Could Pythagoras Hear His Own Comma?
Julien de Channes de Jouvancourt ’22, Petaluma, California
Majors: Physics; Mathematics
Ancient Eastern and Western music theorists predicted a small musical interval would occur when constructing a scale based on a circle of fifths. This interval, now known as the Pythagorean Comma, can clearly be discerned even by non musicians. This musical system however was an idealized mathematical construct. By examining the nature of ancient Greek and Chinese plucked instruments, we consider whether or not a sufficiently rigorous ear-based tuning system could have constructed a music scale that would have a discernible Pythagorean comma. We account for systematic tuning errors associated with string stiffness, amplitude induced pitch errors, finite observation time effects, and psycho-acoustic effects based on listener perception ability. The physical and technological limitations presented above make it unlikely that a Pythagorean comma would have been heard by the ancient Greeks.