Some people who already have experience studying music take a look at the group of shapes and recognize a Circle of Fifths. But if a shape isn’t quite the same as a scale, key, or mode, then is the group of shapes the same as a Circle of Fifths?
It turns out that there are several ways to see a Circle of Fifths in the group of shapes. If you were to choose the note in each shape that organizes the other notes into the Major or minor modes, the progression of those notes across consecutive shapes in the group would give you a progression of fifths.
If you do the same thing for the notes that organize each shape into any mode other than Major or minor, you will likewise see a progression of fifths, but a different progression than would result from emphasizing the Major or minor modes.
Similarly, if you look at the note that changes between each consecutive shape in the group, you will see a progression of fifths as well, that relates to the “order of sharps” when you move from left to right across the group, and the “order of flats” when you move from right to left.
When you look at the progression of shapes themselves, you can see the “Circle of Keys,” or more accurately, of Key Signatures, corresponding to the progressions of fifths that had organized those key signatures into individual modes.
And finally, you can even look at a single shape as being composed of a progression of fifths. That is, if you construct a series of 7 consecutive fifths beginning from each one of the keys on the keyboard, you will have constructed each of the shapes. And if you continue on to 12 consecutive fifths, you will have constructed all the notes represented on the keyboard.
So one way to look at the group of shapes is as many different Circles of Fifths, all at once. Or perhaps better, as something more general than a Circle of Fifths, that has the potential to become any, all, or none of the possible versions of the Circle of Fifths.
After all, these different Circles of Fifths each have different qualities, and different uses. Perhaps most notably for Shapes, the Circles of Fifths that are actually made up of fifths, like the circle of Major or minor keys, or the order of sharps or flats, place a focus on the fifths themselves—the individual notes that comprise the larger whole. And by contrast, the Circles of Fifths that are related by fifths, like the Circle of Key Signatures, place the focus on the broader contexts.
The group of shapes allows for any of these Circles of Fifths, but notably, it also doesn’t suggest or rely on them. You can navigate the group of shapes by remembering the contour of the shape itself, and perhaps also by remembering its name, like “3 to the Right,” or “2 to the Left,” without considering anything else about how the shapes are related to one another, or about how they are constructed.
But significantly, in both the case of navigating the group of shapes, and navigating a Circle of Fifths, you are stepping outside of the immediate experience of playing—outside the world of the shape, the song, and the intuitions that connect the two—and looking at a larger view of the terrain. You are looking at a map of something bigger than you can experience in one moment. It is a theoretical territory, a larger musical space, a system of musical spaces.
A single shape is also a theoretical territory. There may be a sense in which you experience this whole territory at once, and connect it to the experience of playing with a song. And there may also be a sense in which playing in one shape is connected to the experience of playing in other shapes.
The impulse to develop a concept, and then to develop a larger system of relationships between concepts is very much part of our musical curiosity, creativity, and our attempts to make rational sense of our musical experiences. The group of shapes has the potential to enhance the experience of playing with any single shape, because it gives us a way to place that experience in the broader context of all the other shapes.
So it is not necessarily a Circle of Fifths that the group of shapes represents, but the connection between an immediate musical experience, and a broader theoretical terrain. This is exactly what a Circle of Fifths, in whichever form it takes, is intended to represent as well.