Category: Harmonic Origins of the World

Agni, the Indian God of Fire

Those new to Ernest McClain and his The Myth of Invariance, should know this book was a seminal work for anyone in my generation, that opened up a Pythagorean vision; of how number operates in the domain of harmony. This world of harmony can be numerically defined in a quite extraordinary and specific way and we, as human beings, can receive it through our mind whilst also through the senses. This relates to the unusual fact that, whilst all notes can be doubled in frequency through the number two, with a perfect consonance, a new population of notes is then opened up, within an octave, of intervals that are also harmonious, through the use the two next prime numbers: three and five. Thus music, so effective upon the human heart, can build a world of meaning, sometimes referenced in myths as sacred numbers, written through understanding harmony as fundamentally generated through numeric transitions within music.

In 2008 I prepared a summary of Ernest McClain’s statements about Agni because, in the midst of the perfect symmetry of musical harmony lies something new, born to the world opposite its beginnings and endings. I originally made the pdf below for my friend Anthony Blake, part of our attempt to study the origin of creativity within the existing world. It appears that something important comes into being at the centre of this issue of octaval harmony, just as we ourselves come into existence in the middle of the universe, as conscious beings, conscious then of our incompletion.

It occured to me to include this in an email to Ernest and, all in, he said in reply “I can’t imagine anyone improving on your few pages” and “Put it out now on your own website stamped with my approval”. Please enjoy this transmission from the centre of the octave:

What Ernest McClain says about Agni in The Myth of Invariance:

Visit Ernest McClain website: Musical Adventures in Ancient Mythology. In the section of online documents, his books are available for your to study as links to pdf downloads.

The Richard Syrett Interviews on Sacred Geometry: Language of the Angels

I recently recorded a podcast with Richard Syrett and will be talking with him again today (January 2nd) on Coast to Coast, starting 10pm Pacific time. In the UK, this is tomorrow (Sunday the 3rd) at 6am GMT. Both these interviews are in response to my new book Sacred Geometry: Language of the Angels, which goes on release Monday 4th of January 2021.

Ways of Purchasing: This large-format book, richly illustrated in color throughout, can be seen in the sidebar (on mobiles, below the tag cloud) or visit Inner Traditions.

from Book 5: Harmonic Origins of the World

Intelligent Star Systems

The harmony of the spheres can only be found in our world of time, where it is a strong and compelling phenomenon. Such a harmony was no prescientific fantasy. Pythagoras, who coined the term, probably did so based on the geocentric time world, a view lost to history apart from cryptic references that can no longer be interpreted.

In our age of system science, musical harmony is not thought relevant to the design of dynamic systems such as the planets, yet they appear adapted to just intonation seen from the exclusive perspective of our planet. Why should our planet have a harmonious view of time, and what difference does time’s harmoniousness make to life on Earth? Is there some other purpose to this harmony or none at all? To answer such questions one has to recognize just intonation as being a holistic system that demands human insight into the nature of whole phenomena (a so-called gestalt). Such gestalts flow from the need to see higher-level relationships rather than the raw complexity of their parts. All higher structures of meaning subsume lower levels of meaning.  For example, microclimates are a structuring of meaning higher than  trees, water, weather, and topography, usefully integrating these parts within a newly perceived whole. Such insights reveal a higher idea that indicates new potentials within a system. The new level of conceptual order has not changed in the phenomenon but how we relate to it. This profound faculty is the basis of what we call understanding rather than knowing, and it enlarges our “world.” The world is already structured, and a sensory insight re-creates that structure as a simplifying aspect, already present, to expand the intelligibility of the sensory world and with it, our present moment. Insight and the world’s creation were considered similar acts within ancient cosmologies, in that an insight about the world resembles the structure of the world as it would be conceived by any god in the act of creating it. Such a vision involves a special effort but provides a creative view of the world, in which simplicity and relatedness replace functional complexity with a new appreciation of the sensory world. The celestial behavior in Earth’s skies is a prime example of such an action: the rotation of Earth, its orbit around the sun, the moon’s orbit, and its illumination by the sun complicate the observed orbital periods of the other planets and yet, that added complexity has produced harmonic simplicity between synodic periods!

Chapter 1 showed how Late Stone Age astronomers used geometrical counts of synodic periods to discover this harmony of the spheres, which modern astronomers have not seen because scientific calculation methods deal instead with planetary dynamics modeled by equations. Simplicity has somehow adapted our solar system without breaking physical laws. At the level of gravitational dynamics, many complexities were required to achieve just intonation seen only from Earth, especially the lengthening of the lunar month as an intermediary to the planetary synods seen from Earth. Any demiurgic preference for harmony (seen from Earth) resembles the human gestalt that revealed the harmony of the spheres to human sensory intelligence in the Late Stone Age, and it must be noted, humanity has become demiurgic since the Stone Age, creating man-made worlds.

Demiurgic intelligences are probably part of each star system and, if our star has a demiurgic intelligence, this action seems to have used the moon to establish a justly intoned time world for the third planet. It adapted the unchanging orbital pitches of an n-body planetary system to present harmonic synodic systems that planetary orbital periods alone could never express. Our geocentric system is harmonically founded between 1, the zeroth power of 2 (the Saturn synod) and the fifth power of 60 (YHWH, as 365-day year), which is the smallest numerical resolution to contain just intonation of both inner and outer planets, as in the implied holy mountains of our ancient texts.

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
Index

pdf: Astronomical Musicality within Mythic Narratives

Ancient musical knowledge came to Just tuning long before Greek music, in Babylonia. It now seems likely that two sources of musical information, were involved in an early tradition of musical tuning by number: firstly, the early number field is the original template upon which musical harmony is based; and secondly, the prehistoric geocentric astronomy which preceded the ancient world had been comparing counted astronomical time-periods, and had discovered the rational tone and semitone intervals between the lunar year, Jupiter and Saturn . Ernest G. McClain identified a harmonic parallelism within ancient texts in which the anomalous numbers found within mythic narratives inferred a unique array (a matrix) of whole numbers, shaped like a mountain, which could explain plot elements, events and characters of the narrative, as intended parallels to such harmonic mountains. McClain’s matrices allowed the author to locate the harmonic intervals found between planetary synods as a reason why religious texts should have employed harmonic numbers, these relating to planetary time as gods alongside ancient systems of tuning. Based on a talk delivered at ICONEA2013, 5th December at Senate House, University College London.

Harmonic Explorer app

The work of the late Ernest McClain [1918-2014] was based upon a technique in which ever higher numbers appear to have been studied in antiquity as to the harmonic field of intervals possible within that integer limit. Such a single number reference can be mentioned en passant within texts like The Bible, Homer’s Illiad or the Sumerian story of Gilgamesh and be ignored today as a frivolous use of large numbers, such as great ages of the gods, the number of ships, or tithe goods and so on, when in fact the numbers were referring to a musicological field relevant to the narrative and its elements.

McClain’s work was very briefly introduced in  Precessional Time and the Evolution of Consciousness (2011) in its Chapter 3 on the Age of Aries, when such calculational musicology/theology seem to have replaced the megalithic activities in Age of Taurus. After then collaborating with Ernest for a few years, after his death I attempted to make an accessible book on Ernest’ work in my 2018 book Harmonic Origins of the World.

Ernest had a fine sensibility for the Ancient Near East (or A.N.E.), its number science and symbolisms. Through many email exchanges I wanted to be able to generate his tonal diagrams for myself; to both learn more and answer specific questions. I was able to make a web page so that people like myself could more easily enter his world of tonal yantras (that look like mountains) and their corresponding tonal mandalas (the octave circle); without having to learn the method of “limiting the products of powers of three and five and then doubling all numbers to the limiting number”. This Harmonic Explorer app enables ridiculous freedom over the previously required manual calculations, including walking through limiting number space with prime factor buttons, multiplying/dividing by 2, 3, 5, 10 or 12. It can also be very useful for screen grabbing when discussing a given tuning system as in:

TRY IT NOW HERE: Harmonic Explorer

Ernest’s website has study pdf’s of his books and papers plus other resources.

pdf: Musicological Narrative Structures in Biblical Genesis

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.