7-7 · Symmetric Scales: When Geometry Takes Over

At the end of the last lesson, I promised you scales so regular that there's almost nothing to memorize. That's what this section is about, and it's the fifth operation on the module map: repeat.

Think about every scale we've built in this course. Each one is some combination of one-, two-, and three-fret intervals in a seemingly random order. That's the whole reason this course needed rectangles, stacks, and all the other bits and pieces layered around them: the patterns look different depending on where your fingers are, so you need something to hold onto.

The two scales in this section are different. Their interval patterns repeat like wallpaper, and since the pattern repeats, most of what you'd normally have to memorize just isn't there. Will you use them often? Probably not. But they cost almost nothing to learn, and for that reason I think they're worth knowing about.

The whole-tone scale

Take the repeat operation literally, picking one interval and repeating it until you get back to where you started. If that interval is a whole step, you get the whole-tone scale, and on one string it couldn't be simpler: it's every other fret. Here it is from the F at the 1st fret, the way I played it in the video.

Count the notes, though. There are six, not seven. It's the first scale since the pentatonics without seven notes, so the spelling is 1, 2, 3, ♯4, ♯5, ♭7, and one of the degree names, the 6, goes unused.

Here's where the symmetry starts to pay off. Start this scale from any of its six notes, and you get the same six notes back. So the whole-tone scale has no modes; every rotation is the same scale. In fact, in all of music there are only two whole-tone scales. On a single string, it's either the odd frets or the even frets.

Memorize this: The whole-tone scale is 1, 2, 3, ♯4, ♯5, ♭7: every other fret on any string. There are only two of them in all of music, and every rotation of either one is the same scale.

So what does it look like across the strings? It's the same three-note shape on every string, shifted one fret toward the bridge each time you cross a string (two at the warp). In the video, I played it from the G at the 3rd fret of the low E string:

If you'd rather stay in one position, alternate three notes and two notes per string. That gives you fifteen notes (about two and a half octaves) without moving your hand:

And since every note in this scale is the same distance from its neighbors, you can start either fingering from any note you like. The pattern is identical no matter where you begin. There's no real root to anchor to, and no Forms 1 through 5, because every position is the same position.

What it sounds like, and when

You've heard this sound your whole life. It's what movies and cartoons play when a character drifts off into a dream or a flashback, usually on a harp. I'd describe it as unmoored: with no half steps in it, nothing pulls toward anything else, so the scale just floats.

The classic place to use it is over a dominant chord whose fifth has been pushed off its usual spot: a 7♯5, or a 7♯4 with no fifth in it at all. Remember from the extensions lesson that if you keep stacking, a chord ends up containing a whole scale. Stack the whole-tone scale in thirds, and you get 1, 3, ♯5, ♭7, then 9 and ♯11: a 7♯5 chord with a 9 and a ♯11 on top. The chord and the scale are the same set of notes. In the video, I played over this D7♭5 grip, using the three-notes-per-string diagonal from the D at the 5th fret of the A string:

It's a tension scale, not a home scale. You float for a moment, and then you land somewhere.

The diminished scale

The second scale repeats a pair of intervals instead of just one: half step, whole step, half step, whole step, all the way around the octave. That's the diminished scale, and this particular version, the one that starts with the half step, is called the half-whole diminished scale.

This one has eight notes, which is why the books sometimes call it octatonic. With eight notes and only seven letter names, the spelling gets messy; measured from the root, the degrees come out as 1, ♭2, ♭3, 3, ♯4, 5, 6, ♭7, and in the video I mostly just point at frets. Chord charts call the four extra notes by their upper-structure names:

Notice what's left when you take those four away: 1, 3, 5, ♭7, the entire dominant seventh chord. That's why this scale fits a dominant chord so well.

The symmetry works the same way as the whole-tone scale, but with wider spacing. This scale repeats every minor third: move the root up three frets and you get exactly the same notes, which means there are only three diminished scales in all of music.

On the fretboard, the natural way to play it is four notes per string, stretching four frets from the first note to the last. And once again, it's the identical shape on every string, one fret toward the bridge per string, two at the warp. Here it is from the E at the 7th fret of the A string, the way I played it in the video over an E7 drone:

In fact, across the entire fretboard, there are only two fingerings to learn. If your four-note group starts on a half step, it goes half, whole, half. If it starts on a whole step, it goes whole, half, whole. That's the complete list. And that second fingering is the whole-half diminished scale: the same collection of notes, started one note later, and the version that fits diminished seventh chords.

Memorize this: The diminished scale is four notes per string, the identical shape on every string, one fret toward the bridge per string and two at the warp. There are only two four-note cells: half–whole–half and whole–half–whole.

What it sounds like

That ♭9 grinding against the chord is the sound: dominant tension with some snarl to it. And it isn't only a jazz thing. Robben Ford built a signature blues-rock sound out of this scale.

Using them

Neither of these is a scale you'll want to hang out in. They're tension scales that you pass through on the way to somewhere else. So think in short gestures: a few notes that grind against the chord, and then land on a chord tone. If you run all the way up either scale, it will sound like an exercise. A short phrase that resolves is more likely to sound like music.

Practice for this lesson is about learning to trust the symmetry.

Exercise 7-10: Put on a 7♯5 or augmented triad drone. Pick any note of the matching whole-tone scale, anywhere on the neck, and build outward from it: along the string, up the diagonal, or in position. Then pick a different starting note and prove to yourself that the pattern really doesn't change.

Exercise 7-11: Switch to a dominant seventh drone and learn one four-note cell of the half-whole scale, starting on the root of the chord. Slide the cell up a fret on the next string, and repeat. For a challenge, finish every phrase by landing on a chord tone of the drone. Making tension is easy; resolving it is the part that takes practice.

As always, treat these as starting points and make up your own variations.

So that's two new scales, and almost nothing new to memorize. Cheap as they were, we've reached the point of diminishing returns when it comes to learning new scales.