The basic reason for octave equivalence is not from human subjectivity. It's from the fact that something that repeats "x" times is also something that repeats

The basic reason for octave equivalence is not from human subjectivity. It's from the fact that something that repeats "x" times is also something that repeats "x/2" times, eg a sequence such as: ABCABCABCABCABCABC Can be thought of as "ABC" repeated 6 times or "ABCABC" repeated 3 times. If you replace the letters with numbers, you can treat the numbers as samples of a sound wave. Just to be clear: the magical number here is 2 (not 12 or 8 or 7) since "octave equivalence" refers to the fact that you can multiply a frequency by 2 and get the same note. Unless the sound is a perfect sine wave, there isn't a particular frequency associated with it due to these alternative interpretations.