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Music and Numbers through the Looking Glass presents new insights into well known formulas. Dealing with the cyclic nature of reality, as expressed within the harmonics of sound, musical scales, number cycles, the nature of spin, Golden ratio, Fibonacci numbers and various other phenomena.
The Unbroken Thread
It has been said that all is number. What does this mean? Can every formula that glazes the eyes of most non scientists be represented as number? And if so, is there any system held within number that can simplify the whole idea of what number actually is? We see One sun, two feet, five fingers etc, therefore some form of number is necessary in order to distinguish things. Even E=MC^2 has a numerical side to it. The Planck constant, a number. Algebra, can be substituted with numbers.
In a system that is represented in cyclic form, with its duality of spin, can we expect to find a point where this duality is acting as one whole system in perfect symmetry?
The electron is known to behave as a particle and as a waveform. The electron will appear as a particle when it is being observed, whereas when unobserved will appear as a waveform. Particles make up matter, and all matter has a natural frequency. Frequency again is oscillation and waveform. So can cyclic waveform phenomena be seen as dual, positive and negative, clockwise and anti-clockwise, expansion and contraction? And if so, is there again a way of seeing these phenomena as existing within one overall system?
There is even an argument that the electron is only ever a wave, possessing inward and outward spin, and that both these events function as a whole system.
There is a technique that has had very little usage in the past. And yet, it is the very tool that will unearth dual spinning cycles, bring together the expansion and contraction principles, and unify the positive/negative aspects within many systems. That tool is simply the technique called Mirroring; the reversal of formula in its cyclic activity. This technique should not be confused with the word Symmetry, because symmetry is almost always concerned with what the mirror reflects back onto "this side". The mirroring technique discussed in this book is a tool that penetrates "through" the mirror, and describes the relationships existing on the "other side". The difference is vital, because to reflect back onto this side is to see the same phenomena in symmetrical variation. But to penetrate through the mirror sees the emergence of different data that has no bearing on what was placed at the mirror point.
One argument that criticizes the idea of mirroring formulas is that it is merely a reflection, and not exposing a real life situation or solution. This however, is not the truth of the matter. What is really brought into such a question is the assumption that only one side of the mirror is valid. Yet the formulas in question will show their dual nature, that is, they unite to produce one overall formula based on the two sides of the mirror. Which side can rightfully say "you are just a reflection"? It isn't that simple. The claim is that these dual formulas that are being exposed are one formula in its overall expression.
Therefore, if one side of the mirror is considered an illusion, then so is the other side. Both sides are inextricably linked together, and are seen to share information, which transfers to the other side at specific axis points.
Some of the relationships that exist between the two sides of the mirror are quite unique, and show without doubt that they are linked to each other. The four-way relationship evident in Mode boxes, for example, as will be shown at the end of chapter two. Any musician will agree to this. And one must not make the mistake of considering this purely a musical phenomena. Sound relationships exist within nature, in the form of overtones or Harmonics. Nature is cyclic in its behaviour, with clockwise and anti-clockwise spins. The Phi ratio really does have an impact on natural growth of things, and that includes the Fibonacci numbers too.
We see a mode box in chapter two and ask which side is real? We see structure existing between both sides of the mirror, with one side in contrary flow to the other, and ask how on earth this can be an accident?
Why do galaxies spiral, and why is a spiral equated with the Phi ratio, and why is the Phi ratio evident within the Fibonacci numbers and vortex phenomena? These numbers will be shown with their mirror side added, and it will be seen that the two sides act as one whole unit, again asking the question as to which side has the right to call itself the real side.
So then we decide to get to the bottom of exactly what number is, and find out the nature of its cyclic identity. It turns out that all number can be represented in the form of only nine individual cycles. Four of these are mirrors of another four, and the remaining cycle is perfectly symmetrical. Again, there appears structure here, mirror flows, and a point of perfect symmetry between those flows. Exactly as it is in a Mode Box, and, with exactly the same result when these numbers are shown as frequencies. Number cycles and music cycles shouldn't really correlate, because the number cycles are made up of a constant flow of nine numbers, whilst the scales in question flow in sets of eight steps. Yet it is the mirror side again that completes the picture, and shows where the unifying point exists between both sets of flows. All this will become evident within the very first two chapters.
This book will expose the mirror side through applying symmetrical reflection to musical formulas and a variety of number cycles. There is not so much a highlighting of patterns here, but an actual process which is at work, seen through the application of the mirroring technique. The overall structure that resides within every mirroring experiment is a hidden element of many well known natural cycles; things like the natural overtones (also known as harmonics or partials), musical scales, the seven modes and other music theory, , the Vedic Square of numbers, the Phi ratio/Fibonacci numbers, Prime numbers, number pyramids, and even the binary system. All these grids and systems will be shown as never seen before, that is, with their shadow/mirror side added. One will get a sense that this other mirror side does belong, and that it does open up a different meaning for each grid or system.Does the process of mirroring these well known formulas provide structural results? All the formulas show a mirror side, and they expose a dual functioning system. As two halves generally have the potential of uniting at specific points, these dual formulas do so at a specific axis.
The information in this book will require a little groundwork for those that have relatively no knowledge of music theory, but it is not hard theory that is presented here, just the first few basic steps. I will attempt to keep things as simple as is musically possible, and provide many diagrams in order to show the symmetrical flows that exist between both sides of the mirror. From then on the number experiments should pose no great difficulty in understanding for the reader. Therefore, it is not a requirement that one understand every experiment in this book.
The experiments in this book are relatively simple, yet they are using structures that are verified within nature. It is more than a musical or numerical puzzle, because once contemplated that the very cycles within nature reveal the hidden interplay of one overall unifying structure, it should provide one with new ideas within various fields of research. If one agrees that the mirroring process is a valid tool, then they may be able to incorporate it into far more formulas.
The book is in pdf format and also comes with a series of separate animations. You will find the animations numbered and placed in folders that correspond to the chapter within the book. All this is placed in a Rar file for you to download.
To download this book and animations simply right hand click with the mouse on the following link, and choose Save As:
Download - Music and Numbers through the Looking Glass
Here is the pdf book without the animations:
Download - Music and Numbers through the Looking Glass
Copyright - 2004 Lui Di Martino