This article is quite well done, especially from a programmer's perspective, but falls flat (no pun intended) for me because of my terrible ear for pitch.
> Here are five notes. Every one is double the frequency of the one before it. [...] They are different pitches, and yet they sound like the same note.
Nothing about these notes seem similar to me. You could play pretty much any sequence of rising notes and (falsely) claim they're the "same note" and I'd believe it. This is one reason I've always had trouble learning music.
> √2 the awkward one -> 311.13Hz
That one doesn't sound particularly awkward to me. Again, I blame my inability to distinguish pitch.
The only instrument I was able to pick up pretty easily was drums.
I thought the same for a long long time.
At least for me the solution was to grind ear training for a few weeks/ months 10 minutes a day.
I'll certainly never reach the heights of this skill but a bit of persistence to overcome lack of natural talent did propell me forward.
What method/software did you use for the ear training?