Before we understood the science of harmonics, we instinctively knew about octaves. For example, the note of A was recognized with two common octaves before we named it. Using science, we confirmed our perception: we discovered the halving of octave frequencies (880 Hz to 440 Hz).
This embodied knowledge -our body as a tuning fork- can pick up on realities beyond our mental cognition, yet it does not make these realities mystical. What does seem magical, indeed mysterious, is the ability of notes in sequence to create an altered state in humans.