A Note on the Pitch Contour Similarity Index
Ilya Shmulevich · Journal of New Music Research · 2004
of C, and adjusting for the number of ties. Thus, the matrix representation is largely redundant in the sense that it can be uniquely recovered by simply knowing the ranks of each of the notes. This should come as no surprise, since by definition, the combinatorial model of contour is fundamentally ordinal: it ignores the absolute note values and only considers their ranks. By knowing the vector of ranks [R, R2,... , P], where Ri is the rank of note i, we can uniquely write down the matrix C. As mentioned above, the matrix C has been used to define the pitch contour similarity measure CSIM as follows. Given two pitch patterns of equal length, we form their respective matrices and then count the number of entries in each matrix that are common to both. This number is typically normalized by a constant, n (n - 1), representing the total number of possible matches, excluding the diagonal. I will now show that the CSIM similarity measure is essentially the well-known and widely-used Kend