fractals, octaves and the infinite

What is an octave?

Octaves are fractals – self similar tones that magnify into infinity. By doubling and halving frequencies, in ratios of 2, 4, 8… or 1/2, 1/4, 1/8 ad infinitude, octaves reveal themselves, each a universe within a universe, a creation within a creation. What an octave is not, is the 8th note of a scale, nor is it ‘higher’ or ‘lower’ than a particular unison. Octaves are magnifications of the infinite.  Imagine two mirrors faced towards each other, each reflection is an octave of the next.

So then, why is it called an “Oct”-ave?

The prefix “oct” means “8″, a symbol for “∞”, the Lemniscate, which means infinity.  It is perhaps easiest to describe this concept using geometry:

A cube within a cube – one octave:

Three octaves:

This same principle applies to sound, with vibration doubling and halving onto itself:

The infinitely large is just as magnificent as the infinitely small.  Interestingly, conventional science tends to discard the infinitely small numbers, primarily focusing on the infinitely large. Are they not of the same origin?

∞

Images from:
Sacred Geometry Quantum Magic