Music, Number Mysticism and Sacred Geometry: The Legacy of Pythagoras

 

Pythagoras was an ancient Greek mathematician/mystic.  He is most famous for the right triangle theorem named after him: a² + b² = c².  In all likelihood he did not discover it.  It is believed that he learned it while studying with priests in Egypt.  However in the West he gets credit for it.

 

 

 

Pythagoras also studied music and discovered that pleasant sounding musical chords and note sequences are related to each other by whole number string length ratios.  In more recent times this idea has been extended to whole number sound frequency ratios.  Modern western music is based on his studies.  Western music is based on a 12-tone equal temperament tuning system designed to maximize pleasant sounding musical ratios while minimizing unpleasant sounding ratios.  This system generally does not create exact whole number ratios but approximates whole number ratios closely enough that the music sounds good.  It is based on the twelfth root of 2 which is irrational but produces close approximations to whole number ratios.  Pythagoras also studied how music can affect human emotions causing joy, motivation, energetic behavior, melancholy, lethargy, depression, focused seriousness, tension, anger, violence, whimsy, relaxation, peace, pacifism etc.  The western tuning system is sometimes blamed for what some people perceive as the violent nature of western civilization due to the fact that the musical ratios are not generally exact whole number ratios.  The slight deviation from exact ratios creates tension in the nervous system which manifests as anxiety and violence.

 

Pythagoras was the founder of a mathematics based religious cult.  His followers were called Pythagoreans.  He apparently claimed to be a son of the Greek god Apollo.  The group studied numbers, music and geometry and attributed religious significance to their discoveries.  In ancient times understanding mathematics and science was equivalent to understanding the mind of God.  Math and Science were natural ways of showing reverence to and worshiping the creator deity.  The present day split between math/science and religion is due to a corruption of our modern religions.

 

Compass and straightedge geometric constructions were also a major feature of his teachings.  These promoted visualization abilities as well as complex thinking and problem solving skills.  These abilities were applied to artistic design as well as architectural design of temples and other major civic structures.

 

Below is a quick listing of some topics which he influenced.

 

 

 

WHOLE NUMBER MUSICAL RATIOS

 

1/1     2/1     4/1     8/1     Unison, Octave, Double Octave, Triple Octave     2°    2¹     2²     2³

 

1/1     2/1     3/2     4/3     Unison, Octave, Fifth, Fourth     In order of importance, pleasantness of sound

 

Whole number musical ratios are very good for the human nervous system and can reprogram the nervous system to a higher state of functioning.

 

 

 

NUMBER MYSTICISM

 

a² + b² = c²          The Pythagorean Theorem     Right Triangle Mathematics

 

1, 1, 2, 3, 5, 8, 13, 21 …     The Fibonacci Sequence     Named after an Italian mathematician, it was likely known by Pythagoras as learned from the Egyptians.  Important because natural patterns of growth seem to be related to this sequence.  The ratio of adjacent terms of this sequence approaches a number called the golden ratio, approximately 1.618, and its reciprocal .618     The exact value is (1 + √5)/2

 

111, 222, 333, 444, 555, 666, 777, 888 ,999, 000     Numbers consisting entirely of repeating digits     The numbers shown are fractions of 9 scaled up by a factor of 1000 and then truncated to form integers.  To learn more I suggest you read the book “Jesus Christ, Sun of God: Ancient Cosmology and Early Christian Symbolism,” by David Fideler.

 

 

 

SACRED GEOMETRY

 

Pentagram     The five pointed star     Important because it contains segment lengths whose ratio is the golden ratio: approximately .618 or 1.618

This symbol has been slandered and corrupted and is today considered and used as a symbol of satanism.

 

The Vesica Piscis     A shape generated through geometric construction which represents the cross, the female vagina, the intersection between the spiritual and material worlds.  It is symbolic of Tantric Hindu, Tantric Buddhist, Greek Dionysian and Christian Sexual Techniques of Attaining Spiritual Enlightenment.

 

 

The Platonic Solids     Tetrahedron, Cube (Hexahedron), Octahedron, Dodecahedron and Icosahedron     Some sources give Pythagoreans credit for discovering the Dodecahedron.  These solids represent the five elements of earth, water, fire, air and spirit.  They also represent chakras of the human body.  The ancient Greeks used a five chakra system as opposed to the seven chakra esoteric Hindu/Buddhist system popular in the west today.  The platonic solids can be used for visualization during Chakra Based Meditation Techniques.

 

The Tetraktys     Consists of ten circles arranged in the shape of an equilateral triangle.  The base of the triangle has 4 circles, the next higher level has 3 circles, then 2 circles, then 1 circle, as you move higher.  The tetraktys is an ancient Pythagorean symbol encoding certain whole number musical ratios which when played on an instrument stimulate energy movement in the body and results in spiritual development.

 

 

 

 

7-20-2017