The relationship between the frequency range of visible light and the musical concept of an octave is an interesting observation, but it is ultimately a coincidence. The correspondence between light and sound in terms of frequency ranges is not a fundamental or deliberate connection.
The visible light spectrum is a small portion of the overall electromagnetic spectrum, ranging from approximately 400 to 700 nanometers in wavelength. This range corresponds to the colors we perceive, from violet to red. On the other hand, the concept of an octave in music refers to a doubling or halving of a frequency. When you move up one octave, you double the frequency, and when you move down one octave, you halve the frequency.
While the frequency range of visible light roughly spans what would be considered a single octave in music, this is due to the specific nature of the electromagnetic spectrum and the way our visual system has evolved to perceive light. The connection to musical octaves is coincidental and not based on any inherent relationship between light and sound.
It's worth noting that the perception of light and sound occurs through different sensory organs (eyes and ears) and involves distinct physiological and neurological processes. While both light and sound can be described in terms of waves and frequencies, they are fundamentally different phenomena.