Some Interval Map Visualizations

For the past few days I've been experimenting with circular representations of chord, scale and similar kinds of structure. Laying them out in a circle is the right thing to do because then rotation of the circle is equivalent to finding all the modes of the scale or arpeggio.

Here are three experimental visualizations of interval maps of common and uncommon structures; click the image for a higher resolution version:

The blue disc shows a number of triads, the green disc shows all possible symmetrical structures having more than four notes and the reddish disc shows some heptatonics. In each case the outer rings tend to represent more common structures than the inner rings.

The segment at 12 o'clock is the root note, which is always present. Then we count around clockwise in semitones, with the b2 at 1 o'clock, the 2 at 2 o'clock, the b3 at 3 o'clock, the 3 at 4 o'clock and so on, ending with the 7 at 11 o'clock and then going back to the root.

The key thing is that these interval maps can, in theory, be rotated around the circle to create the modes of each scale in the ring. If these seem useful I'll probably design an interactive version that allows you to do the rotations, which I imagine would be a very nice teaching tool for the basic theory of modes.

I'm sure more refinements are be possible; I'll probably post more ideas on this topic in the future since, for me at least, visualization is a key technique for any kind of learning, and especially for learning and understanding more about music.