Circle-of-fifths tunings can be visualized as laser bounces inside a mirrored circle

Evidence

We can think of the progression around the circle of fifths in an intuitive and physical way, visualizing the progression as a clockwise succession of bounces of a laser beam off the interior of a mirrored circle. In each bounce, the angle of incidence measured from a line from the center of the circle (easily shown to be 15.29325 degrees) equals the angle of reflection. In the case of the Pythagorean circle of perfect fifths, we notice not only the approximately 7-degree Pythagorean comma—a gap at the last perfect fifth from F toward (but missing) C—but also the fact that the spacing between the notes, indicated by the sharp apex at each bounce, is uneven. If we want to close exactly after 12 bounces, and get the spacing to be even, we need only to switch the laser beam launched at C to fly off at 15 degrees (or π/12 radians) from the normal rather than 15.29325 degrees, as it does in the Pythagorean system. — Eric J. Heller, Why You Hear What You Hear- An…, 2395

Categorization

• CANDY: The laser-bounce visualization of tuning systems is a vivid, shareable image — the difference between Pythagorean (15.29325°) and equal temperament (15°) collapses to one-tenth of a degree.