Musimathics Quotes

“To communicate about music, we must be able to name the pitches and associate them with frequencies. This is not an engineering problem so much as a design question, and each culture has answered it in a manner that speaks to what is important to that culture. In the West the choices have been profoundly influenced by the ideas of Pythagoras”
― Gareth Loy, Musimathics: The Mathematical Foundations of Music

“Natural examples of chaotic dynamical systems include the earth’s atmosphere and the vibrations of virtually all sources of musical sound, such as the scrape of a bow on the strings or the turbulent flow of air from the player’s lips over the fipple of a flute. Small differences in initial conditions can be amplified by such systems to such an extent that any error in measuring the initial conditions can render any long-range forecast of system behavior wildly inaccurate, even if there is no further disturbance to the system. The weather from day to day is never exactly the same. Notes played on a flute, though they may sound alike, are never exactly the same. Our ears gloss over these differences, hearing sound categorically. But if we wish to understand the precise mechanism of a dynamical system so as to accurately predict its behavior over time, the initial conditions must be known exactly.”
― Gareth Loy, Musimathics: The Mathematical Foundations of Music

“Music is a science which should have definite rules; these rules should be drawn from an evident principle; and this principle cannot really be known to us without the aid of mathematics. Notwithstanding all the experience I may have acquired in music from being associated with it for so long, I must confess that only with the aid of mathematics did my ideas become clear and did light replace a certain obscurity of which I was unaware before.”
― Gareth Loy, Musimathics, Volume 1: The Mathematical Foundations of Music

“it seems that our neural anatomy is wired to perceive an exponential relation between pitch and frequency. Frequency f goes up exponentially as pitch p goes up linearly: to double pitch, we must quadruple frequency.”
― Gareth Loy, Musimathics: The Mathematical Foundations of Music

“Both mathematical notation and musical notation point to universes quite different from the one in which ordinary language functions so well. But, in each too, there is genius in the very notation that has developed for giving representation to ideas that seem to lie beyond ordinary language. There are times in mathematics when the similarities in notation is the first clue to a deeper relationship. Similarly musical notation not only created a structure within which Western music could develop but also shows something other than just the sounds being made. It indicates how the various elements stand in relation to one another, how sound creates a space, it shows how different musical voices move against and through each other.”
― Gareth Loy, Musimathics: The Mathematical Foundations of Music