The most surprising feature of the musical scale is its imperfection – we don’t get everything we could hope for. Allow me to explain.
The pitch of a musical note is related to its frequency, that is, the number of sound waves that pass a given point per second. Frequency is measured in hertz (Hz) – vibrations per second. The human ear can hear sounds with frequency between about 20Hz and 20,000Hz.
Within this range there are an infinite number of possible frequencies that an instrument could sound out. This is clearly impractical for musical purposes – how does one chose between an infinite number of options? The human ear can only distinguish between two frequencies if they differ by about 0.3% or more. But this still leaves over 2000 discernible frequencies within the human ear’s audible range. Imagine a piano with 2000 keys! So how should we go about making music?
Letters to Nature 