I was watching a harp, yesterday, and thought about the mathematics involved. I know that music is closely related to logarithms, because having a string or pipe twice as long produces the same note.
As an octave contains 7 notes, I would expect the strings 8 to be twice as long as the string 1, the string 9 to be twice as long as the string 2, etc.
Instead of that, the strings are strained between an oblic plane and a "S" shaped holder that reminds me a little of a $\frac{\sin(x)}{x}$ function.
I see two possibilities:
- This shape is precisely calculated to produce the right notes.
- This shape is only a matter of esthetic and the right pitch of the notes are mainly produced by the string diameter and tension.
Is there a mathematical reason to make the harps with such a non-logarithm shape?