It's been nicknamed "the loneliest whale in the world". It sings a song like no other. Some say it wanders alone across the Pacific Ocean, crying out for companionship that never comes.

No-one knows for sure whether the whale is male or female, what species it is, or even if it still lives. The last in the original series of recordings was made in 2004.

It's one of the animal kingdom's great mysteries. But we might have been thinking about it the wrong way.

Maybe its unusual song doesn't isolate it after all. Perhaps instead it sings this way to ensure it can be better heard by its companions, or to impress members of the opposite sex. One way or another, this unusual whale can tell us a lot about whales and their songs.

The story begins in 1989. An array of hydrophones called SOSUS, built by the US Navy to detect enemy submarines, picked up some strange signals. They were whale songs, and they were similar to blue whale calls, but there was one big difference.

His findings would be discussed for years to come

The key notes of the song were at a frequency of 52 Hertz. To human ears this is a low bass note, but it is significantly higher than the blue whale, which sings between 10 and 40Hz.

Fin whales also seemed like an unlikely fit, since they sing at 20Hz.

It was Bill Watkins, a marine mammal researcher at the Woods Hole Oceanographic Institution (WHOI) in Massachusetts, who first realised the significance of the Navy's recordings. For Watkins, tracking the 52Hz whale became a passion.

He passed away in 2004, aged 78, but a few months before his death he completed work on a paper that summarised 12 years' worth of recordings. His findings would be discussed for years to come. Watkins had found that the 52Hz whale was not just unusual, but outright unique.

"It is perhaps difficult to accept that if this was a whale, that there could have been only one of this kind in this large oceanic expanse," Watkins and his colleagues wrote. "Yet in spite of comprehensive careful monitoring year-round, only one call with these characteristics has been found anywhere, and there has been only one source each season."

The popular press decided that it was the story of a lonely animal

The finding had all the hallmarks of a great mystery story. There was the renowned and dedicated scientist, the years of collaboration on classified military recordings, and the eventual publication of those findings when the material was declassified.

The popular press decided that it was the story of a lonely animal. In 2013, the Express, a British tabloid newspaper, claimed that the whale's unusual call had "stopped him finding love".

Now, American filmmaker Josh Zeman and actor Adrian Grenier are planning a crowd-funded documentary about the whale.

The film's Kickstarter page strongly emphasises the idea that "52" is a lonesome beast. "The loneliest whale needs some friends," asserts a poster image encouraging donations. In the end, one of those would-be friends was Leonardo DiCaprio, whose foundation gave $50,000 and helped the campaign hit its $300,000 funding target.

It will be like looking for a needle in the world's largest haystack

The funds gathered will be used to mount an expedition in autumn 2015 in which, it is hoped, the 52Hz whale will be found and filmed. Zeman says the rest of the movie's budget will come from elsewhere.

His biggest challenge will be finding the correct whale and filming it. Calls at this loud, low frequency can travel hundreds and sometimes thousands of miles from their source. It will be like looking for a needle in the world's largest haystack.

But Zeman has another problem. Some whale scientists have questioned his whole approach.

One critic is Christopher Willes Clark of Cornell University in Ithaca, New York. He made recordings of the 52Hz whale in 1993 and says it's not quite as anomalous as it might seem.

To ask if the whale is lonely – I don't think that's so far off the mark

Many types of idiosyncratic whale calls have been detected, and some studies suggest that groups of whales living in particular regions have dialects. When you consider that, the 52Hz whale is "not completely mind-bogglingly unique," he says.

Furthermore, Clark and others reject the idea held by some that the 52Hz whale cannot be heard or understood by "normal" blue whales that make lower-frequency calls. "The animal's singing with a lot of the same features of a typical blue whale song," he says. "Blue whales, fin whales and humpback whales: all these whales can hear this guy, they're not deaf. He's just odd."

"It's been a real struggle," admits Zeman, who has disagreed with some over the nature of the 52Hz whale's experience. "Definitely we speak in hyperbole. Is he the loneliest whale? But to ask if the whale is lonely – I don't think that's so far off the mark. My goal is to ask scientists to really consider this."

Complicating the picture further, the whale hasn't been calling at 52Hz for many years, according to John Hildebrand of the Scripps Institution of Oceanography in California. Watkins also noticed this. The whale's call has been gradually deepening and is expected to be closer to 47Hz today, though it’s been a few years since any recordings were identified.

Nobody knows why whales change their calls

It's not alone. Blue whales around the world have been singing at steadily deeper pitches since the 1960s, according to a study Hildebrand published in 2009. This suggests some kind of relationship between the 52Hz whale and blue whales. North Atlantic right whales for example are different – their calls have actually been rising in tone over time.

Nobody knows why whales change their calls like this. In 2009, Hildebrand and his colleague Mark McDonald suggested that blue whales were deepening their calls to make them stand out against shipping noise, which threatens to drown them out.

But that looks wrong, says Hildebrand. "It turns out that, by deepening the pitch of the song, the whales are actually shifting into an area where there's more noise, not less."

Whales respond to man-made noise in an unpredictable way, says Clark. He has watched what happens when an oil and gas exploration ship approaches singing whales and sets off explosives to discover fossil fuel deposits beneath the seabed.

Every season they listen to each other and synchronise their songs

Sometimes the whales' response is dramatic. "In many cases the whales will change their whole behaviour," says Clark. "Males will stop singing, there'll be a quieting of the whole acoustic scene, they'll move out of the whole area." But not always. "At other times it won't make any difference."

Maybe the whales are changing their songs for another reason entirely. Hildebrand suggests that blue whales are competing with each other to be deeper, season after season.

"If the guy next to you is signing a little deeper than you, you better move down to synchronise," he says. "We see this. Every season they listen to each other and synchronise their songs."

That raises another question. If whales prefer to sing similar songs, what would make one of them sing at a completely different pitch?

The leading hypothesis is that the 52Hz whale is a hybrid, the offspring of two whales of different species. Such a whale would have an unusual body, and that might well affect its song.

Nobody has managed to record a hybrid whale's calls

Hybrids of fin whales and blue whales are well-documented and can be identified, according to John Calambokidis of the non-profit organisation Cascadia Research in Olympia, Washington. For instance, their body shape is often similar to that of a fin whale, but with a larger snout and flippers like a blue whale.

Certainly the 52Hz whale behaves a lot like a blue whale, says Kate Stafford of the University of Washington in Seattle. "It had the exact same seasonality as blue whales and if you look at the migratory patterns that Bill and his colleagues found, it's the same thing," she says. "So I feel pretty confident that at least part of this animal is a blue whale."

But we cannot yet be sure. Nobody has managed to record a hybrid whale's calls – even Calambokidis, who got close enough to document their unique appearances. Getting them on tape will be crucial.

Calambokidis is one of several scientists now working on ways to make it easier to study the calls of individual whales. One of the biggest problems has been figuring out which whale is calling when.

As the animal produces the call its whole body seems to vibrate

Scientists often fit whales with microphones to record their calls. But these sometimes pick up the calls of nearby whales as well. So Calambokidis and his colleagues have added accelerometers, just like the ones your smartphone uses to detect motion, to the microphones.

"As the animal produces the call its whole body seems to vibrate and the accelerometer picks up that signal," says team member Peter Tyack of the University of St Andrews in the UK. "It's by far the best way to pick up when an animal in a group is making a call." In a study published in 2014, they showed that they could now match tagged animals to instances of their singing.

And over at WHOI, where Watkins once worked, marine biologist Mark Baumgartner has helped to oversee the development of a listening system which can automatically analyse and digitally publish marine mammal sounds in near real-time.

The apparatus includes a moored buoy off the coast of Massachusetts. An underwater microphone listens out for marine mammal calls and on-board software written by Baumgartner classifies the calls by species.

The signals are then transmitted via satellite to computers at WHOI, which quickly process the data and publish it on the web. "What you're seeing on the website is near real-time data," says Baumgartner. "The latest stuff is less than two hours old."

People often like to imagine that animals experience the same emotions we do

In theory, detection methods like this could pinpoint specific animals, if their call is distinctive enough. "You could use this technology to search for 52Hz," says Baumgartner. However, it would have to be installed where the mysterious whale has been detected in the past, such as off the west coast of the United States.

What they can't tell us is what is going on inside the whale's head. The 52Hz whale may feel lonely, as Zeman suggests, but it's equally possible that it doesn't. There's certainly no reason to assume it does.

The fact is, people often like to imagine that animals experience the same emotions we do. Whales are complex and mysterious creatures. The idea that one might be out there, experiencing something as quintessentially human as loneliness, makes the animal seem somehow closer to us. But it remains a fantasy until there is evidence for it.

That evidence will only turn up if we can find the 52Hz whale again. "No one since Bill [Watkins] has really put any effort into trying to track it down," says Hildebrand. But his team has recently been on the case.

In 2010, sensors off the coast of California picked up whale calls with the same pattern as Watkins' recordings.

The recordings were discovered by an intern, after Hildebrand suggested they look for evidence of the 52Hz whale. "We found it on sensors no more than five or six miles from my office," says Hildebrand. "So I think it's accessible and we should be able to solve it."

Conceivably Hildebrand's team has found a group of hybrid whales

However, Hildebrand's data suggests there is now more than one animal singing at this unusually high pitch. "You could see it on two widely separated sensors at the same time, so that suggests it's not just a single animal," he says. "It may be multiple animals."

Conceivably Hildebrand's team has found a group of hybrid whales, all singing at the same special pitch. The 52Hz whale may be a member of this group that sometimes wanders off on its own. If that's true, there is a happy ending to this story: the whale is not all that lonely after all.

Finding concrete evidence won't be easy. But many, from filmmakers to whale researchers, are now on the lookout. To discover the true nature of the 52Hz whale, we can only wait – and listen.