Tag: Ernest McClain

American Musicologist who decoded the cryptic numerical ciphers in Plato’s Dialogues

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 I originally made the pdf below for my friend Anthony Blake, part of our attempt to study the origin of creativity within the existing world.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.

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.

Harmonic Earth Measures

The Size of the Earth’s Meridian

It appears the ancient world had unreasonably accurate knowledge of the size of the earth and its shape: Analysis of ancient monuments reveals an exact estimate for the circumference of the mean Earth, a spherical version of the Earth, un-deformed by it spinning once a day. Half of this circumference, the north-south meridian, was known to be about 12960 miles (5000 geographical Greek feet of 1.01376 ft), a number which (in those Greek units) is then 60^5 = 777,600,000 geographical Greek inches. One has to ask, how such numbers are to be found very accurately within a planet formed accidentally during the early solar system?


Figure 1 The Earth as a circular Equator and a spherical Mean Earth, whose half circumference approximates the non-circular distance between north and south poles

John Michell’s booklet on Jerusalem found (in its Addendum) that the walls of the Temple Mount, extended for the rebuilding of the Temple of Solomon, was a scaled down model of the mean-earth Meridian in its length. These walls are still 5068.8 feet long, which is the length of a Greek geographical mile. This unit of measure divides the meridian into 12960 parts, each a geographical Greek mile.

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Harmonic Genesis of the Sumerians

The emergence of 2, 3, 5 from ONE then combining as ANU and leading to the differentiation of the World along various paths. The creation proceeds through three prime number dimensions, Ea (as in Earth) through 2, Enki through 3 , Enlil through 5. Anu remains the fountainhead associated with all three and with the Zodiac, which emerged in later Babylonian as a seasonally relevant calendar.

Here I start by publishing an important diagram that shows how the earliest known references to musical tuning (early 4th millennium BC) on clay cuneiform tablets, using “regular numbers” whose factors are products of only the numbers 2, 3 and 5, led to the cosmological vision of their gods, the primary god, Anu, being a balanced mix of all three numbers as 60 but also called ONE. This is the source of their Sexagesimal  or base-60, still employed in measuring angles and time called minutes and seconds. All comes from ONE.

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