Return to Free Library

Return to Number Menu

Previous Article                                                                         Next Article

We will now discuss one important aspect of the Octad – that of Octaves.

We have discussed octaves many times before throughout Cosmic Core.  We will bring that information together here.

Octaves

The octave is totally dependent on the divine, mystical qualities of the 7, but takes it one step farther.

The eight represents the octave.

Octaves show up in music, as the eighth note is the exact same as the first, but in a higher octave, or higher frequency (vibration).

They show up in the electromagnetic spectrum, where the wavelengths of light repeat spiraling in both directions, becoming shorter, faster and more dense as they move up the scale, and longer and slower as they move down.

We can only perceive a tiny portion with our 5 senses…knowing all the while that all these other frequencies exist, and are real, just unseen.

Astronomers tell us that 90% of the universe is invisible to our eyes but can be detected with sensitive equipment.  This includes radio waves, microwaves, X-rays, gamma rays, cosmic rays…etc.

This is a key point of the new scientific paradigm.  Traditional science essentially “cuts off reality” at the Plank scale – claiming that wavelengths shorter than the Plank length do not exist.  This is called renormalization.  It is a pure denial that the spectrum of wavelengths continue to extend to infinity in both directions (the small & large).

As the Reddit commentor oldcoot88 explains…reality should not be cut off at the Planck length.  “The great bulk of ‘What Is’ in terms of energy-density, resides on the ‘other side’ of the Planck length – the subPlanckian Energy Domain – with ever-finer scales of pixelization – each ‘sub-pixel’ of ever-higher energy density, ad infinitum.

We see repeating spiraling octaves to infinity in sound, light & chakras.

Taking it one step farther, as the comment above suggests, it is possible that reality itself is arranged this way – into spiraling octaves of levels of consciousness that our soul journeys through towards infinity.

These levels of consciousness are otherwise known as densities, or ‘seven heavens’ or the ‘Rainbow Bridge’.  These are seven major thicknesses or “quantum densities” of the fluid-like Aether medium.

This concept of spiraling octaves of levels of consciousness is a key teaching in the esoteric stream of knowledge and Perennial Philosophy.

This is the perspective Cosmic Core takes of the journey of transformation through the universe, through life and death and through timelessness.

The Octave in Music

The octave signals the movement to a new level.

The piano has 8 white keys from C to C – the 8^th note signals the octave.

The 8 white keys and 5 black keys produce all the sharps and flats in the chromatic scale making 12 notes, the 13^th note begins the next octave.

Between each step of the chromatic scale there are 12 major overtones.

The 12 major overtones between two notes are a replica of the larger pattern – it is holographic – it goes up and down to infinity.

This is called a geometric progression in harmonics.

There are 12 notes in an octave and 12 overtones between each note making 144 levels between each octave.

All the sub-overtones and sub-sub overtones are superimposed over each other and every point in space and time contains them all.

The Octave

A string length exactly half of the original will result in a tone exactly twice that of the original.

This is the concept of halving = doubling we return to again and again in Cosmic Core.

½ has created its mirror opposite: 2/1 – or halving = doubling.  This is expressed as the ratio of 2:1.

It is a tangible experience of the simultaneity of opposites.

It is an auditory perception of a simultaneous interwovenness of interior with exterior.

It will create the same note, but one octave up.

“An octave sound has the strange characteristic that it is of the same quality as the fundamental tone, so much so that it seems to blend into it, yet it is definitely higher in pitch.”1

The octave creates the tone of concord.

It is the foundation upon which to build the musical scale.

Robert Lawlor tells us, “For Pythagorean thinking, the sounding of the octave (an octave is for example two successive ‘do’s’ on a musical scale) was the most significant moment of all contemplation.  It represented the beginning and goal of creation…  It is the same note, yet it is different; it is the completion of a cycle, a spiral from seed to new seed.  This timeless, instantaneous recognition (more accurate than any visual recognition) is universal among humans.”2

He goes on to say, “The experience of hearing the octave contains the mystery of a simultaneous sameness and difference.  This quality of perceiving both sameness and difference is part of the poise of mind that sacred geometry means to cultivate: one which is precisely discerning yet harmoniously integrating.”3

Geometry of One Octave (Halves)

The octave can be expressed geometrically in various ways.

An equilateral triangle in a circle defines the octave as its circumcircle is twice the diameter of its incircle.

The circumcircle (outer circle) is twice the diameter of the incircle (the inner circle).  This creates a ratio of 2:1 which equals the octave.

The yin yang Taoist symbol expresses the octave in a profound way.  There are two equal circles within the larger circle.  The diameter of each smaller circle is exactly ½ that of the larger circle.

Geometry of Two Octaves (Quarters)

The geometry of two octaves can also be expressed geometrically.

See page 84 in the Quadrivium.

This is seen in:

• A circle within a triangle within a larger triangle – two triangles
• Decomposed squares – Four squares
• A pentagon in a pentagram

Octave-shifting

Cosmic frequencies, like very low frequencies of planetary motions can be octave-shifted, or multiplied by 2 many times over to get the same note in the audible range of frequencies.

For example:

Earth frequency = 1 cycle per year

1 year = 31,556,926 seconds

Earth Frequency = (1/31,556,926) Hz = .000000031556926 Hz

Multiply by 2, 36 times and get 136.1 Hz

136.1 Hz is C#, the note of the Earth year, 36 octaves higher.

Resonance

“The idea of periodic recurrence is at the heart of “resonance,” or resounding, the same note an octave apart.”4

Michael Schneider writes, “Resonance occurs between plucked strings as they are continually halved or doubled in length, creating the same tone in higher or lower octaves.  Similar musical notes across any number of octaves will resonate with each other just as they properties of atoms resonate with those listed above and below them in the Periodic Table.”5

Resonance & Radios

Resonance in oscillating electronic circuits led to the idea of tuning a radio to receive multiple channels.

The radio receiver resonates with the broadcast waves of a specific station.

Taking this idea further, one can image that our consciousness can ‘tune in’ to different dimensions of reality just like a radio tunes into different channels.  Our various brainwave patterns can give a hint into this idea.  We also experience this ‘tuning into’ different dimensions when we dream at night.

Resonance & Seeing through Glass

Light strikes the glass surface.  The silicon dioxide molecules absorb the energy and oscillate with it, ringing like microscopic bells, vibrating in the same range as visible light.

Nearby ‘molecular bells’ absorb the energy through resonance and ring with the same note.

The vibrations reach the other side and emerge as light nearly identical with their entry vibrations.

“In actuality we are seeing light that has resonated through matter.”6

Resonance & the Law of Attraction

The Law of Attraction relates to The Hermetic Doctrine of Correspondences & the Law of Analogy of Similars.

In the Kybalion, a Hermetic text, there are seven principles upon which the Hermetic philosophy is based.  The second of these is the “Principle of Correspondence.”

“This principle embodies the truth that there is always a Correspondence between the laws and phenomena of the various planes of Being and Life. The old Hermetic axiom ran in these words: “As above, so below; as below, so above.” And the grasping of this Principle gives one the means of solving many a dark paradox, and hidden secret of Nature. There are planes beyond our knowing, but when we apply the Principle of Correspondence to them we are able to understand much that would otherwise be unknowable to us. This Principle is of universal application and manifestation, on the various planes of the material, mental, and spiritual universe–it is a Universal Law. The ancient Hermetists considered this Principle as one of the most important mental instruments by which man was able to pry aside the obstacles which hid from view the Unknown.”7

Micheal Schneider writes, “Consider that our inner world is an energy system.  Each urge, desire, emotion, thought, and intuition represents a different wave band of subtle energy.  Each of us unconsciously broadcasts the energy of our inner life and receives only that with which we are in tune.

The ancients knew that unless we purify and tune our inner life and center ourselves at as high a level as we can, we will resonate with whatever passions are blowing in the wind.  This is the root of much unconscious suffering, not knowing the sources that motivate and shape the pliable human psyche.  Our outer experiences only resonate with our inner rattle.  If we don’t like the connections we’ve formed we cannot break them, but we can transform ourselves so as not to resonate with them.  It’s useless to blame anyone or anything outside ourselves.  We carry our inner state with us and will find the same types of friends and relationships wherever we go.  To change what we encounter in the world we change the levels and qualities to which we attune.”8

The Octad & Mitosis – Cell Division

The human body grows and replaces cells through the process of mitosis.

Each cell replicates itself and then divides into two identical ‘sister’ cells.

Cell division is absolutely integral for life.  Without it we could not grow, heal or maintain our health.

The Monad becomes the Dyad as one becomes two, two becomes four, four becomes eight, sixteen, and so on until the organism is complete: the Many.

This involves the Geometric Sequence of Doubling: 1, 2, 4, 8, 16, 32, 64, 128…etc.

It is a process of 8 seamless stages that renews itself upon reaching the 8^th step, where 1 becomes 2.

The Octave and Human Anatomy

On average:

• The thumb, wrist, neck & waist form a series of doubling octaves.
• Thumb base circumference x 2 = wrist base circumference
• Wrist circumference x 2 = neck base
• Neck base x 2 = waist circumference

The Octad & the Periodic Table of Elements

The Periodic Table of Elements is the map of all 92 naturally occurring elements from hydrogen to uranium.

Elements 95 to 118 are only synthesized in labs or nuclear reactors.

The elements are ordered by atomic number (# of protons), electron configurations, and recurring chemical properties.

The Periodic Table was first publicly published in 1869 by Russian chemist Dmitri Mendeleyev.

The Periodic Table and the Law of Octaves

The Law of Octaves in the Periodic Table was discovered by chemist John Newlands (1837-1898) in 1865.  This was prior to Mendeleyev, yet Medeleyev got the credit.

John Newlands

John Newlands wrote in Chemical News in 1865, “If the elements are arranged in order of their equivalents [ie relative atomic masses in today’s terminology] with a few transpositions, it will be seen that elements belonging to the same group appear in the same horizontal line. Also the numbers of similar elements differ by seven or multiples of seven. Members stand to each other in the same relation as the extremities of one or more octaves of music. Thus in the nitrogen group phosphorus is the seventh element after nitrogen and arsenic is the fourteenth elements after phosphorus as is antimony after arsenic. This peculiar relationship I propose to call ‘The Law of Octaves’.”9

Newlands original Periodic Table, 1866

Newlands was the first to group elements according to patterns.

He was originally criticized for his ideas, because he did not leave spaces for undiscovered elements and he grouped two elements into one box.

He was humiliated at a lecture at the Chemical Society on March 1, 1855 for the above two reasons and sadly, the Publication Committee refused to publish his paper.

Not until 1998 did he receive full recognition of his discovery.  He was the true first discoverer of the Periodic Table of Elements.

When the elements are aligned according to their atomic weight, every 8^th element shares similar properties.

He likened it to octaves of music.

The properties repeat in periodic cycles.  This resulted in elements grouped as families.

Hydrogen, fluorine, chlorine, bromine and iodine are all on the same interval.

Inert or Noble gases have full shells: Helium, Neon, Argon, Krypton, Xenon, Radon

The entire Periodic table spans seven ‘octaves’ – nine octaves according to Walter Russell.

Walter Russell’s Periodic Table

Octet Rule

The Octet Rule refers to atoms of main-group elements tending to combine in such a way that each atom has eight electrons in its valence shell.10

This gives it the same configuration as a noble gas which creates stability.

Atoms strive for 8 electrons in their outermost shell – making a ‘full shell’.

When full, another shell will form.

Sodium (atomic number 11) is highly reactive with many other atoms.  The first shell is full with 2 electrons; the second shell is full with 8 electrons; the outer shell has only 1 electron.  It desires to fill this shell so it readily combines with other atoms in order to complete its shell with 8 electrons.

The number of electrons in the outer shell will determine how readily one atom bonds with another, thus creating molecules.

But remember: electrons are not ‘things’ or ‘particles’.  They are vortices of energy and represent processes and probabilities.  They are not solid things.

8 Major Families of Elements

“The periodic table is a modern cosmological model weaving the principles of the Monad, Dyad, and Tetrad.  That is, it depicts a universe woven of polarities, positive and negative charges of subatomic matter and recurring eight step cycles to manifest all matter.  Each horizontal row of the Periodic Table represents another ‘octave,’ or eighth step up the ‘scales.’”11

The families of elements are determined primarily by the number of electrons in the outer energy shell (valence shell).

• Alkali Metals – 1 valence electron
• Alkaline Earth Metals & Transition Metals – 2 valence electrons
• Boron Group or Earth Metals – 3 valence electrons
• Carbon Group or Tetrels – 4 valence electrons
• Nitrogen Group of Pnictogens – 5 valence electrons
• Oxygen Group of Chalcogens – 6 valence electrons
• Halogens – 7 valence electrons
• Noble (Inert) Gases – 8 valence electrons

The Periodic Table represented as a spiral, as it should be.

Elements in the same group have the same number of electrons, between 1 & 8, in the outermost electron orbital shell.

* Note here that electron shells are clouds of probabilities, and electrons are not particles, but corners of Platonic Solid geometry.

Read Articles 130 & 131 for information on the Moon model and how atomic structure relates to the Platonic solids.

It is interesting to note that “Modern chemistry is discovering molecular, atomic, and subatomic structures strikingly similar to the geometric patterns of Islamic art and architecture”12 that we saw in the last article.

The 64 (8 x 8) – An Octave of Octaves

Divisors of 64: 1, 2, 4, 8, 16, 32, 64

It is the smallest number with exactly 7 divisors.

It is the first number that is a perfect square and perfect cube.  Sixty-four is a square cubed: 2² x 2² x 2² = 64.  Paradoxically, sixty-four is also a cube squared: 2³ x 2³ = 64.

Atomic number 64 = Gadolinium

Robert Lawlor tells us “The number 64 is the symbol of the self-reproductive power of mankind, as well as the abstract universal reproductive power of number to bring forth the principle of three-dimensional form necessary for a physical manifestation.  64 represents the world of the body reaching its transcendence in the two-dimensional world of thought.”  This is expressed through many systems of 64.

64 Tetrahedral Grid – Isometric Vector Matrix (IVM)

The ‘ground-state’ structure of the Aether is thought by Buckminster Fuller and Nassim Haramein to be an IVM.

The IVM consists of 64 tetrahedra.

The negative space consists of octahedra.  Therefore it is a tessellating structure of octahedra and tetrahedra or cuboctahedra and star tetrahedra.

The Flower of Life is the curved line version of the IVM.

64  6-part codons Specify Amino Acids in DNA

Dr. Mark White tells us, “Codons are made of nucleotides and nucleotides demonstrate a fundamental symmetry.”

He then says, “Not all codons are alike, but all codons do always inform each other. No codon ever has any meaning outside of the context of all other codons.”

See Articles 168-172 for more information on the geometry and science of DNA as well as the work of Dr. Mark White who discovered the codon table and mapping of amino acids is related to the dodecahdron.

64 Possible Tastes

There are 64 possible tastes according to the Chinese.

These are all combinations of the 6 tastes:

• sweet
• sour
• bitter
• salty
• pungent
• astringent

64 Transformations – I-Ching – Book of Changes – China

The I-Ching is an ancient text from the 9^th century BC that depicts the cosmos as a series of dynamic events in distinct stages of transformation.

The way of natural law is called the “Tao”.

It starts with the circle representing “Grand Ultimate” or “Great Unity”.  In other words, the Monad.

The One produces the Two – the Dyad of opposites – the yin/yang.

“In its circular form, each part contains a small piece of its opposite within itself, causing the parts to endlessly chase each other.”13

Yang – solid line

Yin – broken line

The 64 Transformations are arranged as trigrams – three at a time.

There are 8 possible trigrams.

Pa Kua represents the diagram of the 8 trigrams around the central symbol of yin/yang.

Eight Trigrams – I-Ching

The Eight Trigrams are as follows:

• Chi’en (heaven, creative)
• Tui (attraction, achievement)
• Li (awareness, beauty)
• Chen (action, movement)
• Sun (following, penetration)
• K’an (danger, peril)
• Ken (stop, rest)
• K’un (earth, receptive)

The ‘Former Heaven Sequence’ represents the ideal pattern of transformation in the cosmos.

Each trigram is the complement of its opposite.

Each trigram is combined in pairs, one over the other, forming hexagrams.

This results in 64 combinations, or 64 continuous stages in the cosmic creating process.

The 64 can be arranged as a square representing earth, or a circle representing heaven.

64 Arts of the Kama Sutra – India

The Kama Sutra is a guide to virtuous and gracious living that discusses the nature of love, family life, and other aspects pertaining to pleasure oriented faculties of human life.

Only 20% of Kama Sutra is about sexual positions.

According to the Kama Sutra there are 64 arts to be cultivated to make a person more attractive.  These are gender neutral.  They are:

1. Singing
   2. Playing a musical instrument
   3. Dancing
   4. A combination of singing, using musical instruments and dancing
   5. Writing and drawing
   6. The Art of Tattooing
   7. Adorning an idol with flowers
   8. The art of spreading flowers on a bed or on the ground
   9. Coloring fabrics, nail and body with colors from plants
   10. Fixing colored glass tiles on floor
   11. The art of making a bed
   12. Producing music by striking glasses of water
   13. The art of storing water in reservoirs
   14. The art of picture making and decorating
   15. Making rosaries, necklaces, garlands
   16. Tying turbans
   17. Stage playing
   18. The art of making ear ornaments
   19. The art of making perfumes
   21. Magic (sorcery)
   22. Manual skills
   23. Cooking (culinary skills)
   24. Making combination drinks and flavored drinks i.e.– lemonades, sherbet etc
   25. Tailoring and sewing
   26. Making handicrafts e.g.– parrots, flowers etc. from thread
   27. Skills to solve riddles, puzzles and covert speeches
   28. The skill of Antakshari (a singing game were one must start with the letter with which other    person’s song ended)
   29. The skill of imitating natural sounds
   30. Reading, chanting and intoning
   31. Mastering tongue twisters
   32. Skills at martial arts (the skills to use sword, stick, bow and arrow)
   33. Skill to reach logical conclusions based on given facts
   34. Carpentry
   35. Architecture
   36. Knowledge about gold, silver and gems
   37. Chemistry (knowledge of properties of materials)
   38. The art of coloring jewels or beads
   39. Knowledge of mines
   40. Gardening
   41.The art of cock fighting (getting cocks, quail or rams to fight and make the fowl/animal            victorious)
   42. Teaching parrots or starlings to talk
   43. Applying perfumes on body and hair
   44. Understanding of code language
   45. Spoonerism (purposefully interchanging position of letters of words while speaking)
   46. Knowledge of languages
   47. Knowledge of making flower chariots
   48. Knowledge of making mystical graphics, spells and charms and ways to avoid spells
   49. Mental exercises
   50. Composing poems
   51. Knowledge of dictionaries and vocabulary
   52. The art of impersonation
   53. Impersonation of materials i.e.– make common things appear fine rare substances (make cotton appear to be silk)
   54. Knowledge of gambling
   55. Using mantras (enchantments) to take away others’ possession
   56. Skills in sports and games
   57. The art of social conduct, paying respect and sending compliments
   58. Knowledge of war, arms and army deployment
   59. Knowledge of gymnastics
   60. The skills of knowing a person’s real character from his conduct
   61. The skill of reading and composing verses
   62. The skill of enjoying arithmetic puzzles
   63. Making artificial flowers
   64. Making images with clay

Note – We do not condone #41 – the art of cock-fighting or animal fighting.  These are highly unethical practices, gross transgressions against animal rights and major crimes punishable by law.

Nevertheless it is included here for historical interest.

64 Types of Sexual Acts in the Kama Sutra

The 64 types of sexual acts are included in the ancient Indian Hindu text written by Vatsyayana.

This is the standard work on human sexual behavior in Sanskrit literature.

64 Squares on a Chess Board

The Game of Chess symbolism can be taken farther than just the checkerboard.  This was first discussed in Article 20.

Chess is called “The Royal game of Life”.

The board has 64 alternating white & black or red & black squares.

64 represent an octave of octaves, or eight steps of eight steps.  It has profound symbolic implications relating to the journey of consciousness through the Cosmos.

The 64 alternating squares represent the world’s polarities & the conflicting choices life offers us.

The board itself represents the universe.

The pieces represent the elements and their possible actions.

The interplay among pieces represents the cosmos and our lives as fields of transformation.

There are 20 possible opening moves.

There are 400 possible 2^nd moves.

There are 20,000 possible 3^rd moves…

The number of moves increase exponentially from there.

In Zoroastrian Persia chess represented the struggle between good and evil, understanding and ignorance.

‘Checkmate’ comes from shah mat – “The king is dead.”

Chess arrived in Europe after the 11^th century.  The pieces took on political and religious attributes at that time.

Michael Schneider tells us in A Beginner’s Guide to Constructing the Universe, “A key to understanding the deeper significance of each piece is the geometric way it moves.  A “square” move represents earthly action.  A triangular move represents alignment with the divine within us.”

Schneider analyzes it as follows:

The King

• most important piece
• least powerful in terms of movement – moves 1 step at a time, any 8 directions
• represents the Sun of the Solar System; or more importantly our Higher Self
• “The king [our Higher Self] is virtually hidden from the action, yet the entire game revolves around it.”

The Queen

• most powerful piece – unlimited movement in all 8 directions
• queen of the materially configured world; the Moon that reflects the light of the Sun

The Bishops – 2

• power to slide along diagonals

The Knights – 2

• represent the awakening spiritual initiate
• moves by leaps of intuition along the sides of 30-60-90 right triangles
• moves by alternating between white and black squares, head and heart
• only a knight or pawn can initiate the game…until then, the world waits

The Rooks – 2

• move strictly along straight lines
• represents physical power to act in the world

The Pawns – 8

• represents ordinary men and women attempting to cross the board of life through seven grades of initiation (7 chakras; 7 quantum densities)
• mirrors the purification of the seven chakras
• “A pawn experiences only the simplest interactions with other pieces and does not see the divine forces behind it, being aware of only one step ahead.”
• When a pawn reaches the other side, the 7^th stage, it achieves a higher state or octave and transforms into any piece the player wishes

The Checkerboard & Two Paths of Esoteric Philosophy

On another level, the black and white squares represent the two paths frequently discussed in Cosmic Core.  The white squares represent the path of Unity, and the black squares represent the path of Separation.

The path of unity involves: acceptance, forgiveness, compassion and understanding.

The path of separation involves: control, manipulation, selfishness and ignorance.

The point is: it’s a Choice.  Each person chooses one or the other and can choose to change at any time.  There are no victims.  Each is responsible for themselves.  Each is the captain of their own life and the rate of speed of their own evolution.

The end result of spiritual evolution (choosing a path) is to raise your consciousness to a higher level, help others raise theirs, and everyone learning to live in a world of peace, prosperity, justice, and abundance for all.

Remember – control and manipulation leads to slavery and genocide.

Acceptance and forgiveness rejoices in individuality and leads to freedom and harmony among all humans and all life forms.

1. Lawlor, Robert, Sacred Geometry: Philosophy & Practice, Thames & Hudson, 1982
2. ibid.
3. ibid.
4. Schneider, Michael, A Beginner’s Guide to Constructing the Universe, Harper Perennial, 1994
5. ibid.
6. ibid.
7. The Seven Hermetic Principles, http://www.sacred-texts.com/eso/kyb/kyb04.htm
8. Schneider, Michael, A Beginner’s Guide to Constructing the Universe, Harper Perennial, 1994
9. http://www.rsc.org/education/teachers/resources/periodictable/pre16/develop/newlands.htm
10. https://en.wikipedia.org/wiki/Octet_rule
11. Schneider, Michael, A Beginner’s Guide to Constructing the Universe, HarperCollins Publishers, 1994
12. ibid.
13. ibid.

Return to Free Library

Return to Number Menu

Previous Article                                                                         Next Article