Friday, August 5, 2011

New Perspective on Harmonic Series

The very important and well-known harmonic series i.e. 1 + 1/2 + 1/3 + 1/4 + 1/5 +... is especially associated with Pythagoras who reputedly found in these simple fractions definite links with the manner in which musical notes sound. This pattern of the simple natural fractions, in particular, seemed to correspond perfectly with - what we would recognise as - a harmonious sequence of notes and thereafter it has become known as the harmonic series.

So we have here a very clear link as between simple mathematics and musical harmonics. Subsequently it was shown that this series (and its associated series where the dimensional power of each fraction itself can vary from 1 and ultimately alter over the entire range of complex numbers) has intimate connections with the prime numbers!

So in a certain valid sense there is music in the primes. So just as we are accustomed to give a wave form to musical sounds likewise there is a wave pattern associated with each prime number.

Indeed we could go further and suggest that there are intimate links as between the prime numbers and quantum mechanics with each possessing particle (discrete) and wave (continuous) aspects. The real implication is that just as music itself has quantitative and qualitative aspects which interact to produce the experience that we recognise, likewise - when appropriately understood - prime numbers and quantum mechanics likewise arise from the interaction of quantitative and qualitative elements.

As we have seen the harmonic series is made up of the reciprocals of the natural numbers.

Now each of these numbers has a dimensional aspect as the corresponding fractional powers, which results in a circular - rather than linear - quantitative structure. The corresponding qualitative numbers are then simply the natural numbers, 1, 2, 3, 4, 5.. etc now interpreted in a holistic manner.

Recently I have come to the conclusion that quality in all its aspects ultimately relates to this dimensional appreciation of number (interpreted in a holistic manner). In this context each dimensional number represents a unique way of configuring the fundamental polarities of experience (internal/external and whole/part).

So quality in the most basic sense always arises from a certain manner of configuring these basic polarities (which is given by the qualitative interpretation of dimensional numbers).

Seen in this light the qualitative correspondent of the harmonic series is simply the natural number dimensions. So it is not surprising that our fundamental appreciation of harmony (relating to the manner of configuring polarities) corresponds directly with the simplest dimensional numbers. These are the very ones with which we are implicitly programmed in out attempts to discern qualitative meaning!

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