Maurizio Nicosia

The Lyric of the Universe

What is the most beautiful thing ?
Harmony - a Pythagorean answered -
Giamblico, Pythagorean life.

 

Armonia (Harmony), the daughter of the god of War and the goddess of Love, has inspired three of Eraclitus’ most powerful passages. The philosopher caught at first glance the essence of her mythical origins: «what opposes, converges, and from conflicting elements the most beautiful harmony arises». Armonia derives from the greek verb harmòzo, meaning «connecting, composing»; from the loan translation harmòs, or «junction».
What the etymology doesn’t explain, it emerges in the myth: through Armonia’s mythical origins, Eraclitus hints at a cognitive practise which has its meaning in separating and connecting. Plato will then refer to it in the Fedro.
In Eraclitus’ second passage the mythical setting remains: »harmony that comes back from an extreme to the other, like it is in the bow and in the lyre». The twelve Olympic deities attend to Armonia and Cadmo’s wedding, testifying the entire cycle of the solar revolution: it’s a cosmic wedding.
As wedding gifts, Armonia receives a lyre from Hermes and a golden dress from Athena while Giason’s mother initiates her to the Eleusinians mysteries.
Referring to the extremes, Eraclitus alludes to the opposite limits of time (the beginning and the end), those of the Universe (the Solstices) and those of the existence (life and death). So the harmony, returning to the other extreme, transcends the human sphere and the temporality itself.
Of the mythical narration, Eraclitus keeps the motif of the lyre, adding Apollo’s attribute, the bow. And it is considering these elements that the third passage (dear to architects and musicians of everytime) should be red: «invisible harmony is better than visible».
If it’s feasible to compare such elements to the Pythagorean doctrine of the harmony of spheres, then visible harmony would exist in the phenomenal world, while the invisible could be caught only in those intelligible relationships that determine the visible. Through the lyre, it’s perhaps possible to give back to this passage parts of its meaning: visible in itself, its shape shows the inner relations between the chords and the strings producing them.
Filolaos, a Pythagorean famous both for his harmonic science and for having made available to Platone the famous Pythagora’s books, is the first to state precisely the numerical relations corresponding to the intervals among the lyre’ four strings, whose lengths are equal to six, eight, nine and twelve units.

Il tetracordo di Filolao e i rapporti armonici basati sulle tre consonanze in accordo d’ottava, o diapason (6 : 12 = 1 : 2), quinta, o diapente (6 : 9, 8 : 12 = 2 : 3) e quarta, o diatessaron (6 : 8, 9 : 12 = 3 : 4).

Between the first and the last string, the relation is equal to one half, or diapason (octave); between the first and the third, as well as between the second and the fourth, the intervals are equal to two thirds, or diapente (quint); at last, between the first and the second, and the third and the fourth string the relations are equal to three fourths, or diatessaron (fourth).
In the Rome of the third and fourth century, Porfirio will describe in Armonia tolemaica the nature and qualities of harmonical consonance’s. «Invisible» harmony is therefore based upon the three consonance’s inherent to the first four numbers. In the platonic-Pythagorean discipline this has metaphysical and cosmological implications. The diapason or 1:2, shows the relation between the immovable origin or «deus absconditus» (Hidden God) and the «never-ending diade», or between the One and the manifold or, scholastically, between spirit and matter.
This principle already implies the other two consonance’s and so it constitutes the perfect harmony according to Filolao (6:12 = 6:8 + 8:12 or 6:9 + 9:12 ). In the diapente, or 2: 3, the matter, or female archetype, is related to number three, the revealed principle corresponding to nous or intellectus (Mind), and to the male archetype. In the diatessaron, or 3: 4, the revealed principle represents the «developed» matter, with the shape entering into relationship with the solid. The three consonance’s therefore describe the emanation that from the One goes on to the manifold, by their musical and geometric development. They are the lyric of a living organism, the lyric of the universe.
So, we can understand the reason why Vitruvius, who dedicates a whole chapter to harmony in his treaty on architecture, indicates in the relation 1:2 the ideal basal plan of the temple: it becomes the mirror of the poles between which the whole universe reveals itself, concerted and harmonical image of the world. For the same reason the ideal Masonic Lodge Room should develop according to this proportion, from East to West, from North to South, from Zenith to Nadir.
Leon Battista Alberti, the architect of the Malatesta’s temple in Rimini, build by strict Pythagorean proportions, wrote to Matteo de’ Pasti, the executor who was modifying parts of the project, not to spoil «all that music». So the architect as well has at his disposal a lyre for orchestrating the parts and volumes of a building, he separates and connects, articulating in the space the three consonance’s and the chords deriving from them. By the squares and the compasses, of course.

I tre rettangoli armonici, costruiti secondo le consonanze di diapason, o un mezzo (ill. 1, cioè 6/12), di diapente, o due terzi (ill. 2; 6/9), di diatessaron, o tre quarti (ill. 3; 6/8). Le proporzioni sono in neretto.