12-TET Geometry Examples

A few figures made with my interactive diagram for generating geometric shapes based on the 12 equal-temperament tones.

All the options we have

Triads

Triads result in simple triangles and transposing them (moving them up or down by some interval) is a simple rotation.

Transposition of the C major triad to E♭

Tritone substitution

Rotating a dominant 7th chord by 180°, such that the tritone interval within the chord remains unchanged, gives us the chord for tritone substitution.

Tritone substitution: G7 → D♭7

Modes

Instead of just chords, we can look at full scales. Rotating the Ionian mode gives us the six other modes, for example, the Phrygian.

C Ionian (left) and Phrygian mode (middle and right)

The second and third diagram both depict the Phrygian: in the former, I rotated the geometrical figure, in the latter, the labels on the outside circle.