Regular Stars, Polygons, and Musical Scales

Edge scales are musical scales constructed from the edges and vertices of a regular polygon. Regular polygons are polygons that have specific structure and they can be constructed from regular stars. We will discuss this structure using elements of rational trigonometry and discuss regular stars of order n. A star of order 6 will be used to construct a regular hexagon and motivate the construction of an edge scale. Similar constructions can be used to make other types of musical scales such as stellation scales.