The solution to Gann's Law of Vibration from the 1909 Ticker Interview. Penicka analyzes Gann’s exact words correlating them with the cutting edge science of Gann’s day to develop a system which identifies the “mathematical points of force” behind all market action. The Periodic Table of Elements determines a system of order based upon atomic structure which generates a master number set for each market defining its structure in price and time.

Sean Erikson

Sean Erikson, a trader and fund manager with 25 years’ experience, provides a set of powerful astro-tools for advanced swing trading based upon celestial mechanics. The key tool uses an astronomical component which consistently and beautifully predicts the angle of attack or slope of a forthcoming trend. This is combined with a simple astro-timing tool which indicates the next 1-3 turns out and a geometrical price projection tool which provides the two most probable price projections for each move.

Robert Rundle

Rundle’s expertise lies in decrypting the complex hidden codes that W. D. Gann used to veil his deeper secrets in his book The Tunnel Though the Air. People spend decades studying and attempting to decode the meaning behind this seemingly sappy romance/sci-fi novel, without realizing that it is really a scaffolding for a vast template of knowledge centering around cycles and astrological relationships.

Alexander Straker

Straker's Universal Golden Keys Series uses Circular Scaling thru Time-by-Degrees to provide the key to accessing Pendulum Motion in the financial markets. Straker reveals that the core of Gann Science is dependent upon specific, hidden scaling techniques needed for tools to work. He has cracked Gann's scaling system and shows how Golden Mean is hidden in Gann's work.

Johannes Sundberg

Sundberg's The Secret Science of Squaring elaborates a major series of insights within the field of W. D. Gann’s astrological market forecasting. Sundberg has rediscovered an approach to the application Gann's of astro-geometric price/time conversion and projection principles which operates to square price and time on market charts using a system of planetary geometry and astronomical timing.

Dr Lorrie Bennett

Dr. Lorrie Bennett is one of the only Gann experts to have cracked the Law of Vibration! After 20 years of grueling research she discovered a complex code in Gann's texts which led her to the full solution. Following in Baumring's footsteps, Dr. Bennett lays out the science behind the Law of Vibration in an intensive 4 Volume Advanced Series revealing the Patterns, Numbers, Planets & Geometry behind Gann's secret trading system.

Timothy Walker

A detailed exploration and analysis of W. D. Gann’s Mechanical Trading System illustrating Gann's trading strategy over a period of 15 years. Gann turned $3000 into $6 million over this period, producing a 1400% return in the first 8 months alone. This study provides the foundation that Gann required for ALL of his students before learning to forecast. These techniques still work today producing 570% return in the S&P in 2014 in 3 months!

W.D. Gann Works

We stock the complete collection of the works of W.D. Gann. His private courses represent the most important of his writings, going into much greater detail than the public book series. Our 6 Volume set of Gann's Collected Writings includes supplementary rare source materials, and is the most reliable compliation of Gann's unadulterated vital work.

Table of ContentsPendulum Motion: The Harmony of the Circle

Book 1 of The Universal Golden Keys Series

By Alexander Straker

Introduction

Mathematics of Perfect Price-Time Spiral Symmetry
Pendulum Motion and Harmonic Vector Scaling
Slight Edge Theory
Foreword

Section 1: Harmonic Science & The Golden Mean

Chapter 1: The Science of Harmonics
- Characteristics of Harmonics
- What is a ‘Point of Resonance’ in the Market
- Price Behaviour at Points of Resonance
Chapter 2: Market Harmony and Resonance
- Music as a Model for the Market
- Octave Principle
- Seed Vector Provides Key Information for Future Growth
Chapter 3: The Golden Mean
- Mathematics of the Golden Mean
- A Fresh Look at the Significance of Numbers
- The Golden Mean Divided Spiral
- Deconstructing the Maths of Growth
Chapter 4: Fractal Nature of Markets & Elliott Impulse Waves
- Fibonacci and Fractals in Nature
- The Mathematical Genius of Benoit Mandelbrot
- Market Wave Movement and Fibonacci Based Structure
- Golden Mean and Fibonacci Based Structure
- Golden Mean Key to Growth Patterns of all Living Systems

Section 2: Application of Harmonic Circular Scaled Geometry & Pendulum Motion

Chapter 5: The Inner Workings of Pendulum Motion
- What is Pendulum Motion?
- Time-by-Degrees
- Angle of Pendulum Reaction Applied
- The Bifurcation Principle in the Market
Chapter 6: Alan Andrew’s & Roger Babson’s Action-Reaction
- Newton’s 3rd Law of Motion
- Interpreting Dr. Alan Andrew’s Median Line Rules
- The Action-Reaction Principle at Vector Angle Limits
- Cycles and Nodes of Wave Motion
- Identifying a Node
- Time Flow in Contrary Motion
- Action Reaction Using Elliot Pivots
Chapter 7: Lines of Force and Vector Thrust
- Locating Lines of Force
- The Speed of Price
- Vector Magnitude and Direction
- Parallel Lines of Force
- Correct Scaling Perfects Vector Harmonics
Chapter 8: Why Your Gann Angles Don’t Work
- Gann’s 1:1 Scale Principle and Common Challenges
- Harmonic Scale Adjustment Does Not Always Fix Problems
- What is the Ideal Scale? Next is a Universal Solution
Chapter 9: Harmonic Scaling - Baumring’s Gnomonic Principles
- Harmonic Scaling of a Vector and Pendulum Motion
- Square vs. Circle Based Scaling
- Mathematical Foundation Principle for Circle Based Scaling
- Universal Principles of Pendulum Motion
- Gann’s Key Hint
- Pendulum Forces of a Vector
- Progression of Time-by-Degrees as a Spiral
- Circular Scaling of a Vector
- The Perfection of a Circle
Chapter 10: Circle Based Harmonic Vector Scaling Mathematics
- An Elegant Starting Point
- Squaring Price geometrically with Time as Rotation
- Setting the Pendulum Motion Scale for any Vector
- Angle of Pendulum Reaction (APR) & Angle Critical Support (ACS)
- Harmonic Adjustment of the Scale
Chapter 11: Pendulum Tunnels
- Pendulum Motion Extension Lines
- Scaled Median Lines from a Single Vector
- Powerful NEW Median Line Application using Pendulum Motion
Chapter 12: Pentagonal Harmonic Growth Template
- Seed Vector DNA
- Steps to Building the Template
- Arc Limits of Growth
- Boxes and the Overall Square
- Elliott Wave Impulse & Fractal Growth
- Vector Thrust and Rotation of the Market
- Palindromic Pendulum Motion
Chapter 13: Timing Techniques
- Simple Price Time Squares
- Time Cycle Similarity
- Elliott Wave and Time Retracement Zones
- Applying Time Counts
- Time Cycles and Gann
- Gann Squares
Chapter 14: Targets, Set Ups & Campaigns
- Core Pendulum Angle Set Up
- Pendulum Tunnel Campaign
- Pentagonal Growth Template Campaign
- The Final Frontier Campaign from a Seed of Growth to End of W5

Section 3: Advanced Principles in Numbers, Music and Cycles

Chapter 15: Properties of Golden Mean Harmonics
- Properties of Mathematical Harmonics from the Golden Mean
- The Geometry of a Circle
- The Importance of Natural Cycles, the Golden Mean
- The DNA Spiral is a Golden Section
- Pentagonal Structure of a DNA Cross Section
- The Human Body
Chapter 16: A Fresh Look at the Significance of Numbers
- The Speed of Light
- Golden Mean and the Numbers of the Intangible
- Music and Key Numbers
- The Golden Mean Divided Spiral
- Deconstructing the Mathematics of Pentagonal Growth
- The Golden Mean Ratio and Harmonic Triads
- Extracting the Straker Golden Mean Cycle from a 360° Circle
Chapter 17: The Straker Golden Mean Cycle
- Harmonic Triad Degree Values (18 numbers)
- SGMC Time Counts and Solar Degree Harmonics
- Spiral Growth Harmonic Angles Using Golden Mean/Circle Ratio
- Hurst Nominal Cycles and SGMC Harmonic Triad Key Degrees
- Planetary Cycles and SGMC
- The Nature of Rotational Energy
- The Measurement of Time & The Natural Cycle of One Day
Epilogue: A Final Word

Summary of Theoretical Framework

The Incredible Properties of Mathematical Harmonics from the Golden Mean & the Geometry of the Circle

There are a number of deep mathematical concepts and logic-based proofs that are presented in both volumes which examine numerous subjects in esoteric mathematics and geometry. The following concepts are examined in the text in some depth, many of these ideas being presented for the first time. Experienced researchers may be familiar with some of these concepts already, but these foundations lead into the exploration of the mathematics behind the geometry, behind the markets. Also, some of this information will only make complete sense once other pieces of the puzzle fall in to place later on in the books…

The speed of light is precisely mathematically related to the GOLDEN MEAN = 161.8. The direct relationship may come as a great surprise if you have not seen this before. It will then become clear why the Golden Mean can also be thought of as a Golden Speed. Speed being distance over time (motion), a detailed mathematical framework is offered that unifies the Golden Mean with Light, Time and Motion.

The Speed of Light is shown to be directly proportional to the circumference of the Earth in an exact whole number ratio.

Using pure geometric circle-based mathematics, a ratio calculation is used to extract a numerical cycle from a circle based on the Golden Mean number triad. This will be referred to as the Straker Golden Mean Cycle (SGMC). The circle is then divided into golden mean ratio based ‘units’ and the key single unit to SGMC (in degrees of a circle) is revealed as a result.

If you ponder deeply on how this process is applied, you will see a great truth in the Golden Mean’s relationship with a circle and the growth cycles it produces. This unit is a ‘building block’ harmonically related to the Golden Mean, and offers proof of the validity of the now well recognized and ever present Elliott wave standard wave set: 5 wave impulse set followed by 3 wave retracement set (see works of Ralph Elliott, Jeff Kennedy, Robert Prechter).

All harmonics of the SGMC are then calculated using a matrix of summation triads (triad is a musical term for 3 notes) developed from the SGMC key single unit extracted from the golden mean/circle ratio in the previous step. These harmonics reveal some astounding numerical information and correlations with well-known trading methodologies that will enlighten Gann enthusiasts.

The SGMC harmonic set of degrees is demonstrated to be the numerical basis for the square of nine and presents in mathematical form exactly why any growth sequence comes to a natural end (decomposition). An incredible set of numerical relationships is presented proving the SGMC mathematics is a logic-based reasoning that provides evidence of why the square of nine principle works.

Although somewhat similar viewpoints have been explored before, I believe this is a brand-new way to mathematically examine and prove the Golden Mean connection with the Square of Nine. This deep logic-based insight and incredible viewpoint of market understanding is being openly exposed for the first time ever (to my awareness).

The calculation of the full harmonic degree set is then examined as a composition and decomposition wave with 6 possible harmonics per phase set of triads. The phases are mathematically shown to elegantly solve the movement pattern of the common Elliott Wave Set: 5 impulse + 3 corrective waves.

The same composition and decomposition wave sets derived from the SGMC are shown mathematically to be the basis for completing the musical Octave (OCTave = 8 = 5 + 3) which always results in a ‘squaring of nine’ at the completion of the Octave.

The mathematical reason a ‘squaring of 9’ ALWAYS occurs at the end of a SGMC composition cycle is then clearly presented and explained.

Next, the Speed of sound is shown to be directly proportional to the RADIUS of earth in an exact manner, again the ‘hidden in plain sight’ numerical relationship may shock you if you have not seen it before.

As we will have already proven, the speed of light is inextricably related to the Golden Mean (you will be blown away if you have not seen this before!!). Therefore, by extension the speed of sound is ALSO precisely mathematically related to the Golden Mean and this is shown to be the case mathematically by other means as well.

As many now know, ancient measurements in both time and distance are a function of earth rotation. One DAY is the key natural cycle, being the most important rhythmic cycle we experience throughout our lifetime. As the earth’s circumference is the distance completed by rotation in a circle (cycle), a unified theory that numerically ties together the Golden Mean, Speed of Light and Sound, Natural Cycles and Time and Distance measurements acquired via circular degrees of Rotation is developed.

Using a full cycle (circle of 360 degrees), the numbers representing distance moved over various portions of time by degrees and expressed in minutes and seconds of an arc is also examined for numerical relationships with music. The exact number of minutes in a day, then multiple days of a week (cumulative) will also be examined and again related back to musical frequencies, offering proof that key musical frequencies are harmonically inherent in natural cycles and their measurement by degrees.

The Speed of Sound is examined next for numerical and harmonic significance in relation to the Golden Mean (and by extension Light, Time and Motion!).

The distance in meters per second for the speed of sound will be converted to distance in inches. This number is examined for frequency relationships with music.

Distance will be further examined as inches. This can also be expressed in geodetic feet and inches, yards or nautical miles relating to the circular latitude/longitude circumference measurement of the earth = approximately 21,600 nautical miles. The harmonic value of this is 216, the harmonic language representing 1 rotation of Earth and will become important as we explore the numerical relationships between the Golden Mean, Light, Time, Sound, Motion and Earth.

The distance travelled by sound in inches per second will then be calculated to find out the numerical distance for a full cycle (circle) by multiplying distance per second by number of seconds in a full cycle. The results will be examined in relation to musical frequencies and in particular the relationship between the frequency of the musical note closest to the speed of sound and the frequency relating to the distance travelled during a complete cycle.

Finally, I will present the fully developed conclusion as a brand new Golden Mean based equation never published before: Straker’s Theorem.

Later in the practical applications section of this book, the Straker Golden Mean Cycle (SGMC) mathematical theory will be shown to have a very direct and astounding correlation with the historical cycles research of Hurst, co-validating both pieces of research from a completely different viewpoint.

If that is not enough co-incidence, the same SGMC again accounts for cycle harmonics of the outer planets! Inner planets are left to the reader to discover.