Archiepiscopal Museum & Chapel of Sant'Andrea

Behind Ravenna's Duomo, beside the Baptistry of Neon, a set of ordinary doors leads into an extraordinary problem: what do you do with the relics of a cathedral that no longer exists? The Archiepiscopal Museum is Ravenna's answer - a collection of what survived the first cathedral's demolition, assembled alongside the private chapel a bishop built for himself at the end of the fifth century. Theodoric the Great ruled from Ravenna as an Arian king over an Orthodox population, and his bishops built their answer to that fact in ivory, marble and glass. It is a smaller, quieter museum than Ravenna's basilicas, and better for it.

The main room opens with an inscription: HIC REQUIESCIT IN PACE VIR SBL SEDA IGNUCUS - here lies in peace that eminent man Seda the Eunuch, cubicularius, or bedchamberlain, to Theodoric the Great, buried in 541. It is a small, human detail from a court that otherwise survives mostly in stone.

By the window beneath it stands a reliquary made for two martyred saints, Quiricus and Julietta, whose remains travelled from Tarsus - Saint Paul's birthplace - to Auxerre and finally to Ravenna, where Galla Placidia placed them in the church of San Giovanni Battista. Its four faces keep to the theme of giving: Christ handing the Tables of the Law to Peter, with Paul beside him; Daniel in the lions' den, fed by the prophet Habakkuk with bread and fish; the Three Kings bringing gifts to the infant Christ; and the women seated at his empty tomb.

On the facing wall, a marble rosette carries a harder kind of gift: order. It is a sixth-century Paschal calendar, built to fix the date of Easter so it fell on the same day across a Christendom that could not agree on how to count. The Eastern Church followed the Hebrew lunar calendar; the West followed the sun. The Council of Nicaea had ruled on the matter in 325, and Theophilus had drawn up tables to settle it, but people kept faith with their own reckoning regardless. This calendar follows the eastern lunar cycle - LV on the outer rim, then AN marking the phase of its nineteen-year cycle - with the date of Easter recorded against each recurring phase from 532 to 626.

The mosaic fragments nearby are what is left of the apse of that first, vanished cathedral - not Roman work, as it turns out, but a twelfth-century reconstruction, at its best in a Madonna praying in the eastern manner. Other pieces suggest the rest of the scheme: the life of Sant'Apollinare, Ravenna's founding evangelist, scenes of the Resurrection, Peter and Paul. In the room to the right, a small stele carved with Christ as the Good Shepherd beside a tree marks the grave of Antiphon, who died at seventeen years, five months and twelve days, around the turn of the third century - before Christianity was legally tolerated in the empire. It is the earliest Christian record in Ravenna. Near it stands a headless, handless, footless man carved in red porphyry, his hand caught mid-gesture with a sword, either drawing it or sheathing it. He may be the emperor Theodosius; he recalls, in brute physicality, the Tetrarchs clutching each other outside the Doge's Palace in Venice.

The collection's centrepiece is the Ivory Cathedra, a bishop's throne carved in the sixth century and counted among the finest surviving ivory work in Western art, displayed where the tower of Porta Salustra once stood - the Roman gate that guarded the city's southern approach along the Cardo. The work of several hands, and missing some panels, it remains a masterpiece regardless. The front bench shows John the Baptist flanked by the Evangelists, bordered by a frieze of peacocks, lions, goats and deer moving through vines. The backrest tells the story of Christ's birth, including Mary proving her virginity by immersion; the other side shows his miracles, his baptism, his entry into Jerusalem. The armrests carry the Old Testament story of Joseph, carved to be read left to right by whoever sat in the chair.

Through the museum, in what was once the bishop's private chapel, Theodoric's court left its clearest statement of doctrine. Built at the end of the fifth century and dedicated to Sant'Andrea, the chapel exists because the bishops of Ravenna, Orthodox men serving an Arian king, needed somewhere to say plainly what they believed.

The vault of the narthex, the first thing you see on entering, is a fine working of blues and greens filled with the aquatic birdlife of Ravenna, its lower walls cleverly restored in painted imitation of mosaic. Among the restoration runs an inscription: Aut lux hic nata est, aut capta hic libera regnat - either light was born here, or it was captured and now reigns free. Read one way, it is a line about the beauty of the room. Read another, it may be a pointed dig at the Gothic occupation - light, begotten not made in the language of the Orthodox creed, held briefly captive by Arian rule before its freedom.

Above the door, a lunette shows Christ not as the suffering Man of Sorrows but as a young Roman soldier, shouldering his cross, holding a book that reads I am the Way, the Truth and the Life, treading a lion and a snake underfoot - the forces of evil, and, in context, of Arianism itself. The rest of the chapel was heavily repainted in the Renaissance by the Ravenna painter Luca Longhi, with marbling added to match the narthex's intimacy.

The apse keeps a starry sky, possibly echoing the nearby Oratory of Galla Placidia, beneath a vault where four angels arch inward to support the monogram IX - Iesus Xristos - flanked by the symbols of the Evangelists. In the vault of the apse itself, the first apostles look down: Peter and Paul, James and Philip, Andrew and Jacob, gathered around a Christ absorbed in the Word and its meaning. Robbed of earthly power under an Arian king, Ravenna's bishops built themselves a ceiling of heaven instead. The chapel, like the mosaics beside it, is listed among Ravenna's UNESCO World Heritage monuments - a small, dense coda to the city's larger, more famous set.