The Keys of Atlantis
A Study of Ancient Unified Numerical and Metrological Systems
by Peter Wakefield Sault
Copyright © Peter Wakefield Sault 1973-2012
All rights reserved worldwide
Table of Contents
1. The Ring of Truth: Mathematical Derivation of The Western Musical Intervals
A. Plato's Tale of Atlantis
B. The Life of Pythagoras
C. Principal Data of The Pyramids of Giza
D. Geodesic and Lunar Data
E. Derivation of The Augmented Triad
F. The Parthenon Trapeza
Z. About The Author
“The men of old possessed all knowledge and had no use for it.” - Chuang Tzu
Since the 1970s, man's measures of the Earth and its Moon have achieved an almost incredible precision. This has been accomplished solely through the media of artificial satellites and radio telemetry. Such precise measurements simply cannot be made from the surface of the Earth. This book examines ancient metrological systems whose origins are lost in the mists of time. In the light of modern, space-age, measurements, some ancient units of measure can be seen to be based on equally precise determinations of the dimensions of Earth and Moon. Moreover, they can be seen to have been designed to carry this very message forward to that epoch when technology would yield such precision once again; our own time. Once the means of conveyance has been solidly established, connected material is shown to carry similar messages of prior knowledge of biochemistry and atomic structure. This book is about those messages.
Since completing the research for this book and writing up the first few chapters, I have become acquainted with the work of the late and extraordinary Professor Livio Catullo Stecchini. On the subject of geodesy, he says*
“Some twenty years ago when I arrived at establishing the data that I have just listed I considered them breathtaking. It was only later that I realized that the ancients were aware of the fact that the degrees of latitude become longer as one approaches the poles. I discovered that the units used in Greece and Rome (and also in Mesopotamia, except for the very early period) were based on the length of the degree of latitude at latitude 37° 42'N, latitude of Mycenae. Herodotos refers to it as the latitude of the Heraeum of Samos in comparing Greek units with the Egyptian ones.
“In 1971 I believed that I was uttering a daring statement when I published that the Egyptians had reached the level of precision achieved by the great geodetic surveys conducted at the beginning of the [20th] century. It was only later that I was forced to realize that the Egyptians had reached the level of precision which we have reached in the last decade thanks to the new techniques of space exploration.”
And so I find that I am not the only person to have reached the selfsame conclusion. In view of the fact that his expressed opinion appears to significantly predate my own, I cannot claim origination for the observation even though I arrived at it quite independently. However, I think it no false claim that my work complements and extends his and thoroughly vindicates his stand on the astronomical advancement of the ancients although I must confess it is not yet entirely clear to me how he arrived at that conclusion. It is my hope that I can present a fully supported case, leaving no one wondering how I might have intuited or otherwise divined the claims I make.
It should be understood that no attempt to argue the existence of the legendary Atlantis is being made here, the use of the name in the title being purely poetic. What is established is that an extraordinary and previously unrecognized intellectual development took place over some unidentified period in mankind's history or, more likely, pre-history; a development which does not seem to have a place in the currently accepted catalog but which, however, has left us a legacy which cannot be denied. I must leave it to others to locate its source, being content to identify some small part of the legacy itself. Someone, somewhere, sometime put an inordinate amount of effort - and computing power, presumably of the purely organic kind - into creating this legacy and ensuring that it would not be lost in the hope that it would eventually be recognized for what it is. As to the tale of Atlantis, some of which is reproduced in Appendix A, I can only quote an English proverb - “Where there's smoke there's fire”. Perhaps indeed only beneath the murky waters of a tantalizing anagram, about which no more will be said here. No matter whence it came the legacy itself is nonetheless very real.
What the reader must allow is that without first having read Plato's Timaeus, in the late 1960s, I would never have written this book. Hence it is of no real consequence whether or not Atlantis ever really existed; the tale of it most certainly does, unarguably, and that was my inspiration and deserving of due credit for that alone if naught else. Unlike the tale of Eden that seems to describe allegorically the combined roles of psychoactive mushrooms and feminine curiosity in the birth of self-awareness, if not actual speciation, in the human race, that of Atlantis, whether real or allegorical, describes a post-Eden pinnacle and its subsequent disappearance.
The reader should not, however, think that he is about to enter yet another attempt to translate the Timaeus into even plainer English and to extract some additional meaning from it that has not already been thoroughly pored over by generations of erudite scholars. Clearly neither Pythagoras nor Plato truly understood the nature of sound and music. This is not to diminish their genius in the slightest but merely to identify the missing parts of their worldview. The present author has the advantage of the knowledge accumulated by concerted and highly successful scientific and musicological research over the past several hundred years and has thus been able quite independently to synthesize the full derivation of the musical intervals and thereby of the Babylonian unit of rotation, the ‘degree of angle’. The musical intervals are in fact aeonian and were there sets of intelligent ears on some planet in an unreachably distant galaxy then they too could discover dodekaphonic music and could produce their own Beethoven and Mozart. Nonetheless, once the actual system is laid out, elements of it can be seen quite clearly in the pythagorean model laid out by Plato. Since a defective model cannot be the root and source of the western system of music Pythagoras must have been transmitting knowledge which preceded him and, by his time, reduced to fragments just as so many written works of the ancient Greeks have been lost to us in the here and now.
It is a recognized fact that the most brilliant composing musician needs neither knowledge of acoustics nor anyone's theory of harmony in order to create and perform the most wonderful music. Conversely, all the knowledge in the world of those subjects will not make a musician, let alone a composer, out of anyone. Music seems to be rather like love in that respect.
Preceding statements notwithstanding, the material under discussion must have come from somewhere and that somewhere had to predate all of the somewheres for which we have historical data because they all display both fragments of it and either false rationalizations or even complete unawareness of those fragments, the length of the Silk Road.
Whether or not the original source was Plato's Atlantis, the material documented here stands on its own merits. Pythagoras recognized that the duple-ratio musical interval, the octave, which he called the ‘universal concord’, was at the very heart of it and yet he provided no explanation of why that should be. Hence those who slavishly follow Pythagoras are also unable to provide that explanation. There is indeed a physical reason for the absolute defining nature of the octave and it is spelled out in Chapter 1.
As far as I am aware, the full reconstruction in Chapter 1 of the complete derivation of the dodekaphonic musical intervals, leading to the dependent derivation of the Babylonian unit of rotation and the minute of time, is entirely novel and original, as is the content of all the subsequent chapters.
The reader will occasionally come across the term masonic in connection with names associated with certain ancient stone monuments and their architects and builders. This should not be interpreted as any reference to Scottish Rite Freemasonry, its derivatives or its members, with which neither this author nor this work have, ever had, or will ever have any relationship or association.
The presence of large quantities of numbers and calculations is unavoidable as these are the very quintessence of the argument. It is widely recognized that such things guarantee a minimal, if not non-existent, readership. The author can only hope that the brave reader will be heartened by Professor H.S.M.Coxeter's prefatory comment in his book Regular Polytopes – “What one fool can do, another fool can do” – especially in view of the fact that the content of this book is nowhere near as mathematically challenging as that of the good professor's. Until we get to the last chapter, that is…
* Livio C. Stecchini,
Egyptian Estimates of the Size and Shape of the Earth.
My previous lack of awareness of the extent of Stecchini's work is explained by the fact that most of it has never been published in book form. Its transcription for and publication on the World Wide Web have been proceeding since around 2001.
Copyright © Peter Wakefield Sault 1973-2012
All rights reserved worldwide