## The Samian Foot (of Samos), Saturn and the Moon

- Details
- Category: Planetary Harmony
- Hits: 799

Herodotus, the great 5th century BC historian, mentions that the key south-facing "datum" edge of the Great Pyramid was 800 feet long whilst in English feet, the best survey found it was 756 feet long. Dividing 800 by 756 gives a foot length of 0.945 feet (fractionally 189/200 ft). John Neal has called this foot the Samian foot, since Herodotus lived as a young body on the island of Samos, as did Pythagoras. Neal found another historical reference to the same ("Samian") module in the pre-metrification city standards of at least seven German cities; in Danzig the variation was the Root value for the module (33/35 ft), in Bremen the Root Canonical (x 176/175), in three others the Standard microvariation (i.e. x 441/440) and two more the Root (33/35).

The Samian module is therefore quite well attested by Neal as a historical measure, but my own work finds a new significance in it. Neal's Standard Canonical is a foot 0.945 feet long, where 1000 such feet are 945 English feet which, divided by 32, equals 29.53125 feet, the number of days in a lunar month. At Le Manio Quadrilateral, the 32nd stone from the "sun gate" origin of day-inch counting appears to signify 945 day-*inches* from which I discovered this relationship between 32 lunar months and 945 days of day counting, in any unit. Could the Samian foot (then using feet to count days) have used one thousand such feet to conveniently arrive at 32 lunar months? I will return to this, but also need to point to the apparent coding of 27 feet to represent months at the Crucuno complex. This led to finding that this same 27 regular feet is 29.53125 Iberian feet (each 32/35 feet), allowing days to be counted within a lunar month counted in units of 27 feet! One must also recognise that 27 feet is ten steps (viz. megalithic yards) of the Druzian foot from which the astronomical megalithic yard is derived as 176/175 of 2.7 feet.

## Distribution of Prime Numbers in the Tone Circle

- Details
- Category: Tuning Theory
- Hits: 1321

The ancient notion of holy mountains, intuited by Ernest G. McClain in the 1970s, was based on the cross-multiples of the powers of the prime numbers three and five, placed in an table where the two primes defined two *dimensions*, where the powers are ordinal (0,1,2,3,4, etc...) and the dimension for prime number 5, an upward diagonal over a horizontal extent of the powers of prime number 3. Whilst harmonic numbers have been found in the ancient world as cuneiform lists (e.g. the Nippur List circa 2,200 BCE), these "regular" numbers would have been known to only have factors of the first three prime numbers 2, 3 and 5 and, furthermore, the prime number two would have been seen as not instrumental in placing where, on such holy mountains, each number must appear. Thus, an inherent duality was recognised between seeing each regular number as a whole integer number and seeing it as made up of powers of the two odd two prime numbers, their harmonic composition of the powers of 3 and 5 (see figure 1). It was obvious then as now that regular numbers were the product of three different prime numbers, each raised to different powers of itself, and that the primes 3 and 5 had the special power of both (a) creating musical intervals within octaves between numerical tones and (b) uniquely locating each numerical tone upon a mountain of numerical powers of 3 and 5.

*Figure 1 Viewing the harmonic primes 3 and 5 as a mountain of their products, seen as integer numers or as to these harmonic primes *

## Harmonic Metrology: the Moon and Outer Planets

- Details
- Category: Planetary Harmony
- Hits: 491

The moon has enabled the semi-harmonic orbits of the outer planets (Jupiter, Saturn and Uranus) to become fully harmonic, expressing two of the three intervals necessary for the type of *modal* music found in the earliest civilization of the Sumerians. Harmonic Origins of the World plots how the ancient world from then on interpreted musical harmony as a cosmic principle, in which the harmonic planets were gods. This connection, between harmony, planets, and a divine world can only have emerged from the greatest astronomical culture in prehistory, responsible for building megalithic buildings and earthworks in many regions of the Earth, over the last seven thousand years.

This website uses the basic techniques of these early astronomers,

- alignment to horizon events, exactly counted time periods using fixed measures (
**metrology**), - triangular, square, rectangular and circular
**geometries**to enable comparison, calculation and simulation

to interpret their surviving monuments as to their purpose and thus learn from them what their astronomy might have revealed.

*Figure 1 New Dawn No. 168 for May-June, 56-60.*

Here I present how our historical metrology, which the Neolithic astronomers evolved, comes to have the metrological ratios that enable a single length to have modelled the synodic periods of the Moon (lunar year), Jupiter, Saturn (and Uranus). My recent article for New Dawn (issue 168) progresses, in one graphic, the ratios between the planetary synods and how these are transformed by the lunar year in its present length of 354.367 days. Probability not 100% proof can be offered; instead perhaps joy that such an ancient and important intellectual tradition should have come down to us in recognisable form, without writing.

## Musical Tones of the Outer Planets

- Details
- Category: Planetary Harmony
- Hits: 1314

First Published on Cosmic Harmonist with 6546 views.

The crucial entré to planetary harmony came when I noticed musical ratios in the synodic time periods of Jupiter and Saturn relative to the lunar year. This approach differs from the norm for "harmonies of the spheres" (a.k.a. Musica Universalis) that are geometrical and spatial rather than temporal.

My aim here is to prepare supporting material for my book, published March 2018, called *The Harmonic Origins of the World*, this by reviewing how these synodic periods were parts of my previous work from c. 2000, using "matrix diagrams". I will show (in my new book)how ancient tuning theory seems to have presented the same information. To avoid spilling all the beans I am now connecting the outer planets in a different (and useful) kind of diagram called the Pentad, evolved in the 20th century within *Systematics (more on that in previous article)*.

*Figure 1 The harmonic ratios between the nearest two outer planets and the lunar yearThe four square rectangle with side eaqual lunar year gives, geometrically, the solar year as diagonal length. The outer planetary synods are longer sincethe planets have moved ahead of their last opposition to the sun, whenthey appear to travel in a loop amongst the stars*

## Danielou's India and the Tritone

- Details
- Category: Footnotes
- Hits: 1325

Alain Daniélou wrote *Music and the Power of Sound, The Influence of Tuning and Interval on Consciousness* and a footnote in this is of interest regarding the role of the tritone in India. The trigger was a request to review a new book about Harmonic Geometry by John Oscar Lieben, which quotes a footnote in Daniélou, page 156:

51. The use in Indian music of the augmented fourth, or tritone, at the critical times of midnight and midday reminds us of the magical importance attached to those hours, and of the use of the tritone (

diabolus in musica) by Western musicians for the representation of magic, which is nothing other than the possible intersection, at certain critical hours, of worlds that cannot normally communicate. It is used conspicuously in this way by Schumann for the character of Manfred, by Wagner every time a magician appears, by Berlioz in theSymphonie fantastique, by Weber in Der Freischutz, and so on. In Chinese music theIü rui bin, corresponding to the augmented fourth, represents the summer solstice, the critical moment in the annual cycle when the masculine influx, hot and creative, gives place to the feminine influx, cold and destructive.

The tritone plays an important place in the work of Ernest G McClain's classic work *The Myth of Invariance*, informed by his contact with Antonio de Nicolas who studied the Indian tradition as habing been concerned with harmonic audition rather than extensive vision. Agni, the Indian god of fire, plays the role of tritone within harmony by enabling creativity as a liberating counter to cosmic and human egoity. I wrote this summary document; of what Ernest McClain wrote about Agni. With this in mind one can return to Daniélou's main text:

### The Periods of the Day

Page 2 of 3