Music as a universally accepted form of abstract art
Music as a universal (abstract) language
The abstract nature of most music may seldom occur to us, nor even perhaps to many students of the subject, so 'natural' does it seem to our ears and minds when well-composed and performed. But this naturalism is an in-principle naturalism. It harmonises with the 'composition of Nature' in principle. What do we mean exactly? Simply this: that beneath the apparently haphazard external forms and motions of the Universe, there exist covert orders and principles (traditionally in science called, 'laws') that link or tie everything together and choreograph the unfolding panoply of motion, position and timing. This linkage is metaphorically reflected within the form and syntax of 'music'. [In this document I call many of the Universe's syntactic and ordering principles 'resonant scale structures', in the musical sense of "scale".]
Musical compositions are largely abstract in that they do not usually duplicate, reproduce, or represent the sounds we encounter in day-to-day life (cf. 'representational art'). Rather, they combine timbres and ratios of frequencies of sounds, distributing these abstract 'sequences of notes' (melodies) and chords over rhythmic or rational intervals of time.
Representation in music
On the other hand, composers today have synthesisers and sampling keyboards at hand which have the ability to reflect the 'objective or representational arts' in that they can digitally recreate, by a layering of waveforms, sounds which may very closely mimic a myriad of natural sounds and with which we are all well familiar (e.g. the sound of a car engine, the sound of bell, the sound of a door clicking shut, etc.) This new subset of music is more to do with sound engineering and the synthesis and modulation of wave forms via electronic means.
The concept of music as emphasised in this document
Here we are principally concerned with the former view of music— musical compositions as abstract melodies and chord progressions. In other words, the way they reflect an in-principle naturalism.
This in-principle naturalism is echoed in the syntactical link that exists between the various covert (more regular) scale structures that subtly unify a composition (e.g. key signatures and time signatures) with the less regular patterns of melodies or progressions of chords within most musical compositions. Thus the irregular and asymmetric aspects of both melodies, the sequence of chords, and rhythmic variations in time—are all linked loosely (or more directly) to various underlying regular or logical scale structures that relate the frequencies of notes to one another, timing divisions, etc.
This metaphor has not yet found a significant parallel within the visual arts to this day. We do not yet have (at least in common usage) powerful visual scale structures per se.
This document will present a number of scale structures applying to the visual arts, number theory and geometry, and proposes various ways they might be implemented and, together acting in synchrony, empower the emergence of a new visual language and logic. Later in this document, scale structure theory is applied to discover Pythagoras-like theorems relating to new classes of triangles, and these findings point to a need for a (possibly major) revision of some of the 'fundamentals' of mathematics and of the sciences more generally.
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