Is there a distance generalizing the Hamming distance to $[0, 1]^n$? I'd like to compute a distance between two vectors of $[0, 1]^n$ ($n$ numbers between 0 and 1).
I'm looking for a distance generalizing the Hamming distance which I would have used if the numbers were bits.
Actually, I don't need a real distance, only a pseudo-distance, a measure of similarity / divergence.
I'm comparing spectra of audio samples : I take the Discrete Fourier Transform of both, normalize the spectra, and I'd like to compute the similarity of these spectra. 

What if you used $$d(a,b) = \sum |a_i - b_i|$$  It is continuous, and has the usual metric properties such as the triangle inequality, and for $a,b\in \{0, 1\}^n$ it is identical to the Hamming distance.
