Singing fish is a cute idea, but is there anything in it? Cicadas chirrup, if you can call that singing. Birds certainly sing and it's debatable whether dogs sing although they sometimes howl.
The definition of singing is a largely human oriented one. The Oxford dictionary refers to use of the voice "with musical modulations", especially in a "skilled manner". That probably excludes the common Australian fish known as the "grunter". We caught one once. When we flipped it into the boat it became obvious how it got its name. The poor thing flapped around making a sad wheezing noises like a distressed pig.
Fish have a few ways to make sounds. One is their swim bladder - an air sac they use to maintain buoyancy. Attached to this, is the sonic muscle and when they flex it, it produces a drumming sound. In fact, they do it quickly enough to make them the fastest contracting muscles known in any vertebrate. As you'd expect, the pitch varies depending from one species to another.
A grouper can produce 250-300 Hz (250 Hz is close to middle C on a piano). Most fish sounds are around 40-60 Hz.
This topic gives me the opportunity to use the longest word you'll ever read in an Ask Fuzzy. Springfederapparat is found in some marine catfish.
Given that it's two words bolted together, it has to be German. "Spring" means, well, spring. "Federapparat" means elastic. The springfederapparat is a thin shelf of bone attached to the wall of the swim bladder, forming part of their noise-making apparatus.
If you thought the rock concert was loud, the Australian Mulloway has been recorded at over 172 decibels. You wouldn't want to be close to a fish making that kind of noise, and divers have reported that it is indeed painful. The Goliath grouper also has a booming voice that can be detected 2km away.
Another way fish make noise is similar to cicadas called "stridulation". They rub parts of their skeleton or their teeth together to make a clicking or a grinding noise. The pitch can be between 100 Hz (below piano middle C) and 8000 Hz (well beyond the top note on a piano). These can be amplified by the swim bladder.
A third way that fish can make noise is called "hydrodynamic sound". They do this when they're swimming, by sudden changes of direction with tail and fin slaps. It's suggested that this is one way they can be detected by predators such as sharks.
On the whole fish are a noisy bunch, and if you've ever been snorkelling you may have heard their constant clicking.
Surprisingly though, some fish make almost no noise. The pink snapper is as quiet as a dormouse.