What are Aspects?
Welcome to the Aspects directory — one of the core atomic structures of the Astrology Arith(m)etic system.
This folder contains subfolders that group planetary aspects by harmonic families and geometric frequency. These files are the groundwork for interpreting planetary relationships — angular distances between celestial bodies that form the energetic latticework of every chart. Each aspect carries a distinct frequency, function and psychological/metaphysical tone.
What are Aspects?
Aspects are angular relationships between two or more planets and/or points in a chart, measured in degrees. They are the vibrtational geometry of astrology, influencing how planetary energies combine, clash, or synergize. Aspects reveal activation points in the psyche, soul path, and lived experience.
In Astrology Arith(m)etic, aspects are treated as modular units of archetypal interaction. Each folder within this directory represents a spcific aspect family or harmonic type.
Folder Categories
Harmonic
This category includs aspects derived from dividing the 360° circle by whole numbers — forming the basis of harmonic astrology.
Each harmonic yields a family of aspects with ist own core vibration:
- 2nd Harmonic: Opposition (180°), Duality, Reflection
- 3rd Harmonic: Trine (120°), Flow, Talent
- 4th Harmonic: Square (90°), Tension, Growth
- 5th Harmonic: Quintile (72°), Creative Genius
- 6th Harmonic: Sextile (60°), Opportunity, Movement
These divisions are based on resonant math and form the structure of frequency-based aspect interpretation.
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Septile Family
The Septile (51.43°) and its related angles arise from dividing the circle by 7, a number long associated with sacred or mystical symbolism. This family includes:
- Septile (51.43°) — fate, spiritual compulsion
- Biseptile (102.86°) — karmic tension, breakthrough
- Triseptile (154.29°) — spiritual alignment or disruption
These are non-Ptolemaic aspects and are often used in psychological, soul-based, or esoteric astrology. They are rare, subtle, and deeply patterned.
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Novile Family
From the ninth harmonic, novile aspects are about fulfillment, spiritual learning, and inner completion.
- Novile (40°) — sacred. Work, internal mastery
- Binovile (80°) — double growth
- Trinovile (120°) — overlap with trine energy but with a soul undertone
They resonate strongly in charts that show spiritual contracts, repetive life themes, or subtle callings.
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Decile Family
Based on the 10th harmonic (360°/10), this family focuses on personal ability and refined expression.
- Decile (36°) — subtle skill or gift
- Quindecile (24°) — 360°÷15, 15th harmonic; creativity, refinement, integration
- Tyl Quindecile (165°) — Noel Tyl / Reeves; obsession, drive, compulsion (11×15°; 24th-harmonic multiple of 15°, not 24°)
This group explores psychic intensity and minor-but-critical life currents. Always label 165° as Tyl Quindecile to avoid confusion with the 24° Quindecile.
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Undecile & Vadecile
Aspects from the 11th harmonic are rare and often used in high-weirdness or ultra-specific chart systems.
- Undecile (32.73°) — experimental insight, irregular genius
- Vadecile (18°) — a minor aspect of curiosity, stimulus, and instability.
These aspects are great for odd-numbered rituals, spiritual codes, or exsperimental intermretation techniques.
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Purpose in Astrology Arith(m)etic
This directory is a core layer of the entire Astrology Arithetic system, which is:
- A modular, expandable framework for astrological studies
- Designed to support CLI-based tools and future AI implementation
- Meant to be accessible, teachabe, and programmable for astrologers of all levels
Eventually, this folder will power:
- Custom command-line packages (e.g., ./aspect Mars Venus -date 06-09-2025)
- AI LLM training for interpretation generation
- Scriptable metaphysical engines and Obsidian-integrated prompts
Each aspect file can be thought of as a semantic glyph — a programmable, magical code.
Naming Convention
Files within each folder follow the format:
[Aspect Name].md
Each Contains:
- Glyph
- Exact degree
- Orb tolerance
- Geometric origin
- Interpretations (mental, emotional, physical, spiritual)
- Use in natal, transits, progressions and ritual astrology.
🧮 Master Table of Vault Aspects (exact arithmetic)
| Aspect | Decimal | D°M′S″ | Fraction | Harmonic |
|---|---|---|---|---|
| Conjunction | 0.0000° | 0°00′00.0″ | 1 | H1 |
| Vigintile · Vadecile | 18.0000° | 18°00′00.0″ | 1/20 | H20 |
| Quindecile · 6 | 24.0000° | 24°00′00.0″ | 1/15 | H15 |
| Semisextile | 30.0000° | 30°00′00.0″ | 1/12 | H12 |
| Undecile | 32.7273° | 32°43′38.2″ | 1/11 | H11 |
| Decile · 6 | 36.0000° | 36°00′00.0″ | 1/10 | H10 |
| Novile | 40.0000° | 40°00′00.0″ | 1/9 | H9 |
| Semisquare | 45.0000° | 45°00′00.0″ | 1/8 | H8 |
| Septile | 51.4286° | 51°25′42.9″ | 1/7 | H7 |
| Sextile | 60.0000° | 60°00′00.0″ | 1/6 | H6 |
| Quintile | 72.0000° | 72°00′00.0″ | 1/5 | H5 |
| Binovile | 80.0000° | 80°00′00.0″ | 2/9 | H9 |
| Square | 90.0000° | 90°00′00.0″ | 1/4 | H4 |
| Biseptile | 102.8571° | 102°51′25.7″ | 2/7 | H7 |
| Tridecile | 108.0000° | 108°00′00.0″ | 3/10 | H10 |
| Trine | 120.0000° | 120°00′00.0″ | 1/3 | H3 |
| Sesquiquadrate (Sesquisquare) | 135.0000° | 135°00′00.0″ | 3/8 | H8 |
| Biquintile | 144.0000° | 144°00′00.0″ | 2/5 | H5 |
| Inconjunction (Quincunx) | 150.0000° | 150°00′00.0″ | 5/12 | H12 |
| Triseptile | 154.2857° | 154°17′08.6″ | 3/7 | H7 |
| Quadrinovile | 160.0000° | 160°00′00.0″ | 4/9 | H9 |
| Tyl Quindecile | 165.0000° | 165°00′00.0″ | 11/24 | H24 |
| Opposition | 180.0000° | 180°00′00.0″ | 1/2 | H2 |
| Quadseptile | 205.7143° | 205°42′51.4″ | 4/7 | H7 |
| Quinseptile | 257.1429° | 257°08′34.3″ | 5/7 | H7 |
| Seseptile | 308.5714° | 308°34′17.1″ | 6/7 | H7 |
Trinovile (3/9 = 120°) named in the Novile Family section above is arithmetically identical to the Trine, so it has no separate note.
⚖️ Orb Arithmetic — Two Systems
1. Orb by aspect (modern, used in this vault’s aspect notes). Each aspect note states its own orb range in its header.
2. Orb by planet (traditional, Lilly 1647). Each planet carries an orb; two planets are in aspect when their separation from the exact angle is within the sum of their moieties (half-orbs).
| Planet | Lilly orb | Moiety (½) | Alternative “others say” orb |
|---|---|---|---|
| Saturn | 10° | 5° | 9° |
| Jupiter | 12° | 6° | 9° |
| Mars | 7°30′ | 3°45′ | 7° |
| Sun | 17° | 8°30′ | 15° |
| Venus | 8° | 4° | 7° |
| Mercury | 7° | 3°30′ | 7° |
| Moon | 12°30′ | 6°15′ | 12° |
Example: Sun–Saturn → 8°30′ + 5° = 13°30′ allowed for any Ptolemaic aspect between them. Outer planets and points were later given ~5° by convention.
📐 The Book’s Formula
The published edition expresses the vault’s method as: “Let a represent Celestial Body 1 … the aspect drawing a connection between the two bodies as the type of equation … the houses … an exponent” — (a + 1)² × (b + 2)³ = Interpretation. Aspect arithmetic above supplies the exact operator.
Sources (aspects master)
- William Lilly, Christian Astrology (London, 1647), Book I (houses, orbs p. 107, essential dignities table p. 104) — public domain; orb table transcribed at https://www.renaissanceastrology.com/aspects.html and https://www.skyscript.co.uk/aspectorbs.html
- Claudius Ptolemy, Tetrabiblos (2nd c. CE), Book I — trans. F. E. Robbins, Loeb Classical Library 435 (1940), public-domain text at LacusCurtius: https://penelope.uchicago.edu/Thayer/E/Roman/Texts/Ptolemy/Tetrabiblos/home.html
- Johannes Kepler, Harmonices Mundi (Linz, 1619), Book IV, Props. 9–14 (introduces quintile, biquintile, sesquiquadrate); background: https://www.skyscript.co.uk/kepler2.html
- John M. Addey, Harmonics in Astrology (1976) — harmonic (360°/n) theory of aspects
- Mikah Smith, Astrology Arith(m)etic — The Building Blocks of Astrology (Schizo Studios EPUB, 2025-12-31), vault copy: Astrology Arith(m)etic - Book Text