Page:The age of Justinian and Theodora (Volume 1).djvu/243

 type, to which a peculiar character was sometimes given by the use of quarter tones; and choral singing was purely symphonic. But the vibrational numbers of the scale had been discovered by Pythagoras when making experiments with strings; and each of the eighteen notes and fifteen modes had received a descriptive name. Hence the limited scope of the art did not prevent the theory of music from ultimately becoming elaborated with a complexity not unworthy of the native subtlety of the Greeks. In practice the musical training of pupils consisted in their learning to sing to the lyre.

Such in brief were the component parts of a liberal education, with which, however, under the name of philosophy, it was considered essential that a complement of ethical teaching should be conjoined. This complement was digested into three branches, under which were discussed the duty of the individual to himself, to the household, and to the community at large or to the state. *