Core Principles Behind The Stereotypes

Astrology is a complex and nuanced art form, and personally I believe it to be a science in its own right. Many people might disagree with me, but I wonder if they have truly given it serious contemplation, or have just written it off as apophenic nonsense. Contemplate this: thousands of years before we could simply open a newspaper and read a dumbed-down horoscope, astrology was a scholarly art that required a deep knowledge of mathematics and study of the natural world.

Warning: If you really hate astrology, then don’t bother to read any further! But if you are curious and would like to deepen your understanding of the fundamental stereotypes of the zodiac, let’s do it. Keep in mind that an individual chart is a mandala of all the planetary energies, and the complexity of one’s personality can’t be summarized by a single sun sign.

In my view, astrology serves as an evolutionary tool. The natal chart is like a cosmic mirror that reflects the moment we chose to incarnate on this plane. By looking into this mirror, we can gain insight into the lessons we desired to learn and experience in this lifetime, and also learn to embrace ourselves more fully with all our unique strengths and challenges.

Besides the sun, moon, and planets, the twelve signs of the zodiac are perhaps the most fundamental aspect of astrology. They are named after the constellations of stars that span the great ecliptic circle, but did you ever wonder where their descriptions and qualities come from? It turns out that zodiacal energies go much deeper than rote memorization of surface-level stereotypes, and can be derived from the fundamental principles of harmonic waves.

Harmonic Waves are the Key!

In physics, a harmonic wave is a periodic wave that is described by a sinusoidal function. Harmonic waves are characterized by their frequency, which is the number of cycles they complete in a given period of time, and their amplitude, which is the maximum height of the wave above and below the equilibrium position. Harmonic waves are often described as having a sinusoidal shape, which means that they oscillate around a central axis, reaching a maximum height (the peak) and then returning to the central axis before reaching a minimum height (the trough).

Harmonic waves can be found in a wide variety of physical systems, including sound waves, light waves, and mechanical waves. They are important in many fields, including engineering, physics, and mathematics, and they are often used as a model for understanding the behavior of real-world systems.

For the context of astrology, circular harmonics can be visualized by wrapping a sine wave around a circle, as in Figure 2. Even though it is a continuous pattern of peaks and troughs, for convenience it can be demarcated into equal sectors. By understanding the harmonics and the energies they represent, astrologers can gain a deeper understanding of the core energies and characteristics of each astrological sign. Harmonic charts can also be constructed, to magnify certain aspects for closer inspection. Such divisional charts are frequently used in Vedic astrology, where they are called varga.

Fig. 2 from Addey 1977 showing the 3rd, 4th, and 12th harmonics

In this blog post, we’ll be exploring the 3rd, 4th, and 6th harmonics and how they inform the qualities of each zodiac sign. I will also explain the role of ruling planets in further keynoting the energy of each sign. By the end, you’ll have a deeper understanding of the complexities and nuances of astrological energies, and you’ll be well on your way to decoding the zodiac for yourself!

The 3rd Harmonic: Triplicity and the Four Elements

Have you ever heard someone say that their astrological sign belongs to the element of Fire, Earth, Air, or Water? In relation to the zodiac, the four elements can be derived from the 3rd harmonic, known to the ancients as the Law of Triplicity. If we we divide the twelve sectors of the zodiac into three waves (Figure 2a), we get three groups of four, each group containing the four elements: Fire, Earth, Air, and Water. (The fifth element of Akasha/Space/Ether is not bound to the terrestrial plane, and so is both included and transcended here.)

When we divide the twelve sectors of the zodiac into three groups for four elements, we get the following associations:

Fire	Earth	Air	Water
Aries	Taurus	Gemini	Cancer
Leo	Virgo	Libra	Scorpio
Sagittarius	Capricorn	Aquarius	Pisces

But what do these elements actually represent, and how do they inform the energy of each sign? Rather than reducing them to stereotypes like “Fire signs are passionate” or “Water signs are emotional,” we can think of them as representing primal qualities. In traditional shorthand, the four elements could be said to correspond to Spirit, Body, Mind, and Emotion— though I prefer not to boil them down to such a limiting box. Here’s are a few keynotes with a bit more nuance:

Fire: free-spirited, initiative, restlessness, and impulsive.
Earth: practicality, crystallization, and alchemically transformative
Air: relational connection, understanding, and communication.
Water: deep feeling, emotional sensitivity, and intuition.

Fire signs (Aries, Leo, and Sagittarius) are associated with passion, creativity, and the drive to initiate change. They are energetic, dynamic, and often have a strong sense of purpose.

Earth signs (Taurus, Virgo, and Capricorn) are associated with stability, practicality, and the ability to ground and manifest ideas. They are grounded, reliable, and often have a strong sense of responsibility.

Air signs (Gemini, Libra, and Aquarius) are associated with communication, intellect, and the ability to connect and relate to others. They are curious, adaptable, and often have a strong sense of social awareness.

Water signs (Cancer, Scorpio, and Pisces) are associated with emotion, intuition, and the ability to connect with the unconscious and the spiritual. They are sensitive, emotional, and often have a strong connection to their inner selves.

The 4th Harmonic: Quadruplicity and the Three Modes

Have you ever heard someone say that their astrological sign is cardinal, fixed, or mutable? These three modalities are derived from the 4th harmonic, and can be thought of as different angles of approaching life.

By dividing the twelve signs of the zodiac into four parts, we get three 90º cross shapes that each contain four signs. The cardinal axis covers the equinoxes and solstices, and represents the beginning of the four seasons. The fixed and mutable axes represent the middle and end of the seasons, respectively.

Cardinality is like the axle of a wheel that facilitates movement, and is associated with action, initiation, and change.
Fixity is like the spokes of a wheel that provide support, and is associated with stability, determination, and persistence.
Mutability is like the rim of a wheel that navigates changing environments, and is associated with adaptability, versatility, and changeability.

The four cardinal signs are Aries, Cancer, Libra, and Capricorn. These signs are characterized by their desire to take action and initiate change. They are often seen as brave and decisive, with a natural inclination towards leadership and a strong drive to make things happen. Cardinal signs are associated with the beginning of the four seasons: Aries is the beginning of spring, Cancer is the beginning of summer, Libra is the beginning of fall, and Capricorn is the beginning of winter.

The four fixed signs are Taurus, Leo, Scorpio, and Aquarius. These signs are characterized by their determination and focus, and they are often seen as unyielding and opposed to change. Fixed signs are associated with the middle of the four seasons: Taurus is the middle of spring, Leo is the middle of summer, Scorpio is the middle of fall, and Aquarius is the middle of winter.

The four mutable signs are Gemini, Virgo, Sagittarius, and Pisces. These signs are characterized by their adaptability and versatility, and they are often seen as open to change and resourceful in finding solutions. Mutable signs are associated with the end of the four seasons: Gemini is the end of spring, Virgo is the end of summer, Sagittarius is the end of fall, and Pisces is the end of winter.

For even more nuanced details, check out this blog post on the motivations and pressures of modality in each sign as a response to their elemental needs.

Decomposing the 12th harmonic of the zodiac into its 3rd and 4th harmonics (elements and modes), we can start to flesh out the flavor of each of the zodiac signs from the core components. Putting it all together so far, we have this basic “decoder ring” table for the zodiac:

	Fire	Earth	Air	Water
Cardinal	Aries	Capricorn	Libra	Cancer
Fixed	Leo	Taurus	Aquarius	Scorpio
Mutable	Sagittarius	Virgo	Gemini	Pisces

The 6th Harmonic: Yin/Yang

This isn’t as commonly discussed as much as the 3rd and 4th harmonics, but I found very helpful (especially when we bring in planetary rulers in the next section). Dividing the circle into six parts, we get two groups of six. Aries peaks into yang, Taurus dips into yin, Gemini peaks into yang, Cancer dips into yin, etc. So each subsequent sign has the opposite quality of it’s neighbors. Peaks and valleys are expressions of yang and yin, “outies” and “innies” 😆.

This image is from Robin Armstrong at RASA school of astrology. It shows what he calls "pentans," which are six tiny zodiacs embedded in the circle. Why is it a turtle you ask? I don't know! Likely it is a nod to the Chinese mythology of the Lo Shu tortoise.

In a grossly oversimplified way, some people describe yin as feminine and yang as masculine. But really, these are just energy polarities that are present in all things. They are never absolute, but simply relative qualities to their opposites.

Yin	Yang
introverted, receptive, magnetic	extroverted, expressive, electric
Earth (Taurus, Virgo, Capricorn)	Air (Gemini, Libra, Aquarius)
Water (Cancer, Scorpio, Pisces)	Fire (Aries, Leo, Saggitarius)

Connecting the 6th and 4th harmonics

I discovered this concept on a reddit post about yin and yang in astrology, which introduces the polarity of Thinking vs Feeling along with Introverted (yin) and Extroverted (yang). It is based on the 4th harmonic, so could be thought as a modality of Yin/Yang.

Water and Fire signs are associated with emotions and intuition, and are therefore could be referred to as “Feeling” signs. Water signs, such as Cancer and Scorpio, are known for their emotional depth and sensitivity (feeling internally), while Fire signs, such as Aries and Leo, are known for their passion and intensity (feeling out loud).

Earth and Air signs, on the other hand, are often associated with intellect and reason. Earth signs, such as Taurus and Virgo, are known for their practicality and focus on material realities (thinking internally), while Air signs, such as Gemini and Aquarius, are known for their communication and social skills (thinking externally). These signs could therefore be referred to as “Thinking” signs.

	Introverted	Extroverted
Thinking	Earth	Air
Feeling	Water	Fire

Connecting the 6th and 3rd harmonics

Here’s a bonus thought experiment to play with. Imagine two cycles of a sine wave, rising and falling while transforming through the four elements.

Lava rises up from a volcano, and sinks down as rock and soil, terrestrial creatures (including plants) exhale gases which rise into the sky as air, and condense down as rain that turns into rivers and the ocean.
Alternatively, imagine this wave as the upwelling of spirit and the sinking down of matter, the expansion of the mind and the embodiment of feelings.

The Thema Mundi and Planetary Domicile

Bear with me, because this next section brings in some traditional theory that is not derived from pure mathematics. However, it does follow the empirical ordering of the planets by their distance from the sun. UPDATE: Planetary rulers can be derived from the Fibonacci numbers (see this video for details), but for the moment just take my word for it.

The Thema Mundi is a myth from Ancient Greece that is used as an astrological teaching device. It is said to show the position of the visible planets, sun, and moon at the creation of the Universe. This chart is used to explain many things, but especially what is called planetary domicile or rulership. You can think of it like each planet is the “landlord” of particular zodiac signs.

Beginning at the brightest and warmest time of the year in the Northern Hemisphere, we place the sun as the ruler of Leo, and the moon as the ruler of Cancer. Taking this as a central axis, begin to fill in the zodiac with the planets in order of their distance from the sun. Mercury in Gemini and Virgo, Venus in Taurus and Libra, Mars in Aries and Scorpio, Jupiter in Pisces and Sagittarius, Saturn in Aquarius and Capricorn.

Le Pièce de Résistance: Yin/Yang planetary archetypes!

Combining the 6th harmonic with planetary rulership, we get even more flavors to add to the stew. When this clicked for me it blew my mind with the level of nuanced detail. I could finally understand the zodiac logically without rote memorization and stereotypes!

If you’re not familiar with planetary archetypes, don’t worry. I’ll briefly outline them below. Keep in mind that the Greeks named the planets after their pantheon of gods, and these days we go by the Romanized version of their names.

Luminaries:

Sun: the energy of life. Ego/personality.
- Yang: radiant charismatic shine, desire for attention (Leo).
Moon: reflector of solar light, ruler of the tides, governs the needs of the personality
- Yin: emotional depth, desire for security and comfort (Cancer).

Mercury: messenger of the gods (Hermes). Mind, movement, communication.

Yang: adaptability, curiosity, and love of communication and learning (Gemini).
Yin: analytical mind, attention to detail, and love of order and efficiency (Virgo).

Venus: goddess of love and beauty (Aphrodite). Social, relational, art/aesthetics.

Yin: material abundance, aesthetic beauty, sensual comfort (Taurus).
Yang: relational harmony, social charm, elegance (Libra).

Mars: god of war (Ares). Confidence, assertive energy, strength.

Yang: bold assertiveness, desire for action and leadership (Aries).
Yin: passionate intensity for inward investigation of the unconscious shadow realms (Scorpio).
- In modern astrology, Yin Mars relates to Pluto: Hades, god of the underworld, sex, and death, and transfiguration.

Jupiter: King of the gods (Zeus). Expansion, optimism, enthusiasm, faith.

Yang: yearning for adventure and higher knowledge (Sagittarius).
Yin: spiritual depth, creativity, universal understanding (Pisces).
- In modern astrology, Yin Jupiter relates to Neptune: Poseidon, god of the sea.

Saturn: god of time (Kronos). Ambition, control, harvest.

Yang: independence, innovative thinking, and desire for social justice and progress (Aquarius).
- In modern astrology, Yang Saturn relates to Uranus, which represents eccentricity and electricity.
Yin: discipline, responsibility, desire for material stability and achievement (Capricorn).

The Full Harmonic Synthesis

Now we have all the necessary ingredients to fully keynote the twelve signs of the zodiac from their core ingredients!

Aries ♈️

Cardinal Fire: Initiating Extroverted Feeling
Yang Mars: confident, assertive, direct

Aries is associated with the beginning of spring and is known for its bold and passionate nature. People with strong Aries energies are often seen as courageous and confident, with a natural inclination towards leadership and a strong drive to make things happen. They are energetic and dynamic, with a fierce determination to achieve their goals.

Taurus ♉️

Fixed Earth: Determined Introverted Thinking
Yin Venus: beauty, abundance, sensuality

Taurus is associated with the middle of spring and is known for its stability and practicality. People with strong Taurus energies are often seen as reliable and down-to-earth, with a strong connection to their senses and a natural inclination towards material comfort. They are patient and persistent, with a strong sense of security and a desire for stability.

Gemini ♊️

Mutable Air: Adaptable Extroverted Thinking
Yang Mercury: curious, clever, quick

Gemini is associated with the end of spring and is known for its mental quickness and adaptability. People with strong Gemini energies are often seen as curious and adaptable, with a natural inclination towards communication and learning. They are versatile and resourceful, with a strong sense of wit and a desire to keep things interesting.

Cancer ♋️

Cardinal Water: Initiating Introverted Feeling
Yin Moon: receptive, compassionate, protective

Cancer is associated with the beginning of summer and is known for its emotional depth and sensitivity. People with strong Cancer energies are often seen as nurturing and caring, with a strong connection to their family and home. They are intuitive and deeply emotional, with a natural inclination towards protection and security.

Leo ♌️

Fixed Fire: Determined Extroverted Feeling
Yang Sun: vital, radiant, dynamic

Leo is associated with the middle of summer and is known for its bold and courageous nature. People with strong Leo energies are often seen as confident and self-assured, with a natural inclination towards leadership and creativity. They are energetic and dynamic, with a strong sense of self and a desire to shine in the world.

Virgo ♍️

Mutable Earth: Adaptable Introverted Thinking
Yin Mercury: analytical, organized, detail-oriented

Virgo is associated with the end of summer and is known for its practicality and attention to detail. People with strong Virgo energies are often seen as analytical and detail-oriented, with a natural inclination towards perfectionism and improvement. They are resourceful and adaptable, with a strong sense of service and a desire to be of use to others.

Libra ♎️

Cardinal Air: Initiating Extroverted Thinking
Yang Venus: charming, elegant, social

Libra is associated with the beginning of fall and is known for its balance and harmony. People with strong Libra energies are often seen as diplomatic and fair-minded, with a natural inclination towards justice and fairness. They are socially skilled and able to see both sides of an argument, with a strong desire for balance and harmony in their relationships.

Scorpio ♏️

Fixed Water: Determined Introverted Feeling
Yin Mars: hidden strength, shadowy, intense

Scorpio is associated with the middle of fall and is known for its emotional depth and intensity. People with strong Scorpio energies are often seen as passionate and powerful, with a strong connection to their emotions and a natural inclination towards transformation. They are intuitive and deeply emotional, with a strong sense of mystery and a desire to delve into the unknown.

Sagittarius ♐️

Mutable Fire: Adaptable Extroverted Feeling
Yang Jupiter: adventurous, optimistic, faithful

Sagittarius is associated with the end of fall and is known for its adventurous and optimistic nature. People with strong Sagittarius energies are often seen as open-minded and free-spirited, with a natural inclination towards exploration and expansion. They are adaptable and resourceful, with a strong sense of curiosity and a desire for growth and expansion.

Capricorn ♑️

Cardinal Earth: Initiating Introverted Thinking
Yin Saturn: solid, determined, committed

Capricorn is associated with the beginning of winter and is known for its hardworking and disciplined nature. People with strong Capricorn energies are often seen as practical and ambitious, with a strong work ethic and a natural inclination towards success and achievement. They are focused and determined, with a strong sense of responsibility and a desire to build a solid foundation for the future.

Aquarius ♒️

Fixed Air: Determined Extroverted Thinking
Yang Saturn: disciplined, responsible, methodical

Aquarius, a fixed Air sign, is associated with the middle of winter and is known for its independent and unconventional nature. People with strong Aquarius energies are often seen as innovative and forward-thinking, with a natural inclination towards progress and change. They are open-minded and unconventional, with a strong sense of individuality and a desire to challenge the status quo.

Pisces ♓️

Mutable Water: Adaptable Introverted Feeling
Yin Jupiter: intuitive, understanding, transpersonal

Pisces is associated with the end of winter and is known for its emotional depth and sensitivity. People with strong Pisces energies are often seen as intuitive and emotional, with a natural inclination towards creativity and spirituality. They are adaptable and resourceful, with a strong sense of empathy and a desire to connect with others on a deep level.

Bonus: The Developmental Spectrum of Shadow to Gift

Taking it even further, we can add in a dimension of developmental maturity, where shadows transform into gifts. I have keynoted them as (shadow) → (gift) → (power) in the following chart. These are adapted from the Gene Keys website.

	Fire (bold expression, restless)	Earth (practical, stabilizing, organizing)	Air (relating, communicating, thinking)	Water (sensitivity, depth, feeling/intuition)
Cardinal (initiating, leading)	Aries: assertive warrior. Selfishness → independence → purpose.	Capricorn: wise elder. Authoritarian → humbleness → wisdom.	Libra: social diplomat. Imbalance → cooperation → connection.	Cancer: sensitive caregiver. Isolation → caring → nurturing
Fixed (focused, persistent)	Leo: dramatic leader. Conformity → courage → creativity.	Taurus: embodied sensuality. Stubborness → flowing → presence.	Aquarius: visionary change agent. Cerebral → contemplative → awakened	Scorpio: obsessive alchemist. Deception → authenticity → transformation
Mutable (adaptive, resourceful)	Sagittarius: expansive adventurer. Fundamentalist → explorer → faith	Virgo: intricate ritualist. Censored → ceremonial → centered.	Gemini: intellectual storyteller. Pretense → curiosity → play.	Pisces: empathetic mystic. Delusion → dreaming → remembrance.

Update: check out Part Two for even more thoughts on harmonic patterns.

(This blog post was written with the assistance of ChatGPT)