They say you can’t dance about architecture. But can you hear geometry? I sure think so. Below are a few examples of "shapes" in jazz music. The examples below show that John Coltrane heavily explored this concept, but there were some earlier practitioners too. The examples below are all transposed to the key of C. The Regular Polygons Equilateral Triangle: The song "Giant Steps" is based around Coltrane Changes, which rotates around three key centers. The interval between each of the three key centers spans a major third, which builds an augmented triad. If you connect the tonalities in the circle of fifths you get an equilateral triangle. The name "Giant Steps" may come from the fact that the intervals between the three key centers are much larger than the ears are used to hearing in music. This harmony is used in other Coltrane songs, like "Countdown," Coltrane's reharm of "But Not For Me," and the bridg...