Known as the syrinx, it is the bird's version of the voice box or larynx in humans.
Scientists used 3D imaging to examine the structure, located where the windpipe forks into the lungs.
They showed how muscles, cartilage and bone work together to allow birds to sing highly intricate songs even in flight.
The syrinx has two pairs of vocal cords, allowing songbirds to produce two different notes at the same time.
Songbirds routinely perform a feat equivalent to an orchestra musician playing two instruments at once while dancing.
Lead scientist Dr Coen Elemans, from the University of Southern Denmark, said: "We show how the syrinx is adapted for superfast trills and how it can be stabilised while the bird moves. Also we emphasise how several muscles may work together to control for example the pitch or volume of the sound produced."
There are striking similarities between the way young birds learn to sing and the way babies learn to speak.
"We know quite a bit about how the songbird brain codes and decodes songs and how young songbirds learn to imitate the songs of their adult fathers," said Dr Elemans.
"But we know very little about the instrument itself, the vocal organ called syrinx."