The Greek philosopher, Pythagoras, is widely known for his work with triangles; but what most people don’t know is that he also delved into the realm of circles contributing to the creation of a “musical mandala” that we now call “The Circle of Fifths".
In his investigation of music frequencies and pitch, Pythagoras discovered that there were mathematical ratios between notes. He created a visual map, or musical mandala, depicting the relationships between the 12 semitones of the chromatic scale (the 12 notes of an octave - all the back and white keys in one octave on the piano), their corresponding key signatures (a set of sharp ♯, flat ♭, and natural ♮ symbols placed together on the staff designating notes that are to be played higher or lower than the corresponding natural notes) and the associated major and minor keys. In particular, he discovered that the ratio of frequencies between octaves is 2:1 and that the ratio of frequencies between semitones is 2:3.
Why is it called the Circle of Fifths?
There are twelve semitones in an octave. These are the white AND black notes on a piano.
In about 600 B.C.E., Pythagoras arranged the 12 notes (half-steps) of the octave around a circle in a similar manner to a clock. This depiction became known as the Pythagorean Circle.
Revisions and improvements to the Pythagorean Circle were made by Nikolay Diletsky in the 1670's, and Jonn David Heinichen in 1728, resulting in the version that we have today - the Circle of Fifths.