Songbird duets resonate to beat
Physics underlies rhythms of South American birdsong.
The synchronized rhythms of South American ovenbirds may be driven by simple physics, say researchers, rather than deep-rooted musical talent.
The thrush-sized Hornero, Furnarius rufus, is common to Brazil and Argentina and famed for its oven-shaped nest. When a male and female strike up song, the male begins by singing roughly six notes per second and gradually upping the tempo.
Instead of keeping pace with her partner, the female punctuates his beat with one of her own1. The result is "a most appealing rhythm," say Rodrigo Laje of City University in Buenos Aires, Argentina, and Gabriel Mindlin of the University of California at San Diego.
The male's song 'drives' the pattern of the female song, the researchers think, rather like a pendulum that is set swinging by vibration of the beam from which it hangs. But the songs differ from a simple pendulum, or linear oscillator, that swings with a single, steady rhythm.
Instead, Laje and Mindlin think that the muscles controlling the birds' breathing and syrinx, the sound-generating organ, work like so-called nonlinear oscillators. Nonlinear oscillators can respond to regular 'driving' signals in complex ways.
By studying recordings of duets in Argentina's Villa Elisa nature reserve, Laje and Mindlin find that the number of male and female notes tend to come in simple ratios, which change frequently over several seconds. One female note for every three male notes is a common combination, but they also find ratios like 1:4, 2:7 and 3:10.
At this rapid-fire speed, it would be virtually impossible for human musicians to set up such complex counter-rhythms. But the birds aren't consciously counting beats; they just let their muscles vibrate together. The researchers have previously proposed that songbirds' bodies are hard-wired for singing.
Using mathematical models, Laje and Mindlin find that if one nonlinear oscillator drives another, just like the male and female birdsongs, the two get locked into the same rhythm ratios as those seen in Hornero duets. As the pace of the driving oscillator picks up, the driven oscillator jumps abruptly between fixed ratios.
In theory, a typical sequence might go from perfectly synchronised notes of 1:1 to 2:3, 1:2, 2:5, 1:3, and so on all the way to 1:5. This is just what seems to happen in the real duets as the male speeds up his song.
- Laje, R. & Mindlin, G. B. Highly structured duets in the song of the South American hornero. Physical Review Letters 91, 258104, (2003).