The history of Western music revolves around the fundamental question of tuning. Through the ages theorists and composers worked to create an ordered system whereby all sounds, all pitches would be in reference to an established scale, which resulted in our octave of twelve notes, so perfectly represented by the piano’s symmetrically ordered keyboard.
The problem in such a system is that there is no way to perfectly divide the pitches in an octave by twelve, there is always a slip, a compromise, a fraction of a note that gets swept under the carpet. In music theory these fractions are called commas: a minute interval, the difference resulting from tuning one note two different ways. Various theorists from Pythagoras to Mercator have proposed their own variants of the comma. In 1692 William Holder Published A Treatise on the Natural Grounds and Principles of Harmony, and in it he proposed a new comma that solved the tuning problem better than any previous ones, but there was a catch: Holder’s Comma was an irrational number, a number that existed in theory, but no physical instrument could ever be tuned to its intervals exactly.
There would always remain this crack in the foundation of the perfect order of harmony.