Bird Song Analysis: The Hidden Math of Birdsong
Bird Song
Up above our heads the whirling, twittering world of the bird unfolds. It sounds beautiful, and it truly is, but it is also a complex web of communication. Birds use song to warn of danger, attract a mate, stay in touch with their flock and call to their offspring. Our bird song analysis tool looks at the song, and tried to make mathematical sense of it.
The sounds are complex and have meaning. Birds are one of the few animals that acquire communication like humans do. Young birds must learn the language of their species, or they will never acquire it — much like the window of time in which children must be exposed to language.
Bird song has a syntax with its own set of rules and order. Birds manipulate order to create different meanings. In experiments, Japanese researchers found that scrambling song order affected whether the bird understood the sequence.
It is obvious listening to birds that there is a fixed order of notes. But what does that sequence of notes look like, and just how ordered is it?
What is a Hurst value?
We can look at this by calculating the Hurst value. For those interested, this guide, goes into further discussion of the math behind the sound.
Our bird song tool displays two Hurst values. In the recordings we have tested, we generally see the waveform H at around 0.5, meaning that it is random or almost random. However, when we look at pitch, the Hurst values are high — 0.7, 0.8 or higher — meaning that pitch is ordered and predictable.
Why the difference? Waveform H is affected by many things in the environment: temperature, other birds, wind. But when we look at pitch, the note sequence of the song is deeply orderly.
The Beauty of Bird Song
But numbers are numbers, cold in the loveliness of our hidden world. What is beautiful is the shape of the songs themselves. In our tool above, you can see bird song captured as a 3D image. We used a similar tool for music and prose, and bird song — like the output of those other tools — shows an orderly, complex, predictable shape.
Try putting in audio files of your own at try your hand at bird song analysis. Different species of bird are immediately identifiable by sound shape. The Ornithology Department at Cornell University offers individual bird sound downloads at allaboutbirds.org.