Tuning – Sacred Number Sciences

Goddess of Time in the Sky

Explores the relationship between ancient astronomical practices and megalithic cultures, highlighting how early societies understood time through celestial cycles. It contrasts matrilineal hunter-gatherer societies with later patriarchal agricultural ones, suggesting that megalithic structures reflect deep, sacred knowledge of the cosmos and have influenced subsequent architectural designs across civilizations.

Above: (center) The form of the Minoan “horns of consecration”, on the island of Crete, followed (outside) the form of the manifestations of Venus in her synodic period.

Time appears to march on at what seems a constant rate. In this way time has two opposite directions, the somewhat known past and the largely unknown future. However, events in the sky repeat and so they can be predicted as seasons within a year or lunar phases within a month. Even before modern calendars, stone age humans counted the days in a month to understand recurrence of the menstrual period and know when moonlight would be strong again at night.

Figure 1 (above) L’Abri Blanchard Tally Bone 30,000 BP with (below) Alexander Marshack’s interpretation, showing marks as days shaped to express the moon’s phase, over 59 whole days or two lunar months.

Two months happen to equal 59 whole days: a lunar month is 29.53 days long, just over twenty-nine and a half, which is half of 59. In the artifact shown on the top of figure 1, each day was carved upon a flat bone, each mark appearing varied in shape and depth to show the moon’s changed phase on a given day. The flat bone enabled a cyclic shape to be used, of 59 marks, which “ate its own tail”: showing there were always the same number of days in two “moons”. This sameness emerges from dividing the recurring time of the solar day into the time of the month’s phases over two months, to give the recurring whole number of 59, then forever useful as a knowledge object.

The solar day is clearly the same duration every day and two lunar months clearly repeat twice after 59 days. But our modern life is the extended straight line of day numbers belonging to unequal months of the sun so that the loops that recur are lost in the framework of man-made time. The stone age “lesson from nature” was, that events in the sky largely run according to a definite schedule along cyclic paths, most of these being along the path of the sun, along which the sun, moon, and planets follow their own cyclicities, seen from the earth. This reliable cyclicity shaped our notion of an unchanging realm of Eternity, different to Life upon the Earth as our ever-developing present moments within Existence. In this way, knowledge from the sky came to be considered sacred, and interconnected through numbers when counted as days and months, especially through counting the often identically sized discs of the Sun and Moon and their respective years.

While astronomy started as a stone age hobby it later became a tribal science quite unlike our own astrophysics. Only latterly could farmers support city specialists that would assimilate this prehistoric science, by forming religious sciences and cosmologies in the East, of Egypt, Babylonia, India, China and so on. But millennia later, the 16th century altogether discarded this geocentric view-from-the-Earth and adopted a new heliocentric view of a solar system: this enabled the planetary orbits of the sun to be clearly seen as mathematical ellipses by Kepler, a system soon seen to be held together by Newton’s newly intuited force called gravity, of the central sun’s large mass.

If counting the moon had synchronised both female fertility and male hunting then this shaped the format we call the hunter-gatherer, who foraged for food before there was farming. Their women formed a naturally less-mobile core for the tribe and its children, the men hunting over extensive ranges. All adults were used to working together for the greater good and, since they were in-common descended from the women, so a matrilineal society was an effective format for problems requiring larger groups.

Stone age art of the goddess seems to have been very varied and geometrical (see Language of the Goddess by Marija Gimbutas). In Sacred Geometry in Ancient Goddess Cultures, myexperience in analysing megalithic sites had caused me to question whether the megalithic monuments were the work of Neolithic or New Stone Age farming revolution moving west from the Middle East where it started. Because the farming revolution was only slowly advancing through central Europe towards the Atlantic coast (see figure 2) it was pretty much avoiding the Mediterranean. For a start, the megalithic revolution was largely taking place within the islands and hinterlands of the Mediterranean and Atlantic Coast of Europe, between 5000BC and 2500BC. It was therefore much more likely to have have been carried out by the late middle stone age (Mesolithic) people, before the farming way-of-life arrived. And the indigenous culture of old Europe was mesolithic, well established and centred around women, foraging, and matrilineage (using your mother’s name) rather than the neolithic norm, led by men, farming and patrilineage (using your father’s name).

Figure 2 The journey of the Neolithic from the Middle East (see colored circles), via central Europe, was in stark contrast to the dating (dark circles) of megalithic sites on the Mediterranean and Atlantic coasts: And the neolithic were patriarchal farmers using the seasonal year while the late middle stone age were matriarchal foragers, truly interested in the sacred time world of the celestial objects, and hence building and using the megalithic observatories. [Globe by Google Earth, data from Barry Cunliffe and Bettina Schulz Paulsson]. Figure 1.1 in Sacred Geometry in Ancient Goddess Cultures.

The Clash of the Titans

Being indigenous, the matrilineal tribes were far more likely and able to innovate the megalithic astronomy which effectively inherited from the long tradition of day counting seen on the stone age tallies like the Blanchard plaque. But this continuity of interest in the sky conflicts with the today’s model of history and our foundation myth for modern science, as grandchild of ancient Near Eastern civilizations and exact sciences, fuelled by farming on fertile soils using irrigation.

Through comparing day counts, sky time could be given geometrical forms such as the circle, square and rectangle/triangle, these rightfully considered sacred by the coherent megalithic culture on Europe’s shores. The civilization was numerate, intelligent, but not stone age in the vernacular sense, of having no ability to reason. Having an extended family of adults and no urgent need to seasonally grow crops, conserve seeds or tend their animals, nature already provided food through foraging There was a natural collaborative workforce and this perhaps explains the dearth of neolithic settlement noted alongside the earliest megalithic monuments.

Having overcome this misnomer that megaliths were automatically neolithic, a further work is required to see why our own science cannot understand the sky phenomena in the way the stone age must have. We do not today study the synodic periods of the planets because they are seen as a merely incidental composite of the planetary orbits and our solar year. But, and quite unexpectedly, the view from the Earth is supremely important since the structure of time on earth is a phenomenon reflecting the form and structure of the numerical world. This would suggest that the earth was, in some way, influenced by the abstract world of numbers to have formed this type of time environment. This might also suggest that the evolution of Life was an intended outcome for the third planet.

Having discarded the earth-centred model of the universe and having rid ourselves of the religions and gods proposed to explain this phenomenon, modern humans are free to live in an accidental universe where one is just alive on an existential line-of-time with no end except for death, and without any appreciation of the deeper structural recurrences, implicate within the sky. Instead there is a hotch potch Roman calendar whose roots were literally man-made.

Figure 3 Fibonacci Golden Mean. 1.618 is found in the Fibonacci approximation of 8/5 = 1.6 of the practical year of 365 days to the Venus Synod 584 days. Venus was seen as the youthful goddess, Earth as the mother of all that lives and the Moon as the wise older goddess, these together forming the ancient Triple Goddess. [photo by C. Messier for Wikipedia] see section Statues representing Knowledge in Sacred Geometry in Ancient Goddess Cultures, pages 106 to 111.

The Greek myths referred to women, but in ways designed to put matrilineage norms in a bad light. The patriarchal farmers of Jupiter-Zeus had defeated the religion of the Goddess, whose representatives had snakes (perhaps the dreadlocks of the Medusa or knowledge of the snake shaped ecliptic, see figure 3) or had kept men sexually enslaved on an island (as in the Odyssey) or sacrificed a sacred king after “a year …” (of 364 days) “… and a day” (making 365 in all). Our 7-day week derived from this Saturnian year of 364 days (52 weeks), named because the synod of Saturn is exactly 378 days (54 weeks) while the synod of Jupiter is 57 weeks. In this one is seeing through a series of invisible filters, that the ancient Greeks were against the tribal age that had preceded farming and cities, when women rather than men were most important to that way-of-life. And the western Enlightenment adopted the heliocentric planets as a binary removing the foundations of a vast past cultural corpus of religious and pre-scientific thought that had quite reasonably shown something special about the world that modern science would never choose to see. If we can fathom megalithic astronomy, its uniquely powerful discoveries will reveal what the religious texts were about: that the environment of the earth is no accident within in the universe, but that it is that of a planet for the evolution of Life.

Megalithic discoveries had been transmitted, only subconsciously, into the cultural subconscious of the later civilizations, and it was and is still informing and infecting our arts and the classical form of numeracy called mathematics. This diffusion had benefited from the clash of the Titans, namely between the matriarchal and patriarchal ways-of-life in the Eastern Mediterranean and Levant. It would be recorded in the intellectual life of the Greeks and Hebrews, thus informing Islamic then Christian world view, as a code of numbers and stories often agreeing with those of the East.

Continuity in Sacred Building

If you know how to look, one finds the units of measure and geometries of the megalithic repeated in later sacred buildings, built under disparate religions as if the design of sacred buildings had some sort of megalithic origin. The Chinese, Indian, Buddhist, Minoan, Classical Greek, Romanesque, Islamic, South Asian, Amerindian, Gothic, Sufi, and Renaissance buildings draw upon common geometric and metrological blueprints relating, for example, to the relative size of the Earth and Moon, and the sophisticated celestial time cycles such as the eclipse phenomena, as if to celebrate the cosmic environment even though many religions had conceptualized the heavens as if not found in the sky.

For this reason, my books can explore buildings of the historical period in the same way as megalithic buildings, to demonstrate this continuity of an invisible language, as if there were people with megalithic knowledge behind the construction of buildings without the outer religion officially acknowledging this fact. And in some strange way, I and others are recapitulating ancient works as to their meaning, by employing skills belonging to the past. For example,

In Cappadocia, Turkey, stone cut churches inexplicably contain high levels of meaning in their dimensions and definition of circular apse and rectangular naos occupied by hermit monks.
Angkor Wat is shown to be a massive statement of astronomical cyclicities alongside an outer meaning of Vedic mythological carving and Indian temple design.
St Peter’s Basilica was a renaissance rebuilding involving many great architects, including Michaelangelo who displayed sacred geometrical skill in translating a Greek square-cross basilica design into a Latin cross cathedral design, through the golden mean relationship of a square to such a rectangle (see figure 4). St Peter’s tomb is then in the centre of a model of the Earth and Moon.

Figure 4: St Peter’s Basilica: Sacred buildings followed geometrical and numerical rules that reflect both the cycles of the sky and the geometrical methods and numerical results of the megalithic. [plan courtesy The New York Metropolitan Museum]

Chapter 11 demonstrates that the equal perimeter model of the earth and moon had been related to the now-abandoned geocentric model. The Earth is at the centre (of course) and a system of growing square areas, for each planet’s synod, grows to embrace the whole figure to show it was the archetypal form taken as the norm for Buddhist Mandalas. And mandalas have recently been used by Jungian therapists and others to enable interaction with the subconscious mind. This suggests that our very being, as micro-cosmos, is part of the Earth and its planetary Sky environment of time. Celestial time appears to be a carrier wave for reality and not just a straight line.

Figure 4 The geometry of Equal Perimeter circle and square, with moon circles, showing the influence of the time world of the earth and moon, as the true basis for far-eastern designs called mandalas.
[photo: Cesar Ojeda 17th century Tibetan -Five Deity Mandala from Sacred Number: Language of the Angels. Fig 7.20]

References

Cunliffe, Barry. Europe Between the Oceans: 9000 BC to AD 1000. Yale 2008.

Gimbutas,Marija. The Language of the Goddess. Thames & Hudson 1989.

Heath, Richard.

______Sacred Geometry in Ancient Goddess Cultures. Inner Traditions 2024.

______Sacred Geometry: Language of the Angels. Inner Traditions 2021.

______Tragic Loss of the Geocentric Arts and Sciences: When Poetry was the Language of Cosmology, NewDawnMagazine.com #185***

Marshack, Alexander. The Roots of Civilization: The Cognitive Beginnings of Man’s first Art, Symbol and Notation. Weidenfeld and Nicolson 1972.

Paulsson, Bettina Schulz. Time and Stone. The Emergence and Development of Megaliths and Megalithic Societies in Europe. Archaeopress 2017.

Medieval Solfeggio within the Heptagonal Church of Rieux Minervois

This paper responds to Reichart and Ramalingam’s study of three heptagonal churches[1], particularly the 12th century church at Rieux Minervois in the Languedoc region of France (figure 1a).

image: The Church in situ

Reichart and Ramalingam discuss the close medieval association of the prime number seven[2] with the Virgin Mary, to whom this church was dedicated. The outer wall of the original building still has fourteen vertical ribs on the inside, each marking vertices of a tetraheptagon, and an inner ring of three round and four vertex-like pillars (figure 1b) forming a heptagon that supports an internal domed ceiling within an outer heptagonal tower. The outer walls, dividable by seven, could have represented an octave and in the 12^th century world of hexachordal solmization (ut-re-mi-fa-sol-la [sans si & do])[3]. The singing of plainchant in churches provided a melodic context undominated by but still tied to the octave’s note classes. Needing only do-re-mi-fa-sol-la, for the three hexachordal dos of G, C and F, the note letters of the octave were prefixed in the solmization to form unique mnemonic words such as “Elami”.It is therefore possible that a heptagonal church with vertices for the octave of note letters would have been of practical use to singers or their teachers.

The official plan of Rieux Minervois

12^th Century Musical Theory

In the 10^th Century, the Muslim Al-Kindi was first to add two tones to the Greek diatonic tetrachord of two tones and single semitone (T-T-S) and extend four notes to the six notes of our ascending major scale, to make TTSTT. This system appeared in the Christian world (c. 1033) in the work of Guido of Arezzo, a Benedictine monk who presumably had access to Arabic translations of al-Kindi and others [Farmer. 1930]. Guido’s aim was to make Christian plainsong learnable in a much shorter period, employing a dual note and solfege notation around seven overlapping hexachords called solmization. Plainsongs extending over one, two or even three different hexachords could then be notated.

Cologne Cathedral Facade as Double Square

image: The Gothic cathedral of Cologne by night, by Robert Breuer CC-SA 3.0

On the matter of facades of Gothic cathedrals, I hark back to previous work (February 2018) on Cologne cathedral. This was published in a past website that was destroyed by its RAID backup system!

As we have seen with Chartres, some excellent lithographs with scales can often exist online from which one can interpret their sacred geometrical form and even the possible measures used to build that form. The Gothic norm for a facade seem more closely followed at Cologne facade which has two towers of (nearly) equal height.

We saw at Chartres that an underlying geometry using multiple squares may have been used to define a facade and bend it towards a suitable presentation of astronomical time, in a hidden world view that God’s heaven for the Earth is actually to be found in the sky as a pattern of time. This knowledge emerged with the megaliths and, in the medieval, it appeared again in monumental religious buildings built by masons who had inherited a passed-down but secret tradition.

A Prologue to Cathedral Music

Gurdjieff, Octave Worlds & Tuning Theory (2019)

This is a paper I suggested for the All and Everything conference in Cumbria, but it was not selected. It developed a number of strands, which I offer here as a snapshot of my thinking and research around 2019. This text was modified to become appendix 3 of my Sacred Number and the Language of the Angels (2021).

Abstract

The first part presents what has only recently become known about ancient musical theory, to better understand the All and Everything of Gurdjieff’s intellectual output. This must include In Search of the Miraculous (Search, 1916-18) Beelzebub’s Tales (Tales, 1949) and Meetings with Remarkable Men (Meetings, 1963). In part 2 ancient monuments are shown to record a ‘lateral octave’ connecting humanity to the planetary world, 24. Part 3 explores the significance of the Moon in Gurdjieff’s lectures and writing. An appendix reviews the conventional virtues of the Moon as accepted by modern science, stabilising earth, enabling life and beings such as we, to evolve into appropriate habitats.

Part 1: Ideas relating to a ‘science of vibrations’

Part 2: Where are the Lateral Octaves?
Part 3: The Significance of the Moon
Appendix 1: A Moon that created Life?
Appendix 2: Reference Charts from Search
Appendix 3: Index of the Moon in Search & Tales
Moon in Search
Moon in Tales
Bibliography

Introduction

Publications about Gurdjieff’s ideas appeared after he and Ouspensky had died. The main works of Gurdjieff’s words are Search, Tales and Meetings. Beyond these lie autobiographical books and compendia of Gurdjieff’s ideas, by his students. Some of his students also looked into traditional sources such as Sufism and Vedanta, and followed up on new scholarship relating to cosmological ideas such as world mythology (Hamlet’s Mill, The Greek Myths); the number sciences of Pythagorean schools and Plato (Source books); ancient buildings (Megalithic Sites in Britain, Ancient Metrology, The Temple of Man); and musical tuning theory (The Myth of Invariance, Music and the Power of Sound).

Primacy of low whole numbers

What we call numbers start from one, and from this beginning all that is to follow in larger numbers is prefigured in each larger number. And yet, this prefigurement, in the extensive sense {1 2 3 4 5 6 7 etc.}, is completely invisible to our customary modern usage for numbers, as functional representations of quantity. That is, as the numbers are created one after another, from one {1}, a qualitative side of number is revealed that is structural in the sense of how one, or any later number, can be divided by another number to form a ratio. The early Egyptian approach was to add a series of unitary ratios to make up a vulgar* but rational fraction. This was, for them, already a religious observance of all numbers emerging from unity {1}. The number zero {0} in current use represents the absence of a number which is a circle boundary with nothing inside. The circle manifesting {2} from a center {1} becomes the many {3 4 5 6 7 …}.

The number one manifests geometrically as the point (Skt “bindu”) but in potential it is the cosmological centre of later geometries, the unit from which all is measured and, in particular, the circle at infinity.

Two: Potential spaces

Music, part 1: Ancient and Modern

We would know nothing of music were it not that somewhere, between the ear and our perceptions, what we actually hear (the differences between different frequencies of sound, that is, different tones) is heard as equivalent musical intervals (such as fifths, thirds, tones, semitones, etc), of the same size, even when the pitch range of the tones are different. This is not how musical strings work, where intervals of the same size get smaller as the pitch at which tones occur, grows larger. On the frets of a guitar for instance, if one plays the same intervals in a different key, the same musical structure, melodic and harmonic, is perfectly transposed, but the frets are spaced differently.

The key is that human hearing is logarithmic and is based upon the number two {2}, the “first” interval of all, of doubling. This can only mean that the whole of the possibilities for music are integral to human nature. But this miraculous gift of music, in our very being, is rarely seen to be that but, rather, because of the ubiquity of music, especially in the modern world, the perception of music is not appreciated as, effectively, a spiritual gift.

Music is often received as a product like cheese, in that it is to be eaten but, to see how this cheese is made from milk requires us to see, from its appearance as a phenomenon, what music perception is made up of . Where does music come from?

Normally a part of musicology, that subject is full of logical ambiguities, confusing terminology, unresolved opinions, and so on. Those who don’t fully understand the role of number in making music work, concentrate on musical structures without seeing that numbers must be the only origin of music.

The ancient explanation of music was that everything comes out of the number one {1}, so that octaves appear with the number two {2/1}, fifths from three {3/2}, fourths from four {4/3}, thirds from five {5/4} and minor thirds from six {6/5}. Note that, (a) the interval names refer to the order of resulting note within an octave, (b) that intervals are whole number ratios differing by one and that, (c) the musical phenomenon comes out of one {1}, and not out of zero {0}, which is a non-number invented for base ten arithmetic where ten {10} is one ten and no units.

Another miracle appears, in that the ordinal numbers {1 2 3 4 5 6 7 8 9 etc.} naturally create, through their successiveness, all the larger intervals before the seventh number {1 2 3 4 5 6 7} leaving the next three {8 9 10} to create two types of tone {9/8 10/9} and a semitone {16/15} thereafter {11 12 13 14 15 16}: by avoiding all those numbers whose factors are not the first three primes {2 3 5}. Almost the whole potential of western music is therefore built out of the smallest numbers!

This simplicity in numbers has now been obscured, though the structure of music remains in the Equal Temperament form of tuning evolved in the last millennium. By having twelve equal semitones that sum to the number two, we can now transpose melodies between keys (of the keyboard) but we have pretty much lost the idea of scales. Instead, each key is the major diatonic {T T S T T T S} (where T = tone and S = semitone intervals) starting from a different key. The fifth is called dominant and fourth subdominant and the black notes (someway fiendish to learn) required to achieve the major key in all keys but C which is all white keys.

The old church scales are achievable by over ruling the clef with accidental notes, and the reason for different keys sounding different is that they contain aspects of what were the scales. So a pop song, for example, is usually in a scale. “Bus Stop” by the Hollies was in the Locrian scale.

Equal Temperament enabled the Western tradition to create its Classical repertoire but it has made ancient musical theory very distant and has abandoned the exact ratios it used to use since every semitone is identical and irrational. Plato described this kind of solution as the best compromise, where every social class of musical numbers has sacrificed some thing of their former self in order to achieve the riches versatility bestows upon modern musical composition.

To be continued.

Category: Tuning