The Harmonic Origins of the World
Key Terms
- Harmonics
- PYTHAGORAS
- PLATO
- NICOMACHOS of Gerasa
- IAMBLICHOS of Chalkis
- THEON of Smyrna
- JOHANNES KEPLER (1571-1630)
- ALBERT VON THIMUS (1806-1878)
- HANS KAYSER (1891-1964)
- RUDOLF HAASE (* 1920)
- Joscelyn Godwin
- Ernest G. McClain
- Richard Heath
- Tone Circles
- Jain Cosmic Wheel of Time
- Buddhist Wheel of Life
- Sacred Science
- Music Theory
- Quadvirium
- Circle of Fifths
- Tuning Theory
- Pythagorean Comma
- Tritone
- Symmetry
- Pythagorean Tuning
- Diatonic Tuning
- Pentatonic Tuning
- Yug Cycles
- The Great Year
- Algebraic Geometry
Source: https://sacred.numbersciences.org/harmonic-origins-of-the-world/
“We have long known, thanks to Ernest McClain, that the ancients were obsessed with harmonic numbers and that the Bible encodes these from beginning to end. Now new evidence appears, as these numbers correlate with the planetary periods, and their discovery is pushed far back into the prehistoric era. Richard Heath’s work, based not on speculation but on objective data, challenges all accepted notions of cultural evolution and religious origins.”
–JOSCELYN GODWIN, author of Harmonies of Heaven and Earth and Atlantis and the Cycles of Time
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 interact to give us the harmonic relationships of music.
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 the Carnac stones, discoveries that informed later myths and stories, including the Epic of Gilgamesh, the Resurrection of Osiris, the Rg Veda, the Hebrew Bible, Homer’s epic tales, 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 and sacred geometry 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.
Recasting our understanding of the solar system, Heath seeks to reawaken humanity’s understanding of how sacred numbers structure reality, offering an opportunity to recover this lost harmonic doctrine and reclaim our intended role in the outer life of our planet.
Harmonic Origins of the World
Contents (272 pages, 100 b&w illustrations)
Preface
Introduction: The Significance of Planetary Harmony (5)
PART 1: RECOVERING LOST KNOWLEDGE OF THE WORLD SOUL
1 Climbing the Harmonic Mountain (20)
2 Heroic Gods of the Tritone (19)
3 YHWH Rejects the Gods (15)
4 Plato’s Dilemma (22)
PART 2: A COSMICALLY CREATIVE HARMONY
5 The Quest for Apollo’s Lyre (25)
6 Life on the Mountain (23)
PART 3 THE WAR IN HEAVEN
7 Gilgamesh Kills the Stone Men (16)
8 Quetzalcoatl’s Brave New World (31)
9 YHWH’s Matrix of Creation (19)
10 The Abrahamic Incarnation (15)
Postscript: Intelligent Star Systems
APPENDIX 1: Astronomical Periods and Their Matrix Equivalents
APPENDIX 2: Ancient Use of Tone Circles (11)
Notes
Bibliography
IndexRICHARD HEATH is a development engineer with degrees in systems science and computer-aided design. His interest in megalithic astronomy and ancient metrology has resulted in 6 books, including, in January 2021, Sacred Geometry: Language of the Angels. He lives in the Preseli hills of West Wales.
Source: https://sacred.numbersciences.org/2022/06/07/introduction-to-my-book-harmonic-origins-of-the-world/
Introduction
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 metrologyThe 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 alignmentsA 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 solsticeThe 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, Ernest McClain 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 synodic 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:
Preface
Introduction: The Significance of Planetary Harmony
PART 1
RECOVERING LOST KNOWLEDGE OF THE WORLD SOULPlato’s description of how the Creator designed the world using only the intervals of musical fifth (3/2), whole tone (9/8) and fourth (4/3), within a purely numerical framework (6 8 9 12).
1 Climbing the Harmonic Mountain
2 Heroic Gods of the Tritone
3 YHWH Rejects the Gods
4 Plato’s Dilemma
PART 2
A COSMICALLY CREATIVE HARMONY5 The Quest for Apollo’s Lyre
6 Life on the Mountain
PART 3
THE WAR IN HEAVEN7 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 SymmetryNotes
Bibliography
Index
Source: The Harmonic Origins of the World
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Key Sources of Research
The Harmonic Origins of the World
Sacred Number at the Source of Creation
https://www.simonandschuster.com/books/The-Harmonic-Origins-of-the-World/Richard-Heath/9781620556122
https://sacred.numbersciences.org/harmonic-origins-of-the-world/
https://sacred.numbersciences.org/2022/06/07/introduction-to-my-book-harmonic-origins-of-the-world/
https://www.innertraditions.com/books/the-harmonic-origins-of-the-world
Matrix of Creation
Sacred Geometry in the Realm of the Planets
https://www.simonandschuster.com/books/Matrix-of-Creation/Richard-Heath/9780892811946
Precessional Time and the Evolution of Consciousness
How Stories Create the World
Sacred Number and the Origins of Civilization
The Unfolding of History through the Mystery of Number
Sacred Number and the Lords of Time
The Stone Age Invention of Science and Religion
Sacred Geometry: Language of the Angels
Ernest G. McClain
Harmonic Explorer
Ancient Musicology by Limiting Numbers
Richard Heath
https://www.harmonicexplorer.org/mountain.html
Harmonic Explorer App
Sacred Geometry in Ancient Goddess Cultures
Richard Heath
Feb 2024
https://www.innertraditions.com/books/sacred-geometry-in-ancient-goddess-cultures
Jain cosmology
Wikipedia
https://en.wikipedia.org/wiki/Jain_cosmology
https://exhibits.stanford.edu/ruderman/catalog/bp830ft1058
The Living Cosmos of Jainism: A Traditional Science Grounded in Environmental Ethics
Christopher Key Chapple
Jain Cosmography
https://www.academia.edu/43650937/Jain_Cosmography
VISUAL AND CONCEPTUAL LINKS BETWEEN JAINA COSMOLOGICAL, MYTHOLOGICAL AND RITUAL INSTRUMENTS*
Julia A. B. Hegewald
International Journal of Jaina Studies (Online) Vol. 6, No. 1 (2010) 1-20
The Jain Cosmology
Authors Colette Caillat, Ravi Kumar
Publisher Ravi Kumar, 2004
ISBN 1588860582, 9781588860583
Length 196 pages
Cosmology Old & New, Being a Modern Commentary on the Fifth Chapter of Tattvārthādhigama Sūtra
Volume 5 of Jñānapīṭha Mūrtidevī granthamālā.Jñānapīṭha Mūrtīdevī granthamālā. English series
Volume 5 of Jñānapīṭha Mūrtidevī granthamālā: English series
Volume 5 of Murtidevī granthamālā
Author G. R. Jain
Publisher Bharatiya Jnanpith Publication, 1975
Original from the University of Michigan
Digitized Oct 6, 2006
Length 219 pages
Victorious Ones: Jain Images of Perfection
Author Phyllis Emily Granoff
Editor Phyllis Emily Granoff
Contributor Rubin Museum of Art (New York, N.Y.)
Edition illustrated
Publisher Rubin Museum of Art, 2009
ISBN 0944142834, 9780944142837
Length 308 pages
Elements of Jaina Geography: The Jambūdvīpasaṃgrahaṇī of Haribhadra Sūri : Critically Edited and Translated with the Commentary of Prabhānanda Sūri
Authors Haribhadrasūri, Frank van den Bossche
Editor Frank van den Bossche
Compiled by Frank van den Bossche
Publisher Motilal Banarsidass, 2007
Original from the University of Michigan
Digitized Jun 22, 2009
ISBN 8120829344, 9788120829343
Length 327 pages
Jainism and its Cosmic View
https://www.peepultree.world/livehistoryindia/story/living-culture/jainism-its-cosmic-view
Salakapurusa
https://en.wikipedia.org/wiki/Salakapurusa
HISTORY OF HARMONIC THINKING
WERNER SCHULZE
Symmetry: Art and Science Buenos Aires Congress, 2007
Circle of fifths
https://en.wikipedia.org/wiki/Circle_of_fifths
The circle of fifths developed in the late 1600s and early 1700s to theorize the modulation of the Baroque era (see § Baroque era).
The first circle of fifths diagram appears in the Grammatika (1677) of the composer and theorist Nikolay Diletsky, who intended to present music theory as a tool for composition.[7] It was “the first of its kind, aimed at teaching a Russian audience how to write Western-style polyphonic compositions.”
A circle of fifths diagram was independently created by German composer and theorist Johann David Heinichen in his Neu erfundene und gründliche Anweisung (1711),[8] which he called the “Musical Circle” (German: Musicalischer Circul).[9][10] This was also published in his Der General-Bass in der Composition (1728).
Heinichen placed the relative minor key next to the major key, which did not reflect the actual proximity of keys. Johann Mattheson (1735) and others attempted to improve this—David Kellner (1737) proposed having the major keys on one circle, and the relative minor keys on a second, inner circle. This was later developed into chordal space, incorporating the parallel minor as well.[11]
Some sources imply that the circle of fifths was known in antiquity, by Pythagoras.[12][13][14] This is a misunderstanding and an anachronism.[15]Tuning by fifths (so-called Pythagorean tuning) dates to Ancient Mesopotamia;[16] see Music of Mesopotamia § Music theory, though they did not extend this to a twelve note scale, stopping at seven. The Pythagorean comma was calculated by Euclid and by Chinese mathematicians (in the Huainanzi); see Pythagorean comma § History. Thus, it was known in antiquity that a cycle of twelve fifths was almost exactly seven octaves (more practically, alternating ascending fifths and descending fourths was almost exactly an octave). However, this was theoretical knowledge, and was not used to construct a repeating twelve-tone scale, nor to modulate. This was done later in meantone temperament and twelve-tone equal temperament, which allowed modulation while still being in tune, but did not develop in Europe until about 1500. Although popularized as the circle of fifths, its Anglo-Saxon etymological origins trace back to the name “wheel of fifths.”
The Development of Musical Tuning Systems
Peter A. Frazer
2001
Pythagorean comma
https://en.wikipedia.org/wiki/Pythagorean_comma#History
Chinese Cyclic Tunings in Late Antiquity
McClain, Ernest and Ming Shui Hung.
Ethnomusicology Vol. 23 No. 2, 1979. pp. 205–224.
Pythagorean tuning
https://en.wikipedia.org/wiki/Pythagorean_tuning
The system dates to Ancient Mesopotamia,[4] and consisted of alternating ascending fifths and descending fourths; see Music of Mesopotamia § Music theory. Within Ancient Greek music, the system had been mainly attributed to Pythagoras (who lived around 500 BCE) by modern authors of music theory; Ancient Greeks borrowed much of their music theory from Mesopotamia, including the diatonic scale, Pythagorean tuning, and modes. The Chinese Shí-èr-lǜ scale uses the same intervals as the Pythagorean scale and was invented between 600 BCE and 240 CE.[2][9]
Because of the wolf interval when using a 12-tone Pythagorean temperament, this tuning is rarely used today, although it is thought to have been widespread. In music which does not change key very often, or which is not very harmonically adventurous, the wolf interval is unlikely to be a problem, as not all the possible fifths will be heard in such pieces. In extended Pythagorean tuning there is no wolf interval, all perfect fifths are exactly 3:2.
Because most fifths in 12-tone Pythagorean temperament are in the simple ratio of 3:2, they sound very “smooth” and consonant. The thirds, by contrast, most of which are in the relatively complex ratios of 81:64 (for major thirds) and 32:27 (for minor thirds), sound less smooth depending on the instrument.[10]
From about 1510 onward, as thirds came to be treated as consonances, meantone temperament, and particularly quarter-comma meantone, which tunes thirds to the relatively simple ratio of 5:4, became the most popular system for tuning keyboards. At the same time, syntonic-diatonic just intonation was posited first by Ramos and then by Zarlino as the normal tuning for singers.
However, meantone presented its own harmonic challenges. Its wolf intervals proved to be even worse than those of the Pythagorean tuning (so much so that it often required 19 keys to the octave as opposed to the 12 in Pythagorean tuning). As a consequence, meantone was not suitable for all music. From around the 18th century, as the desire grew for instruments to change key, and therefore to avoid a wolf interval, this led to the widespread use of well temperaments and eventually equal temperament.
Pythagorean temperament can still be heard in some parts of modern classical music from singers and from instruments with no fixed tuning such as the violin family. Where a performer has an unaccompanied passage based on scales, they will tend towards using Pythagorean intonation as that will make the scale sound best in tune, then reverting to other temperaments for other passages (just intonation for chordal or arpeggiated figures, and equal temperament when accompanied with piano or orchestra). Such changes are never explicitly notated and are scarcely noticeable to the audience, just sounding ‘in tune’.
Viewpoints which Matter 