Harmonic Rectangles 2022

Contained within each symmetry system are one or more harmonically proportioned rectangles, commonly used for creating repeatable pattern units for larger-scale designs. This piece explores the process of deriving the harmonic rectangle from the initial circle divisions, by way of constructing regular polygons.

For example, we can divide a circle into six (or twelve) through the same method we use to construct a regular hexagon. We can then derive the harmonic rectangle by drawing lines connecting specified circle divisions at the circumference.

Each of these harmonic rectangles (a square is considered here to be a specific kind of rectangle) can be scaled up or down according to its own proportional rhythm. The final (left side) column demonstrates these scaling rhythms.