- Category: Planetary Harmony
- Hits: 798
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 Neal found another historical reference to the same ("Samian") module in the pre-metrification city standards of at least seven German cities; in Danzig the variation was the Root value for the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.
- 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 the Symphonie fantastique, by Weber in Der Freischutz, and so on. In Chinese music the Iü 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
- Category: Planetary Harmony
- Hits: 286
NE Cairn; half an hour before sunset [photo: Ian B. Wright, 2009]
My recently released book, Harmonic Origins of the World (HoW) spliced,
- the ancient tuning theory implied by a wide ranging use of harmonic numbers in the ancient world (post 3000 BC) onto
- the advanced solar and lunar horizon astronomy of the megalithic in Brittany, Britain, and Ireland.
using my early finding (Matrix of Creation, 2002), that the lunar year has harmonic ratios to the visible outer planets.
In other words, the megalithic were led to find the whole tone and semitone ratios to Jupiter and Saturn through their work of counting the synodic period between the loops of these two planets, these results being responsible for that information (and their wider astronomical tradition) leaking into the foundations of what we call history. Later traditions, such as The Harmony of the Spheres, would allude to this prospectus: that the Earth had a musical planetary environment.
This article explores a megalithic complex called Clava Cairns, near Inverness, Scotland, and finds first evidence that the megalithic counted the synodic periods of Jupiter and Saturn and used this knowledge to inform the dimensions and design of these cairns. This might give clues as to how sun, moon, and outer planets were informing the design of monuments of those and later sacred spaces. A previous article on the alignments found at Clava cairns is in the British Megaliths section of this site
Some Metrology at Clava Cairns
Alignments to the solstice sun are at least symbolic of the solar year in between of 365 days. At Le Manio Quadrilateral one finds a count over three solar years of 1095 day-inches along the mid-summer solstice sunrise alignment and so counting was tied to the solstice sun in 4000 BC, in Brittany, and the strongest solstice alignment at these cairns is that of the passageways of the NE and SW cairns towards midwinter sunset. I will therefore look at the distance between these two cairns whilst also looking at other features and geometries associated with accurate time counting in days.
Figure 3 The distance between the small circular centres is 399 feet
- Category: Footnotes
- Hits: 1494
page 1: Agni, savior and god of fire, is himself "the holy Singer who precedes the sages . . . waxen mighty by laudations" and the secret he alone can impart is a certain "lofty Hymn". (3.5.1-2 and 4.5.3)
page 6: [regarding tenfoldness] ... and ten is the number of piles of wood for the fire in which Agni is born as well as the number of his secret "dwelling places."
page 37: [regarding tone mandalas] But it is equally legitimate to consider D = 360 = 720 at the top of the circle as "1" also, in the sense of the geometric mean whose "appearance" has been changed to avoid fractions. Now a-flat lies somewhat askew from the symmetrical [Asvin] twins we have been studying; it is near the locus of the square root of 2 which would have put the equal tempered A-flat = G-sharp precisely at the bottom of the circle, directly opposite D. It is in this region of the of the circle, I believe, that Indra will be born later as Indra-Agni, god of fire, not as a "point" in the circle but as a segment of the circle. The Rg Veda describes this birth as that of a kind of "breach baby": "Forth from the side obliquely will I issue" (R.V. 4.18.12). There is no integer at the locus in question. The great expansion of the number sets in later diagrams is motivated, I believe, by the effort to approximate as exactly as possible the irrational square root of 2 which is needed to locate a tone symmetrically opposite the mean on D, that is, precisely in the middle of our octave.
page 40: [regarding Vishnu's three steps]
Among the skillful Gods most skilled is he,
who made the two world-halves which
bring prosperity to all;
Who with great wisdom measured both the
regions out, and established them
with pillars that shall ne'er decay.
- Category: Tuning Theory
- Hits: 1725
Marduk is a character like Indra who was associated with a very large number and antediluvian floods, though Noah seems adapted not to mention 8,640,000,000. The reality of these floods is based upon an idea revealed in this number. The head number 864 is the earliest which can form the seven note heptatonic octave whose intervals are far from perfect. Winds can be viewed as blowing into the octave's tone circle, and the heptatonic has seven but having defined seven tones (including the tonic here to be called D) the gaps remaining between B and C and between E and F, that we call semitones, are unplanned so as to be numerically and acoustically imperfect as equal the ratio 256/243, This imperfection was called by Pythagoreans the leftovers (leimmas), and they highlight the fact that when a cycle of fifths and fourths emanate from D (clockwise and anticlockwise within in the octave's tone circle), powers of three can only be eliminated to achieve the exact 2 required of octave doubling, by a semitone fraction involving three to the power of five = 243 (figure 1).
Figure 1 The Serpentine cycle of ascending and descending fifths leading to the Pythagorean Heptatonic using imagery generated by Harmonic Explorer.
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