convinced I become that this exercise is money.

Of course, harmonized scales can (and probably should) be practiced on the remaining two string sets, but I recommend focusing on the top four strings as much as possible (at least my brain struggles to handle more).

Chord function

The nice thing about the Becker exercise is that it forces you to see how the shapes connect, and which chords are “closest” in terms of shared notes. I suspect this is particularly helpful for “voice leading” (finding chord inversions).

It led me to a bit of an epiphany regarding chord function (tonic/dominant/sub-dominant). I always knew that Am was the “relative minor” of C, and that the key of Am shared all the same notes as C Major, so it made sense to me that both C and Am (the I and vi chords) were in the “tonic” family. Both sound like “home.”

I never understood why Em (the iii chord) was also considered in the tonic family, though. Now I know. Both Em and Am are very closely related to C. You only need to change one note to get to either triad.

I recently came across this terrific article about chord function. That article coupled with the Becker Triad exercise really helped me learn something that I only vaguely understood before.

C to G is an interval of a fifth. The G triad functions as a dominant (C is the tonic, of course). F to C is also an interval of a fifth (C to F is a fourth) which is why it’s called the sub-dominant. Both share a note with the C triad. Playing a cadence of G Major to C Major gives a strong sense of resolution. Playing F Major to C Major also resolves, but not quite as strongly.

G is closely related to Bdim (only one note changes). Similarly, F is closely related to Dm (again, just one note differs). Both Bdim and Dm are utterly dissimilar to C. They share no common notes. C is spelled CEG, Bdim is BDF, and Dm is DFA. Bdim and Dm are as far from the tonic as you can get. Both G and Bdim perform the dominant function, and both F and Dm are sub-dominants.

To summarize: