What Instrument Does Mr Tumnus Play In The Chronicles Of Narnia?

I've been trying to find out. Turns out the instrument is fictional; they just added in the sounds of other instruments. The "duduk" is the one with the melody. However, it's single-chambered and only produces one tone, not two. It'd be cool to invent such an instrument, though,

Mr. Tumnus plays the flute to Lucy Pevensie in The Chronicles of Narnia. Lucy is one of the four main characters in The Chronicles of Narnia. The story of the book which is entitled The Chronicles of Narnia is set in the fictional world of Narnia. It was written by C.S. Lewis.

Mr. Tumnus is the name of a faun in the story which is entitled The Lion, the Witch and the Wardrobe. In addition to The Lion, the Witch and the Wardrobe, Mr. Tumnus has also appeared in the stories which are entitled The Horse and His Boy and The Last Battle.

He is described as a faun whose skin is reddish in colour. He has curly hair, a short, pointed beard, horns on his forehead and cloven hooves. His legs, which resemble those of a goat, are shiny and black in colour and he has a long tail which he carries over his arm.

I thought that Mr Tumnus, being a faun, played the pan pipes.  But perhaps I am wrong.