I love this topic and love to see some rigor put into testing for this effect.
I bought a pair of HE-500 headphones a few years back. Straight out of the box, they had NO bass - I mean, NONE ... to the point I was seriously concerned they were broken.
Before sending them back, though, I decided to "break them in" using frequency sweeps, played on a loop over the weekend when I was out of town.
When I returned, the headphones sounded COMPLETELY different, with bounteous bass. They never sounded any different at that initial change.
So while Amir's test appears to show there was no change WITH THESE SPECIFIC SPEAKERS, I know what I heard. There was no chance for my ears to "get used to" the sound (as I was out of town), and the headphones went from literally no bass at all to clear and present bass.
Will continue to follow this topic with great interest
I was once break-in/burn-in curious, like you, having gone through a similar situation with many a headphone. I don't mean to negate your experience, but I'd ask you to reconsider your notion that the you were able to break them in over the weekend. There are
so many variables that can make a pair of headphones sound different after some time - yes, even if you haven't been listening to them for a while.
Here's one fun anecdote. The biggest case of headphone "break-in" I ever experienced was actually with a pair of high end noise cancelling headphones. Except it wasn't break in at all that had changed the sound.
When I first tried them, they had almost no bass with noise cancelling off, and sometimes showed distortion with noise cancelling on when playing loud. I'd been into headphones for about a decade ago that point, so I knew how important seal was, but as far as I could tell, everything was fine in that regard. Mind you, at this point I was already quite skeptical of burn in.
The headphones sounded 'resolving' or whatever but lacking 'body' and 'oomph' (fun words I used often back in the day). I was ready to write them off as being headphones only for people who like bright headphones, and to complain they couldn't play loud without distorting with ANC on
Then I put them away for a few days and left them plugged into my computer to burn in, just in case.
Miraculously, they sounded better next time I tried them. I was almost ready to start believing in burn in again. The bass was there even with ANC off, and the distortion was gone! Surely the answer was burn-in? No.
The answer, I soon realized, was that I'd gotten a haircut.
See, I have pretty poofy hair, and at the time, my hair was extra poofed up. I had never really noticed any headphone-related problems because of my hair before, but my hair was bigger than usual and it turns these headphones were
particularly sensitive to a good seal, so even when I thought I had that, I did not.
The hair-induced gaps in the seal were enough to cause all the low bass to leak out. When using them in passive mode. When using them with ANC on, it turns out that the DSP uses the microphones to regulate bass, and that had some funny interactions. The headphones 'work harder' to maintain the right bas level with a poor seal. The distortion was gone after my haircut, but I could easily make it come back by simply loosening the fit on my head a bit.
Unsurprisingly, as my hair grew poofier again, the headphones started to sound worse, like those first few days.
This particular anecdote aside, I'm willing to bet that earpads softening up and improving seal has a bigger effect on a headphone's sound than anything going on with the drivers.