I misteri di San Miniato al Monte. ll significato dello zodiaco della navata (4)

Poiché attraverso il simbolo del Cristo-Pesci siamo saliti in cielo ed ora ne discendiamo, ossia ci incarniamo attraverso l’immagine del Toro, è naturale che questa immagine sia disposta in modo particolarmente significativo, forse in modo da metterci nuovamente in rapporto con il moto del sole.

Il mistero del Toro è legato al singolare orientamento della chiesa stessa. Durante il Medioevo quasi tutte le chiese erano orientate con l’altare verso est. S. Ambrogio ci conferma che fatto di volgersi dall’occidente verso oriente, in quanto parte del rituale, è un atto di rinuncia al Diavolo e di accettazione della luce di Cristo. Ogni giorno Cristo ‘sorge’, come il sole che sorge ad oriente.

Ora, una delle caratteristiche più straordinarie della basilica di S. Miniato è che contraddice il complesso delle norme stabilite per l’orientamento delle chiese. Non è assolutamente orientata verso est. Lo si vede facilmente se, uscendo dalla chiesa, ci si affaccia su Firenze: si noterà che tutte le altre chiese della città (il Duomo in maniera più evidente) hanno gli assi longitudinali orientati in modo del tutto diverso da S. Miniato. È chiaro comunque che, se S. Miniato fosse stata rivolta ad oriente, obbedendo alle leggi di costruzione delle chiese, il miracoloso effetto di luce sul piede di Cristo non avrebbe potuto verificarsi in nessun giorno dell’anno. E quindi possibile che l’orientamento sia stato stabilito proprio allo scopo di permettere questa magia di luce sul piede di Cristo.

Scopriamo comunque che una sorprendente deviazione nell’orientamento rende possibile anche questo importante simbolismo legato al sorgere del sole. Il fatto è che lo zodiaco è sfato orientato in modo tale che il sole si levi ogni giorno nella direzione del settore occupato dal Toro! E l’arco di 30° del Toro che ogni giorno saluta il sole nascente, perché è orientato ad est.

Come la luce dei Pesci è usata per indicare un miracolo di luce che si rinnova simbolicamente ogni anno, troviamo adesso che il sorgere del sole ogni giorno è in relazione con lo zodiaco, attraverso il segno del Toro. Il toro mancante, simbolo del Cristo-Logos, si trova proprio dove nasce il sole. E proprio qui che troviamo il ‘Toro’ mancante, risuscitato ogni giorno come il Cristo-Pesci è risuscitato ogni anno. Il sole sorge e tramonta all’interno della chiesa secondo i ritmi legati ai due importanti simboli cristiani del Toro e dei Pesci.

Sia l’orientamento dello zodiaco che quello della chiesa stessa sono in stretto rapporto con il movimento del sole. Quando l’insigne scultore Antonio Rossellino ultimò la tomba del Cardinale Principe del Portogallo a S. Miniato, doveva essere a conoscenza del nesso fra il Toro ed il sorgere del sole. Lo spigolo di questa tomba era esattamente allineato con il Toro e la direzione del sole, per cui l’artista collocò all’angolo, in modo da sfuggire ad una visione frontale, l’immagine di un toro! Si tratta di un Toro Mitriaco, sul punto di essere sgozzato.

Abbiamo così completato il ciclo di questo mistero di S. Miniato. Abbiamo cominciato dal disco solare al centro dello zodiaco, siamo stati trasportati dai Pesci nella traiettoria del sole al tramonto, e siamo stati ricondotti allo zodiaco solo per essere nuovamente proiettati al di là della chiesa verso il sorgere del sole. I Pesci ed il Toro irradiano intorno a noi il loro simbolismo solare. Se solo ci soffermiamo un poco sul prodigio di pensiero e di tecnica che hanno reso possibile questa splendida concatenazione di simboli, cominciamo a capire perché questa fosse la chiesa preferita di giganti quali Dante e Michelangelo, che sicuramente dovevano conoscerne i segreti.

Il vero mistero del Toro-Logos deve tuttavia essere ancora pienamente esplorato. Per renderci conto di un ulteriore piano simbolico dobbiamo considerare nuovamente la data dello zodiaco, chiaramente incisa sul marmo. Ricerche specifiche hanno recentemente dimostrato che nell’anno di fondazione dello zodiaco si verificò un evento celeste piuttosto unico. Il 28 Maggio 1207 ci fu un accumulo di non meno di cinque pianeti nel segno del Toro! Quel giorno il Sole, la Luna, Mercurio, Venere e Saturno si trovavano tutti nel segno del Toro, a pochi gradi di distanza l’uno dall’altro. L’oroscopo per l’alba di quel giorno indica nel Toro una situazione planetaria ripetibile solo a distanza di migliaia di anni!

Vediamo dunque che il tema del Toro non è solo legato al simbolico sorgere del sole, ma si riferisce alla stessa fondazione della chiesa. In questo simbolismo incentrato sul Toro vediamo realizzata l’armonia che gli antichi artefici ricercarono – un’armonia tra Cielo e Terra. Con fondatezza perciò lo scalpellino che incise la data definì lo zodiaco rumine cœlesti, ‘una divina immagine del Cielo’.

Incidentalmente noteremo che il simbolismo segreto espresso con tanta arte all’interno della chiesa si riflette anche all’esterno, sulla facciata che guarda su Firenze. Il simbolo dei due pesci si ritrova nel riquadro intarsiato sotto la grande croce che domina la facciata. Qui ci sono due esseri semi-umani, che si mettono ciascuno un pesce in bocca. Si tratta di un’evidente allusione all’aspetto sacramentale dell’Eucaristia, l’assorbimento del Corpo di Cristo in noi.

Anche il simbolo del Toro mancante si esprime sulla facciata. Alla sommità della chiesa, c’è su di un piano l’aquila appoggiata sopra una balla di lana, simbolo dei Lanaioli che contribuirono maggiormente alla costruzione della basilica. Si tratta naturalmente dell’aquila simbolo di S. Giovanni, parallela a quelle già trovate nel mosaico absidale e sul leggio del pulpito. Sotto, all’estremità delle due gronde, c’è da ambo le parti un essere umano, nella posizione generalmente indicata dagli storici dell’arte come l’orante. E la raffigurazione antica dell’essere umano spiritualizzato, ed è qui l’equivalente dell’essere umano alato di S. Matteo che abbiamo visto anche nel mosaico dell’abside e sul pulpito. Più in basso, alla base delle due colonnine che incorniciano la finestra quadrangolare al centro, vediamo due teste leonine. Questi sono naturalmente i leoni simbolo di S. Marco. In nessuna parte della facciata troviamo l’immagine del toro… Eppure, se la nostra interpretazione del simbolismo nascosto dell’interno è esatta, dovremmo vedere il toro come simbolo nascosto del Cristo-Logos, che ha sacrificato il proprio sangue per gli uomini. Potremmo riconoscere questo ‘Toro mancante’ nell’immagine della croce trionfante che domina la sommità della facciata. Il toro si aggiunge alle altre tre immagini per costituire la quadruplicità fissa dello zodiaco, che nella tradizione cristiana rappresenta la croce sacrificale. E qui, sulla facciata, che il simbolo dell’Incarnazione e della Redenzione (la Croce) si incontra con il simbolo dello Spirito (il Pesce) nella croce innalzata sull’immagine dei Pesci!

Abbiamo osservato tre diversi ritmi nella Chiesa, tutti legati allo zodiaco. Abbiamo per primo il ritmo quotidiano, espresso dall’orientamento del Toro verso il sorgere del sole. In secondo luogo abbiamo il ritmo annuale espresso dal culminare della luce esattamente sul piede di Cristo, e lo chiameremo il ritmo dei Pesci. Infine abbiamo i ritmi planetari, espressi dalla data dello zodiaco. Ciascuno di questi ritmi richiede la partecipazione attiva dell’essere umano: dobbiamo personalmente metterci sul sole dello zodiaco, salire i gradini, sperimentare la magia della luce solare, ritornare allo zodiaco dietro suggerimento del leone, e così di seguito. C’è una perfetta coordinazione di movimento tra gli elementi simbolici della chiesa. Il sole dello zodiaco dentro la chiesa, i raggi del sole che penetrano nella chiesa, il sorgere ed il tramontare del sole ogni giorno nel nostro sistema solare, sono tutti integrati in questo gioco di simboli, e muovendoci tra i simboli della chiesa, noi stessi facciamo eco al moto del sole. Il sole è usato per offrire una sorprendente immagine del Cristo, che domina l’interno della chiesa dal Suo trono di gloria e all’esterno regna sulla terra. E perfettamente integrato in questa armonia di interno ed esterno è l’essere umano, che porta il Cristo in sé.

Autore: Fred Gettings
Pubblicazione:
I misteri di San Miniato al Monte
Editore
Arti Grafiche
Luogo: Firenze
Anno: 1978
Vedi anche
I misteri di San Miniato al Monte. ll significato dello zodiaco della navata (1)
I misteri di San Miniato al Monte. ll significato dello zodiaco della navata (2)

I misteri di San Miniato al Monte. ll significato dello zodiaco della navata (3)

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Early Christian Sources of Platonic Geometry: Augustine (1)

Ambrose presumably had less need for Latinizers because of his own knowledge of Greek. It was partly this and his enthusiasm for Greek thought, both classical and Christian, and in particular the Platonists whom he regarded as the ‘aristocrats of thought’ that contributed to his standing as one of four Doctors of the Western Church.
In addition to adapting Basil’s Hexaemeron,
he eagerly collected other Greek works, especially those of Origen, from whom he acquired his own understanding of allegory. Ambrose’s contact with the Greek world evidently made his sermons the most progressive in the West and it was into this environment that Augustine (354-430) arrived in 384.

Symmachus, the Prefect of Rome and one of the leading pagans of his day, had recommended Augustine for the post in rhetoric at the court of Milan. On his arrival from Rome, however, Augustine soon fell deeply under the influence of Ambrose and his sermons. In just two turbulent years he had contemplated withdrawing from the world with a band of amateur philosophers; he had been introduced to various Neoplatonic writings in the translations of Victorinus, including probably the Enneads of Plotinus; then
having turned to Simplicianus who particularly impressed him with the earlier conversion of Victorinus, Augustine underwent his own conversion; and, following a breakdown, he penned four Dialogues during his convalescence which marked his arrival as a Christian Platonist thinker, teacher and writer.

It is of crucial importance to this study that his massive output, together with his command of classical and Christian thought and his ability to conduct an argument derived from personal reflection, ensured his place along with Gregory as the foremost authority for the Latin Church in the tenth century and either side of it.
Being comprehensive in span, his writings are concerned not only with purely theological interpretations of scripture and the Christian revelation but with Christian philosophy as well. In this he reveals the Platonic underpinning of his own thought, particularly that related to the universe, harmony and numbers, to the extent that he is credited with transmitting to the medieval Church the best account of Plato’s teaching, thereby securing its acceptance by the Church.
Among the first of the early Dialogues was De ordine. Another Platonic work, De musica,
was started a year later in 387 along with his treatise De quantitate animae. After an interval of ten years his Confessiones,
compiled over a period of four years, also contains an exposition of Platonic metaphysics. This was overlapped by his treatise De Trinitate which was written between 399 and 419. During this time he commenced his greatest undertaking, De civitate Dei,
a work of twenty-two volumes which was perhaps the most widely read of all books early in the middle ages apart from the Bible itself. It was written throughout the years 413 to 427, with what can be considered the Platonic volumes of the work, VIII-XI, coming over two years from 415. Finally, as he was nearing the end of De civitate Dei,
he issued his Retractationes in about 427.

It needs to be borne in mind, however, that since Augustine’s search for truth had already caused him several revisions, the views expressed in this huge collection of writings are neither uniform nor unchanging. For example, De ordine is a treatise dealing with the liberal arts as the path leading to comprehension of the universal order. It shows that their evolution was rational because it was orderly and it concludes with a generous tribute to Pythagoras. This and the predominance accorded the liberal arts were subsequently moderated, though by no means actually retracted, in his Retractiones. De musica, on the other hand, constitutes a six-volume work on rhythm that was meant to be complemented by a further six on melody. The first five serve as an introduction to Book VI which places number and music in a cosmological scheme that is essentially Platonic and reflects material in Timaeus. The work as left by Augustine largely follows a Greek treatise on music written in the second century by Aristides Quintilianus.
However, the Platonic content of De musica and the early Dialogues which it followed was shortly to be put into perspective in Confessiones as being but a preparation, albeit a necessary one, for understanding the Christian mysteries. This was a similar conclusion to Clement’s, yet the importance of Platonism was hardly diminished thereby, for it is abundantly evident from his later De civitate Dei that the discipline of Platonic thought and the basic precepts of its natural philosophy remained indispensable for such an understanding.

However, this did not place Platonists beyond criticism, especially those who found the idea of the Incarnation of the Son of God profoundly distasteful. Augustine recalled Simplicianus recounting how one Platonist had maintained that the quotation, “The Word was in the beginning of all things, and the Word was with God”, should be displayed in gold in every church. This was sufficient, it was argued, and some could not accept the Christian sequel that “The Word was made flesh”. Porphyry in particular was repelled by the suggestion that the Word, as Christ Incarnate, should appear as a body from a woman, bleed on the Cross and become resurrected. This earned Augustine’s dismissal:

But god, the great teacher, became of no account in the eyes of the proud [Porphyry and the Platonists] simply because “the Word became flesh

De civitate Dei X.29

I read there that the Word, God, “was born not of the flesh, but of God”. But, that “the Word was made flesh and dwelt among us” – I did not read that there that “in due time He died for the ungodly” and “that Thou didst not spare Thine Only-begotten Son, but didst deliver Him up for us all” – that is not there.

Confessiones V.II.9.14

That all gods should be worshipped, as urged by Plato, was also repudiated by Augustine together with the doctrine of metempsychosis. Porphyry was again criticized for upholding both these teachings along with Origen who, as recently as 400, had been criticized at a council in Alexandria for some of his
views.

Despite these differences, it can be seen that the two traditions remained essentially compatible. This was still partly explained by the belief that Plato may have learnt some scripture in Egypt,
a belief based on what was taken to be internal evidence as, for example, when Augustine compares Timaeus with Genesis:

“In the beginning God made heaven and earth. But the earth was invisible and unformed, and there was darkness over the abyss, and the spirit of God soared above the water (Genesis 1.1f)”. Now in the Timaeus, the book in which he writes about the creation of the world, Plato says that God in that work first brought together earth and fire (Timaeus 31B); and it is obvious that for Plato fire takes the place of the sky Plato goes on to say that water and air were the two intermediaries whose interposition effected the junction of those two extremes
(Timaeus 32B). This is supposed to be his interpretation of the biblical statement: “The spirit of God soared above the water”.

De civitate Dei VIII. 11

And when God declared, “I am He who is ” (Exodus 3,14), it was the “truth Plato vigorously maintained and diligently taught”. Augustine’s own exegesis of Plato’s moral philosophy acknowledged that, to Platonists, the highest good was to be found not in the mind or body, but in God, and that goodness, being equated with virtue, is only to be found through knowledge of God.”

[Platonists] acknowledge a God who transcends any kind of soul, being the maker not only of this visible – heaven and earth, in the familiar phrase – but also of every soul whatsoever, a God who gives blessedness to the rational and intelligent soul – the class to which the human soul belongs – by giving it a share in his unchangeable and immaterial light.

De civitate Dei, VIII.1

Platonists assert that the true God is the author of the universe, the source of the light of truth, and the bestower of happiness.

De civitate Dei VIII.5

His synthesis of the two traditions appears as effortless as Clement’s had been.

The philosophy that is true has no other function than to teach what is the First Principle of all things – Itself without beginning, – and how great an intellect dwells therein, and what has proceeded therefrom for our welfare, but without deterioration of any kind. Now, the venerated mysteries teach that this First Principle is one God omnipotent, and that He is tripotent, Father and Son and Holy Spirit.

De ordine II.5.6

In his expositions of the cosmos, the elements, the liberal arts and the understanding of numbers, it may be seen that Augustine again very much continues the teaching of Clement.

But what are the higher things ? Where there is no time, because there is no change, and from where times are made and ordered and changed, initiating eternity as they do when the turn of the heavens comes back to the same state, and the heavenly bodies to the same place, and in days and months and years and centuries and other revolutions of the stars obey
the laws of equality, unity and order. So terrestrial things are subject to celestial, and their time circuits join together in harmonious succession for a poem of the universe.

De musica VI. 11.29

In this is contained the original sense of universe as unus versus,
namely one that is turning.

From him derives every mode of being, every species, every order, all measure, number and weight he has not left them without a harmony of their constituent parts, a kind of peace.

De civitate Dei V.11, paraphrasing Wisdom 11.20

there is nothing which is not brought into being by him, from whom comes all form, all shape, all order …

De civitate Dei XI. 15

However, understanding the orderliness of the creation and what a Christian’s attitude towards it should be was naturally difficult, particularly following the shock of the sack of Rome in 410 which prompted the writing of De civitate Dei. In achieving such an understanding, Augustine evidently differs somewhat from Clement for, whereas Clement excluded the uneducated from the path to knowledge, Augustine seems prepared to include anyone even at the risk of holding back the educated.

If only the weak understanding of the ordinary man did not stubbornly resist the plain evidence of logic and truth! The result is that we are forced very often to give an extended exposition of the obvious …

De civitate Dei II. 1; see also VII. Pref.

In all these branches of study, therefore, all things were being presented to reason as numerically proportioned Then, reason gained much coinage and preconceived a great achievement; it ventured to prove the soul immortal. It treated diligently of all things. It came to feel that it possessed great power, and that it owed all its power to numerical proportions. Something wondrous urged it on. And it began to suspect that it itself was perhaps the very number by which all things are numbered, or if not, that this number was there whither it was striving to arrive But, false images of the things which we number drift away from that most hidden something by which we ennumerate, snatch our attention to themselves, and
frequently make that hidden something slip away even when it has been already in our grasp.

De ordine II. 15.43

If a man does not yield to these images, and if he reduces to simple, true and certain unity all the things that are scattered far and wide throughout so many branches of study, then he is most deserving of the attribute learned. Then, without being rash, he can search after things divine …

De ordine II.16.44

Open though this may be for anyone to attempt, Augustine both warns of the difficulties that lie ahead and at the same time describes the milestones that must be attained in order to succeed:

… no one ought to aspire to a knowledge of those matters without that twofold science, so to speak – the science of right reasoning and that of the power of numbers.

De ordine II.18.47

only a rare class of men is capable of using [reason] as a guide to the knowledge of God or of the soul; either of the soul within us or of the world-soul.

De ordine II.11.30

If you have a care for order you must return to those verses, for instruction in the liberal arts produces devotees more alert and steadfast and better equipped for embracing
truth

De ordine I.8.24

But since all the liberal arts are learned partly for practical use and partly for the knowledge and contemplation of things, to attain the use of them is very difficult except for some very gifted person who even from boyhood has earnestly and constantly applied himself.

De ordine II.16.44

Autore: Nigel Hiscock
Pubblicazione:
The Wise Master Builder. Platonic Geometry in Plans of Medieval Abbeys and Cathedralsl
Editore
: Ashgate
Luogo: Aldershot
Anno: 2000
Pagine: 64-69

Early Christian Sources of Platonic Geometry: the Latin Encyclopedists

In the foregoing sections, it has been shown that the passage of Platonic and Neoplatonic thought from Alexandria to Asia Minor and the Greek Fathers produced writings of sufficient importance that they were immediately to find their way to the West, reaching not only Ambrose in Milan but Rome as well, whence the teachings of Origen were to spread in the translations of Rufinus. In the meantime, however, Neoplatonism had already reached Rome with the arrival of Plotinus in 244.

It was Plotinus’s pupil, Porphyry (233-c.300), a leading Neoplatonist himself, who edited the work of his master and whose own writings included commentaries on Timaeus and apparently the Elementa as well. Writing in Greek though living in Rome, he was to be highly regarded by Augustine as a pagan philosopher, though this was a tribute Augustine was to qualify because of Porphyry’s anti-Christian stance, manifest for example in his treatise Adversus Christianos.

Marius Victorinus, who taught rhetoric in Rome and became a Christian convert in the middle of the fourth century, translated writings of Plotinus and other Neoplatonists into Latin which may have numbered among the works of Victorinus recorded by Alcuin at York. He was in touch with
Simplicianus, the priest in Milan who prepared Ambrose for baptism the year before the latter became bishop of that city in 374.

At about the time of Victorinus’s conversion, Chalcidius was producing his celebrated Timaeus translation and commentary, copies of which, as already stated, were a necessary possession for all medieval libraries of note.
This was in spite of the text ending prematurely at a point which immediately precedes Plato’s treatment of the elements and the regular solids. Nevertheless, the work remained the most important of all Platonic sources for the Latin middle ages.

This was followed by two more Platonic works of hardly less importance, namely the Commentarii in Ciceronis Somnium Scipionis of Macrobius and Martianus’s De nuptiis Philologiae et Mercurii. Macrobius’s Commentarii,
second only to Chalcidius’s, was written late in the fourth century or early in the fifth based on a lost commentary on Timaeus by Porphyry. Yet it is less a commentary than an encyclopedia of Neoplatonism illustrated with diagrams. Its starting-point is Plato’s Republic,
Cicero’s original work also being entitled De republica,
and it is with Scipio’s Dream that he ends it as an obvious counterpart to Plato’s Vision of Er. Martianus’s De nuptiis was approximately contemporary, being written between 410 and 439, and uses the allegorical marriage between Philology and Mercury as a setting for summarizing the seven liberal arts, in which each appears personified as a bridesmaid at the wedding.

Whilst Somnium Scipionis is among the works most frequently referred to in early medieval manuscripts and is itself among the most common manuscripts from that time, so De nuptiis was perhaps the most widely used schoolbook, its popularity during the ninth and tenth centuries being matched by that of Somnium Scipionis possibly from early in the tenth. Their influence in transmitting Plato’s cosmology was second only to Chalcidius partly as a result of expositions of number theory that deal not only with numerical relationships but with their powers as well, the attributes of the Pythagorean decad for example and the discovery of his musical ratios being relayed extensively in medieval literature. This is not to say that the transmission was exact and unvarying since tradition was always open to interpretation and development. For example, Plato’s and Clement’s concept of 7 planets revolving around an eighth, which is Earth, becomes in Somnium Scipionis 7
planets revolving within an eighth which is an all-encompassing celestial sphere. This is composed of 5 zones. Because justice is even-handed, to Clement it was represented by 4, by Martianus 2 and by Macrobius 8. 7, being a virgin number, is identified with Pallas Athene. In De nuptiis, 9 is also a perfect number and signifies the Muses. Nevertheless, it seems fair to say that these are additions to, not an undermining of, the basic precepts, for these remained those of Pythagoras and Plato as recognized by Martianus.

Meanwhile the august company of the gods… acknowledged [Arithmetic] herself… to be in very truth the procreator of the gods. And the host of philosophers, too, who stood nearby – in particular, Pythagoras, with all his disciples, and Plato,
expounding the cryptic doctrines of his Timaeus – worshipped the lady with words of mystic praise….

Martianus, De nuptiis 803

According to this whole tradition as transmitted, 1 is confirmed as the monad and the generator of numbers. 2, being the first departure from unity, represents discord and is the female number because it lacks a middle term.
3 is male because it possesses a middle term and is therefore the first number that is wholly odd. In other words, because,

1 + 1 + 1=3,

it is the first number comprising a mean and two extremes; it also stands for the triangle and the three divisions of the soul.
By the same reasoning, 4 is the first number wholly even because it is the first consisting of two means; it is the terminal number of the tetrad as well as that of the geometric elements of point, line, plane and solid; it represents the quadrangle and the
4 elements and seasons.

The pentad comes next, the number assigned to the universe. This identification is reasonable, for after the four elements, the universe is a fifth body of a different nature.

Martianus, De nuptiis 735

To this Macrobius adds that 5,

. . . alone embraces all things that are and seem to be

Macrobius, Commentarii, 1.6.19

Yet in conveying Plato’s association of the macrocosm with the human microcosm, Martianus adds that 5 also stands for marriage, being the sum of the male and female numbers, as well as the sum of the human senses. 6 is a perfect number because it is the sum of its parts. In other words,

1 x 2 x 3 = 1 + 2 + 3 = 6

Moreover, it is the product of the male and female numbers and so signifies creation. Because 7 begets no numbers in the decad,
it is virgin; as the sum of 3 + 4, it is the number by which the World-Soul is generated, according to Timaeus;
and, the Moon being the seventh planet, it also relates to the phases of the Moon measured in 7-day periods and the lunar stages of each month.
8 is the first cube and is perfect because it has 6 surfaces.

(10 is) the highest degree of perfection of all numbers…

Macrobius, Commentarii, 1.6.76

It contains within itself all numbers with their varied attributes and degrees of perfection…

Martianus,
De nuptiis 742

Interestingly, it is important to note that Martianus has Geometry preceding Arithmetic at the wedding. Her Book is the longest in the work and contains more geography than geometry, yet it does incorporate a ten-page summary of Euclid’s Elementa. Here a classification of angles, planes and solids leads to a description of how solids are generated from planes. Having described the basic solids, among which are found the pyramid and cube, Martianus concludes with the ‘noble’ figures of the octahedron, dodecahedron and icosahedron. Not surprisingly, geometric thinking finds its counterpart in arithmetic for, just as the sphere is recognized as containing all other figures, and in particular the regular solids, so 10 contains all numbers. And since geometric solids are recognized as being based upon plane figures, this would explain Macrobius’s allusion to 5 embracing all things.
Because 5 is the first figurate number of the pentagon, which is the plane figure of the dodecahedron which signifies the universe, Macrobius seems clearly to be associating 5 directly with the macrocosm, as indeed does Martianus.

Had Augustine written his text-books on the liberal arts, he would undoubtedly have belonged to the encyclopedic tradition of his near-contemporaries Macrobius and Martianus. As it is, his importance for the present study is arguably even greater, not only for transmitting Platonic thought within a theological framework but also for securing thereby its acceptance by the Church. Consequently, his contribution will be considered next.

Autore: Nigel Hiscock
Pubblicazione:
The Wise Master Builder. Platonic Geometry in Plans of Medieval Abbeys and Cathedralsl
Editore
: Ashgate
Luogo: Aldershot
Anno: 2000
Pagine: 61-64

Architettura cristiana ravennate – Edifici Basilicali: Conclusioni (1)

Nell’accingerci a trarre qualche conclusione dall’analisi compiuta sugli edifici a pianta longitudinale, dobbiamo innanzitutto riconoscere in tutte le espressioni basilicali il comune anelito ad una semplicità d’impostazione architettonica che ci sorprende ad attrae.

L’univoca scelta ddl’elementare impianto planimetrico denuncia, meglio di ogni altro argomento, l’adesione più convinta alla tradizione architettonica cristiana incentrata su Roma. Nello spartito generale — dall’atrio fino all’abside esclusa — i caratteri romani sono certo evidenti e ben più marcati a Ravenna che nella edilizia sacra della precedente capitale lombarda, come pure della vicina Dalmazia ed in Grecia. Anche il gusto per l’unitaria ampiezza degli spazi interni, l’assenza del transetto e delle conseguenti « navate avvolgenti », delle gallerie superiori, degli endonarteci e di soluzioni comunque ricercate e complesse, confermano fedeltà alle origini cristiane e fermezza di ideali artistici.

Questa esemplare stabilità programmatica — non scossa e forse nemmeno scalfita dalle contrastate vicende e traversie politiche, di cui Ravenna subì i più forti contraccolpi — deve commuoverci per la fede che certo l’animò e la sorresse. Ravenna non soltanto rifiuta, per la tipologia basilicale, un allineamento con l’Oriente e con Bisanzio in particolare; ma si mostra refrattaria nell’accogliere alcuna delle tanto variate esperienze lombarde, suscitate dall’attivismo architettonico di S. Ambrogio, ed assai poco sensibile alle lusinghe dei mondo adriatico e ionico.

 

Siffatta limpida, indiscutibile visione di fondo si precisa a Ravenna, ma non si irrigidisce, attraverso l’uso di schemi proporzionali ora rintracciati. Mentre il rapporto più frequente, posto a base delle costruzioni chiesastiche, è di una volta mezzo tra lunghezza e larghezza, anche gli altri riscontrati (√2, √3 ed il numero d’oro) rispondono ad affermate consuetudini di modulazione classica.

Le modalità applicative di tali semplici proporzionamenti meritano particolare attenzione. Qualunque sia il rapporto, lo schema proporzionale in questi monumenti ravennati non riguarda — più o meno studiatamente — aspetti o particolarità dell’edificio, ma la costruzione nel suo complesso, non concerne lo spazio interno, ma le dimensioni esteriori comprensive degli spessori murari; in sostanza prende in considerazione il volume della fabbrica con esclusione della parte absidale. Ciò attesta la concretezza degli architetti che consideravano l’edificio nella sua unità e si preoccupavano di poterne indicare preventivamente sul terreno i punti e gli allineamenti estremi.

Che queste mie osservazioni — cui sono pervenuto soltanto attraverso il concorde esame dei dati monumentali — siano sicuramente fondate, dando peso e valore a tutta la fioritura delle basiliche ravennati, è confermato in pieno dal citato passo di Agnello (Liber Pontificalis, ed. Testi Rasponi, p. 71,5-8; 77,3-6) in cui si indicano due successive fasi nella costruzione di una basilica. La fabbrica veniva iniziata, difatti, dai muri perimetrali per poi essere completata nelle suddivisioni interne; anzi il protostorico, per il secondo tempo impiega addirittura il verbo implere.

Tale unico metodo di ideazione e di lavoro indica perciò lo schietto desiderio dei costruttori di dar ordine ed unità alle loro semplici fabbriche, direi agli stessi cantieri, più che rivelare particolare gusto per raffinati accordi o per le pure ricerche teoriche.

Per le strutture in elevato, la proporzione tra l’altezza e la larghezza della nave centrale — predominante per chi entri in chiesa o ne esca — si attua in diverse, ma non abnormi soluzioni. A parte l’esempio dello Spirito Santo, il rapporto è abbastanza alto (1,6) in S. Giovanni Evangelista e tende a diminuire gradatamente, attraverso S. Agata e S. Apollinare Nuovo — imperniati ambedue su √2 come le loro piante lo sono nel numero d’oro — per giungere alla basilica classense che prende il valore maggiormente beante di 1,33, di indubbio gusto classico.

Autore: Guglielmo De Angelis D’Ossat
Pubblicazione:
Studi ravennati: problemi di architettura paleocristiana
Editore
: Dante
Luogo: Faenza
Anno: 1962
Pagine: 31-34
Vedi anche:
Architettura cristiana ravennate – Edifici Basilicali: Basilica Ursiana

Architettura cristiana ravennate – Edifici Basilicali: Basilica di Santa Croce
Architettura cristiana ravennate – Edifici Basilicali: Basilica di San Giovanni Evangelista
Architettura cristiana ravennate – Edifici Basilicali: Basilica Apostolorum (San Francesco)
Architettura cristiana ravennate – Edifici Basilicali: Sant’Agata Maggiore
Architettura cristiana ravennate – Edifici Basilicali: Anastasis Gothorum (Basilica dello Spirito Santo)
Architettura cristiana ravennate – Edifici Basilicali: Sant’Apollinare Nuovo
Architettura cristiana ravennate – Edifici Basilicali: Sant’Apollinare in Classe
Architettura cristiana ravennate – Edifici Basilicali: San Michele in Africisco
Architettura cristiana ravennate – Edifici Basilicali: Santa Maria Maggiore e chiese minori

Early Christian Sources of Platonic Geometry: Basil and Gregory

Basil (c.329-79) read philosophy and rhetoric in the young capital of the Eastern Empire, Constantinople, before continuing his studies in Athens with, among others, Julian, the apostate emperor of the Byzantines. It was only later in life, in 364, that he was ordained priest and only seven years before his premature demise that he was consecrated metropolitan of his native Caesarea, whereupon he made his younger brother Gregory (c.335-c.95) bishop of Nyssa. Before his ordination, Basil had spent some time as a hermit studying Origen and when Gregory stayed at his brother’s cell he too studied ‘his master Origen’ along with everything Basil had learned in Athens. On Basil’s death, Gregory came into his own as a churchman and teacher to the extent that he became known as the ‘Father of Fathers’. In 381 he was summoned by the Emperor Theodosius to the Second Oecumenical Council in Constantinople, as a result of which he was recognized as a principal interpreter of the emergent orthodoxy of the Eastern Church.

Of chief interest to this study is Basil’s Hexaemeron, a series of sermons on the 6 days of Creation delivered morning and evening during Lent to a congregation of workmen. As he acknowledges,

I know that many artisans, belonging to the mechanical trades, are crowding around me. A day’s labour hardly suffices to maintain them; therefore I am compelled to abridge my discourse, so as not to keep them too long from their work.

Hexaemeron III.1

Although the sermons are systematically arranged, the final homily which should have described the creation of man seems to end prematurely and was supplemented by Gregory’s treatise De hominis opificio. Such was the importance of Hexaemeron that its teaching quickly spread to the West.
Ambrose produced an adaptation of it which was soon translated into Latin by Eustathius in about 440 and, whether or not this was the work of Basil’s already noted on Alcuin’s shelves at York, a vernacular abbreviation of Hexaemeron was produced in Anglo-Saxon in 969 by Aelfric. As has been remarked elsewhere, the circulation of shortened versions of texts can usually be taken as evidence that such texts had become standard reading. In addition to manuscripts of several of Gregory’s writings surviving from the tenth century onwards, including no less than three of De hominis opificio from the tenth century itself, this same work had already been translated into Latin by John Scotus in the previous century.

At first sight Basil appears largely to repudiate classical philosophy as he recounts how one theory about the origin of the universe became supplanted by another.

Those who have written about the nature of the universe have discussed at length the shape of the earth … all these conjectures have been suggested by cosmographers, each one upsetting that of his predecessor. It will not lead me to give less importance to the creation of the universe, that the servant of God, Moses, is silent as to shapes … Shall I then prefer foolish wisdom to the oracles of the Holy Spirit? … It is this which those seem to me not to have understood, who, giving themselves up to the distorted meaning of allegory, have undertaken to give a majesty of their own invention to Scripture …

Some have said that heaven is composed of four elements … Others have rejected this system as improbable, and introduced into the world, to form the heavens, a fifth element after their own fashioning. There exists, they say, an aethereal body which is neither fire, air, earth, nor water, nor in one word any simple body … But yet another speaker arises and disperses and destroys this theory to give predominance to an idea of his own invention. Do not let us undertake to follow them for fear of falling into like frivolities; let them refute each other, and, without disquieting ourselves about essence, let us say with Moses ‘God created the heaven and the earth’. Let us glorify the supreme Artificer for all that was wisely and skillfully made … Because … the objects which on all sides attract our notice are so marvellous, that the most penetrating mind cannot attain to the knowledge of the least of the phenomenon of this world.

Hexaemeron IX.1, I.11

Basil seems intent here on keeping the minds of his workaday congregation upon simple devotion. He lived, after all, at the time of violent religious disputes such as those caused by Julian’s apostacy and Valens’s Arianism, and
both needed to be answered by an insistence on orthodoxy, particularly concerning the Holy Trinity, rather than by raking over old arguments about classical cosmogony. In fact, it was Basil himself who has been credited with precipitating the end of the Arian dispute, to be ratified soon after his death at the Council of 381 in the presence of his brother. Given the determination to hold the line on orthodoxy which this indicates, Basil is hardly likely to have encouraged cosmological speculation from his own pulpit, especially since he considered such matters to be above the heads of his artisan audience. Certainly the tradition of teaching he inherited from Clement and Origen of knowledge being reserved for the educated, leaving faith to the uneducated, would seem to support this. Indeed, it will be shown that the early Church actually developed its liturgy in a way that protected its innermost secrets from the uninitiated.

Ambiguity in this passage over the fifth essence being ether still seems unabated for, although Basil appears to dismiss it here, when dealing elsewhere with God’s command, ‘Let there be light’, he refers to it as a matter of course.

Up it sprang to the very aether and heaven. In an instant it lighted up the whole extent of the world … For the aether also is such a subtle substance and so transparent that it needs not the space of a moment for light to pass through it … With light the aether becomes more pleasing …

Hexaemeron III. 3

Here it is surely the fifth essence, being distinct from the elements and yet associated with heaven. Later in the same homily, the implication again must surely be that ether is the substance surrounding the 7 planets which therefore fills the universe.

These circles, they say, carried away in a direction contrary to that of the world, and striking the aether, make sweet and harmonious sounds, unequalled by the sweetest melody …

Hexaemeron III.3

That such matters may sometimes be implied is clear from his treatment of the elements:

… ‘In the beginning God made heaven and earth.’ … Thus, although there is no mention of the elements, fire, water and air, imagine that they were all compounds together, and you will find water, air and fire, in the earth … Do not ask, then, for an enumeration of all the elements; guess, from what Holy Scripture indicates, all that is passed over in silence.

Hexaemeron 1.7

The underlying view here seems clearly to be Platonic as well as Christian, as it is when Basil deals with the divine order and the sensible and intelligible worlds.

… ‘In the beginning God created.’ What a glorious order!

It appears, indeed, that even before this world an order of things existed of which our mind can form an idea, but of which we can say nothing, because it is too lofty a subject for men who are but beginners and are still babies in knowledge. . . . The Creator and the Demiurge of the universe perfected His works in it, spiritual light for the happiness of all who love the Lord, intellectual and invisible natures, all the orderly arrangement of pure intelligences who are beyond the reach of our mind and of whom we cannot even discover the names.

Hexaemeron I.2, 5

You will finally discover that the world … is really the school where reasonable souls exercise themselves, the training ground where they learn to know God; since by the sight of visible and sensible things the mind is led, as by a hand, to the contemplation of invisible things.

Hexaemeron I.6

This anagogical doctrine of the path that leads from the sensible to the intelligible, or from the material to the spiritual, was not only a logical corollary of Plato’s world of Forms but, of importance to this study, it also justified religious art and architecture, as Suger was to write in explaining the design of his abbey of St Denis in the twelfth century.

Gregory’s completion of his brother’s Hexaemeron seems similarly Platonic.

Now all is beautiful and good that is closely related to the First Good … If, then, … that which is truly good is one, and the mind itself also has its power of being beautiful and good, in so far as it is in the image of the good and beautiful, and the nature, which is sustained by the mind, has the like power, in so far as it is an image of the image, it is hereby shown that our material part holds together, and is upheld when it is controlled by nature; and on the other hand is dissolved and disorganized when it is separated from that which upholds and sustains it, and is dissevered from its conjunction with beauty and goodness.

De hominis opificio XII.11

Although, like his brother, Gregory sometimes appears to refute a conventional Platonic doctrine, it reappears later albeit in slightly altered
guise. For example, in referring to humans as a microcosm of the universe, he
says,

… how unworthy of the majesty of man are the fancies of some heathen writers, who magnify humanity as they supposed, by their comparison of it with this world! for they say that man is a little world, composed of the same elements with the universe.

De hominis opificio XVI.1

Yet when he answers:

In what then does the greatness of man consist, according to the doctrine of the Church? Not in his likeness to the created world, but in his being in the image of the nature of the Creator.

De hominis opificio XVI.2

surely he is simply equating Creator and created with Origen’s own distinction between the intelligible and sensible worlds. His description of rational man certainly appears purely Platonic:

Now since man is a rational animal, the instrument of his body must be made suitable for the use of reason …

De hominis opificio VIII.8; cf. Plato, Timaeus 44D

Likewise, in another treatise, Plato’s world of Forms lies just beneath the surface as Gregory celebrates the liberal arts as the path to virtue. A virtuous man is one who,

… has been led to the apprehension of a Master of the creation; he has taken the true Wisdom for his teacher, that Wisdom which the spectacle of the Universe suggests; and when he observed the beauty of this material sunlight he had grasped by analogy the beauty of the real sunlight….

Has a man who looks at such spectacles procured for himself only a slight power for the enjoyment of those delights beyond? Not to speak of the studies which sharpen the mind towards moral excellence, geometry, I mean, and astronomy, and the knowledge of the truth that the science of numbers gives, and every method that furnishes a proof of the unknown and a conviction of the known, and, before all these, the philosophy contained in the inspired Writings, which affords a complete purification to those who educate themselves thereby in the mysteries of God.

De infantibus praemature abreptis 377-8

Once again it may be seen that the doctrines of Plato and Clement are conveyed in the importance given by Gregory to education and purification as preparations for the ‘apprehension of a Master of the creation’ and ‘the spectacle of the Universe’. Part of this apprehension is to be gained in the understanding of numbers:

… number is nothing else than a combination of units growing into a multitude in a complete way … accordingly, in order that we may be taught by Holy Scripture that nothing is unknown to God, it tells us that the multitude of the stars is numbered by Him, not that their numbering takes place as I have described, [for who is so simple as to think that God takes knowledge of things by odd and even, and that by putting units together He makes up the total of the collective quantity?] … For to measure quantity by number is the part of those who want information. But He who knew all things before they were created needs not number as His informant. But when David says that He ‘numbers the stars’, it is evident that the Scripture descends to such language in accordance with our understanding, to teach us emblematically that the things which we know not are accurately known to God.

Contra Eunomium librum II 293

Autore: Nigel Hiscock
Pubblicazione:
The Wise Master Builder. Platonic Geometry in Plans of Medieval Abbeys and Cathedralsl
Editore
: Ashgate
Luogo: Aldershot
Anno: 2000
Pagine: 56-61

Macrobio: armonia universale e curiositas musicale

La figura storica di Macrobio è ancora alquanto oscura, sebbene fra le fonti più importanti del neoplatonismo medievale vi furono proprio le sue due principali opere, i Commentari al Sogno di Scipione e i Saturnalia. Le varie ipotesi tentate per dare un’identità biografica a Macrobio convergono nel collocare la sua opera negli anni 420-30 d.C., entro un quadro di sostanziale affinità tra la cultura neoplatonica cristiana e quella pagana.

Come in Calcidio con il Timeo, anche il commento di Macrobio impiega il procedimento dell’explanatio delle sole sezioni di testo per lui di maggior interesse. Qui si tratta della sezione finale del De republica di Cicerone, conosciuta col titolo Somnium Scipionis. La Repubblica ciceroniana era un dialogo filosofico di cui restano solo frammenti, di chiara ispirazione platonica. In essa, Cicerone intendeva mostrare come la costituzione repubblicana romana fosse la forma perfetta di Stato. Nel Sogno,
egli pone in bocca a Scipione l’Africano, apparso in sogno al nipote Scipione l’Emiliano, protagonista del dialogo, un ampio discorso sulla gloriosa ed eterna esistenza celeste riservata allo stesso Emiliano dopo la morte, parimenti gloriosa, che lo attende mentre salverà la patria conquistando Cartagine. Il dialogo onirico si svolge in cielo, sulla Via Lattea, da dove l’Emiliano ammira la bellezza e perfezione dell’universo. Ciò offre a Cicerone l’opportunità per una breve illustrazione della struttura del cosmo, ricalcata sul modello platonico, e per una specificazione a proposito dell’armonia celeste. E questa la sezione del dialogo che ha interessato maggiormente i teorici medievali della musica, i quali a loro volta illustrarono l’esegesi del testo proposta da Macrobio. Ecco i punti essenziali della dottrina dell’armonia cosmica:

  1. il suono è prodotto dalla rotazione delle orbite planetarie;
  2. i pianeti più distanti dalla Terra emettono suoni più acuti e la Luna produce il suono più grave, avendo orbita più piccola e dunque minore velocità di rotazione;
  3. Venere e Mercurio, satelliti del Sole, risuonano all’unisono;
  4. i sette suoni risultanti dipendono dalla distanza delle sfere dalla Terra (dal più acuto al più grave la sequenza è: stelle fisse, Saturno, Giove, Marte, Sole, Venere/Mercurio, Luna);
  5. coloro che hanno riprodotto sulla Terra l’armonia musicale celeste, con gli strumenti musicali o con la voce, sono come coloro che si sono dedicati alle scienze divine;
  6. l’armonia universale è impercepibile a causa delle rapidissime rivoluzioni dei corpi che la producono, e l’udito umano non riesce a distinguerla, così come l’occhio non può fissare il Sole.

Macrobio risponde ai vari problemi messi in campo dalla visione dell’universo tratteggiata da Cicerone, organizzando la trattazione in “blocchi” disciplinari: l’aritmetica, la geometria (più simile alla nostra geografia che alla disciplina euclidea), la musica e l’astronomia, dunque le discipline quadriviali, indagate da Macrobio attraverso due prospettive privilegiate. Da una parte quella della vetustas,
cioè della sincera venerazione per il sapere antico, sentito come patrimonio da salvare, proteggere e trasmettere; dall’altra
quella della curiositas,
dello sguardo sul mondo che rintraccia e scopre le verità partendo dall’osservazione diretta delle apparenti bizzarrie e delle particolarità della natura. Tenendo presenti le due prospettive, risulta evidente che l’insistenza sul tema dell’anima mundi nel corso della trattazione musicale si nutre tanto di doverosi omaggi alla tradizione solenne della filosofia di Platone, adeguatamente mediata da fonti neoplatoniche (Porfirio e il commento di Proclo al Timeo),
quanto di attenzione per la natura, la cui molteplice e variegata facies esprime l’ordine unitario universale. Così, come Calcidio, anche Macrobio apre la sua indagine sul suono partendo dai cieli. Il suono nasce dal girare vorticoso delle orbite per un principio naturale, cioè la violenta collisione di due corpi. L’idea della collisione è di derivazione aristotelica, ma manca del tutto il concetto di vibrazione dell’aria nel mezzo di trasmissione. Se i suoni prodotti sono esprimibili con un rapporto matematico, allora si ha armonia; dunque,

dal girare delle sfere celesti vengono prodotti dei suoni musicali perché, da un lato, è inevitabile che dal moto nasca il suono e, dall’altro, il suono come armonia è il prodotto della razionalità intrinseca alle realtà divine

(Macrobio, II, 1, 5-7)

La modulazione celeste è dunque sì suono, in quanto effetto di moto, ma “razionale”, poiché scaturisce dalla ratio intrinseca all’universo: nulla di nuovo rispetto a quanto sostiene Nicomaco o Calcidio, anche se in Macrobio questa tematica è sviluppata alla luce della teologia astrale (più diffusamente trattata nei Saturnalia).
E infatti, anche se egli rispetta l’ormai consolidata abitudine di riferire come Pitagora scoprì la razionalità dei suoni consonanti nell’officina del fabbro, una diversa prospettiva filosofica pervade la mitica vicenda.

Contrariamente all’affermazione di Nicomaco per cui è «la mente guidata dal numero» che muove Pitagora alla scoperta, il più pragmatico Pitagora di Macrobio «ha capito con gli occhi e con le mani ciò che prima cercava col pensiero» (II, 1, 10). Ecco dunque che da questa osservazione, potremmo dire, empirica e sperimentale, Pitagora ha desunto la «legge dei pesi» da cui dipende la consonanza dei suoni. Macrobio procede così a illustrare la convergenza fra i rapporti matematici e le consonanze, ma allo stesso tempo delinea anche un computo delle stesse basato su principi musicali. Avendo individuato il più piccolo intervallo nel semitono minore (diesis o leimma),
egli identifica ogni consonanza in una somma di
toni e semitoni. Per questo motivo computa anche il tono fra le consonanze, anche se poi ne elenca in via definitiva solo cinque: quarta (diatessaron),
quinta (diapente),
ottava (diapason),
ottava più quinta e doppio diapason. Macrobio impiega il termine symphonia per indicare ogni armonia terrena scaturita dalle consonanze, mentre harmonia,
usato con grande parsimonia, è riferito alla musica delle sfere, la quale però, quanto a modo di produzione e “scala di valori” di costruzione, non è altro che un naturale proseguimento delle consonanze terrene:

Ma questo numero di sinfonie riguarda la musica che, con la sua tensione, può generare il fiato umano o che può essere percepita dall’udito umano. Molto più in là si estende la soglia dell’armonia celeste, cioè fino a quattro volte il diapason e diapente [usque ad quater diapason kai diapente]

(id. II, 1, 24)

Quanto si estende in termini di gamma acustica l’armonia cosmica? Se si interpreta «fino a quattro diapason e un diapente», l’estensione della musica celeste coincide quasi con l’ampiezza della scala musicale proposta nel Timeo, mancando di un solo tono a raggiungerla; se invece, seguendo la traduzione, si intende «fino a quattro volte il diapason e diapente», allora l’armonia cosmica si estende per quattro intervalli di dodicesima (ottava + quinta), comprendendo una gamma molto più ampia di suoni. Alla lapalissiana affermazione segue un richiamo alla struttura numerica del cosmo, voluta dalla provvidenza del dio artefice, e che si riflette in ogni legame proporzionale che governa l’universo. Ma c’è bisogno di un chiarimento: poiché il testo di Cicerone è oscuro, occorre spiegarlo alla luce del Timeo,
il quale però, a sua volta, ha bisogno di essere delucidato premettendo alcuni concetti chiave della disciplina matematico-musicale. Nell’esegesi “al quadrato” proposta da Macrobio la teoria armonica è riferita con notevoli semplificazioni. Ma questo non è rilevante, ciò che importa è ben altro:

Proprio tutti questi concetti mostrano tanto la causa del moto cosmico, che è impresso dal solo impulso dell’anima universale, quanto la necessità di
quell’armonia musicale che l’anima inserisce nel movimento da essa prodotto, perché connaturata ad essa fin dall’origine

(id. II, 2, 24)

Partendo dall’inscindibile legame causale che struttura nel movimento l’universo intero, cosmico e terreno, Macrobio può infine far convergere questo tema centrale del neoplatonismo, l’armonia cosmica, con l’antica mitologia greca delle Muse, di Apollo e delle Sirene, e può far confluire la teologia astrale degli etruschi con la ratio di ogni umano comportamento, dalla cura delle esequie alla terapia medica. L’ethos musicale pervade il cosmo naturale e anche quello animale, e:

non c’è da stupirsene perché, come abbiamo premesso, le cause della musica sono insite nell’anima universale che da esse è appunto costituita; a sua volta poi, l’anima universale dispensa a tutti gli esseri la vita […]. È logico dunque che il cosmo vivente sia rapito dalla musica e la causa è che l’anima celeste, da cui l’universo riceve la vita, ha preso origine dalla musica

(id. II, 3, 11)

Con Macrobio, la musica celeste è davvero un fondamento filosofico universale: è ragione costitutiva dell’anima del mondo, che dà vita col movimento a ogni realtà, cosmica e terrena; è, in conseguenza, primo principio causale del corpo naturale; è, inoltre, il fine teleologico, il premio di beatitudine cui aspira l’anima dopo la morte, che finalmente si ricongiunge alla sua originaria armonia; ma è, ancora, legge universale che controlla e ordina il vivente, dalla conduzione delle azioni umane a quelle animali.

Una suggestiva annotazione, che sarà ripresa dagli autori medievali, esprime la profonda affinità che lega la musica terrena e cosmica: gli inni intonati agli dèi, in cui venivano usati metri diversi per strofe e antistrofe, ricalcano per Macrobio «quel primo inno che la natura ha destinato alla divinità», espresso dal moto del cielo stellato e da quello, di opposta direzione, dei pianeti (II, 3, 5). Per ogni singolo uomo e per ogni comunità umana, bruta o civilizzata, la musica è dunque imprescindibile, conclude Macrobio introducendo un’interessante nota antropologica di segno del tutto opposto alla psicologia platonica: non esiste musica “cattiva”, ogni uomo e ogni popolo cercano nel suono e nel canto di attingere per quanto possono a quello stato di eterna dolcezza e soavità che ogni cuore, anche il più rozzo, non può non sentire, e che perfino gli animali percepiscono come tensione naturale, esprimendola nei loro sonori gorgheggi.

Autore: Cecilia Panti
Pubblicazione:
Filosofia della Musica. Tarda Antichità e Medioevo
Editore
: Carocci (Studi Superiori, 541)
Luogo: Roma
Anno: 2008
Pagine: 45-49

Early Christian Sources of Platonic Geometry: Clement of Alexandria (2) and other Greek Fathers

Therefore just as the equation of the law with perfection appears safe so, it seems, can references to law and perfection be equated with 10.

It may also be seen that the meaning of number was as integral to Clement’s universal view as it had been to those of Pythagoras and Plato, the sole distinction between them being that he acknowledged his authority to be biblical as well as Platonic.

They say, then, that the character representing 300 is, as to shape, the type of the Lord’s sign.. Now the number 300 is 3 by 100. Ten is allowed to be the perfect number…

‘The days of men shall be,’ it is said, ‘120 years’ (Genesis 6.3). And the sum is made up of the numbers from 1 to 15 added together.

Stromateis VI. 11

Numbers were not endowed with specific significance arbitrarily. For example, because the Greek letter T served as the numeral for 300 and resembled a cross, 300 became regarded as the Lord’s sign. Yet numbers were also held to be expressions of the divine order because of the order to be found within them. If the tetrad was given importance partly because the sum of the first 4 numbers is 10, then 120 was important partly because it is the sum of the first 15 numbers. Moreover, Clement continues:

On another principle, 120 is a triangular number, and consists of the equality of the number 64, [which consists of eight of the odd numbers beginning with unity], the addition of which in succession generates squares; and of the inequality of the number 56, consisting of seven of the even numbers beginning with 2, which produce the numbers that are not squares.

Stromateis VI. 11

In other words,

64 + 56 = (8 x 8) + (7 x 8) = 120

64 is composed thus:

1 + 3 = 4, + 5 = 9, + 7 = 16, + 9 = 25, + 11 = 36, + 13 = 49, + 15 = 64

where each sum is a square number which, when added to the next odd number in the series, produces the next square number in the series. As for the series of the first 7 even numbers adding up to 56, each sum, whilst being even, is not square.

2 + 4 + 6 + 8 +10+ 12+ 14 = 56

2 + 4 = 6; 4 + 6 = 10; 6 + 8 = 14; 8 + 10 = 18; 10 + 12 = 22

Following this, Clement continues:

Again, according to another way of indicating, the number 120 consists of four numbers – of one triangular, 15; of another, a square, 25; of a third, a pentagon, 35; and of a fourth, a hexagon, 45. The 5 is taken according to the same ratio in each mode. For in triangular numbers, from the unity 5 comes 15; and in squares, 25; and of those in succession proportionally.

Stromateis VI. 11

It can be seen that in this apparently numerical analysis, geometry is clearly implicit. In addition to the importance given to numbers when they relate rationally to each other, the relationship is perceived and expressed in geometric terms, with the concept of figurate numbers standing for square, triangular and polygonal arrangements of numbers, originally in the form of pebble figures. This, together with the inherent order to be found in numbers themselves was to be treated by the Latin encyclopedists and Augustine.

Clement’s successor at the Didascaleon was his former pupil Origen (c.185-c.254) who went on to study philosophy under Ammonius Saccas. He in turn had abandoned an earlier conversion to Christianity and was a Neoplatonist.
One result of Origen’s varied education was a certain flexibility in calling upon the authority of Plato, not invariably, but when it supported his own theological speculations. In a huge output of literature, these were largely a development of Clement’s and organized into his famous treatise, De principiis, which enjoyed particular influence in both the West and the East. Before they caught the attention of Ambrose and others in Italy, Origen’s ideas had spread to Cappadocia reaching the generation of Basil the Great and his brother Gregory of Nyssa and, although some of his ideas were soon to be condemned, his main thesis remained intact.
Ammonius Saccas also taught Platonic philosophy in Alexandria to the Greek Egyptian Plotinus (c.205-70) whose principal contribution lies in incorporating Plato’s thought with Aristotle’s methods and in bringing to this his own theories concerning progressive planes of spiritual existence. As the doctrine of emanation, this was to have a profound effect on mystical thinkers, setting him among the greatest of the Neoplatonists. Care, it should be said, needs to be taken in the understanding of Neoplatonism as a term, since it is comprehensive rather than specific, referring to various individual developments of Platonic thought, some of which are more Christian than Platonic, or more theological than philosophical, or more mystical than intellectual, or vice versa. Despite such distinctions, however, Neoplatonists at the time called themselves Platonists. As for Plotinus, his importance for this study is that in 244 he moved to Rome, where he taught and eventually died, and it was in Italy that Augustine may well have read his essay On Beauty from his Enneads (I, VI).

Autore: Nigel Hiscock
Pubblicazione:
The Wise Master Builder. Platonic Geometry in Plans of Medieval Abbeys and Cathedralsl
Editore
: Ashgate
Luogo: Aldershot
Anno: 2000
Pagine: 54-56