Scale Structures

A key principle of this document is that Nature is full of interconnecting scale structures. This will be elaborated in later sections, but first the terminology needs to be defined.

The term scale structure is applied here in the broadest sense of a musical scale: relative dimensions and relations among parts that together form logical wholes.


…ordering divisions, combinations, ratios, or operations, applying to fields of elements, or events. Scale structures may apply horizontally across a range of parameters of any generic quality or quantity; and/or may apply vertically spanning hierarchies or dimensions; or may apply complexly and variously as syntactical organization (frequently reflecting the emergent, self-organizing behavior of complex systems). They will often exhibit the phenomenon of ‘resonance’ and recursion. Many are fractals, or have fractal-like properties. They organize, and are organized. They determine, and are determined.
W. Roberts2, 1996

To qualify as a scale structure in this document, the structure or principle (which may be abstract or ‘ideal’ as in geometry) must be applicable in more than one situation: it must tend to the generic rather than the specific; it must concern relative values rather than so-called ‘absolute values’. In this there is no room for absolute pitch, absolute measurement, etc. Every entity can only be defined in terms of some other entity or entities. This follows from the profound interconnectedness of the universe.

The meaning, understanding, and relevance of scale structures will become apparent as we look at the precedents for scale structures and their ubiquitous occurrence in nature, mathematics, music, science, history, language, and finally, their potentially enormous application in the visual arts and ‘thinking’.

Visual art which syntactically links its apparently haphazard external forms to the rhyme and measure of various covert scale structures will result in visual works of enormous diversity which combine logic and intuition in concord with the physiology of the mind. Progress in this direction is likely to occur hand-in-hand with the development of new paradigms for thinking across the disciplines.

This haphazard arrangement of forms may be the future of artistic harmony. Their fundamental relationship will finally be able to be expressed in mathematical form, but in terms irregular rather than regular.
W. Kandinsky3, 1911