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PYTHAGORAS, THE FIRST PHILOSOPHER[1]

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During his youth, Pythagoras was a disciple of Pherecydes and Hermodamas, and while in his teens became renowned for the clarity of his philosophic concepts. In height he exceeded six feet; his body was as perfectly formed as that of Apollo. Pythagoras was the personification of majesty and power, and in his presence a felt humble and afraid. As he grew older, his physical power increased rather than waned, so that as he approached the century mark he was actually in the prime of life. The influence of this great soul over those about him was such that a word of praise from Pythagoras filled his disciples with ecstasy, while one committed suicide because the Master became momentarily irritated over something he had dome. Pythagoras was so impressed by this tragedy that he never again spoke unkindly to or about anyone.

From Historia Deorum Fatidicorum

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PYTHAGORAS[2]

Pythagoras of Samos (Ancient Greek: Πυθαγόρας ὁ Σάμιος ; 570 – 495 BCE) was an Ionian Greek philosopher, mathematician, and founder of the religious movement called Pythagoreanism. Most of the information about Pythagoras was written down centuries after he lived, so very little reliable information is known about him. He was born on the island of Samos, and might have travelled widely in his youth, visiting Egypt and other places seeking knowledge. Around 530 BC, he moved to Croton, a Greek colony in southern Italy, and there set up a religious sect. His followers pursued the religious rites and practices developed by Pythagoras, and studied his philosophical theories. The society took an active role in the politics of Croton, but this eventually led to their downfall. The Pythagorean meeting-places were burned, and Pythagoras was forced to flee the city. He is said to have ended his days in Metapontum.

Pythagoras made influential contributions to philosophy and religious teaching in the late 6th century BCE. He is often revered as a great mathematician, mystic and scientist, but he is best known for the Pythagorean theorem which bears his name. However, because legend and obfuscation cloud his work even more than that of the other pre-Socratic philosophers, one can give only a tentative account of his teachings, and some have questioned whether he contributed much to mathematics and natural philosophy. Many of the accomplishments credited to Pythagoras may actually have been accomplishments of his colleagues and successors. Whether or not his disciples believed that everything was related to mathematics and that numbers were the ultimate reality is unknown. It was said that he was the first man to call himself a philosopher, or lover of wisdom, and Pythagorean ideas exercised a marked influence on Plato, and through him, all of Western philosophy.

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THE PYTHAGOREAN THEORY OF MUSIC AND COLOR[3]

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TOPICS COVERED

THE PHILOSOPHY OF MUSIC

THE MUSIC OF THE SPHERES

THE PHILOSOPHY OF COLOR

SUB-TOPICS COVERED

THE INTERVALS AND HARMONIES OF THE SPHERES

THE CONSONANCES OF THE MUNDANE MONOCHORD

THE MUNDANE MONOCHORD WITH ITS PROPORTIONS AND INTERVALS

THE THEORY OF ELEMENTAL MUSIC

THE FOUR ELEMENTS AND THEIR CONSONANTAL INTERVALS

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THE INTERVALS AND HARMONIES OF THE SPHERES

(THE PHILOSOPHY OF MUSIC)

In the Pythagorean concept of the music of the spheres, the interval between the earth and the sphere of the fixed stars was considered to be a diapason--the most perfect harmonic interval. The allowing arrangement is most generally accepted for the musical intervals of the planets between the earth and the sphere of the fixed stars: From the sphere of the earth to the sphere of the moon; one tone; from the sphere of the moon to that of Mercury, one half-tone; from Mercury to Venus, one-half; from Venus to the sun, one and one-half tones; from the sun to Mars, one tone; from Mars to Jupiter, one-half tone; from Jupiter to Saturn, one-half tone; from Saturn to the fixed stars, one-half tone. The sum of these intervals equals the six whole tones of the octave.

From Stanley's The History of Philosophy.

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THE CONSONANCES OF THE MUNDANE MONOCHORD

(THE PHILOSOPHY OF MUSIC)

This diagrammatic sector represents the major gradations of energy and substance between elemental earth and absolute unconditioned force. Beginning with the superior, the fifteen graduated spheres descend in the following order: Limitless and Eternal Life; the superior, the middle, and the inferior Empyrean; the seven planets; and the four elements. Energy is symbolized by Fludd as a pyramid with its base upon the concave surface of the superior Empyrean, and substance as another Pyramid with its base upon the convex surface of the sphere (not planet) of earth. These pyramids demonstrate the relative proportions of energy and substance entering into the composition of the fifteen planes of being. It will be noted that the ascending pyramid of substance touches but does not pierce the fifteenth sphere--that of Limitless and Eternal Life. Likewise, the descending pyramid of energy touches but does not pierce the first sphere--the grossest condition of substance. The plane of the sun is denominated the sphere of equality, for here neither energy nor substance predominate. The mundane monochord consists of a hypothetical string stretched from the base of the pyramid of energy to the base of the pyramid of substance.

From Fludd's De Musica Mundana.

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THE MUNDANE MONOCHORD WITH ITS PROPORTIONS AND INTERVALS

(THE MUSIC OF THE SPHERES)

In this chart is set forth a summary of Fludd's theory of universal music. The interval between the element of earth and the highest heaven is considered as a double octave, thus showing the two extremes of existence to be in disdiapason harmony. It is signifies that the highest heaven, the sun, and the earth have the same time, the difference being in pitch. The sun is the lower octave of the highest heaven and the earth the lower octave of the sun. The lower octave (Γ to G) comprises that part of the universe in which substance predominate over energy. Its harmonies, therefore, are more gross than those of the higher octave (G to g) wherein energy predominates over substance. "If struck in the more spiritual part," writes Fludd, "the monochord will give eternal life; if in the more material part, transitory life." It will be noted that certain elements, planets, and celestial spheres sustain a harmonic ratio to each other, Fludd advanced this as a key to the sympathies and antipathies existing between the various departments of Nature.

From Fludd's De Musica Mundana.                                

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THE THEORY OF ELEMENTAL MUSIC

(THE PHILOSOPHY OF COLOR)

In this diagram two interpenetrating pyramids are again employed, one of which represents fire and the other earth. It is demonstrated according to the law of elemental harmony that fire does not enter into the composition of earth nor earth into the composition of fire. The figures on the chart disclose the harmonic relationships existing between the four primary elements according to both Fludd and the Pythagoreans. Earth consists of four parts of its own nature; water of three parts of earth and one part of fire. The sphere of equality is a hypothetical point where there is an equilibrium of two parts of earth and two parts of fire. Air is composed of three parts of fire and one part of earth; fire, of four parts of its own nature. Thus earth and water bear to each other the ratio of 4 to 3, or the diatessaron harmony, and water and the sphere of equality the ratio of 3 to 2, or the diapente harmony. Fire and air also bear to each other the ratio of 4 to 3, or the diatessaron harmony, and air and the sphere of equality the ratio of 3 to 2, or the diapente harmony. As the sum of a diatessaron and a diapente equals a diapason, or octave, it is evident that both the sphere of fire and the sphere of earth are in diapason harmony with the sphere of equality, and also that fire and earth are in disdiapason harmony with each other.

From Fludd's De Musica Mundana.

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THE FOUR ELEMENTS AND THEIR CONSONANTAL INTERVALS

(THE PHILOSOPHY OF COLOR)

In this diagram Fludd has divided each of the four Primary elements into three subdivisions. The first division of each element is the grossest, partaking somewhat of the substance directly inferior to itself (except in the case of the earth, which has no state inferior to itself). The second division consists of the element in its relatively pure state, while the third division is that condition wherein the element partakes somewhat of the substance immediately superior to itself. For example the lowest division of the element of water is sedimentary, as it contains earth substance in solution; the second division represents water in its most common state--salty--as in the case of the ocean; and the third division is water in its purest state--free from salt. The harmonic interval assigned to the lowest division of each element is one tone, to the central division also a tone, but to the higher division a half-tone because it partakes of the division immediately above it. Fludd emphasizes the fact that as the elements ascend in series of two and a half tones, the diatessaron is the dominating harmonic interval of the elements.

From Fludd's De Musica Mundana.

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[1] Hall, Manly P., THE SECRET TEACHINGS OF ALL AGES, “The Life and Philosophy of Pythagoras”, Copyright 1928 (http://www.sacred-texts.com/eso/sta/sta15.htm)

[2] “Pythagoras” (http://en.wikipedia.org/wiki/Pythagoras)

[3] Hall, Manly P., THE SECRET TEACHINGS OF ALL AGES, “The Pythagorean Theory of Music and Color”, Copyright 1928 (http://www.sacred-texts.com/eso/sta/sta19.htm)