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, both on the chromatic circle and the circle of fifths. Here’s Lydian above and Locrian below:

C Lydian mode

C Locrian mode

Does this geometric relationship mean anything musically? Turns out that it does.

You can think of a seven-tone Western scale as a series of toggles. Each note can be flatted or natural (except for the fourth, which can be sharp or natural.) Toggles flipped up give a scale a brighter feeling, and toggles flipped down give it a darker feeling. For example, major scales have the third toggle flipped up, and minor scales have the third toggle flipped down.

Lydian has all of the possible toggles flipped up, so it’s the brightest major scale mode–brighter than the major scale itself. Locrian has all of the toggles flipped down, so it’s the darkest major scale mode. They’re mirror images in feeling, not just as necklaces. Here are all of the major scale modes, from brightest to darkest:

Lydian mode

Lydian mode toggles

 

 

Major scale

Major scale toggles

 

Mixolydian mode

Mixolydian toggles

 

Dorian mode

Dorian mode toggles

 

Natural minor scale

 

Natural minor scale toggles

 

Phrygian mode

Phrygian mode toggles

 

Locrian mode

Locrian mode toggles

 

How well does the brightness toggle method work to understand scales generally? Not all of them fit the paradigm, but I tried some of the ones that do.

Harmonic minor scale

Harmonic minor toggles

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.

Melodic minor scale

Melodic minor toggles

Melodic minor would seem to have the same brightness as Mixolydian mode. I don’t know if I would characterize it that way; Mixo 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 toggles

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.

The very 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 strong case for Mixo being the fundamental scale; it’s closer to the natural overtone series than major is. For now, we’re stuck with the terminology we have. But it’s worth looking at it critically.

One thought on “Scale necklaces and symmetry

  1. Hello Ethan,
    I am fan of circular representations of musical structures and I follow your blog posts with keen interest. However I am not sure whether I would draw the comparison between rhythm patterns and tonal patterns.
    There are many interesting regularities within the field of tonal modes. Inspired by Milton Mermikides’ I have designed a representation where the mentioned symmetry plays a role.
    Image here: https://flic.kr/p/ri4yis
    Annotated image here: http://mashupforge.com/map/modal_compass/

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