TITLE: Why isn't a harp in a logarithmic shape?
QUESTION [24 upvotes]: 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?

REPLY [2 votes]: Another factor which many of you are missing is the fact that harp strings are made of different materials in different areas of the harp. I am a harpist myself by the way. The three types of strings are (from the large bass end to the small high end) wire, catgut, and nylon. These different materials require different lengths (and diameter and tension as well). 
The long wire strings are different lengths because the body of the harp is angled down, while the neck (top part) is relatively straight here. These strings are changed primarily by tension rather than length or diameter.
The center portion (gut strings) has the most dramatic length change. The diameter is also significantly varied as you compare strings from different octaves.
Finally, the top portion (nylon strings) has the least variety in length, with the neck and body almost parallel. I do not now exactly why this is (the diameter is not greatly altered). My guess is that the tension makes the greatest impact on these strings. I can tell you that turning the tuning key results in a larger change on the nylons than the catgut, but not as much as on the wire strings.
I hope this is helpful! The shape of a harp is fascinating and surprisingly logical and mathematical.