Humans can speak making precise movements of our tongues, teeth and vocal chords.
I want a sentient creature whose carnivorous mouth-parts are completely unsuitable for speech to be able to communicate fluently with others of its species.
A trumpet can certainly make different notes by vibrating the lips against the mouthpiece whilst blowing.
A manatee can finely control its flatulence as an alternative to a swim bladder. https://youtu.be/ktLwBHsA_vk
Humans have been known to be able to inhale both air and water through their anus.
The great early 20th Century French flatulist, Le Petomane, was able to do this, ... By sucking in large quantities of air [through his anus], he was able to perform lengthy shows on stage, and could imitate musical instruments, farm animals, and bird songs, whistle melodies, and play the ocarina. https://megafart.wordpress.com/2012/02/18/is-it-possible-to-inhale-suck-in-air-via-ones-anal-opening/
EDIT - On following this up, I fear the claims made above of what he could do were greatly exaggerated. The main point was that he could draw air in at will which is something most people can't.
Could an alien anus-breather evolve to communicate entirely by taking in and expelling wind? Would it have to evolve extra appendages to do so?
I'm talking about a complex language similar to that of humans. Not just alarm calls.