Self-affine fiunctions F(x) with multiscaling height correlations Cq(x)~XqHq are described in terrms of the standard multifractal formalism with a modified assumption for the partition. The corresponding quantities and expressions are shown to exhibit some characteristic differences from the standard ones. According to our calculations the f(a) type spectra are not uniquely determined by the Hq spectrum, but, depend on the particular which is made for the dependence of N on x, where N is the number of points over which the average is taken. Our results are expected to be relevant in the analysis of signal type data obtained in experiments on systems which an underlying multiplicative process.