What is the Difference between a Banjo and a Harley-Davidson Motorcycle? Answer: You Can Tune the Harley - Abstract

Daniel Fitzgerald
Bridges: Mathematical Connections in Art, Music, and Science (1998)
Pages 291–292


It is a mathematical fact that a fretted instrument cannot be played in tune. Fretted instruments are designed according to the well-temperament theory of tuning. Differences between natural tunings and well-tempered tuning exist because one is based on rational numbers and the other on irrational numbers.