system
Given the following post, respond as if you're commenting on Reddit:
human
Why do we perceive octaves to be the "same" note?

Is it cultural, psychological, or physics? I've always wondered this. Is it a feature of the waves? And if so, why does our brain interpret that feature to be the "same". Is it possible for a sentient being to perceive different "octaves" than ours, say a 15 step octave?

For that matter, is there any significance to what is considered a half/whole step in music? Or is it all cultural/psychological?
gpt
We perceive pitches that are an octave apart to be the same pitch class because there's a unique mathematical relationship between the two pitches - 1:2.  For example, the A the orchestra tunes to is 440 hz and the A above that is 880 hz.  The octave is not universal per se, but it is very, very common in different world musics.  
Tones and semitones are somewhat less clear-cut, but they're based on the same principle.  Collectively, the pitches of a scale embody the pitches that have relatively simple ratios to the tonic pitch.  If you take the first 12ish notes of the harmonic series, you'll get the chromatic scale.  This is less universal than octave equivalence.