Over the last seven thousand years, hunter-gathering humans have been transformed into the “modern” norms of citizens (city dwellers) through a series of metamorphoses during which the intellect developed ever-larger descriptions of the world. Past civilizations and even some tribal groups have left wonders in their wake, a result of uncanny skills – mental and physical – which, being hard to repeat today, cannot be considered primitive. Buildings such as Stonehenge and the Great Pyramid of Giza are felt anomalous, because of the mathematics implied by their construction. Our notational mathematics only arose much later and so, a different maths must have preceded ours.
We have also inherited texts from ancient times. Spoken language evolved before there was any writing with which to create texts. Writing developed in three main ways: (1) Pictographic writing evolved into hieroglyphs, like those of Egyptian texts, carved on stone or inked onto papyrus, (2) the Sumerians used cross-hatched lines on clay tablets, to make symbols representing the syllables within speech. Cuneiform allowed the many languages of the ancient Near East to be recorded, since all spoken language is made of syllables, (3) the Phoenicians developed the alphabet, which was perfected in Iron Age Greece through identifying more phonemes, including the vowels. The Greek language enabled individual writers to think new thoughts through writing down their ideas; a new habit that competed with information passed down through the oral tradition. Ironically though, writing down oral stories allowed their survival, as the oral tradition became more-or-less extinct. And surviving oral texts give otherwise missing insights into the intellectual life behind prehistoric monuments.
The texts and iconography of the ancient world once encrypted the special numbers used to create ancient and pre-historic monuments, using a numeracy which modelled the earth and sky using the invariant numbers found in celestial time, and in the world of number itself. Oral stories spoke from a unified construct, connecting the people to their gods. Buildings were echoes of an original Building, whose dimensions came to form a canon within The application of units of length to problems of measurement, design, comparison or calculation.; the ancient science of measure. But the language of the gods within this Building was seen to be that of musical tuning theory, the number science which concerns us here. The gods in question are primarily the planetary and calendric periods seen from earth, and it was only through the astronomy associated with the earliest, megalithic buildings that the ancient maths could have naturally evolved.
To see musical harmony in the sky, time was counted as lengths of time between visible astronomical events such as sun rise, moon set, or full moon. Geometry evolved to set A name special to Carnac's three successive groups of parallel rows of stones, starting above Carnac called Le Menec, Kermario, and Kerlescan and another found near Erdevan. to horizon events, such as the The extreme points of sunrise and sunset in the year. In midwinter the sun is to the south of the celestial equator (the reverse in the southern hemisphere) and in midsummer the sun is north of that equator, which is above the geographical Equator). sun or, to place long lengths of day-counting within geometries such as the trigonometric triangle. Megalithic astronomy (chapter one) consisted of a set of quantified lengths of time and the geometrical relationship between them. It would have discovered that some of the ratios between time periods were especially simple: most significantly the two outer planets Jupiter and Saturn, related as 9/8 (a musical whole tone interval) and 16/15 (a semitone interval) to the lunar year. In each ratio the lunar year is the denominator and the planetary synods are the numerators. If we make the denominators the same (by multiplying the ratios by each other’s denominator) we obtain (times 15) 135/120 and (times 8) 128/120. Because the lunar year is 12 lunar months long, the lunar month must comprise ten sub-units of time; the Jupiter synod must be 13.5 months long; and Saturn’s synod must be 12.8 months long.
The idea that astronomy could have caused the ancient world to have any great interest in musical tuning theory runs against the standard musicological model of history in which, it was the making of music which drove the Babylonian tuning texts to appear on Cuneiform tablets from Nippur and other places. However, lists of regular numbers and tables of reciprocals counting down from sixty to the power of four (12,960,000) hardly seem relevant to practical music. 12,960,000 is a significant number belonging in my work to Venus, the bright planet of the inner solar system, in its synod relative to the lunar year. The number is a large one because she is higher in “heaven”, becoming Quetzelcoatl in the Olmec’s cult of astronomical time inherited by the Maya and Aztec cultures (chapter seven). Tuning theory must have found its way to Mexico before the devastating Bronze Age collapse circa 1200 BC; a date when Mexico’s likely contact with the eastern Mediterranean would have ceased. The future of European tuning theory in the ensuing Iron Age then lay in the hands of the Archaic Greeks (Homer and Hesiod) and surprisingly, the Jewish school responsible for the early Bible (chapter five).
Whenever civilizations fall they pass on information. When megalithic astronomy died, it bequeathed the idea that the planets were gods related to the Moon through musical harmony, also leaving the ancient world their metrology. When temples were built or stories to the planetary gods passed on, these could express musical numbers and ratios within architecture, iconography and myth. In classical Greece, the power of writing had won over the oral world whereupon Athens enshrined musical harmony in the Parthenon and in Plato’s writings about the ancient tradition of musical tuning theory (chapter six).
I first noticed the musical resonances (of Jupiter and Saturn to the lunar year) in 2000, for which I could find no traditional setting except mythology [Heath 2004]. The extensive works of the Pythagorean tradition for instance, concerned with planetary harmony, are complex and appear more influenced by Greek mathematics than by the ancient world. After some decades though, understanding came through the work of Ernest G. McClain, and through my collaboration with him in the last years of his life. These outer planetary resonances slotted perfectly into McClain’s frameworks for ancient tuning theory. The primary sources for McClain’s work were the surviving texts of the ancient world [McClain, 1976] but his key to these texts were Plato’s dialogues, for which he had provided a definitive interpretation [McClain, 1978], as being a cryptic textbook for ancient tuning theory.
McClain found harmonic numbers (*which only have factors of two, three and five) referred to (as if arbitrarily) in various guises within ancient stories, allowing the initiated to reconstitute a much larger array of harmonic numbers belonging to the god or to a spiritual locale, which the story was intended to animate. (**This resembles the aboriginal habit of recitations before painted caves or cliffs, where an initiate recounts the story illustrated by the paintings, thus “joining the dots”. Our word esoteric perhaps hails from this practice of leaving cryptic clues within texts, in this case linking to musical tuning theory.) In his popular work, The Myth of Invariance, American Cryptologist and Pythagorean Musicologist who decoded Plato's cryptic numerical ciphers in The Pythagorean Plato. The Myth of Invariance showed limiting numbers had been an ancient way of defining the onset of key musical tuning realities, then coded into many religious texts. Wikipedia. recreated many otherwise hidden harmonic worlds from number references within texts; from India, Mesopotamia, Egypt, Greece and the New World.
It became obvious to me that the common denominators (see earlier ratios of the Jupiter and Saturn The recurring time cycle of a given celestial phenomenon seen from the Earth. periods) would “place” them in the corner of McClain’s “holy mountains” (**his arrays of regular numbers which could be inferred from a single number limiting the array as for the high do for an octave). More and more “characters” from astronomical time started appearing “on the mountain”, in parallel with McClain’s own interpretations from the Bible, Homer, Babylonian texts, the RgVeda, etc.
The astronomical significance of harmonic numbers left in ancient texts explains the mystery of why they should be there in the first place and it confirms the important role texts have played in carrying a whole system of knowledge, within an oral tradition. In their heyday, texts were only in the heads of reciters and listeners of all sorts – some hearing a good story and others learning new facets of harmonic knowledge. Such a tradition evidently thought the world had come into existence due to musical harmony (chapter eight) and that relationships to the gods were organised according to harmonic laws. Indeed, the astrology that so obsessed the Babylonians was probably rooted in a harmonic model of fate involving planets and calendars. One can see how stories such as Gilgamesh reveal the Sumerians knew of it (c. 3000 BC), placing planetary gods like Iaana/Ishtar/Venus in heroic stories that make better sense if referring to “holy mountains” (chapter two) located in a harmonic heaven.
Click here to view the publisher page , where extra information on this and my other books, including reviews, can be found. The contents of Harmonic Origins of the World are:
Introduction: The Significance of Planetary Harmony
RECOVERING LOST KNOWLEDGE OF THE WORLD SOUL
1 Climbing the Harmonic Mountain
2 Heroic Gods of the Tritone
3 YHWH Rejects the Gods
4 Plato’s Dilemma
A COSMICALLY CREATIVE HARMONY
5 The Quest for Apollo’s Lyre
6 Life on the Mountain
THE WAR IN HEAVEN
7 Gilgamesh Kills the Stone Men
8 Quetzalcoatl’s Brave New World
9 YHWH’s Matrix of Creation
10 The Abrahamic Incarnation
Postscript: Intelligent Star Systems
APPENDIX 1: Astronomical Periods and Their Matrix Equivalents
APPENDIX 2: Ancient Use of Tone Circles
Reunification of Tuning by Number with Tuning by Ear, through Reason and Visual Symmetry