We were drifting in an inflatable raft just off the rocky shores of Niue, when suddenly a deep humming noise vibrated through the boat.
"That's a whale," said BJ Rex, our Niue Dive skipper. "Must be close."
I pulled my mask and snorkel into position, slipped over the side and looked down through the dark-blue water. There, right underneath, was a huge shape.
I was floating on top of a humpback whale, which was lying on the ocean floor singing.
It sounded, to my ears, like a mournful melody about the sad life of a bachelor whale obliged to swim alone on the long journey from the whale feeding grounds in the Antarctic Ocean to the Pacific Ocean, where the warmer waters are better for raising calves.
But then again, it may have been a song of celebration about arriving back at Niue. Whatever the theme, it sounded quite emotional.
I've listened to whalesong before, mostly during videos about whales, and I once went to a physiotherapist who used to play humpback hits while administering acupuncture. I also heard humpback singing through the hull of a boat when I tried to swim with whales off the Tongan island of Vava'u a few years ago (we followed a mother and calf for hours but, unfortunately, it was too rough for us to go into the water).
But this was quite different. This time the singer was right before my eyes, and the singing was so powerful you could actually feel it in the water. As I drifted on the surface, the sound vibrated through my body. It was an amazing experience.
Soon the others in the boat, including my wife, Chris, were also in the water. I swam over and held her hand. For a while we just hovered together, looking down at the whale and absorbing the sound. Not being overly confident in the ocean, she swam back to the boat, hung on to a rope and watched from there.
For maybe 15 minutes we all floated while the whale sang, its basic melody occasionally interspersed with brief bursts of "hoof-hoof-hoof".
Slowly, its huge pectoral fins began to move, the tail waved gently and the massive body moved slowly towards the surface.
It looked as though it was going to emerge right in front of us but distances in that clear water are deceptive.
It turned out the whale was probably 50m down, and it broke the surface and blew the traditional spout of water about 50m away. Mind you, it was so big that it was quite close enough.
For a few minutes the whale lay on the surface taking in more air, before diving and disappearing from sight. We waited for about 20 minutes - the whale reappeared and dived almost underneath us. This time when I got into the water it looked even bigger because it was resting only about 30m down.
Once again we floated above, feeling the force of its song, until it moved on after about a quarter of an hour.
Annie Gray, one of the owners of Niue Dive who was skippering a second boat, said she thought we had been watching a young male about 12m long.
"Did you enjoy that?" she asked, as we clambered back into the boats.
"More than enjoy," I replied, still a bit overwhelmed by the encounter. "It was almost a spiritual experience."
It was made all the more special by the fact that initially it had looked as if I would miss out on a whale encounter for a second time.
For most of the time we were staying in Niue, at Matavai Resort, there had been humpback whales and spinner dolphins playing in the sea just off the restaurant's big deck.
But when the time came for our trip there was no sign of whales off Matavai Resort - next to the Niue Dive base - and reports of a whale seen off the island capital of Alofi prompted Annie to launch there.
Of course as soon as we dropped the two inflatables into the sea with the aid of a crane, husband Ian Gray's voice crackled over the radio with the news that a whale was now off Matavai.
By the time we got to Matavai the whale had disappeared but a pod of dolphins was playing close to the shore.
We motored closer, and I slipped over the side and looked down to see if I could spot which way they were going.
"Sometimes," said BJ, "the dolphins play off the bow and you can take turns hanging on to the boat, watching their games, while we go with them."
Not on this occasion, unfortunately, because by the time I had got my head into the water they had vanished.
While we waited for action, I passed the time by making whalesong noises.
Then suddenly through the sea came the sound of the real thing. "Keep going, Jim," said one of the other divers. "You're obviously attracting him."
But with a whale nearby I was suddenly shy. And, moments later, there he was right under us, singing with a power that I couldn't remotely imitate.
Getting there: Air New Zealand has a weekly service to Niue, which runs on Saturdays.
Where to stay: Matavai Resort
What to do: See the whales with Niue Dive.
Further information: See niueisland.com.
Jim Eagles visited Niue as guest of Air New Zealand and Niue Tourism.