A New Model of Rank-Frequency Distribution

Abstract

We assume that if there is a homogeneous class of musical or linguistic elements set up on the basis of a property that is relevant for the use of music or language, then the exploitation of these elements abides by its own laws in the sense that their frequency of occurrence displays a regularity which can be modelled by a monotone decreasing rank-frequency distribution. This assumption has three consequences: (i) The frequencies of occurrence of members of any linguistic or musical (jointly “textual”) class are not equal, i.e., they do not follow the discrete uniform distribution, (ii) it is a consequence of some generating mechanism, i.e., it is lawlike (cf. Bunge, 1967, p. 16: “Everything abides by laws”), and it must have developed historically in order to fulfil some human needs (cf. Köhler, 1991), (iii) if one succeeds in finding some laws capturing this phenomenon (and there are a number of successful models) then these laws are in turn the best criteria of “correctness”, “naturalness”, “prolificness” of class formation, i.e., a class is prolific if its rank-frequency distribution follows the given law. As a matter of fact, hypotheses of this kind are well known both in linguistics and in musicology. The most famous is, of course, the “Zipf-Mandelbrot law” (cf., e.g., Orlov, Boroda & Nadarejšvili, 1982; Guiter & Arapov, 1982; Tuldava, 1998) but there are a number of other hypotheses (cf. Chitashvili & Baayen, 1993; Martindale et al., 1996; Wimmer & Wimmerová, 1998; Altmann, 1991; Rothe, 1991; Arapov, 1989, etc.) which still build membra disiecta and wait for systematization. Most probably we shall never obtain a theory encompassing all cases of rank-order laws – because the “causes” and modes of ranking are infinite – so that at present it is necessary to look for ever new foundations of ranking. In this contribution we shall try to show another way of setting up hypotheses of this kind.