Birdsongs and People-Songs Share the Same Math

It shouldn't be an enormous surprise to find birds that sing according to human musical scales. Those scales, after all, are hardly arbitrary, representing mathematical relationships that transcend human aesthetics. In a sense, it's like counting and logic: Humans build deep, complex languages and systems of thought based on some mathematical/philosophical principles, yet those principles are just as much fundamental features of nature.

A group of researchers led by University of Vienna evolutionary biologist W. Tecumseh Fitch examined in intense detail the collected songbook of the male hermit thrush, a tiny bird known for its flute-like melodies. Using recordings collected from locations spanning North America and dating back 50 years in some cases, Fitch and his team were able to isolate 71 distinct songs, each one comprising a minimum of 10 distinct notes.

The researchers then created spectrograms of each of the songs and compared them to the harmonic series. Fifty-seven of those songs shared harmonic relationships. The team's results are published in this week's edition of the Proceedings of the National Academy of Sciences.

Music is simpler than most band class teachers would have us believe. Every sort of musical scale, Western and non-Western, is harmonic. What that means is every note, or acoustic frequency, is a whole number multiple of some base note (or frequency). So, if you have some note x, the next highest note is simply 2x. The next highest after that: 3x. And so forth.

That's music, and most musical instruments attempt to replicate that relationship as closely as possible. The base note is called the fundamental frequency, and this single note sets up the entire musical relationship within a given scale or harmonic. A note itself is a combination of many different other frequencies, each one adhering to this principle of whole number multiples.

So, we don't even need to think in terms of scales to experience harmonics. Just sing a tone to yourself. That tone is the result of vibrating vocal cords. If you were to look at the vibration of a string through time, it's clear that the amplitude (height) of that vibration has many other amplitudes packed inside of it. A wave is just the sum of other waves, which is one of the most fundamental mathematical observations of nature (see: Fourier analysis).

These other sub-waves are called partials, and they too adhere to this harmonic whole number multiple relationship. It looks like this:

Weird, eh? It's actually infinite, what's called a divergent series. Visually, it looks like this.

The harmonics of a given frequency are made up of an infinity of partials, though those subwaves fairly quickly become trivial as they become really tiny. At some point, we're just adding new terms that are "basically" equal to 0.

'"Our findings add to a small but growing body of research showing that a preference for small-integer ratio intervals is not unique to humans," Fitch concludes, "and are thus particularly relevant to the ongoing nature/nurture debate about whether musical predispositions such as the preference for consonant intervals are biologically or culturally driven."

Otherwise, it's just a nice idea. Culture might seem like a far off realm from the natural world, with all of its dirt, noise, and survival of the fittest, yet it's hardly so simple. From Beethoven to Throbbing Gristle, where there are notes, there is wildness, or at least its mathematics.