The pagan philosophers under Constantine had but few pupils and met with but little encouragement. Alypius of Alexandria and his friend Iamblichus, however, still taught the philosophy of Ammonius and Plotinus. The only writings by Alypius now remaining are his _Introduction to Music_; in which he explains the notation of the fifteen modes or tones in their respective kinds of diatonic, chromatic, and enharmonic. His signs are said to be Pythagorean. They are in pairs, of which one is thought to represent the note struck on the lyre, and the other the tone of the voice to be sung thereto. They thus imply accord or harmony. The same signs are found in some manuscripts written over the syllables of ancient poems; and thereby scholars, learned at once in the Greek language, in the art of deciphering signs, and in the science of music, now chant the odes of Pindar in strains not dissimilar to modern cathedral psalmody. Sopator succeeded Iamblichus as professor of platonism in Alexandria, with the proud title of successor to Plato, For some time he enjoyed the friendship of Constantine; but, when religion made a quarrel between the friends, the philosopher was put to death by the emperor. The pagan account of the quarrel was that, when Constantine had killed his son, he applied to Sopator to be purified from his guilt; and when the platonist answered that he knew of no ceremony that could absolve a man from such a crime, the emperor applied to the Christians for baptism. This story may not be true, and the ecclesiastical historian remarks that Constantine had professed Christianity several years before the murder of his son; but then, as after his conversion he had got Sopator to consecrate his new city with a variety of pagan ceremonies, he may in the same way have asked him to absolve him from the guilt of murder.