If basic music theory were the high school algebra of music math, then the work of Noam Elkies, Dmitri Tymoczko, and David Wright would be considered advanced college calculus. Last week these three researchers presented their various math related musical endeavors at the annual meeting of the American Association for the Advancement of Science.
While each researcher had their own unique angle, all three revolved around finding some order or divine math hidden behind the entropy of music.
Elkies was the first to present, and explored the idea of “how many songs are possible”. While not perfect, his approach involved the use of advanced statistics to identify how much a song needs to change before it is considered unique or different. He used his data to randomly generate a piece of music not based on standard musical rules, but instead the numbers of Pi.
Following that was Dimitri Tymoczko, who was drawing parallels between classical musical composition (involving ideas like counterpoint) and geometry. Here’s an excerpt of his intriguing work…
In his scheme, a note is a point on the real line, turned into a circle with the identification of octaves; chords are higher-dimensional generalizations. Voice leading is represented by vectors in the tangent space of these manifolds.
Last was David Wright, who tackled the ethereal world of tuning and overtones. For those of you who may not be aware, our modern scales are built off of the golden ratio and the work of Pythagorus (yeah that same guy who made A² + B² = C²). Wright’s presentation explored the concept of equal temperament, and how it could not create truly perfect intervals besides octaves.
For those of you who may not be familiar, instruments used to be specifically built to play in one key, in which all the intervals would be perfectly in tune. However, instruments like a piano utilized equal temperament, which allows a musician to play in any key.
However, Wright used recorded examples to show that the various intervals are not perfect on a microtonal level when utilizing this method of tuning. Mind. Blown.