That's not "Merlin hum" (Merlin Song) that I'm hearing. That's more exhaust + prop than anything. You're only about a month away from hearing the true song.
It’s called the Merlin Hum because it’s unique to the Merlin.
What causes it is irrelevant (though interesting) regarding the name because it’s only heard on Merlin engines, primarily the Mustang. It is partly due to the Doppler effect which is why it is only briefly heard. That Bob Hoover video I posted last year in your Sounds thread has a longer interval of it than this video.
There’s also one in the Crazy Horse 2 aerobatic video but the music playing is in the way (and that woman won’t shut up with her narration so we can enjoy it).
https://m.youtube.com/watch?v=aXqnCI1B_9g (0:12.8-0:13.9 and 0:38.5-0:39.9. The exhaust masks it at 01:04) - It’s the humming not the popping of exhaust that follows it. The sound system didn’t capture it very well but you can still hear it if you know what you’re looking for.
https://m.youtube.com/watch?v=-IkSQF2MbSU (02:12.4-02-13.2 though the exhaust crackle is being picked up by the mic too much and is drowning it out. 02:37.5-02:40 is better. 03:46-47 catches it briefly as well. It’s that thrum that moves down in pitch tone, very subtle in these recordings and quick. Your ears hear it better in person.)
Merlin Hum is a unique and special sound that is highly transient. Nobody who has heard it can forget it but sound equipment is terrible at capturing it.
Looking forward to what you come up with.