Pythagorean Harmony and Cosmic Order in Plato's Timaeus

The text is evidently divided into 3 fundamental parts preceded by a small initial prologue dealing with Atlantis: the first part treats the constitution of cosmic intelligence, the archetypal structure of the cosmos, the World Soul, its formation, the beginning of time and the creation of planets; the second treats the formation of the world, and therefore its material principle, the structuring of forms through the four elements and the cosmic solids later called Platonic: All material bodies are formed from the four elements which are geometrically represented by the 4 Platonic solids: earth = cube; air = icosahedron, water = octahedron, fire = tetrahedron and finally the fifth element represented by the dodecahedron. The third speaks of the nature and constitution of man: from the World Soul indeed various souls divide and these in turn constitute the various bodies. All the discourse as mentioned is not made by Socrates but by Timaeus of Locri who is precisely an exponent of Pythagorean doctrines. And who speaks of the World Soul reproposing Pythagorean doctrines. At the base of the entire Timaeus lies the awareness that the Universe is a living whole, indivisible, there exists no part independent from another. Why is the Timaeus important? Because the Timaeus constitutes the basis of our approach to analyze and see the Universe. What does the Timaeus say? Visible harmony is the expression of an invisible Harmony, an archetypal order: that is, harmony before being visible harmony, auditory harmony, harmony of the senses, first of all harmony is an Idea and the purest and clearest description of this idea can occur through mathematical relationships. This is the fundamental nucleus for which it will be fundamental in the centuries. The Harmony of the Universe, the mechanism of the Universe, everything that exists and that regulates universal phenomena: 1. is Harmonic and 2. can be expressed and traced back to numerical laws (Everything is ruled by Number). If you think about it, this is a vision very similar to our current one (the idea of being able to trace back to mathematical laws what happens in the Cosmos). Clearly the Pythagoreans did not have our vision of modern Physics, quantitative, speculative and rational, they had another, qualitative, practical and intuitive. The Tetraktys and Musical Harmony. In the Pythagorean tradition the mysteries of all creation were contained by a single number: the number 4. This is affirmed by Iamblichus in theologia arithmetica who calls this number the "guardian of nature's secrets". The Pythagoreans thought of the Cosmos as a whole, as a single Soul, precisely the World Soul that Timaeus speaks of, which was arranged and harmonized according to this number 4. This most probably refers to the mystery of the number 4 to the mystery of the creation of the Tetragrammaton the divine name of four letters etc... In particular the Pythagoreans developed this number four making it derive from unity with a symbol that subsequently became very famous: The divine Tetraktys. The idea of the Tetraktys corresponds to the idea of the development of the One Absolute and transcendent God that develops according to various aspects and various personalities the last of which is the most corporeal and the source of eternal nature, the 4 is as if it were the body of God, the corporeal manifestation of divinity, indeed in subsequent Christian qabbalistic speculation it is put in relation to Jesus Christ (In the name of God the Father, Son, Holy Spirit and of Jesus Christ). So this symbol, on one hand represented divine interiority, but which was mirrored in natural interiority so it represented the mirror of eternal nature, the interiority of all mysteries and of the structure of the cosmos which were evidently structured according to harmonic relationships. Why? Because the fundamental harmonic relationships of musical harmony derived precisely from these 4 numbers. Indeed if we take two strings of equal make and consider them of length $1:2$ we obtain an octave interval which is indeed the diapason. between 2 and 3 we obtain the fifth interval which is the diapente; between 3 and 4 we obtain the fourth interval which is the diatesseron. To give you an idea if we give the value 1 to the note C we obtain the diapason with the C of the upper octave, with the diapente which is the fifth and is G, and with diatesseron which is the fourth which is F. These four notes were called the tetrachord of Philolaus and have importance because they are the tonic, dominant and subdominant of the Eighth musical mode, a derived mode having C as tonic, G as dominant and F as subdominant. The Tonic, dominant and subdominant represent the classical centers of gravity of melody. For example, a canonical way of composing music in antiquity was to start from the Tonic and rise to the dominant pausing on the subdominant. Then from the dominant return to the tonic pausing on the subdominant and then rise again to the dominant and again to the tonic but of the octave above. Five-pointed Star and Golden Proportion. Another element present in the Timaeus is that this is the first writing in which a relationship that will be fundamental for the history of art is explicitly described. A proportion so special that it will be called divine or golden: "And the most beautiful of bonds is that which of itself and of the bound things makes one thing in the supreme degree. And this by its nature in the most beautiful way fulfills the proportion. For when of three numbers or masses or powers whatever you want, the middle stands to the last as the first stands to the middle, and furthermore, in turn that middle stands to the first as the last stands to that middle, then the middle becoming first and last, and the last and the first becoming both middle, in this matter it will necessarily happen that all the proportions are the same, and, having become the same among themselves, all will be one unity." Plato, Timaeus [32-33]. Here Plato makes clear the importance of proportion itself which manages to create a living relationship of union among all parts while leaving them hierarchically distinct. Plato concludes precisely saying that...