Pythagorean Harmony and Kepler's Cosmic Order

The cosmos was evidently structured according to harmonic ratios. Why? Because the fundamental harmonic ratios of musical harmony were derived precisely from these 4 numbers. Indeed, if we take two strings of equal quality and consider them of length $1$ to $2$, we obtain an octave interval - the interval 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 assign 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 and is F. These four notes were called Philolaus's tetrachord and are important 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, dwelling on the subdominant. Then from the dominant return to the tonic dwelling on the subdominant and then rise again to the dominant and again to the tonic but of the octave above. Just as melody is attracted by particular notes that express its movements, so the human soul also has centers of gravity that represent its expression. We will see how in subsequent speculation, particularly with Fludd, attention will be placed on a correspondence between musical notes, states of soul, consciousness and points of the body. Therefore, fundamental point: Classical harmony is regulated by the first 4 numbers: $1, 2, 3, 4$ which can be seen as the tetraktys. When instead one wants to develop the musical scale more thoroughly, the other notes with other intervals are also inserted, but for what we need for the moment this is enough. In subsequent speculation, the Pythagoreans, then taken up by Plato, had defined a true mathematics of harmony, an objective science of harmony that defined what was beautiful and harmonic in contrast to what was casual and disharmonic. It is important to understand therefore that in this context harmony is no longer just a set of consonant notes, but harmony is an idea: the visible or intelligible manifestation of an archetypal order of Divine Being through a Universal Hierarchy. Visual harmony is equal and governed by the same laws as auditory harmony, which is why these proportions are used for example in the construction of Gothic temples that are structured following this aesthetic approach. Harmony therefore is the visible manifestation of an archetypal order that reveals Divine Being. In this context the most important harmony is the celestial Harmony of the planets and the Cosmos which are structured according to archetypal proportions: Hermeticism, Neoplatonism and the Harmony of the Spheres. "Moreover, knowing music is nothing other than knowing the order of all things and the divine design that has thus ordered them; the order indeed, in which all individual things have been united in a single whole by the intelligence of a creator, will produce a kind of sweetest and true harmony of divine music." Hermes Trismegistus, Asclepius, 13. Here is the starting point that moves Kepler in his investigations of the cosmos. Kepler and the structure of the Cosmos. Kepler's Heliocentrism. This is another important point. Kepler embraces the Copernican theory because, he says in Dissertatio cum Nuncio Sidereus: "The Sun is truly at the center of the cosmos, it is the heart of the cosmos, the source of light, the source of heat, the origin of life and the movement of the world." Against the Copernican system there were various fundamental objections: the first, as Heisenberg notes, is the experimental one. Around the sun rotate the eight spheres that depend on it: that of the fixed stars, the six spheres of the planets and the unique sphere that surrounds the earth. Angels depend on these spheres, men on angels and thus everything and everyone are dependent on God. Corpus Hermeticum, discourse XVII, 17. Universal Harmony is expressed by the celestial spheres because the Heavens sing the Glory of God. Therefore -says Kepler- "All investigations of the external world should lead to discovering the order and harmony imposed by God. Astronomers are priests of the Most High God in relation to the Book of Nature, therefore it is our duty not to seek our glory, but the glory of God above all else." Therefore Kepler begins in 1596 the investigation of universal harmony based principally on Geometry. Geometry in fact allows us to highlight the hidden structure of things and grasp the order that is the harmony that these have. The Mysterium Cosmographicum. Harmony and Geometry. Studying the influence of planets on human life, Kepler realizes that the relative positions of planets that Ptolemy reports and that influence man, are expressed by simple geometric aspects in relation to regular geometric figures. Kepler conceives that if such a discourse is valid for the influence of planets on man then it must also be valid for the motion of the planets themselves which for theological reasons occurs around the sun. Thus Kepler, placing the sun at the center of the cosmos and embracing the Copernican theory, after years of study realizes that the planets, the orbits of the Copernican theory can be derived by inscribing and circumscribing Platonic solids. Since each Platonic solid corresponded to an element, Kepler assigns this solid to the element corresponding to the planet whose orbit he wants to find and thus finds the right succession of planets. Kepler remains ecstatic about the discovery which he will always consider as his greatest result. This result indeed made him known. The Harmonices Mundi. However in the discourse of astrological aspects there is another element that he has not yet managed to find and that...