Yes - the training used an approach called “melody triggers”, and was part of a very clever English jazz musician’s PhD research in 2020. I don’t know if he published it in the end.
The idea is that you pick 12 tunes, one for each note in the Western scale. Then the training program plays a random note, and you have to guess which of the tunes starts with that note.
It’s based on the observation that even untrained humans can usually sing the starting note of familiar songs within 1-2 semitones absolute error (known as the Levitin effect).
The training ramps this up very intensely. When you pass the first (recognition) stage, the next stage is about imagining the tone (audiation) for a named tune. I found this part difficult and improved very slowly.
At least for me, it was one of those skills where you make a huge improvement at the beginning, but then see diminishing returns. At the beginning it feels like there are 12 confused voters in your head, but after even just a couple of weeks, hearing a tone is like 1 voter raising their hand very clearly while the others sit down.
I kept doing the training for a couple of years, then stopped because I was sick of “hearing” those 12 tunes pop up when I heard a note.
Basically every time I recognised a note (usually automatically, if it was an isolated note, but not so much when complex music is playing), it instantly recalled that specific tune. So I’d hear a car horn on the street sounding a C# and the “Chariots of Fire” theme starts playing in my head. Similarly, if I’m tuning my violin and want to sing an E before testing that string, I’ll think of Fur Elise, which starts on that note. But actually I don’t want that… I want to just think of “E” without bringing the context of another tune into mind.
Since I stopped doing the training, the associations have faded a little, but my absolute pitch sense is still pretty good. But nowhere even remotely close to people like Jacob Collier who can instantly decode a complex chord – I’m only really able to pick out single notes.
And I don’t really tune my violin using absolute pitch because mine isn’t accurate enough (although I was surprised to discover some research that most people with perfect pitch aren’t perfectly accurate either, and can be “tricked” by gradually detuning things). If I hear a D# and think “oh, Voodoo Child, right, D#” and you tell me “wrong, that was a D”, I’ll get confused and not be sure if I was right or wrong. The researcher highlighted a possible distinction between someone with “enhanced tonal memory” and “absolute pitch encoders”. I’m probably more in the former category, while someone like Collier would be in the latter category (exceptionally reliable, stable and accurate even at microtonal levels).
Anyway I’m exploring some other ideas now because I still want to be able to one-shot transcribe complex chords, but I’ve not yet found any methods more effective than that training some years ago.