That sine wave sounds a bit "fuzzy" to me, maybe the generator adds a small amount of overtones or aliasing. I tried another generator (http://onlinetonegenerator.com/) and the consonance feels weaker.
Interesting, I still hear it the same, dissonant and consonant, perhaps western music ruined me. Thanks for sharing.
Edit: Didn't see the url, makes my old reply obsolete:
Interesting. I tried to avoid clipping/aliasing by using audacity with as high quality audio as my system allows and I can still reproduce pretty much exactly what you hear on those websites. https://vocaroo.com/i/s0Be5CexLgVs is 440hz, then 440hz+880hz, then 440hz+850hz. But I would be interested in any repeatable signal that does not harmonize at all so do share!
Edit: Didn't see the url, makes my old reply obsolete:
Interesting. I tried to avoid clipping/aliasing by using audacity with as high quality audio as my system allows and I can still reproduce pretty much exactly what you hear on those websites. https://vocaroo.com/i/s0Be5CexLgVs is 440hz, then 440hz+880hz, then 440hz+850hz. But I would be interested in any repeatable signal that does not harmonize at all so do share!