Transmission of Astronomical Musicality into Mythic Narrative

Heath Transmission of Astronomical Musicality into Mythic Narrative By Richard Heath https://independent.academia.edu/HeathRichard ICONEA 2013 ©2013 all rights reserved, not for independent distribution

Introduction to the Parts 1. The Planetary Gods of Myth have Musical Ratios with respect to each other’s astronomical time periods 2. Before the gods were characterised, could Prehistory have discovered astronomical ratios using the prearithmetic form of Numeracy, found in the Upper Paleolithic and Megalithic monuments ? 3. …..

Parts 3 and 4 3. The numeric origin of musical invariance actually originates from the structure of the early number field (1-81). 4. Beyond these smaller numbers lies a world of rational tonal LIMITS, studied through balanced tuning, within an arithmetic Numeracy developing in the A.N.E. - this inherited by Plato and pioneered in our time by Ernest G. McClain (for whom I wrote the web application: Harmonic Explorer.) 5. ….

Part 5 5. The Nub of my work has been my use of Harmonic Explorer to locate the planetary ratios of “the gods”, in the numerical limit for 1440 Astronomical Musicality arises naturally out planetary resonance, which prefers to stabilise gravitational systems around such ratios, like the human ear, around products of 2, 3 and 5.

Part 6 6. Numeracy: The role of pre-arithmetic numeracy in prehistory is necessary for interpreting what the Upper Paleolithic and megalithic achieved before the A.N.E., through their study of numerical invariants.

1. Planetary Musical Ratios These became clear to me in 2000 (CE) At that time I knew little about the structure of music I published Matrix of Creation with my findings My next two books, Sacred Number and Precessional Time, saw further connections between cultural narratives about gods, built structures and numerical and musical ratios

Some Planetary Musical Ratios 1. 1.1 Jupiter and the Moon • Jupiter, the largest planet, appears to have brought the lunar year into the harmonic ratio of a Pythagorean wholetone, 9/8, relative to its synod. • In Hesiod’s Cosmogony, Jupiter deposes Saturn, father of the Titans, and forces the God of Time into retirement.

Some Planetary Musical Ratios 1. 2. Saturn and the Moon • Saturn, the second largest planet, appears to have brought the lunar year into a harmonic ratio of the Just semitone, 16/15, relative to its synod. • Saturn, God of Time would have a whole tone to the lunar year if the month was 28 days.. but, Saturn’s synod has the semitone instead, having been “deposed” • Saturn’s synod is exactly 52 7-day weeks, 13 x 28 day “months”, 27 to the 09/09/2016 ICONEA 2013 “Saturnian year” of 364 daysSlides andof Richard 18 toHeath 19 for relative to the Jupiter synod

Some Planetary Musical Ratios 3. Venus The Evening and Morning Star • Venus, the largest inner planet, has a synod that is a Fibonacci of 8/5 earth years and an orbital period of 8/13, thus approaching the golden mean through a musical ratio. • Venus arose when Cronos Saturn cut the genitals of Okeanos/uranos, the sky god, creating LIMITS bounding the outer solar system • Notice Venus stands on Saturn’s shell sickle, used for the emasculation • FIVE has become symbolic of Life and Beauty along with Golden Mean

Some Planetary Musical Ratios 4. Venus and Mars 3:4 Venus’ 584 days also generates a musical fourth to Mars’ synod of 780 days • In Homer’s Odyssey: Venus-Aphrodite, lover of Mars, was caught by husband and smith Hephestos when he cast a “net” over the couple’s love making • Venus and Mars link the two species of 1. Inner planets which only appear around the Sun 2. Outer planets which, like the Moon, traverse the sun’s path of their own volition

Some Planetary Musical Ratios 5. Eclipse to Solar Year 256/243 • The Eclipse Year* (346.62 days) defines a Pythagorean Leimma to the solar year (365.2422 days). * the time taken for the Sun to revisit one of the Moon’s nodes • The Leimma is found in Pythagorean heptatonic tuning. • Megalithic chambered tombs often point to the maximum standstill of the lunar nodes every 18.6 years

Some Planetary Musical Ratios 6. Lunar Month to Lunar Orbit 27/25 • The Lunar Month* (29.53 days) defines a semitone of 27/25 to the lunar orbit (27.322 days). * the time taken for the same phase to be repeated • This ratio of 1.08 is 1/100th of the 108 associated with the Moon and Shiva

2. Stone Age Astronomy In 1992, my brother introduced me to a triangle he thought in use by the Megalithic in Britain, to compare solar and lunar years – he calls the Lunation Triangle. This led to the utility of seeing relative astronomical periods as geometrical ratios (Musical Harmony also uses ratios usually normalised to N:N+1, as in 8:9) In 2009 we discovered a lunation triangle where the megalithic yard had been defined by a triangular comparison of two day-inch counts How could this happen without arithmetic?

Stone Age Astronomy: Geometry and Lengths The Lunation Triangle at STONEHENGE as proposed by Robin Heath in 1992, was only found in 2010 at Le Manio, near Carnac.

2 Stone Age Astronomy: Numeracy • Were there earlier forms of Numeracy? Such as Upper Paleolithic, on bones The Ishango Bone, a bone tool dated to the Upper Paleolithic era and now believed to be more than 20,000 years old. It has been interpreted as a tally stick but also as a medium for a Stone Age awareness of prime numbers. It was found in 1960 by Jean de Heinzelin de Braucourt while exploring what was then the Belgian Congo. Image courtesy of 09/09/2016 Wikipedia.

2 Stone Age Astronomy: Counting In Roots of Civilisation, Alexander Marshack stayed upon a rich seam of apparently notated bones in European Museums These marks appeared to focus on the possibilities of making a daily mark on the bone whilst the moon was visible and then counting invisibility according to some difference in marking a technique Marshack called time-factoring

Thais Plaque Fashioned from a Midden Bone NON-ARITHMETIC COUNTING of days, months and half years As oi Dated to terminal Madgalenian or early Azilian c. 10,000 BC E. ce e e esxe a F e ai de si a 4v 4 St) x | eee CAS A E AB pe LULU Vi Soon 8, no 12 ASdes È EE.mm 8 rcr 14ry+: MLL L nen) 5 8 3 a Pr = e eu 14 y —_ PAUL _® _14_l 16 ., 12 i ae 1 ALL mitt Lg Lu ne) pali MIR 1 L 26 fi qui N ul un 23 mn) U iy MMM IAN LL ni = tong DEP 12 Pi mio me 6 qqmmm =]8 seve eM gi dg si gi tig iae 7 Alexander Marshack (1991). The Tai Plaque and Calendrical Notation in the Upper Palaeolithic. Cambridge Archaeological Journal, 1, pp 25-61 doi:10.1017/5095977430000024X

2 Stone Age Astronomy day-inch counting • Around 5,000 years after the Thais Plaque, megalithic were being constructed, again in France, this time in Southern Brittany near Carnac • One unique site, called Le Manio, is carefully laid out with a stone kerb geometry, the Quadrilateral, north of a large Menhir Geant using 34-5 and 12-13-5 triangles in Megalithic Yards.

CF)+ Le Manio Quadrilateral .» Late Fifth Millennium Rectalinear Kerb of Stones near Carnac in southern Brittany. France PRE-ARITHMETIC COUNTING AND COMPARISON of days and months over three years e using day-inches *. and right angled triangle ser I Q’ — — — — e THREE Lunar Years — — — — — — — — — —— THREE Solar Years — — — — — — — PRE-ARITHMETIC COUNTING of days, months and halfyears — — ——— Ul — _

2 Stone Age Astronomy: The Inchometer This enables the development and understanding of invariant ratios based upon whole number day counts or simple musical ratios of string length We can see that • numbers-as-lengths and • Angular comparison Was a • Simple to access technology • Proceeded from Stone Age time-factoring Le Manio’s Quadrilateral was 09/09/2016 an Inchometer

Ancient “Whiteboard” at Cachao-da-Rapa (3500-3000 BCE) Multiplication as Unit Areas HH 2x2=4 E Colour Coded by factors of primes 7 2,3 and 5 4x 4=16 4 fingers + 1 thumb 6 missing diagonal = 5 3 x 4 Squares

3. Musical Invariance We have seen that astronomical periods provided an ongoing signal which the stone age appeared to receive, the sort of signal that was an external invariant rather than the signals left by evidence To understand artifacts derived from an invariant signal requires that one study that invariance Some planetary periods relate according to the additional invariance we call musical harmony, and megalithic artifacts and techniques were naturally suited to studying the lengths of strings

How the Number System “packs” the Octave’s Tone Circle Successive numbers “Just” tuning applies “closure” on the would divide up the “tone tonal field for the Fifth and Fourth using universe” without end only Harmonic Numbers (4/3 is 5/4 times 16/15) B SCALE DESCENDING 15/14 C= 16/15 pue de ASCENDING D 16/15 9/8 AT > 2/3 LI MAJOR FOURTH % rm OCTAVE

7 # 76 25/2476 10/9 4 9/8 Bus EKO 16/15 10/9 È | 1/150 È E iii 10/9 -- ge u: E 9/8 9/8 25/24> = 1615 À 98 E = de (Pi; 5 Nabnitu XXXII* — fedi = . u © la > i i ge i 3 mei i Hin SE 4 | ©! ¡31 = (PGE A =; Al en ii ii 4 aa 9/8 Too sul = td ia i! a)a; ins: i =; 5 = izi ini iQ a eni : 2 di ] fl h E order of tones. E 4°. - - - - - 98 si B I32 A is o: 5 LU de ee + 306 16/15- ce o Fri AI «e er cere Mi SIR RR — * See Dumbrill, ICONEA 2008, Evidence and Inference in Texts of Theory in the Ancient Near East = POT Ga Se mn — a eee dye TTT 10/9 ei GSi Pb — bie a TssF ll - nié (e iP u u STO E A bi length capable of = il +ar were the least string {EL - generating a coherent -.- i} ie —i 1615 > E ie i i. ETS described in * ¡A iL _ | o GE —27/25 RE ES 2 RA RA A A nt Vem Gan A A A — E A A u A, IA A — . — . —. — fiere Direct Transmission of Just tuning from the Number Field, via String Lengths up to 80 units of length by Richard Heath mm (n MIO SM ie iene Emmen Gue Heme) eh O ec

The Hindu Temple Plan with “Just” God in the Centre Extracted from George Michell's The Hindu Temple by Richard Heath, September 2013 | “Accompanying this penetration inwards towards the cave is the ascent upwards to the symbolic mountain | peak, whose summit is positioned over the centre of the cave-sanctuary. This means that the highest point of the elevation of the temple is aligned with the most sacred part of the temple, the centre of the inner sanctuary which houses the image of the god. “The temple becomes an architectural facsimile of the sacred places of the gods, providing for the worshipper the merit that would be his through an actual visit to the mountains. Meru is the centre or 'navel' of the universe, standing as a reference point for the surrounding and concentrically arranged continents, oceans and heavenly bodies. “The mandala governing the temple plan, following the Brihatsamhita, a text dating from the Gupta period. Brahma occupies the central nine squares and is surrounded by various planetary divinities, including the Sun and Moon”, within 9 by 9 squares equalling 81. “The mandala governing the temple plan, 9 following the Brihatsamhita, a text dating from the Gupta period.” “Brahma occupies the central nine squares “ [and is surrounded by various planetary divinities, including the Sun and Moon, within 9 by 9 squares equalling 81.] y oo, o E oo o

4. Invariance within LIMITS In 1976 Ernest McClain published The Myth of Invariance. He proposed that our greatest ancient literature had an undercurrent of numerical reference to the realities of musical invariance. His work on reconstructing the underlying rules of numerical tuning theory lead to “holy mountains” generated by a single limiting number as D, our “note” signifying do on the axis of symmetry, within octave tone circles and on modern keyboards.

How Holy Mountains are Numerically Born, First by products of 3 and 5 Then by 2 to reach Octave Limit = Using A.N.E. Arithmetic and obtaining large 32 48 36 54 relative string lengths as numbers \ 3125 5° 54 625 1875 Step 2: Double to N > 30 (Powers of 2) 125 25 E 5 15 es 1 52 | 9 i 1: Building 225 675 Blocks for N < 60 y (Powers of 3 and 5) 51 15 45 135 405 27 — Step 75 1125 45 es 3 25 375 5 1 3 9 27 81 243 KK

The Harmonic Trinity Primes 3":4":5" interacting to form Plato’s “4/3 mated with 5” Archetype of Harmonic Mountains

4.3 Invariance within LIMITS: 60

4.4 Invariance within LIMITS: The World of 60 Plato’s TWINS are symmetrical in ascending and descending and shown darkened

4.5 Invariance within LIMITS: 12 – Three Tones

4.6 Invariance within LIMITS: 144 Pentatonic Diminished Minor Thirds

Pythagorean Heptatonic Limit: 864 { 25 33 5°} with 7 reciprocals among 19 bricks

LIMIT = 864 Pythagorean Heptatonic 9 /

4.10 Invariance within LIMITS: 8640 Just Chromatism The Cure for the serpent is to be raised as D by FIVE and become a “ten-borne one”, giving Just tuning alternatives to comma sticken cyclic fifths as was the case with 60 earlier.

A Vedic “lightning” strike: “one auspicious moment” in the “flood” of new insight Musicological relationships based upon the ideas of Ernest G. McClain and Antonio de Nicolas PIERCING THE TWENTY ONE MOUNTAINS of the Himalayas (Mahabharata) wer 620) : 22277773 H (Swen ces! t 159003 241) a (es ize) { (Rae 616) ; wei | mc H (rua ci) i (ems 415) FOR Foo 900) TOBSSELED | SSHnme uses.| 8970866055 | HBEORHNFEL | SSTOLLES | SO0LPEOESO | ugroseser |¿POSTEOS | GOT ES a Y "= eo Y ias vasSo) rs 7 aa 7) i se Lightning on the Mountain Te metaphor of Tregunta, Indra, SEELOFIIES l'osceorerze 0259095975 DOCSLELESO | OHTOSDTESFr Pr)i| O9LESGTOLE | OPESSÉTHES |OTT'IPESSTL | 0205674 O Ay nn i a |HR à 3 ad gad Tea aa) OSTSOOLSFD | OOTHFESONS | 00ST9S66LS OOFOSLTS9L |“costes tors am Tea MR Marduk, Zeus, &ar ‘nies pal "1° asa rest.| 009LI99F09 | O0SOSTTONS (ewes si) | er medie an i (5030 500) Hi (RIO po + 3 PTT asas als were Br 0 ce + The Mountain “upside down” is iscrreesse sia a Garuda's body of symmetries i. OSFZLUHE plus that eagle’Ss matie RESO TESS Limit: 8,640,000,000 (2123 57) among 166 bricks . sa aeons me en ons:2 Fat Basen 00054 od1679 | 000/8098888 TSI and TWENTY ONE brick foundation STD SOLE0ES sco oooscrise: sos . at the v2 AGNI Point (A b -G#) . is KILLED by an Indra Flood in which 8640 (inset below), Did |” Srish fesso gan) Steno ize To) ? : TWELFTH symmetrical Fifth | (containing the SEVEN Tones of Heptatonic) is raised to the SEVENTH power of FIVE SLESSTZAGE | 00571099 000549 82F+ | 0000064065 | 00000ZELSL | The Sinofthe oes 2 OSTIILRLES | OOOSISTLGL | OODOIFFIES : 00DOBESBOL| OOOOZEEZLE 000095869| with 73 reciprocals VedicLightningStrike drawn: Richard Heath, June 2013 e OOTLELEESL costo | seas 00r 9880119 è, un das er NC orti Bn ela | ] STVOFSOSES | OSESFFLTE 000696 780 + | 00OTEZLLED | 000950£058 0007018995 | OOOTLTESSL | 0008188805 | OU FOF SIL [OPEN a nNOS SU No | Semo agi (mo) rs 20000 STTEOTEI9E| 00514 8640 rises up the side of the mountain with SIX fifths & a full set of Just tones above and below VRITRA’s HEAD

5. Orbital Resonance In celestial mechanics, an orbital resonance occurs when two orbiting bodies exert a regular, periodic gravitational influence on each other, usually due to their orbital periods being related by a ratio of two small integers. In physics, the n-body problem is an ancient, classical problem[1] of predicting the individual motions, and forces on same, of a group of celestial objects interacting with each other gravitationally. http://en.wikipedia.org

5.1 The Key to Jupiter and Saturn • The 9/8 of Jupiter is a Pythagorean wholetone • The 16/15 of Saturn is a Just Semitone • This would imply in the world of LIMITS, a tuning system having 9 = 32 and 5 in its limit which gives a ROOT of 45, the root of Plato’s Calendar Octave

The Anatomy of Plato’s Calendar Octave developed from 45:90:180 to 360:720::720:1440 Where 18 Platonic male Version. 1-2 elements of 3x5<720 reduce to drawn for Ernest McClain and Antonio de Nicolas 12.6 pairs through the uncounted by Richard Heath, September 2013 center LIMIT 720 The mixed powers THREE & FIVE on u at ensure cyclic return to D=45, and characterize the a nO Adam (as irreducible 45) and yn AS wf octave's tones, as with, in Hebrew, 625° y + Abram (as “explorer” at 243). x 125 | 478] 1125), > > Mi =. 25.1 75 | 225 | 6754 + 9 ~ uy = pr" > 45-4 45-1:(45)1-135-4-408]-12415-1-> LS 20°” squat v ETA AS av AAA y ———- 9 | 27 AA x 2 % [781 | 243.) 729 >> Et "à Reciprocal powers of 3 and 5 ensure reflection to the center in a self-restorina Universe. Plato’s "Small and Great" 12-tone chromatic octave 360 is "no more than half" of 720, and 1440 is also "no more than double," but rather it is BOTH through the double octave, 1440:720::720:360, > a range of 4:2::2:1; Pythagorean Justice thus remaining "on 360." For Plato this meant 2 years ofpreliminary training, reversing course the 2nd year. For Babylon it meant only the 180 days of the half-year, taken twice.

Limit: 1,440 {253251} with 13 reciprocals among 21 bricks G= 960“ D=720:1440 A=1080 12 Lunar Months 9:18 13.5 Lunar Months Lunar Year Lunar Months Jupiter Synod a » 1024 12.8 Lunar Months Saturn Synod UNITS = Lunar Month + 80 = 0.369 days

6. Prehistoric Numeracy It seems quite clear that a lack of A.N.E. arithmetic need not have held back the Neolithic inheritors of a fruitful interest in the sky and the carving of time-factored bones. Indeed, the megalithic of NW Europe has left evidence in the megalithic of a number science based upon numbers-aslengths (and areas) and the utility of right angled triangles and circles. Useful calculation was possible without arithmetic.

6.1 Prehistoric Numeracy: Numeracy and Invariance The megalithic understanding of astronomy was of invariant ratios between synodic periods, some musical. Unlike our own astronomy, this requires some familiarity with what monuments might have been seeking to achieve. Numbers-as-lengths could give access to musical invariance through forming musical string lengths and studying interval ratios

The Value of Invariance to Ancient Studies Invariance within evidence has been an unpopular “language” within ancient studies, perhaps because people believed it signified an unscientific and religious idea, of a Designer. However, in the case of the musical ratios between planetary time periods, orbital resonance is known to be a stabilisation of planetary orbits into low number relationships. Musical invariance involves low numbers and so it appears as dominant in the musicality of the Moon, Jupiter and Saturn. Hence, our gods naturally obtained a myth of invariance involving their behaviour.

The Different Levels of Numeracy to be Expected within Prehistoric, Ancient and Classical Peoples Level ONE Level TWO Level THREE TIME FACTORING METROLOGY ARITHMETIC Mathematics of the Eastern Mediterranean | 1,000 BC Egyptian and Babylonian Mathematics u. | >> + 2,000 BC British Isles, Sumeria and Egypt | nt 3,000 BC Megalithic of Carnac and Brittany ad ' ee 420222220200, 5,000 BC 8 Late Paleolithic - of Central : France 0

Where Next? • Do try out www.harmonicexplorer.org and onpage links to a related blog and late Ernest G. McClain webpage. • A paper for this talk is soon to be published by ICONEA.org as Conference Proceedings for ICONEA 2013 • For megalithic: see slides for my Megalithomania 2015 talk at academia.org and look at www.numbersciences.org • My author website is www.richardheath.info