#CosmicWisdomGr • Pythagoras • on Harmony of Spheres

 

Pythagoras • on Harmony of Spheres

Harmony is a state recognized by great philosophers as the immediate prerequisite of beauty. A compound is termed beautiful only when its parts are in harmonious combination.

 

The world is called beautiful and its Creator is designated the Good because good perforce must act in conformity with its own nature; and good acting according to its own nature is harmony, because the good which it accomplishes is harmonious with the good which it is. Beauty, therefore, is harmony manifesting its own intrinsic nature in the world of form.

 

Harmony & Tradition

 

ত According to Iamblichus, a Neoplatonist who lived from the third to the fourth century AD, Pythagoras’s journey to discover the arche of the universe started when he walked by a blacksmith shop and heard the sounds of various hammers hitting metal.

 

He realized that certain combinations of hammers produced sounds pleasing to the ear, where others did not. According to the legend, he went into the shop and after observing for a time, surmised that the differing weights of the hammers in combination produces either consonance or dissonance.

 

He noticed that consonance was produced by hammers that had a certain weight proportionate to one another. He then started to ponder why this was so – why proportion was so important.

 

Once, he was engrossed in the thought of whether he could devise a mechanical aid for the sense of hearing which would prove both certain and ingenious. Such an aid would be similar to the compasses, rules and optical instruments designed for the sense of sight. Likewise the sense of touch had scales and the concepts of weights and measures.

 

Using a monochord, Pythagoras is said to have determined the numerical ratios corresponding to the musical concordances: 1/2 for the octave, 2/3 for the fifth and 3/4 for the fourth.

 

 

If the notes of two strings, one string half the length of the other, were played simultaneously, this combination would make what is called a perfect octave.

The ratio of this harmonious proportion is 2:1. If the ratio of the string lengths is 3:2, then we have a perfect fifth and if the ratio is 4:3, we have a perfect fourth and so on. As such, Pythagoras discovered that mathematical proportions govern the relationship between notes.

It was a major achievement to discover that the pitch of a note was determined by the rate of the string’s vibration and that it depended upon its length. This discovery started the prominence in Pythagoreanism of the relationship between mathematics and music.

 

In 1618, Robert Fludd devised a mundane monochord (also celestial or divine monochord) that linked the Ptolemaic universe to musical intervals.
"Was it [Mersenne's discoveries through use of the monochord (1637)] physical intuition or a Pythagorean confidence in the importance of small whole numbers? ... It was the latter."

Harmony of Spheres

The Greek world compares the cosmos to a musical scale where the highest sounds are attributed to Saturn and to the heaven of the fixed stares. The Sun is indispensable for the realisation of harmony, since it corresponds to the central note that link two tetrachords, that is, two scales each composed of four sounds.

 

 

 

The astronomy of the Pythagoreans marked an important advance in ancient scientific thought, for they were the first to consider the earth as a globe revolving with the other planets around a central fire.  They explained the harmonious arrangement of things as that of bodies in a single, all-inclusive sphere of reality, moving according to a numerical scheme.

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

ত The sum of these intervals equals the six whole tones of the octave.

• Earth - Moon ~ a tone
• Moon - Mercury ~  a semitone [1/2 tone]
• Mercury - Venus ~ a semitone  [1/2 tone]
• Venus - Sun ~ three semitones [1 + 1/2 tone]
  
• Sun - Mars ~ a tone
• Mars - Jupiter ~ a semitone [1/2 tone]
• Jupiter - Saturn ~ a semitone [1/2 tone]
  
• Saturn - fixes stars ~ three semitones [1 + 1/2 tone]

The "harmony" as Kepler used the term is the universal order,embracing equally planetary laws, harmonies of music, weather and the patterns of man's life.

These are pure harmonies whereas sensory harmonies we hear while listening to music are echoes of the pure form. Inborn instinct in man makes his soul resonate to music and this provides the clue to the nature of the mathematical harmonies at its source.

Harmony & Life

 

ত Because the Pythagoreans thought that the heavenly bodies are separated from one another by intervals corresponding to the harmonic lengths of strings, they held that the movement of the spheres gives rise to a musical sound.

 

They believed that the distances between various planets in proportion to one another produced a celestial harmony.

 

They applied these principles to the human body, thinking of the soul as a kind of harmony.

• If our bodies and our souls are in correct proportion, then we will be in harmony and thus be healthy.
• When our bodies and souls are unharmonious, then we get sick and even die.
• The musical harmonies had a nourishing effect upon the soul and thus the body.

The Pythagoreans extended this concept of human music to ethics, morality, and government. A good government is one that governs harmoniously with itself and society. A person will live a harmonious life if he or she lives within ethical means and avoids the extremes.

Pythagoras believed that harmony was a virtue that played a central role in the life well-lived. He believed that harmony between individuals and groups with different needs and preferences was crucial for communities and societies to prosper, and that some form of harmony between humanity and nature was indispensable for a good and sustainable way of living.

He believed that the pursuit of harmony through music, knowledge, and virtuous living was essential for achieving human flourishing. He believed that the pursuit of harmony was not only a means to an end, but also an end in itself, and that it was a fundamental aspect of Eudaimonia.

Pythagoras believed that an understanding of the universe and its beauty could bring with it a participation in that beauty, and that this could elevate the soul to a higher level of immortality.

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Wrap up to Farewell...

Harmony, the immediate source of beauty, unites the parts into a beautiful whole. The world's beauty stems from the Good's innate harmony, for goodness acts in accordance with its nature.

Pythagoras' discovery began with the sounds of hammers in a blacksmith's shop, leading to the realization that proportion and mathematical ratios govern harmonious combinations.

This harmony extends to the cosmos, with planets representing harmonious intervals, and to the human body and soul, where proper proportion leads to health.

Embracing harmony in all aspects of life, from ethics and governance to a connection with the universe's beauty, is essential for human flourishing and the elevation of the soul to a higher level of immortality.

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Related #CWGR Articles :

Proclus • Universe Harmony & Methexis
Plotinus • on Symmetry, Beauty, and Unity

#CosmicWisdomGr • Pythagoras

Articles Index • Philosopher's threshold

#CWGR Archway

 

Available readings on Bookshelf :

Pythagoras and the Delphic Mysteries - Edouard Schure

Iamblichus' Life of Pythagoras - Thomas Taylor 

 Secret teachings of All Ages - Manly P. Hall

 

 

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