Scale necklaces and symmetry

While I was doing some examination of rhythm necklaces and scale necklaces, I noticed a symmetry among the major scale modes: Lydian mode and Locrian mode are mirror images of each other.

Does this geometric relationship mean anything musically? Turns out that it does. Lydian and Locrian are mirror images in feeling, not just as necklaces. Read on!

Here’s the entire chromatic scale, centered around C. Each pitch is labeled with its possible scale functions within the diatonic modes. The pitches labeled in green are major intervals above the root, the pitches labeled in blue are minor intervals above the root, and the pitches labeled in purple are perfect intervals above the root.

You can think of a seven-note Western scale as a series of toggles. Each note (other than the root) can exist in two versions, the “bright” one and the “dark” one. I’ve represented this concept on the circle by putting the “bright” notes on the outer ring and coloring them green. I’ve put the “dark” notes on the inner ring and colored them blue. Some notes are “neutral”, meaning neither bright nor dark; these I’ve colored purple. You make scales by setting the different toggles to their bright or dark setting.

Having more toggles flipped in the “brighter” (sharper, clockwise) direction give a scale a brighter feeling. Having more toggles flipped in the “darker” (flatter, counterclockwise) direction give it a darker feeling. For example, all major scales have the toggle for their third scale degree flipped in the bright direction, and all minor scales have the toggle for their third scale degree flipped in the dark direction.

Here are all of the major scale modes, in order from brightest to darkest. You can play all of them on the aQWERTYon!

Lydian mode

Lydian mode has all of the possible toggles flipped in the “bright” direction, so it’s the brightest major scale mode–brighter than the major scale itself!

Major scale

Flip Lydian’s sharp fourth to natural fourth to get the major scale.

Mixolydian mode

Flip the major scale’s natural seven to flat seven to get Mixolydian mode.

Dorian mode

Flip Mixolydian mode’s natural three to flat three to get Dorian mode.

Natural minor scale

Flip Dorian mode’s natural six to flat six to get the natural minor scale (Aeolian mode.)

Phrygian mode

Flip natural minor’s natural two to flat two to get Phrygian mode.

Locrian mode

Flip Phrygian mode’s natural five to flat five to get Locrian mode. This is the darkest possible mode: everything that can be flipped to the dark side has been.

Here’s a graphical summary of flipping all the toggles. Notice that each toggle is a tritone away from the previous one. Cool!

But wait. We haven’t flipped every note yet. What if we move the root down a half step from C to B? Then we’d end up with B Lydian mode, and the whole cycle would start over again a half-step lower.

By the way, compare this toggle system to the way you can move through the diatonic modes by rotating a necklace around the circle of fifths.

The “brightness toggle” method works great to understand the feeling of the major scale modes. Unfortunately, it doesn’t work so well for other scales. For example:

Harmonic minor scale

Just by counting toggles, it would appear that harmonic minor is as dark as Dorian mode, which seems wrong to me. The natural seventh in harmonic minor doesn’t feel so much “bright” as just mysterious and attention-grabbing. It functions more like a sharped flat seventh, if that makes sense.

Melodic minor scale

Melodic minor would seem to have the same brightness as Mixolydian mode. I don’t know if I would characterize it that way; Mixolydian makes me feel at home, while melodic minor makes me feel unsettled. But maybe that’s a different thing from brightness and darkness. Or maybe this definition of brightness and darkness is too simple.

Lydian dominant mode

Lydian dominant is as bright by this formulation as the major scale. Again, I’m not so sure that’s the right way to think about it. But it’s interesting to consider.

Blues scale

The eternal question with the blues scale: does it use sharp four or flat five? Really, it’s both.

The language we use to describe these scales carries strong cultural assumptions. By describing the major scale degrees as “natural,” the baseline against which we define everything else, we assert that the major scale is somehow more fundamental than all the other scales. In Western European music, that’s a reasonable enough assertion. But it isn’t true of all music everywhere, even in Western societies. Rock guitarists learn the pentatonic scales as being fundamental, and usually learn other scales by adding notes to them. That’s the way I learned, and it still makes sense to me. In blues, the blues scale is fundamental. You could make a case for Lydian dominant mode as being the fundamental scale, since it’s closest to the natural overtone series. For now, we’re stuck with the terminology we have. But it’s worth looking at it critically.