We will now move into a three part series on the Heptad, or sevenness. Then we will move into a two-part series on music and how music relates to the Heptad.
The Heptad – 7: The Symbol of Transformational Processes
Seven is perhaps the most venerated number of the Dekad.
It is called “The Virgin” and “The Vehicle of Life”.
It is nicknamed “sebo” in Greek, meaning “veneration”.
Seven is a symbol of mystery, divinity and eternity.
John Michell tells us, “Being without birth and unreproductive, the number 7 represents the principle of eternity.”
The Heptad predominated in mythology, mysticism, magic, ceremony & superstition.
Seven expresses a complete event (beginning, middle, end) passing through 7 stages that keep repeating.
“Seven represents a complete yet ongoing process, a periodic rhythm of internal relationships.”1
All configured efforts are led in seven stages to perfection.
Atomic Number 7 = Nitrogen
Nitrogen is the 7th most abundant element in the universe. It is the 4th most abundant element in the human body. About 2.5% of the weight of living organisms comes from nitrogen.
Direct contact with liquid nitrogen causes severe frostbite. When nitrogen bubbles from in the bloodstream (the bends) the condition can be fatal for divers or astronauts.
Nitrogen is used for fertilizers for plants and is essential for plant health and growth. The nitrogen cycle is of crucial importance for all life on the planet.
The Nitrogen Cycle: Essential for Life
Atomic Number 70 = Ytterbium
Ytterbium is a bright, soft, silvery-white rare earth metal. It is not found free in nature but is found in many minerals. It is moderately toxic.
Ytterbium is used in x-ray machines, stress gauges, fiber laser amplifiers, catalysts in organic chemistry, and in alloys added to stainless steel to improve grain refinement and strength.
Atomic Number 77 = Iridium
Iridium is a rare, hard, lustrous, brittle, very dense platinum-like metal. It is very nonreactive and the most corrosion-resistant metal known. It resists attack by any acid.
Iridium is the densest element. It is used in platinum alloys, and equipment used at high temperatures. It is also used to make heavy-duty electrical contacts.
Arithmetic Properties of 7
1 x 2 x 3 x 4 x 5 x 6 x 7 = 7 x 8 x 9 x10 = 5040
1 x 2 x 3 x 4 x 5 x 6 = 8 x 9 x 10 = 720
As shown above, “Whether the value of 7 is present or absent, its location serves as a pivot balancing the ten.”2
Seven is the “Virgin”. No number less than 7 divides or enters into it.
2 divides 4, 6, 8, 10
3 divides 6, 9
4 divides 8
5 divides 10
Seven is the “Childless”. It produces no other number (by multiplication) within the 10.
The 7 cannot be entered (divided), cannot procreate (produce numbers within the dekad), and cannot be captured (irrational angle of the heptagon) – because it is not born in the physical. It exists in the metaphysical.
When any number is divided by 7 it forms an endlessly looping trail of repeating decimals, 142857, leaving out 3, 6, and 9.
1/7 = 0.142857…
2/7 = 0.285714…
3/7 = 0.428571…
4/7 = 0.571428…
5/7 = 0.714285…
6/7 = 0.857142…
7/7 = 1.000000…
8/7 = 1.142857…
9/7 = 1.285714
10/7 = 1.428571
“Multiply the numerator by the denominator and the last number of the product is the last number of the sequence for that fraction. Thus, 2 x 7 = 14, so the sequence for 2/7 must end in 4 and we can write down 0.285714.”3
Hence 3 x 7 = 21, so the sequence 3/7 will end in a 1.
4 x 7 = 28, so the sequence 4/7 will end in an 8. (Here a 28)
5 x 7 = 35, so the sequence 5/7 will end in a 5.
6 x 7 = 42, so the sequence 6/7 will end in a 2. (Here a 42)
However, the formula here begins to break down after 7/7.
8 x 7 = 56; 9 x 7 = 63; 10 x 7 = 70 (In these three cases you will use the next number up from the last digit. So for 56 use 7. For 63 use 4. For 70 use 1.
999,999 divided by 7 = 142857
There are 7 border geometries or 7 possible kinds of border symmetry.
Six circles surround a 7th perfectly.
Seven takes the physical dimensions of the Hexad and adds the 7th point: the still center point of mystery and divinity – the doorway to the metaphysical.
Powers of Seven
Divisors of 49: 1, 7, 49
The sum of the digits of the square of 49 = √49.
In other words 49 x 49 = 2401. 2 + 4 + 0 + 1 = √49 = 7.
1/49 = .020408163265306122448979591836734693877551
(This is 42 repeating digits that grow in octaves: 2, 4, 8, 16, 32…etc.)
The repeating number can be obtained from 02 and repetition of doubles placed at two places to the right:
Atomic Number 49 = Indium
49 days Siddhartha Gautama (the Buddha) spent meditating as a holy man.
49 days is one of the lengths of the intermediate state (bardo) between life and death in Buddhism.
The speed of sound in dry air at 20° C (68° F) is 343 m/s.
The Theology of Arithmetic – Iamblichus
As we have been doing, we will now take a look at the meaning of the Heptad as prepared by Neo-Platonist philosopher, biographer of Pythagoras, Greek mystic and mathematician Iamblichus (245-325 AD).
The Heptad (Hebdomad)
Seven is not born of any mother and is a virgin.
The sequence from the monad to it added together totals 28. (1+2+3+4+5+6+7= 28)
There are 28 days of the moon (fulfilled by the heptad).
28 is the 2nd perfect number.
Starting with the monad and making a sequence by doubling, seven numbers yield 64, the first square which is also a cube: 1, 2, 4, 8, 16, 32, 64.
Doing the same, but trebling, seven numbers yield 729, the second square and cube: 1, 3, 9, 27, 81, 243, 729.
The heptad consists of the three dimensions (length, width, depth) and the 4 limits (point, line, surface, and solid).
Seven is the number of the primary concord, the fourth (4:3) and of geometric proportion (1, 2, 4).
It is called ‘that which brings completion’.
We see seven things – body, distance, shape, size, color, movement and rest.
There are seven movements – up, down, forward, backward, right, left and circular.
Plato composed the soul out of seven numbers.
There are seven alterations of voice: (7 ways a vowel can be sounded): acute, grave, or circumflex accent, aspirated, unaspirated, long or short).
The heptad is also called ‘forager’ because its structure has been collected and gathered together in a manner resembling unity, since it is altogether indissoluble.
It is also called ‘guardian’ due to the 7 celestial spheres inhabited by the 7 hosts of heavenly guards.
The heptad is not similar to the other numbers. It deserves reverence for it is an instrument of the most authoritative limb of the divine and has gained the power of creativity. For by nature, and not by our own devices, the heptad is a mean between the monad and decad.
The heptad is akin to an acropolis since it is a ‘strong fortification’ within the decad.
By mingling with any of the numbers within the decad, it does not produce any of the numbers within the decad, nor is it produced by the intercourse of any of the numbers within the decad, but, with a principle which is all its own and is not shared, it has been assigned the most critical place.
The Heptad is also called ‘Chance’ because it accompanies everything which happens.
All seeds appear above ground, during growth, in the course of the seventh day or thereabouts.
The four phases of the moon each last for a seven-fold season and reasonably complete the month of this heavenly body which consists of about 28 days.
We also see that the ocean is disposed by the moon in accordance with hebdomadic numbers (the tide).
Women’s menstruation occur by means of the heptad.
An interval of seven hours at least elapses between the natural severance of the baby’s umbilical cord and its appearance and delivery.
For seven days the embryo resembles a membranaceous, water-bearing kind of thing.
The heptad is particularly responsible for viability, for seven-month children are no less likely to survive than nine-month children, however eight-month children often perish.
Just as fetuses were sown and ordered in the womb by the heptad, so also the birth in seven hours they reach the crisis of whether or not they will live – they will be confirmed at the critical 7th hour one way or the other – either towards life or towards death.
Children cut their teeth at seven months, and at twice seven (14 months) sit up and gain an unswaying posture, and at three times seven (21 months) they begin to articulate speech and make their first efforts at talking, and at four times seven (28 months) they stand without falling over and try to walk, and at five times seven they are naturally weaned and milk ceases to be their food.
At seven years they shed their natural teeth and grow ones which are suitable for hard food, and at twice seven years (14 years) they come to puberty and acquire in an articulated manner the full range of expressed speech, as well it becomes possible for them to have children and substitute others for themselves for the fulfillment of the universe.
In the third heptad of life (21 years), they generally conclude growth in terms of length, and in the fourth (28 years) they complete growth in terms of breadth, and there is no other bodily increase remaining to them; for 28 is a complete number.
Finally, when the principle of the decad is blended with that of the heptad, and ten times seven (70 years) is reached, then man should be released from all tasks and dedicated to the enjoyment of happiness, as they say.
The heptad has the property of being the most critical number, not only in pregnancy and in the ages of life development, but also in disease and health, because it is the most akin and cognate to the human constitution: for there are seven so-called black internal organs (tongue, heart, liver, lung, spleen, and two kidneys); 7 channels in the face (2 for eyes, 2 for ears, 2 for nostrils, and one for mouth); and 7 which transmit breath and food (throat, gullet, stomach, guts, intestinal membrane, bladder and rectum).
All types of fever meet at the seventh day and at no other before it, and so they reach crisis at this point.
It is also possible to live for 7 days with no intake of food.
Quality and color and light accompany corporeal magnitudes in three dimensions and evidently fall under the pentad; ensoulment and the condition of life fall under the hexad, completion and thought fall under the heptad.
Linus tells us, “The four sources of everything are controlled by triple bonds.”
There are 7 types of source in geometrical research: point, line, surface, angle, shape, solid and plane.
The heptad is called ‘Athena’ because it is virgin and unwed, born neither of mother (even number) or father (odd number) but from the head of the father of all (the monad, the head of number).
Sevens in Music, Culture, and Nature
There are 7 musical notes in the traditional scale (white keys on piano) – C, D, E, F, G, A, B.
There are 7 colors we see of the electromagnetic spectrum – red, orange, yellow, green, blue, indigo, violet.
6 spheres fit perfectly around the central 7th. Seven functions as the spiritual center of six.
There are 7 days in a week: 7 x 4 = 28.
This is very close to one moon cycle (“moonth”) of 29.5206 days.
The 7 days of the week are related to a specific metal and celestial body:
- Monday – silver – Moon
- Tuesday – iron – Mars
- Wednesday – quicksilver – Mercury
- Thursday – tin – Jupiter
- Friday – copper – Venus
- Saturday – lead – Saturn
- Sunday – gold – Sun
There are 7 groups of crystal structures.
There are 7 coils in a traditional labyrinth.
There are 7 traditional heavenly bodies – Moon, Mercury, Venus, Sun, Mars, Jupiter, and Saturn.
There are 7 liberal arts – logic, rhetoric, grammar, number, music, geometry, cosmology.
There are 7 traditional metals in alchemy – silver, mercury, copper, gold, iron, tin, lead.
The Rebis image appeared in the work Azoth of the Philosophers by Basil Valentine in 1613. Wikipedia states, “The Rebis (from the Latin res bina, meaning dual or double matter) is the end product of the alchemical magnum opus or great work. After one has gone through the stages of putrefaction and purification, separating opposing qualities, those qualities are united once more in what is sometimes described as the divine hermaphrodite, a reconciliation of spirit and matter, a being of both male and female qualities as indicated by the male and female head within a single body.”
There are 7 modes of the major scale (music) – Ionian, Dorian, Phrygian, Lydian, Myxolydian, Aeolian, Locrian.
Opposite sides of dice add to 7.
There are 7 tetrominos (shapes) in Tetris.
Seven shuffles is the amount it takes to create randomness when shuffling a deck of cards.
Sevens in the Body
There are 7 chakras – root, sacral, solar plexus, heart, throat, brow, and crown.
There are 7 endocrine glands – pineal, pituitary, thyroid, thymus, adrenal, pancreas, gonads.
There are 7 levels of Self – physical, etheric, astral, ego, manas, buddhi, atma.
Naturally, the chakras, endocrine glands and levels of self are interrelated.
Sevens in Religion, Myth, Folklore
Buddha meditated for 7 years under the Bodhi Tree before achieving enlightenment.
There are 7 stages of the soul in Sufism: compulsion, conscience, inspiration, tranquility, submission, service, perfection.
There are thousands of references in the Bible of ‘sevens’:
6 days of Creation with 7th day as rest
7 lions in the den with Daniel
7 locks of Samson’s hair cut
7 trumpeters of Joshua circled Jericho 7 times
‘Clean’ animals admitted to Noah’s ark by sevens, unclean by twos
There are many 7’s in Revelations:
7 churches; 7 kings; 7 angels; 7 mountains; 7 crowns; 7 vials; 7 plagues; 7 thunders; 7 golden candlesticks; 7 stars; 7 lamps; 7 heads; 7 seals; and the four and twenty elders surround a throne on which stands “a Lamb as it had been slain, having 7 horns and 7 eyes, which are the 7 spirits of God.”
John Michell shows that the “7 horns and 7 eyes” symbolizes a septagram with an eye in each inner triangle.4
Michell writes, “The ‘Lamb in the midst of the throne.’ in Revelation 5:6 has ‘seven horns and seven eyes, which are the seven Spirits of God.’ the geometer’s image of this creature is the heptagram with seven horns ad seven triangles containing eyes. The eyed triangle of the heptagon, which has a base angle nearly the same as that of the Great Pyramid in Egypt, may be the origin of the mystic symbol of the eye in the pyramid.”
There are 7 Stations of the Cross.
The 7th day in Christianity is the Sabbath (from Hebrew ‘shabbat’ – to cease from labor).
There are 7 deadly sins (abominations) – pride, envy, gluttony, lust, anger, envy, sloth.
There are 7 virtues – Faith, Hope, Charity, Fortitude, Justice, Prudence, Temperance.
There are 7 Ages of Man – infant, schoolboy, lover, soldier (warrior), [one who seeks] justice, Pantalone (top of the social order, wealthy), old age
Shakespeare wrote: “All the world’s a stage,
And all the men and women merely players;
They have their exits and their entrances,
And one man in his time plays many parts,
His acts being seven ages.”
There are 7 Heavens in ancient Mesopotamian religions, Hinduism, Islam, Judaism, and Catholicism.
There are the 7 Hermetic Principles:
- The Principle of Mentalism
- The Principle of Correspondence
- The Principle of Vibration
- The Principle of Polarity
- The Principle of Rhythm
- The Principle of Cause and Effect
- The Principle of Gender
As it is said in the Kybalion, “The Principles of Truth are Seven; he who knows these, understandingly, possesses the Magic Key before whose touch all the Doors of the Temple fly open.”
There are the 7 Samurai, the 7 Sisters, the 7 Virgins, the 7 Veils (Dance of the Seven Veils of Salome).
There are the 7 pillars of wisdom, the 7 voyages of Sinbad, the 7 wonders of the Ancient World, the 7 circles made around the Kaaba at Mecca, and the 7 petals of the pomegranate and of the Chinese lotus.
There is Snow White & the 7 Dwarves, the 7 hills of Istanbul, the 7 hills of Rome, and the 7 gates and 7 doors of the Sumerian temple of Nintu at Adab.
Athena was the Greek Goddess of wisdom, courage, inspiration, civilization, law & justice, mathematics, strength, war strategy, the arts, crafts, and skill.
This virgin Goddess is represented by a heptagon.
Athena was born in an unusual way. Her father Zeus swallowed his pregnant wife. Athena, fully clothed and mature, then sprang forth from his head after his crown was split with an ax.
She remained virgin and bore no children.
This unusual birth will be represented geometrically in the next article.
- Schneider, Michael, A Beginner’s Guide to Constructing the Universe, Harper Perennial, 1994
- Jagadguru Sri Bharati Krishna Tirthaji Maharaja, Vedic Mathematics: Sixteen Simple Mathematical Formulae from the Vedas, Motilal Banarsidass Publishers, 2015
- Michell, John, The Dimensions of Paradise, Inner Traditions, 2nd edition, 2008, page 88