Music: the missing Humboldt system

William Abler identified a common principle of pattern generation underlying the open-ended diversity of forms exhibited by chemistry, genetics and human language. He named this generative principle "the particulate principle of self-diversifying systems". In passing Abler mentioned music as an instance of the principle, but did not develop the idea. Most extant music does not use the sound content of the continua of frequency (pitch) and time directly in the creation of musical patterns. Rather, those patterns are formed on the basis of elements drawn from a discretisation of the pitch continuum into "pitch sets" and, in all rhythmic music, from a discretisation of the time continuum into metrically based durations with proportional values. Musical patterns formed of these elements are perceived not as simple collections of unconnected elements, but as perceptual objects with identities of their own, capable of being combined into more complex patterns. Music thus exhibits all essential characteristics of a particular system, and can be added to language as a so far unrecognized particulate system of the human world. It may even relate to language in the way chemistry relates to genetics, namely as a necessary but not sufficient antecedent.