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Authors: Christopher Knight,Alan Butler

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5. Repeat the experiment on successive nights if necessary, to account for the differing speed of Venus within the zodiac. The longest pendulum achieved during the full cycle of Venus will be exactly half of the most accurate geodetic Megalithic Yard.

Note:
This technique represents one way in which the Megalithic builders could have reproduced the half Megalithic Yard. Time and study might provide others. This horizon method could be subject to very slight inaccuracy as a result of ‘refraction’ of the rising or setting Venus when it is close to the horizon. (Refraction is the distortion of the size or position of an object caused by atmospheric conditions and proximity to the horizon.) It is most likely that Venus was tracked when it was above approximately 15 degrees above the horizon, in order to obviate distortion due to refraction.

Our astronomical associate, Peter Harwood, considers that on balance the setting Venus may have been used, rather than Venus rising as a morning star, though his consideration here has more to do with ease of observation than as a result of any technical considerations.

A
PPENDIX
2
The Formula for Finding the Volume of a Sphere

In Chapter 3 we discussed the capacity of cubes with sides of a length that conform to the Megalithic system, for example the 4 Megalithic-Inch cube that would hold one imperial pint of water. But we also experimented with spheres, both of the same and of different Megalithic sizes as the cubes.

In order for interested readers to be able to check our findings for themselves, we thought it might be useful for those whose schooldays may be now far behind them to be reminded of how the volume of a sphere is achieved.

The formula is as follows:
πr
3
. So, for example, if we want to establish the volume of a sphere of 5 Megalithic Inches in diameter (10.37082 centimetres) we first need to establish the radius, which in this case is 5.18541 centimetres.

The radius cubed is 139.4277 cubic centimetres.

Multiplying this by π we arrive at 438.0252 and
of this is 584 cubic centimetres.

In the case of a 6 Megalithic-Inch diameter sphere (12.444984 centimetres) the radius will be 6.222492 centimetres.

The radius cubed will be 240.931198 cubic centimetres.

Multiplying this by π we arrive at 756.9076 and
of this is 1,009 cubic centimetres.

A
PPENDIX
3
More about Megalithic Music

Music appears to be not only interesting but also absolutely essential to our species. Our research could not turn up one culture, contemporary or historical, that has been shown to be without music and rhythm. Indeed, experiments carried out in prehistoric caves and the structures created by our Megalithic ancestors seem to indicate that even the acoustic capabilities of natural and created structures have been important to humanity for many thousands of years.
1
Archaeologists have also discovered percussive instruments and extremely well-made bone and antler flutes of Stone Age date.

Developing civilizations have classified music in a number of different ways. In the modern western method of musical notation there are considered to be eight notes to a scale of music, allowing for the fact that the starting note and finishing note are the same, but one octave apart, for example C, D, E, F, G, A, B and C again.

The tuning of musical instruments has long been a problem. If the method of tuning by fifths (supposedly credited to Pythagoras) is employed, it is not possible to play a particular instrument in different keys without retuning it because some notes will sound discordant. In order to compensate for this difficulty, western culture has adopted a method known as ‘even tempered tuning’, which allows a compensation to be ‘written into’ the tuning that spreads the accumulating pitch problem in such a way that most ears cannot identify the discrepancies.

The modern convention of having eight notes to an octave is by no means the only possibility. Across the world there have been and still are many other ways of handling the musical scale and none is more correct than any other. It follows therefore that the pitch of specific notes will also vary from culture to culture.

The tuning of musical instruments was once a very local matter. All that concerned the musicians was that their instruments were in tune, one with another. But as soon as music began to cross boundaries, local tunings were no longer possible, especially for many woodwind and brass instruments that are not easily retuned. As a result, much of the world now conforms to international concert tuning, in which each note has a specific frequency, for example A, which is 440 Hz.

It was because of international concert tuning that we were able to define Megalithic mathematics and geometry in musical terms. As the Earth turns on its axis the 366 degrees of the Megalithic divisions of the Earth at the equator pass across a given point in one sidereal day. If we look at the situation in terms of the Megalithic Yard, we know that one Megalithic Second of arc of the Earth has a linear distance of 366 Megalithic Yards. Using Megalithic geometry it is possible to work out the frequencies involved.

A Megalithic Second is more than a geometric division as far as the Earth is concerned. It is also a finite measurement of time and is equal to 0.653946 modern seconds of time. This is how long it takes the Earth to turn one Megalithic Second of arc on its axis. We have called one beat per Megalithic Second of time one Thom, or Th, and since there are 366 Megalithic Yards to a Megalithic Second of arc of the Earth, there are 366 Megalithic Yard beats to one Megalithic Second of time (one 366 Th). If we translate this into modern musical conventions and modern timekeeping, 366 Th is equal to 560 Hz, which in international concert tuning would give a note a little above C# (C sharp). But this is looking at things in terms of frequency. If we think about the Megalithic Yard in terms of wavelength, we discover that 82.96656 centimetres produces a wavelength very close to that relating to the note we would presently call G#, so both C# and G# could be said to have a very special relationship with the Megalithic system.

With regard to rhythm, 1 beat per Megalithic second is the same as a modern expression of timing of 91.5 beats per minute. Using simple harmonics, timings of 15.25, 30.5, 45.75, 61, 76.25, 106.75, 122, 137.25, 152.5, 177.5 and also 183 beats per minute would seem to be appropriate, in the sense that they all have a harmonic relationship with 91.5 beats per minute. We therefore looked at as much indigenous music as we could from around the world in order to establish whether or not Megalithic music actually existed and in order to understand if there might be something instinctive about these pitches and timings. As far as was possible we restricted ourselves to pieces of music with a rhythms shown above and to pieces played in either C# or G#.

It would certainly not be fair to suggest that anything like all indigenous music conforms to these patterns, because it definitely does not. Neither do we claim that we have carried out a valid scientific experiment in the case. What we can report is that we came across music from many different parts of the world that conformed in whole or part to the Megalithic system, and that these pitches and timings appear to show up more regularly than chance would dictate.

Both the key and the rhythm were common among indigenous North American cultures, where many of the sampled chants and songs are particularly significant with regard to their rhythmic patterns. We found some examples in South America, though much of that music has been affected by Spanish and other influences and authentic recordings of Pre-Columbian music are hard to come by.

Examples of old long-playing records created on site in Senegal, Ethiopia, Morocco and Algeria proved interesting and appeared to demonstrate strong elements of the patterns we were seeking in Africa. Some of the best examples came from much further north and east however, with Tibetan Buddhist chants showing a strong resemblance to Megalithic rhythms and keys. Probably related were Siberian songs, particularly those created by ‘overtone’ or ‘throat’ singers, some of which proved to be near perfect examples of Megalithic tunings and rhythms. Australian Aboriginal songs were also interesting, the more so because C# didgeridoos are extremely common. Rhythms vary markedly between examples we have collected, but 91.5 beats per minute, together with its mathematical subdivisions and multiples, are not uncommon.

The greatest difficulty in this research lies in the fact that even ethnic songs and tunes are now invariably recorded in studios, where the natural inclinations of musicians, both in terms of rhythm and tuning, are subservient to the requirements of modern recording techniques. This could also account for the fact that in places such as the British Isles, it is almost impossible to access true, indigenous music. Many English, Scottish, Welsh and Irish traditional songs approximate Megalithic rhythms, but it is impossible to say for certain that this is the case. Timings of 100 beats per minute are extremely common but we suspect this owes more to engineers using electronic metres rather than to the natural caprices of musicians or the turning of our planet.

1
Devereux, P.:
Stone Age Soundtracks.
Vega, London, 2001.

A
PPENDIX
4
Music and Light

In all our discoveries during the research for this book the potential association between sound, specifically music, and light has proved to be one of the most surprising. We fully appreciate that science does not recognize a relationship between these two apparently unrelated phenomena and we have itemized the generally-stated differences between them below.

Sound is created by a source, for example a clanging bell, and sound waves represent generally small areas of high and low pressure caused by the sound source. These variations in pressure cannot travel except through a medium, so in outer space nobody can hear you scream. However, sound can travel through wood, metal, paper, plastic, water, sulphuric acid or almost any other medium. Much of the time sound travels to our ears via the atmosphere.

Sound can be thought of as similar to waves in water, which pass outward, like ripples caused on a pond when a stone is thrown into the water. The ear of any animal, including a human being, is specifically designed to detect the differences in pressure caused by sound waves and to pass these on to the brain, where they are interpreted as sounds. Like all waves, sound waves have frequency, so they can be measured in hertz (cycles per second).

Light waves form part of the electromagnetic spectrum. All electromagnetic waves emanate from bodies such as suns. They are caused by charged particles thrown off from such bodies, which can travel across great distances to reach us here on the Earth. Electromagnetic waves cover a large number of frequencies from very high-frequency shortwave gamma rays, up to extremely low-frequency longwave radio waves. Many parts of the electromagnetic spectrum are harnessed by humanity, for example radio, television, electrical power, X-rays, microwaves and so on. The very world we inhabit only gave birth to life because of the electromagnetic spectrum. Plants cannot live without light, which they transpose into energy, and if it were not for plant life we could not exist either.

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