Monday, 6 October 2014

A Musical Speculation about Absences

I've been reviewing some slightly head-banging papers on information theory today. This stuff is very difficult, and it would be quite easy to get sucked in to the language of mathematical communication theory and lose touch with those phenomena which it really tries to describe. So I feel the need to write something quite cryptic about music. This is probably incomprehensible (although I think I know what it means): basically it's about accompaniments and melodies, but it can be expanded to deal with harmony, tonality, form, rhythm, etc.  It's about the journey that music takes us on towards some kind of unity or resolution. How is this achieved? 

I want to speculate on the way that absence and redundancy might be related in music. Absence is a context that bears upon everything. Changes to the context create changes to the relations between tangible parts (between melodies, motifs, tonalities, etc). (Feyerabend argues something similar for the way that scientific theories are adopted: a previously unaccepted theory is accepted not through some new proof, but because of a deeper mood-change in the scientific environment) In music different harmonisations of the same melody create radically different effects. 

It may be that absences relate to redundancies (repeated patterns, etc) in ways which are decomposable: a redundant pattern R may comprise redundant patterns R' and R''. A melody over R'' may decompose into a redundant pattern R'''. Decomposition of redundancies into R'' and R''' create subdynamics which might reveal a new melody, M'. The difference between the redundancies and the melodies is that whilst both derive from absence, only melodies map on to unities (that is how we know they are melodies: they have an identity). Absence and redundancies are, by contrast isomorphic. (Are melodies monomorphic?) Decomposition creates the conditions in overlapping of redundancies for new ideas to emerge. Decomposition is caused by the inherent instability of different limits. A melody exists as a kind of 'knot' which ties up its unity with absences. That which is tied encompasses many aspects which are not tied (not knots!): these decompose to change the limits of the knot with new redundancies. The knot is untied and something new begins. 

This dialectical process is one of revealing ordering. Orders emerge over time as limits and objects are created and transformed. Only gradually does the relation between the order of things, its relation to unity, and its journey from nothing become revealed. When it finally is revealed, we have reached the end.  

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