§ Octaves are double frequency apart (TODO)

As I am reading BasicSynth, I learnt that:

Each half-step between notes in the
musical scale represents a frequency ratio of $2^{1/12} \simeq 1.059$.

The $(\cdot)^{1/12}$ is reasonable, because an octave contains 12 semitones. The base $2$ is quite mysterious! I wanted to know why this is.
a multiple oCochlea and why frequencies are 1:2

https://physics.stackexchange.com/questions/44469/octave-equivalence-biological-or-more