Reducing Music to Math

lonelysandwich:

Science Daily reports on the research of a team of music professors who have devised a complex method of mapping musical systems onto mathematical ones.

I’ve performed, composed, and over-analyzed music for most of my life, and I’ve come again and again to a central theory: a large part of musical enjoyment comes from the brain automatically inferring complex mathematical relationships between sounds.¹

You don’t need to know the math behind the whole-tone scale. You hear it; you know it is special. But if you analyze it with standard Western theory, set theory, geometric models, etc., you will clearly see the relationships you hear.

A more simple example: when you hear 440 vibrations per second (Hz), you interpret that as a note.² When you hear another sound, you think, “That’s the same note, but higher.” You’re hearing a multiple of 440Hz: 880, 1760, 3520, etc. Somehow, your brain is imposing a system that recognizes an abstract theory of pitch class³ onto mathematically-related vibrations.

The modeling method discussed in this article is yet another way of confirming what we already hear. And, as with any descriptive method, it can also be used to find new relationships, to lead composers ever onward in their quest to explore all sonic relationships.

But here’s where your head will begin to spin. Yes, there are complex relationships between notes in the standard, 12-tone, equally-tempered scale developed in the West. However, these relationship don’t come “straight from nature.” Instead, they’re physical relationships that have been pushed and prodded into a system of our creation, a system that is part human invention, part natural occurrence. This is the case with any culture’s musical system(s).

The question then becomes: are these models of sound as it is or as we imagine it to be?