Richard D Heath - Academia.edu (original) (raw)
Megalithic by Richard D Heath
A flyer for my book 2014 which proposed a historical narrative in which the neolithic in NW Europ... more A flyer for my book 2014 which proposed a historical narrative in which the neolithic in NW Europe could have built megaliths, to count and compare time periods, developing a later ancient metrology, study latitude and land surveying so as to evolve a model of the Earth accurately corresponding to our present geoids. The result is the contemporaneous monuments of the Giza Pyramid and Stonehenge, both models of the earth.
2014
Slides used in the John Michell Memorial Lecture, 9th May 2015, in Glastonbury Town Hall, where R... more Slides used in the John Michell Memorial Lecture, 9th May 2015, in Glastonbury Town Hall, where Richard Heath presents Stone Age Counting as key means for megalithic understanding of astronomy as a highly structured "time-factored" reality which explains the shape and dimensions of the monuments as representing both the means and end results of that astronomy. The paper also esplores the evolution of early metrology into the measures known to history, the geometrical ideas of Carnac's astronomers and their unique art preserved within Gavrinis Cairn (recently scanned by Laurent Lescop) as complementary to the astronomy as "information boards" gathered from Carnac's many monuments, surviving, inundated or lost. Supporting articles can be found at MegalithicScience.org and in author's Sacred Number and the Lords of Time.
This paper presents the theory that in the Megalithic period, around 4500-4000 BCE, astronomical ... more This paper presents the theory that in the Megalithic period, around 4500-4000 BCE, astronomical time periods were counted as one day to one inch to form primitive metrological lengths that could then be compared, to reveal the fundamental ratios between the solar year, lunar year, and lunar month and
hence define a solar-lunar calendar. The means for comparison used was to place lengths as the longer sides of right angled triangles, leading to a unique slope angle. Our March 2010 survey of Le Manio supports this theory.
Following the discovery of such a triangle at Le Manio near Carnac,Brittany, the authors conducted a theodolite survey to accurately establish that both three and four solar year counts had been made in day-inches along the azimuth associated with the midsummer sunrise at that latitude, an angle itself generated between the longer sides of a 3:4:5 triangle (the simplest Pythagorean triangle). The difference in day-inches between three solar years and three lunar years was confirmed as being a megalithic yard of 32.7 inches within the monument, showing that the megalithic yard emerges naturally from day-inch counting the sun and moon over three years.
The invariant proportion of this soli-lunar triangle can be seen at Le Manio as that formed by the diagonal between four squares of equal side length and this generates a natural reading of metres since the modern metre is 4/3 the day-inch count for a lunar month. Finally, the angle of the Quadrilateral is revealed as adapted to the right angled of the three year triangle towards the East of its southern kerb.
It can be inferred that later metrology was derived from such a starting point since the inch and an “English” foot of twelve inches are commensurate with the metrological units of the historical period.
Our survey at Le Manio revealed a coherent arc of radial stones, at least five of which were equa... more Our survey at Le Manio revealed a coherent arc of radial stones, at least five of which were equally long, equally separated and set to a radius of curvature that suggested a common centre. They can be found set into the public walkway at Le Manio, Carnac, Brittany, between the southern kerb of the Quadrilateral and the recent dry stone wall that defines the pathway. This southern kerb has been shown to incorporate a day-inch count for three solar years to its extreme eastern tip [from Point P to Q’ on our plan]. These stones were found to have a centre of curvature at stone 29 of the southern kerb and the arc they suggest would represent, if complete, a circle of 82 similar stones 17 inches apart whilst the radius of curvature was determined to be 221 inches or 13 times 17 inches. This provides a reasonable approximation to 2 times Pi as a ratio 82/13.
The angle of the southern kerb was measured in our survey as being 22.3 degrees north of east, the acute angle in comparison to an east-west line creating the geometry of a right-angled triangle whose two longer sides form the ratio 12.368 to 13.368, an invariant triangle based upon the frequencies of lunar synodic months to lunar sidereal orbits occurring in a solar year. The known day-inch count for three lunar years on the southern kerb is 88.59 feet long which becomes the hypotenuse of a right-angled triangle whose baseline runs east-west and is of length 82 feet. This reveals 82 beneath the fragment of an 82 stone ring as being the length of 36 lunar sidereal orbits in day inches versus the 36 month day-inch count above.
It appears therefore that the astronomers at Le Manio understood that following three lunar sidereal orbits, after 82 days, the moon would appear again at the same point on the ecliptic at the same time of day , a very important observational fact and one that would have enabled them to build circular 82-stone circles representing the ecliptic in which a moon marker could be moved by three stones a day, completing an orbit in 27.333 days and returning to the original ‘start’ stone after 82 days had elapsed.
This paper proposes that an unfamiliar type of circumpolar astronomy was practiced by the time Le... more This paper proposes that an unfamiliar type of circumpolar astronomy was practiced by the time Le Menec was built, around 4000 BCE. This observatory enabled the rotation of the earth and ecliptic location of eastern and western horizons to be known in real time, by observing stellar motion by night and solar motion by day. This method avoided stellar extinction angles by measuring the circular motion of a circumpolar marker star as a range in azimuth, which could then be equated with the diameter of a suitably calibrated observatory circle. The advent of day-inch counting and simple geometrical calculators, already found at Le Manio’s Quadrilateral, enabled the articulation of large time periods within Carnac’s megalithic monuments, the Western Alignments being revealed to be a study of moonrises during half of the moon’s nodal period. Le Menec’s Type 1 egg is found to be a time-factored model of the moon’s orbit relative to the earth’s rotation. This interpretation of Le Menec finds that key stones have survived and that the gaps seen in the cromlech’s walls were an essential part of its symbolic language, guiding contemporary visitors as to how its purpose was to be interpreted within a probably pre-literate megalithic culture.
Two key lengths are found at Le Manio and Le Menec: The first, of 4 eclipse years is a day-inch count of the Octon eclipse cycle; the second is a four solar year count that, with the first, forms a triangle, marked clearly by stones at Le Menec. The principles worked out at Le Manio appear fully developed in Le Menec’s western cromlech, including the use of an 8 eclipse year day-inch count, consequently forming a diameter of 3400 megalithic inches which equals in number the days in half a nodal period. The scaling of the Western Alignments is found to be 17 days per metre, a scaling naturally produced by the diagonal of a triple square geometrical construction. A single sloping length on the top of the central stone initiating row 9, indicates a single lunar orbit at 17 days per metre, a length of 1.607 metres. This control of time counting within geometrical structures reveals that almost all of Le Menec’s western cromlech and alignments express a necessary form, so as to represent a megalithic study of (a) circumpolar time as having 365 time units, (b) the moon’s orbit as having 82 times 122 of those units and (c) the variations of successive moonrises over most of a lunar nodal period of 18.6 solar years.
This article explores the use of axe motifs within a form of carved schematic art unique to the m... more This article explores the use of axe motifs within a form of carved schematic art unique to the megalithic monuments near Carnac, southern Brittany, France, as relating to the astronomy enacted through the monuments. The "Roof Axe" of Kercado appears to express an elegant schematic and metrological presentation of both astronomy on the eastern horizon at Carnac and circumpolar astronomy, which can predict which part of the sky is currently rising and hence also, which part of the ecliptic is rising.
This article is based upon notes made in 22 May 2014 whilst the 32/29 relationship between AMY an... more This article is based upon notes made in 22 May 2014 whilst the 32/29 relationship between AMY and day-inch lunar month was discovered by autumn 2009 (after this paper), being driven to use day-inch counting to explain the origins of megalithic monuments evidently created in the pursuit of astronomical knowledge yet measuring time as lengths. The movement from counting days as inches to using megalithic yards to stand for lunar months was partly explained in my Sacred Number and the Lords of Time by the fact that the excess of lunar months in the solar year is 7/19ths of a lunar year, a residue which adds up over nineteen years to lead to the Metonic period having 235 lunar months in nineteen years. If the AMY is 19/7 feet then it cancels with the residue if and when the megalithic astronomers counted in lunar months. Until last year, there seemed no way to derive the astronomic megalithic yard short of a Metonic scale of monument but the work on this site, on numeracy, and a growing set of techniques such as scaling, proportioning to cancel factors from denominators and hence "clear" fractions, has revealed the 32/29 relationship as deducible in the megalithic and necessary for the quantification of N = 32.585 inches, the measure Robin Heath referred to as the astronomic megalithic yard [2008].
This paper, published on the web, gives time-factoring as an interpretation of the form of Thornb... more This paper, published on the web, gives time-factoring as an interpretation of the form of Thornborough Henge in North Yorkshire (near Ripon). The three henges appear to align to the three notable manifestations to the north west of the northerly moon setting at maximum standstill and then finds the distances between henges as representing 3400 day-feet, enabling a "there and back again" counting of the 6800 days (18.618 solar years/19.618 eclipse years) between lunar maximum standstills.
This paper from 2009 was first published in the DuVersity Newsletter number 25 and marks the star... more This paper from 2009 was first published in the DuVersity Newsletter number 25 and marks the start of a period of work culminating in Sacred Number and the Lords of Time, Inner Traditions, 2014. It comes from a period before the theory developed that days were counted in inches, a theory supported by the subsequent discovery of exactly that at Le Manio, near Carnac, Brittany in Equinox 2010 Theodolite Survey with Robin Heath (see paper The Origins of Megalithic Astronomy as found at Le Manio).
This document was prepared by Richard Heath as a letter for Nature magazine and submitted on 14th... more This document was prepared by Richard Heath as a letter for Nature magazine and submitted on 14th April 1994 but remained unpublished. It marks the discovery of a unit of time proposed and named the Chronon, as being 1/10000th of the Moon's orbit and also the difference between the sidereal and tropical day of the Earth. The paper also documents a discovery made, with Robin Heath, that one can divide up the solar year by its excess over the eclipse year to reveal an 18.618:19.618 ratio between these years, and many other interesting numerical facts not mentioned here. The puzzle is a connection between the rotation of the Earth, the solar year and the precession of the Moon's orbit which (a) may be explainable by science (b) appears to have puzzled Megalithic astronomers and (c) should puzzle us today. We find that the Earth's rotational day divides the year according to the 18.62 year cycle of the Lunar Nodes. The tropical solar year in days is factorised almost exactly by 18.618 times 19.618 and the Moon travels one ten thousandth of its orbit in the time difference between sidereal and tropical days. We have been considering a range of numerical coincidences present in arithmetical and geometrical analyses of astronomical cycles involving the Sun-Moon-Earth system. But here is an apparently lawful relationship concerning the Earth, Sun and Moon, one that is most unusual.
Musicology by Richard D Heath
Explains how the modern system of equal temperament, trans-positional notation, 12 note class key... more Explains how the modern system of equal temperament, trans-positional notation, 12 note class keyboard and key signatures were four causes which transformed western music and culminated in symphonic synchronism and jazz improvisation.
Music and Deep Memory, 2018
Front papers and contributions by Richard Heath to Ernest G. McClain's In Memoriam called Music a... more Front papers and contributions by Richard Heath to Ernest G. McClain's In Memoriam called Music and Deep Memory, in particular his 'Musicological Interpretation Of Ancient Texts' at end. This paper attempts to interpret the first two books of the Bible, according to Ernest McClain’s methods. It is contended that the compositions of ancient texts, as Plato insinuated, were both inspired and used for the science of numerical harmonics. The invariant properties of harmonic numbers, and their evolution through limiting whole numbers, offer a large variety of distinctive scenarios which can be set into compatible narrative forms such as the Seven Days of Creation, the Garden of Eden, the Flood, the Patriarchal development of the Twelve Tribes and Moses meeting with YHWH. They are all set within a single harmonic frame of the 5th power of 60, and have features shared with other ancient texts. This paper
takes numerical references, such as ages, numbers of objects, numeric values of names (as sequences, sums or as exponents), orders of the products of 3 and 5, and considers them as dimensions (and any other features) of integer matrices which McClain called ‘holy mountains’, and symbols such as the Star of David and other elements belonging to the octave tone-circle of a holy mountain.
ICONEA Proceedings, 2013
I open this paper with a diagram of its structure (figure 1). This purportedly ancient symbol cam... more I open this paper with a diagram of its structure (figure 1). This purportedly ancient symbol came to light around 1914 as the (nine fold) Enneagram [BLAKE,1996]: Literary analysis has shown ancient writers using very similar Ring Compositions [DOUGLAS, 2010] as just one of many techniques, often employed within mythic texts to insert hidden structures of meaning. I will be introducing another such technique rediscovered by Ernest McClain [MCCLAIN, 1976, 1978] in which he has “offered a persuasive explanation of crucial passages in texts of world literature—the Bible, the Rig Veda, the Egyptian Book of the Dead, and Plato’s dialogues -- that have defied experts in the concerned disciplines.” – Wikipedia. His work finds harmonic parallelism within texts and finds a purpose for the anomalous often “astronomical” numbers, found within mythic narratives whose meaning is explainable by reconstructing a unique array (a matrix) of whole numbers lesser than the number within the text, numbers evoked purely by consequence of limiting the harmonic generative power to that number. McClain finds that a limit’s matrix, naturally shaped like a mountain, explains the plot elements, events and characters of the narrative, which run parallel to the harmonic concerns found within these mountains. The most significant question emerging from such harmonic parallelism within texts is why the harmonic facts implicit within different limiting numbers were ever thought an important substratum for mythic narrative. What could have made harmonic facts relevant to spiritual tales involving divine worlds and heroic dramas?
BOOK: The Harmonic Origins of the World, 2018
As modern humans first walked the Earth roughly 70,000 years ago, the Moon’s orbit came into harm... more As modern humans first walked the Earth roughly 70,000 years ago, the Moon’s orbit came into harmonic resonance with the outer planets of Jupiter, Saturn, and Uranus. The common denominators underlying these harmonic relationships are the earliest prime numbers of the Fibonacci series—two, three, and five—the same numbers that give us the ratios of musical harmony.
Exploring the simple mathematical relationships that underlie the cycles of the solar system and the music of Earth, Richard Heath reveals how Neolithic astronomers discovered these ratios using megalithic monuments like Stonehenge and those surrounding Carnac, discoveries which informed later myths and stories including the Epic of Gilgamesh, the Resurrection of Osiris, the Rg Veda, the Hebrew Bible, the Odyssey of Homer, and the Return of Quetzalcoatl. He explains how this harmonic planetary knowledge formed the basis of the earliest religious systems, in which planets were seen as gods, and shows how they spread through Sumer, Egypt, and India into Babylon, Judea, Mexico, and archaic Greece. He exposes how the secret knowledge encoded within the Bible’s god YHWH was lost as Greek logic and reason steadily weakened mythological beliefs.
Revealing the mysteries of the octave and of our musical scales, Heath shows how the orbits of the outer and inner planets gave a structure to time, which our Moon’s orbit could then turn into a harmonic matrix. He explains how planetary time came to function as a finely tuned musical instrument, leading to the rise of intelligent life on our planet. He demonstrates how this harmonic science of numbers can be read in the secret symbolism of ancient cities such as Teotihuacan and in temples such as the Parthenon, connecting the higher worlds of planetary time and harmonics with the spiritual and physical life on Earth.
ICONEA 2014, 2014
The Bible, Homer and other myths were largely written down long after their inception, from memor... more The Bible, Homer and other myths were largely written down long after their inception, from memorable oral narratives composed by a type of author who was not a writer. Plato saved the number science implicit in oral works from extinction through including it in his own literary output. A number science can develop without a formal arithmetic through using only geometric procedures and these are to be found in the terminal Stone Age, famous for its enduring megalithic monuments. This paper illustrates the structure of this harmonic science as it is found within historical texts and monuments, whilst suggesting that the harmonic ratios between astronomical periods would most simply explain how our oldest myths were orally composed and performed cosmographies, skillfully woven around the invariant structure of numerical harmony and the sky, these being taken as responsible for creating and maintaining the world.
Harmonic allusions have been found in the ancient literature of the ancient near east and India a... more Harmonic allusions have been found in the ancient literature of the ancient near east and India and these may well refer to harmonic resonances of outer planets to our moon's lunar year noted in my first book Matrix of Creation (2002). These slides for the annual musicological conference of ICONEA in 2013 discusses how ancient astronomy could have become reflected in our oldest religious/ mythological ideas.
Books by Richard D Heath
Sacred Geometry: Language of the Angels, 2021
Examining the angelic science of number, Richard Heath reveals how the development of human consc... more Examining the angelic science of number, Richard Heath reveals how the development of human consciousness was no accident. The beauty and elegance we see in sacred geometry and in structures built according to those proportions are the language of the angels still speaking to us.
Ancient Greece by Richard D Heath
In Memoriam volume for Ernest G. McClain, Music and Deep Memory, 2018
This note responds to Kapraff and McClain’s preceding paper, in which they discover a many-facete... more This note responds to Kapraff and McClain’s preceding paper, in which they discover a many-faceted musical symbolism in the Parthenon. Specifically, Ernst Berger’s new measurements include the shorter side of the triple pedestal of the monument as an accurate length to represent one second of the double meridian of the earth. By applying a knowledge of ancient metrology, Anne Bulckens’ doctoral derivations of a root foot can resolve to a pygme of 9/8 feet, of which one second of latitude would contain 90 such feet. However, as a ‘hundred footer’, the foot length should then be 81/80 (1.0125) feet, the ratio of the syntonic comma. This would indicate a replacement, by Classical times, of the geographical constant of 1.01376 feet within the model of the earth since the original model, by the late megalithic, assumed that the meridian was exactly half of the mean circumference of the earth. These alternative geographical constants co-incidentally represent the ubiquitous theme in ancient musicology of the transition between Pythagorean and Just tunings and their respective commas.
The fields of ancient Greece were organised in a familiar way: strips of land in which a plough c... more The fields of ancient Greece were organised in a familiar way: strips of land in which a plough could prepare land for arable planting. Known in various languages as furlong, runrig, journel, machen etc, in Greece there was a nominal length for arable strips of 600 feet called a stadia. The length of foot used was systematically varied from the foot we use today, using highly disciplined variations (called modules); each module a numeric ratio to the Greek module; whose root foot was the English foot [Neal, 2000]. These modules are found employed throughout the ancient world, lengthening or reducing lengths such as the stadia, to suit geometrical problems; such as the division of land into fields
The unique fired-clay disk, found by Luigi Pernier in 1908 within the "palace" of Phaistos (aka F... more The unique fired-clay disk, found by Luigi Pernier in 1908 within the "palace" of Phaistos (aka Faistos), now called the Phaistos Disk, has had its purpose or meaning has been interpreted many times, as linguistic or technical. We provide a calendric interpretation based on the lunar calendars known to apply in Minoan times, finding an elegant solution to predicting repeated eclipses within the Saros period and an observation that the Metonic is just one lunar year longer, true to the context of the Minoan culture before 1700 BC.
A flyer for my book 2014 which proposed a historical narrative in which the neolithic in NW Europ... more A flyer for my book 2014 which proposed a historical narrative in which the neolithic in NW Europe could have built megaliths, to count and compare time periods, developing a later ancient metrology, study latitude and land surveying so as to evolve a model of the Earth accurately corresponding to our present geoids. The result is the contemporaneous monuments of the Giza Pyramid and Stonehenge, both models of the earth.
2014
Slides used in the John Michell Memorial Lecture, 9th May 2015, in Glastonbury Town Hall, where R... more Slides used in the John Michell Memorial Lecture, 9th May 2015, in Glastonbury Town Hall, where Richard Heath presents Stone Age Counting as key means for megalithic understanding of astronomy as a highly structured "time-factored" reality which explains the shape and dimensions of the monuments as representing both the means and end results of that astronomy. The paper also esplores the evolution of early metrology into the measures known to history, the geometrical ideas of Carnac's astronomers and their unique art preserved within Gavrinis Cairn (recently scanned by Laurent Lescop) as complementary to the astronomy as "information boards" gathered from Carnac's many monuments, surviving, inundated or lost. Supporting articles can be found at MegalithicScience.org and in author's Sacred Number and the Lords of Time.
This paper presents the theory that in the Megalithic period, around 4500-4000 BCE, astronomical ... more This paper presents the theory that in the Megalithic period, around 4500-4000 BCE, astronomical time periods were counted as one day to one inch to form primitive metrological lengths that could then be compared, to reveal the fundamental ratios between the solar year, lunar year, and lunar month and
hence define a solar-lunar calendar. The means for comparison used was to place lengths as the longer sides of right angled triangles, leading to a unique slope angle. Our March 2010 survey of Le Manio supports this theory.
Following the discovery of such a triangle at Le Manio near Carnac,Brittany, the authors conducted a theodolite survey to accurately establish that both three and four solar year counts had been made in day-inches along the azimuth associated with the midsummer sunrise at that latitude, an angle itself generated between the longer sides of a 3:4:5 triangle (the simplest Pythagorean triangle). The difference in day-inches between three solar years and three lunar years was confirmed as being a megalithic yard of 32.7 inches within the monument, showing that the megalithic yard emerges naturally from day-inch counting the sun and moon over three years.
The invariant proportion of this soli-lunar triangle can be seen at Le Manio as that formed by the diagonal between four squares of equal side length and this generates a natural reading of metres since the modern metre is 4/3 the day-inch count for a lunar month. Finally, the angle of the Quadrilateral is revealed as adapted to the right angled of the three year triangle towards the East of its southern kerb.
It can be inferred that later metrology was derived from such a starting point since the inch and an “English” foot of twelve inches are commensurate with the metrological units of the historical period.
Our survey at Le Manio revealed a coherent arc of radial stones, at least five of which were equa... more Our survey at Le Manio revealed a coherent arc of radial stones, at least five of which were equally long, equally separated and set to a radius of curvature that suggested a common centre. They can be found set into the public walkway at Le Manio, Carnac, Brittany, between the southern kerb of the Quadrilateral and the recent dry stone wall that defines the pathway. This southern kerb has been shown to incorporate a day-inch count for three solar years to its extreme eastern tip [from Point P to Q’ on our plan]. These stones were found to have a centre of curvature at stone 29 of the southern kerb and the arc they suggest would represent, if complete, a circle of 82 similar stones 17 inches apart whilst the radius of curvature was determined to be 221 inches or 13 times 17 inches. This provides a reasonable approximation to 2 times Pi as a ratio 82/13.
The angle of the southern kerb was measured in our survey as being 22.3 degrees north of east, the acute angle in comparison to an east-west line creating the geometry of a right-angled triangle whose two longer sides form the ratio 12.368 to 13.368, an invariant triangle based upon the frequencies of lunar synodic months to lunar sidereal orbits occurring in a solar year. The known day-inch count for three lunar years on the southern kerb is 88.59 feet long which becomes the hypotenuse of a right-angled triangle whose baseline runs east-west and is of length 82 feet. This reveals 82 beneath the fragment of an 82 stone ring as being the length of 36 lunar sidereal orbits in day inches versus the 36 month day-inch count above.
It appears therefore that the astronomers at Le Manio understood that following three lunar sidereal orbits, after 82 days, the moon would appear again at the same point on the ecliptic at the same time of day , a very important observational fact and one that would have enabled them to build circular 82-stone circles representing the ecliptic in which a moon marker could be moved by three stones a day, completing an orbit in 27.333 days and returning to the original ‘start’ stone after 82 days had elapsed.
This paper proposes that an unfamiliar type of circumpolar astronomy was practiced by the time Le... more This paper proposes that an unfamiliar type of circumpolar astronomy was practiced by the time Le Menec was built, around 4000 BCE. This observatory enabled the rotation of the earth and ecliptic location of eastern and western horizons to be known in real time, by observing stellar motion by night and solar motion by day. This method avoided stellar extinction angles by measuring the circular motion of a circumpolar marker star as a range in azimuth, which could then be equated with the diameter of a suitably calibrated observatory circle. The advent of day-inch counting and simple geometrical calculators, already found at Le Manio’s Quadrilateral, enabled the articulation of large time periods within Carnac’s megalithic monuments, the Western Alignments being revealed to be a study of moonrises during half of the moon’s nodal period. Le Menec’s Type 1 egg is found to be a time-factored model of the moon’s orbit relative to the earth’s rotation. This interpretation of Le Menec finds that key stones have survived and that the gaps seen in the cromlech’s walls were an essential part of its symbolic language, guiding contemporary visitors as to how its purpose was to be interpreted within a probably pre-literate megalithic culture.
Two key lengths are found at Le Manio and Le Menec: The first, of 4 eclipse years is a day-inch count of the Octon eclipse cycle; the second is a four solar year count that, with the first, forms a triangle, marked clearly by stones at Le Menec. The principles worked out at Le Manio appear fully developed in Le Menec’s western cromlech, including the use of an 8 eclipse year day-inch count, consequently forming a diameter of 3400 megalithic inches which equals in number the days in half a nodal period. The scaling of the Western Alignments is found to be 17 days per metre, a scaling naturally produced by the diagonal of a triple square geometrical construction. A single sloping length on the top of the central stone initiating row 9, indicates a single lunar orbit at 17 days per metre, a length of 1.607 metres. This control of time counting within geometrical structures reveals that almost all of Le Menec’s western cromlech and alignments express a necessary form, so as to represent a megalithic study of (a) circumpolar time as having 365 time units, (b) the moon’s orbit as having 82 times 122 of those units and (c) the variations of successive moonrises over most of a lunar nodal period of 18.6 solar years.
This article explores the use of axe motifs within a form of carved schematic art unique to the m... more This article explores the use of axe motifs within a form of carved schematic art unique to the megalithic monuments near Carnac, southern Brittany, France, as relating to the astronomy enacted through the monuments. The "Roof Axe" of Kercado appears to express an elegant schematic and metrological presentation of both astronomy on the eastern horizon at Carnac and circumpolar astronomy, which can predict which part of the sky is currently rising and hence also, which part of the ecliptic is rising.
This article is based upon notes made in 22 May 2014 whilst the 32/29 relationship between AMY an... more This article is based upon notes made in 22 May 2014 whilst the 32/29 relationship between AMY and day-inch lunar month was discovered by autumn 2009 (after this paper), being driven to use day-inch counting to explain the origins of megalithic monuments evidently created in the pursuit of astronomical knowledge yet measuring time as lengths. The movement from counting days as inches to using megalithic yards to stand for lunar months was partly explained in my Sacred Number and the Lords of Time by the fact that the excess of lunar months in the solar year is 7/19ths of a lunar year, a residue which adds up over nineteen years to lead to the Metonic period having 235 lunar months in nineteen years. If the AMY is 19/7 feet then it cancels with the residue if and when the megalithic astronomers counted in lunar months. Until last year, there seemed no way to derive the astronomic megalithic yard short of a Metonic scale of monument but the work on this site, on numeracy, and a growing set of techniques such as scaling, proportioning to cancel factors from denominators and hence "clear" fractions, has revealed the 32/29 relationship as deducible in the megalithic and necessary for the quantification of N = 32.585 inches, the measure Robin Heath referred to as the astronomic megalithic yard [2008].
This paper, published on the web, gives time-factoring as an interpretation of the form of Thornb... more This paper, published on the web, gives time-factoring as an interpretation of the form of Thornborough Henge in North Yorkshire (near Ripon). The three henges appear to align to the three notable manifestations to the north west of the northerly moon setting at maximum standstill and then finds the distances between henges as representing 3400 day-feet, enabling a "there and back again" counting of the 6800 days (18.618 solar years/19.618 eclipse years) between lunar maximum standstills.
This paper from 2009 was first published in the DuVersity Newsletter number 25 and marks the star... more This paper from 2009 was first published in the DuVersity Newsletter number 25 and marks the start of a period of work culminating in Sacred Number and the Lords of Time, Inner Traditions, 2014. It comes from a period before the theory developed that days were counted in inches, a theory supported by the subsequent discovery of exactly that at Le Manio, near Carnac, Brittany in Equinox 2010 Theodolite Survey with Robin Heath (see paper The Origins of Megalithic Astronomy as found at Le Manio).
This document was prepared by Richard Heath as a letter for Nature magazine and submitted on 14th... more This document was prepared by Richard Heath as a letter for Nature magazine and submitted on 14th April 1994 but remained unpublished. It marks the discovery of a unit of time proposed and named the Chronon, as being 1/10000th of the Moon's orbit and also the difference between the sidereal and tropical day of the Earth. The paper also documents a discovery made, with Robin Heath, that one can divide up the solar year by its excess over the eclipse year to reveal an 18.618:19.618 ratio between these years, and many other interesting numerical facts not mentioned here. The puzzle is a connection between the rotation of the Earth, the solar year and the precession of the Moon's orbit which (a) may be explainable by science (b) appears to have puzzled Megalithic astronomers and (c) should puzzle us today. We find that the Earth's rotational day divides the year according to the 18.62 year cycle of the Lunar Nodes. The tropical solar year in days is factorised almost exactly by 18.618 times 19.618 and the Moon travels one ten thousandth of its orbit in the time difference between sidereal and tropical days. We have been considering a range of numerical coincidences present in arithmetical and geometrical analyses of astronomical cycles involving the Sun-Moon-Earth system. But here is an apparently lawful relationship concerning the Earth, Sun and Moon, one that is most unusual.
Explains how the modern system of equal temperament, trans-positional notation, 12 note class key... more Explains how the modern system of equal temperament, trans-positional notation, 12 note class keyboard and key signatures were four causes which transformed western music and culminated in symphonic synchronism and jazz improvisation.
Music and Deep Memory, 2018
Front papers and contributions by Richard Heath to Ernest G. McClain's In Memoriam called Music a... more Front papers and contributions by Richard Heath to Ernest G. McClain's In Memoriam called Music and Deep Memory, in particular his 'Musicological Interpretation Of Ancient Texts' at end. This paper attempts to interpret the first two books of the Bible, according to Ernest McClain’s methods. It is contended that the compositions of ancient texts, as Plato insinuated, were both inspired and used for the science of numerical harmonics. The invariant properties of harmonic numbers, and their evolution through limiting whole numbers, offer a large variety of distinctive scenarios which can be set into compatible narrative forms such as the Seven Days of Creation, the Garden of Eden, the Flood, the Patriarchal development of the Twelve Tribes and Moses meeting with YHWH. They are all set within a single harmonic frame of the 5th power of 60, and have features shared with other ancient texts. This paper
takes numerical references, such as ages, numbers of objects, numeric values of names (as sequences, sums or as exponents), orders of the products of 3 and 5, and considers them as dimensions (and any other features) of integer matrices which McClain called ‘holy mountains’, and symbols such as the Star of David and other elements belonging to the octave tone-circle of a holy mountain.
ICONEA Proceedings, 2013
I open this paper with a diagram of its structure (figure 1). This purportedly ancient symbol cam... more I open this paper with a diagram of its structure (figure 1). This purportedly ancient symbol came to light around 1914 as the (nine fold) Enneagram [BLAKE,1996]: Literary analysis has shown ancient writers using very similar Ring Compositions [DOUGLAS, 2010] as just one of many techniques, often employed within mythic texts to insert hidden structures of meaning. I will be introducing another such technique rediscovered by Ernest McClain [MCCLAIN, 1976, 1978] in which he has “offered a persuasive explanation of crucial passages in texts of world literature—the Bible, the Rig Veda, the Egyptian Book of the Dead, and Plato’s dialogues -- that have defied experts in the concerned disciplines.” – Wikipedia. His work finds harmonic parallelism within texts and finds a purpose for the anomalous often “astronomical” numbers, found within mythic narratives whose meaning is explainable by reconstructing a unique array (a matrix) of whole numbers lesser than the number within the text, numbers evoked purely by consequence of limiting the harmonic generative power to that number. McClain finds that a limit’s matrix, naturally shaped like a mountain, explains the plot elements, events and characters of the narrative, which run parallel to the harmonic concerns found within these mountains. The most significant question emerging from such harmonic parallelism within texts is why the harmonic facts implicit within different limiting numbers were ever thought an important substratum for mythic narrative. What could have made harmonic facts relevant to spiritual tales involving divine worlds and heroic dramas?
BOOK: The Harmonic Origins of the World, 2018
As modern humans first walked the Earth roughly 70,000 years ago, the Moon’s orbit came into harm... more As modern humans first walked the Earth roughly 70,000 years ago, the Moon’s orbit came into harmonic resonance with the outer planets of Jupiter, Saturn, and Uranus. The common denominators underlying these harmonic relationships are the earliest prime numbers of the Fibonacci series—two, three, and five—the same numbers that give us the ratios of musical harmony.
Exploring the simple mathematical relationships that underlie the cycles of the solar system and the music of Earth, Richard Heath reveals how Neolithic astronomers discovered these ratios using megalithic monuments like Stonehenge and those surrounding Carnac, discoveries which informed later myths and stories including the Epic of Gilgamesh, the Resurrection of Osiris, the Rg Veda, the Hebrew Bible, the Odyssey of Homer, and the Return of Quetzalcoatl. He explains how this harmonic planetary knowledge formed the basis of the earliest religious systems, in which planets were seen as gods, and shows how they spread through Sumer, Egypt, and India into Babylon, Judea, Mexico, and archaic Greece. He exposes how the secret knowledge encoded within the Bible’s god YHWH was lost as Greek logic and reason steadily weakened mythological beliefs.
Revealing the mysteries of the octave and of our musical scales, Heath shows how the orbits of the outer and inner planets gave a structure to time, which our Moon’s orbit could then turn into a harmonic matrix. He explains how planetary time came to function as a finely tuned musical instrument, leading to the rise of intelligent life on our planet. He demonstrates how this harmonic science of numbers can be read in the secret symbolism of ancient cities such as Teotihuacan and in temples such as the Parthenon, connecting the higher worlds of planetary time and harmonics with the spiritual and physical life on Earth.
ICONEA 2014, 2014
The Bible, Homer and other myths were largely written down long after their inception, from memor... more The Bible, Homer and other myths were largely written down long after their inception, from memorable oral narratives composed by a type of author who was not a writer. Plato saved the number science implicit in oral works from extinction through including it in his own literary output. A number science can develop without a formal arithmetic through using only geometric procedures and these are to be found in the terminal Stone Age, famous for its enduring megalithic monuments. This paper illustrates the structure of this harmonic science as it is found within historical texts and monuments, whilst suggesting that the harmonic ratios between astronomical periods would most simply explain how our oldest myths were orally composed and performed cosmographies, skillfully woven around the invariant structure of numerical harmony and the sky, these being taken as responsible for creating and maintaining the world.
Harmonic allusions have been found in the ancient literature of the ancient near east and India a... more Harmonic allusions have been found in the ancient literature of the ancient near east and India and these may well refer to harmonic resonances of outer planets to our moon's lunar year noted in my first book Matrix of Creation (2002). These slides for the annual musicological conference of ICONEA in 2013 discusses how ancient astronomy could have become reflected in our oldest religious/ mythological ideas.
Sacred Geometry: Language of the Angels, 2021
Examining the angelic science of number, Richard Heath reveals how the development of human consc... more Examining the angelic science of number, Richard Heath reveals how the development of human consciousness was no accident. The beauty and elegance we see in sacred geometry and in structures built according to those proportions are the language of the angels still speaking to us.
In Memoriam volume for Ernest G. McClain, Music and Deep Memory, 2018
This note responds to Kapraff and McClain’s preceding paper, in which they discover a many-facete... more This note responds to Kapraff and McClain’s preceding paper, in which they discover a many-faceted musical symbolism in the Parthenon. Specifically, Ernst Berger’s new measurements include the shorter side of the triple pedestal of the monument as an accurate length to represent one second of the double meridian of the earth. By applying a knowledge of ancient metrology, Anne Bulckens’ doctoral derivations of a root foot can resolve to a pygme of 9/8 feet, of which one second of latitude would contain 90 such feet. However, as a ‘hundred footer’, the foot length should then be 81/80 (1.0125) feet, the ratio of the syntonic comma. This would indicate a replacement, by Classical times, of the geographical constant of 1.01376 feet within the model of the earth since the original model, by the late megalithic, assumed that the meridian was exactly half of the mean circumference of the earth. These alternative geographical constants co-incidentally represent the ubiquitous theme in ancient musicology of the transition between Pythagorean and Just tunings and their respective commas.
The fields of ancient Greece were organised in a familiar way: strips of land in which a plough c... more The fields of ancient Greece were organised in a familiar way: strips of land in which a plough could prepare land for arable planting. Known in various languages as furlong, runrig, journel, machen etc, in Greece there was a nominal length for arable strips of 600 feet called a stadia. The length of foot used was systematically varied from the foot we use today, using highly disciplined variations (called modules); each module a numeric ratio to the Greek module; whose root foot was the English foot [Neal, 2000]. These modules are found employed throughout the ancient world, lengthening or reducing lengths such as the stadia, to suit geometrical problems; such as the division of land into fields
The unique fired-clay disk, found by Luigi Pernier in 1908 within the "palace" of Phaistos (aka F... more The unique fired-clay disk, found by Luigi Pernier in 1908 within the "palace" of Phaistos (aka Faistos), now called the Phaistos Disk, has had its purpose or meaning has been interpreted many times, as linguistic or technical. We provide a calendric interpretation based on the lunar calendars known to apply in Minoan times, finding an elegant solution to predicting repeated eclipses within the Saros period and an observation that the Metonic is just one lunar year longer, true to the context of the Minoan culture before 1700 BC.
As Greece began to develop the notion of a Polis (or people), temple design went from using small... more As Greece began to develop the notion of a Polis (or people), temple design went from using small dedicated buildings to creating, in the first Heraion, on Samos, the first Hecatompedos or hundred footer, whose walled room's only entrance faced east [Herwit 1989]. Its axis was 14 degrees south of east, an angle familiar as that of the diagonal of a four-square rectangle, whose diagonal stands in relation to the four-square base as being the solar year relative to the lunar year. At the western end we believe there stood a statue of Hera, wife of Zeus, after whom the monument is named. Herwit's excellent The Art and Culture of Early Greece 1100-480 B.C. shows the monument's early evolution with a plan indicating the most likely metrology for the monument was of 100 common Egyptian feet of 48/49 feet (0.9788) which gives 36 megalithic yards of 2.72 feet along the axis. The diagonal is then 37.1 megalithic yards long so that these two lengths show exactly the sort of count found at the Le Manio Quadrilateral in southern Brittany.
This note gives a new logographic interpretation of the Phaistos Disk as a scribal procedure base... more This note gives a new logographic interpretation of the Phaistos Disk as a scribal procedure based upon counting whole lunar months to track the Saros Eclipse period, employing three types of aggregate counter, for 1, 12 and 37 lunar months. Evidence for such counting appears in megalithic Brittany, and this work revealed the fact that in three 364 day Saturnian years there are 37 whole lunar months. Extracted from authors website; PDF includes links.
Wikipedia gives a helpful resume of theories considering what the spirals of grouped symbols might mean, of two types, linguistic and logographic. Linguistic theories look for a text and logographic look for meanings such as an astronomic meaning. I will provide the latter, as another demonstration of the utility of the number 222 as one less than 223, the number of lunar months making up the Saros period of 18 solar years and 11 days (after which an almost identical eclipse recurs). Of the few eclipse periods, the Saros is the definitive one, because similar eclipses belong to the recurrence of the same actual orbital conditions of sun and moon. The difficulty in predicting Saros events is a problem of counting numbers something simple (the lunar months) which is a natural integer and does not require too many to be counted, when numeracy might be a problem for ancient cultures. The author suggests that the disk side A containing a petal in the center box shows astronomical eclipse information, which belong to a complete Saros cycle beginning −1377 and valid for the Phaistos Palace location only. In 2009, Wolfgang Reczko interpreted the disk: His summary of the disk is useful and he is also tying the disk to specific eclipse data. The outer disk on both faces has twelve groups of symbols with a small excess which could be remarking on the 0.368 (7/19ths) of a lunar month after twelve whole lunar months. Rectzko then points to the spiral on both sides having eighteen blocks of symbols and these inner spirals with 18 divisions he interpreted as solar years so that the small boxes linking these to the rim are the 11 days excess over eighteen years of the Saros period. The disk is about 15 cm (5.9 in) in diameter and covered on both sides with a spiral of stamped symbols. Its purpose and meaning, and even its original geographical place of manufacture, remain disputed, making it one of the most famous mysteries of archaeology. This unique object is now on display at the archaeological museum of Heraklion.
A perforated vessel (#2646) exists in the Heraklion Museum, Crete, found at Knossos and thought o... more A perforated vessel (#2646) exists in the Heraklion Museum, Crete, found at Knossos and thought of the Late Palace Period. Consisting of painted pottery punctuated by circles of similar holes, this paper demonstrates how the vessel could have been used to predict eclipses based upon the rational relationship of the synod of Saturn to the lunar month and year. Thirty eight eclipse seasons can be seen, the seven fold iconography of Chronos (=Cronos) as the seven-day week which divides into various celestial periods and hence is a good reason for choosing the week the West now observes. The paper also discusses how the disk may reflect the cultural transormation between Chronos and his son Zeus, born on Crete within Greek mythology.
This paper extrapolates from the work of Peter Halldorsson, which finds similar landforms to that... more This paper extrapolates from the work of Peter Halldorsson, which finds similar landforms to that found by Einar Palsson (English:1993), but in other parts of Europe and Middle East such as London, Athens, Rome and Jerusalem. The details of Halldorsson's circular structures, called " cosmic images " , vary in size, and in peripheral alignments to the central point, but two constants appear to have been (a) a diameter of 216,000 feet, belonging to different modules, and (b) a central square of 36,000 feet, of the same module 1. The circle and square of Halldorsson's 2017 cosmic image in London (see figure 1) will here be central to reconstructing (a) the practical lengths used to generate such images and (b) the simple geometrical scheme used for their geodetic construction. The proposed image for London employs the English foot, which was the root of the Greek module and also the root of ancient metrology as a system [Neal, 2000]. Figure 1 Halldorsson's cosmic image in London. [Annotated] 1 In ancient metrology, feet are varied by ratios to each other and the similar variation within each module.
Einar Palsson [1] saw the myths of foundation for Iceland's settlement (in 930) had Pythagorean r... more Einar Palsson [1] saw the myths of foundation for Iceland's settlement (in 930) had Pythagorean roots. This manifested as a geometric connection between places on the landscape, especially on the south-western region near Reykjavik, its only city. Coherence was established through organising space according to centres (things), circles and their diameters, the circles punctuated with places and alignments to other places, horizon events or cardinal directions. This paper extends John Neal's analysis of Palsson's landform geometry in its connotation as being a model of the mean earth radius and circumference.
An essay by Richard Heath first published in DuVersity Magazine no 36 In order to think about the... more An essay by Richard Heath first published in DuVersity Magazine no 36 In order to think about the cosmic world one has to recognise that it is more than the world of life found on the earth and the living world, or biosphere, is most probably a result of how the cosmic world organised evolution on the earth. The cosmic world is made up of large bodies; planets and the suns around which planets orbit with sophisticated, some say musical, regularity. However, the cosmic world shares with the living world the basic stuff of materiality, that is the atoms and molecules under the sway of various type of force field. The world of material stuff and forces is characteristically less complex than that exhibited in life and therefore seems "less than" or below life, leading to John Bennett's naming of it as being hyponomic (literally "under laws "). Bennett then called the world of Life autonomic and, since Life arises within a cosmic structure, this higher world was termed hypernomic ("above laws"). Bennett's prefix scheme, of hypo-, auto-and hypernomic, divides the whole universe into three naturally different types of structures. The sky appears as the realm of the hypernomic 'above' life on earth with celestial bodies moving across it in various patterns. As far as we know, humanity has always projected onto
Retrieved from https://sacred.numbersciences.org/2023/10/19/plato-and-the-quran/, 2023
Multiplication of the consecutive numbers 1 to 6 equals 720 and this, applied, to the equal perim... more Multiplication of the consecutive numbers 1 to 6 equals 720 and this, applied, to the equal perimeter model, numerically scaled it up to the cosmic size of the Earth and Moon in miles. The Quranic formula, to instead multiply the numbers 3 to 8 and generate 20160, doubled the cosmic model's 10080 and hence the whole geometry was doubled in scale. The further addition of the consecutive numbers 3 to 8, further signalled 33 years, pointing to the equal area model of the Solar Hero and to the Moon's nodal period because, 33 divided by 18.618 equals √ = 1.778 and the area function squares that. This equality of a circle's perimeter and a circle's area to the same square can then be drawn to unite the cosmic model of Earth and Moon's size, to the relationship of the Solar Hero period of 33 years, as the square, to a circle of radius 18.618 years, as appears quite clearly in the plan of Islam's Dome of the Rock 1 .